Finite Group Databasebeta

← #25020045

Subgroups — #25020045

Order 11008.

3166 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063299C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
3C2×#14582777C211yesmaximal, characteristic, complemented
4C2×#14582776C211yesmaximal, characteristic, complemented
5C2×#14582776C211yesmaximal, characteristic, complemented
6C2×#14582776C211yesmaximal, characteristic, complemented
7C22×C43⋊#95C211yesmaximal, characteristic, complemented
8#19132847C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132835C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C22⋊D43C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C24×Dic43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063299—24no—
23C2×#13063299—24no—
24C2×#13063299C418yescomplemented
25C2×(C22⋊D43)⋊C4—24no—
26C2×(C22⋊D43)⋊C4—24no—
27C2×(C22⋊D43)⋊C4—24no—
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14582777—24no—
41#14582776—24no—
42#14582776—24no—
43#14582776—24no—
44C2×C43⋊#95—24no—
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C24×C4×C43C2211yescharacteristic
56C22×C22⋊C4×C43C2211yescharacteristic
57C22×C22⋊C4×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C2×#95×C43C2211yescharacteristic
61C2×#95×C43C2211yescharacteristic
62C24×D43C2311yescharacteristic
63C24×D43C2311yescharacteristic
64C22×D172—22no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—41no—
69C22×D172—41no—
70C22×D172C2×C414yescomplemented
71C22×C22⋊D43—22no—
72C22×C22⋊D43—22no—
73C22×C22⋊D43—22no—
74C22×C22⋊D43—22no—
75C22×C22⋊D43—22no—
76C22×C22⋊D43—22no—
77C22×C22⋊D43—22no—
78C22×C22⋊D43—22no—
79C22×C22⋊D43—22no—
80C22×C22⋊D43—22no—
81C22×C22⋊D43C2×C414yes—
82C22×C22⋊D43C2×C414yescomplemented
83C22×C22⋊D43D414yes—
84C22×C22⋊D43D414yes—
85C23×Dic43—22no—
86C23×Dic43—22no—
87C23×Dic43—22no—
88C23×Dic43—22no—
89C23×Dic43—22no—
90C23×Dic43—22no—
91C23×Dic43—22no—
92C23×Dic43—22no—
93C23×Dic43—22no—
94C23×Dic43—41no—
95C23×Dic43—41no—
96C23×Dic43—41no—
97C23×Dic43—41no—
98C23×Dic43D414yescomplemented
99C23×Dic43C2311yescharacteristic
100C23×Dic43C2311yescharacteristic
101C23×Dic43C2311yescharacteristic
102C23×Dic43C2311yescharacteristic
103C23×Dic43C2311yescharacteristic
104C23×Dic43C2311yescharacteristic
105C22×C4×D43—22no—
106C22×C4×D43—22no—
107C22×C4×D43—22no—
108C22×C4×D43—22no—
109C22×C4×D43—22no—
110C22×C4×D43—41no—
111C22×C4×D43—41no—
112#13063299—232no—
113(C22⋊D43)⋊C4—232no—
114C2×C4⋊Dic43—22no—
115C2×C4⋊Dic43—22no—
116C2×C4⋊Dic43C2×C414yescomplemented
117C2×Dic43⋊C4—22no—
118C2×Dic43⋊C4—22no—
119C2×Dic43⋊C4—22no—
120C2×(C2×D43)⋊C4—22no—
121C2×(C2×D43)⋊C4—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×(C2×D43)⋊C4—22no—
125C2×(C2×D43)⋊C4—22no—
126C2×(C2×D43)⋊C4—22no—
127C2×(C2×D43)⋊C4—22no—
128C2×(C2×D43)⋊C4—22no—
129C2×(C2×D43)⋊C4—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4—22no—
132C2×(C2×D43)⋊C4—22no—
133C2×(C2×D43)⋊C4—22no—
134C2×(C2×D43)⋊C4—22no—
135C2×(C2×D43)⋊C4—22no—
136C2×(C2×D43)⋊C4—22no—
137C2×(C2×D43)⋊C4—22no—
138C2×(C2×D43)⋊C4—22no—
139C2×(C2×D43)⋊C4—41no—
140C2×(C2×D43)⋊C4—41no—
141C2×(C2×D43)⋊C4—41no—
142C2×(C2×D43)⋊C4—41no—
143C2×(C2×D43)⋊C4—41no—
144C2×(C2×D43)⋊C4—41no—
145C2×(C2×D43)⋊C4C2×C414yescomplemented
146C2×(C2×D43)⋊C4C2×C414yescomplemented
147C2×C4×Dic43—22no—
148C2×C4×Dic43—22no—
149C2×C4×Dic43—22no—
150C43⋊#95—22no—
151C43⋊#95—22no—
152C43⋊#95—22no—
153C43⋊#95—22no—
154C43⋊#95—22no—
155C43⋊#95—22no—
156C43⋊#95—22no—
157C43⋊#95—22no—
158C43⋊#95—22no—
159C43⋊#95D414yescomplemented
160C25×C43C2311yescharacteristic
161C23×C4×C43—22no—
162C23×C4×C43—22no—
163C23×C4×C43—22no—
164C23×C4×C43—22no—
165C23×C4×C43—41no—
166C23×C4×C43—41no—
167C23×C4×C43C2×C414yescomplemented
168C23×C4×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C23×C4×C43C2311yescharacteristic
172C23×C4×C43C2311yescharacteristic
173C23×C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—22no—
175C2×C22⋊C4×C43—22no—
176C2×C22⋊C4×C43—22no—
177C2×C22⋊C4×C43—22no—
178C2×C22⋊C4×C43—22no—
179C2×C22⋊C4×C43D414yescomplemented
180#95×C43—22no—
181#95×C43—22no—
182#95×C43—41no—
183#95×C43—41no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43C22×C412yes—
193C24×C43C2×D412yes—
194C24×C43C2×D412yes—
195C24×C43C2×D412yes—
196C24×C43C2×D412yes—
197C24×C43#4112yes—
198C24×C43#4112yes—
199C24×C43C2411yescharacteristic
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—21no—
203C23×D43—21no—
204C23×D43—21no—
205C23×D43—21no—
206C23×D43—21no—
207C23×D43—21no—
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211C23×D43—21no—
212C23×D43—21no—
213C23×D43—21no—
214C23×D43—21no—
215C23×D43—21no—
216C23×D43—21no—
217C23×D43—21no—
218C23×D43—21no—
219C23×D43—21no—
220C23×D43—21no—
221C23×D43—21no—
222C23×D43—21no—
223C23×D43—21no—
224C23×D43—21no—
225C23×D43—21no—
226C23×D43C22×C412yes—
227C23×D43C22×C412yes—
228C23×D43C2×D412yes—
229C23×D43C2×D412yes—
230C22×C4×C43—28no—
231C22×C4×C43—28no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—44no—
269C22×C4×C43—44no—
270C22×C4×C43—44no—
271C22×C4×C43—44no—
272C22×C4×C43—44no—
273C22×C4×C43C22×C412yes—
274C22×C4×C43C22×C412yes—
275C22×C4×C43C2×D412yes—
276C22×C4×C43C2×D412yes—
277C22×C4×C43C2×D412yes—
278C22×C4×C43#4112yes—
279C2×C22⋊D43—28no—
280C2×C22⋊D43—28no—
281C2×C22⋊D43—28no—
282C2×C22⋊D43—28no—
283C2×C22⋊D43—28no—
284C2×C22⋊D43—28no—
285C2×C22⋊D43—28no—
286C2×C22⋊D43—28no—
287C2×C22⋊D43—28no—
288C2×C22⋊D43—44no—
289C2×C22⋊D43—44no—
290C2×C22⋊D43—44no—
291C2×C22⋊D43—44no—
292C2×C22⋊D43C22⋊C4116yescomplemented
293C22×Dic43—28no—
294C22×Dic43—28no—
295C22×Dic43—28no—
296C22×Dic43—21no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—21no—
301C22×Dic43—21no—
302C22×Dic43—21no—
303C22×Dic43—21no—
304C22×Dic43—21no—
305C22×Dic43—21no—
306C22×Dic43—21no—
307C22×Dic43—21no—
308C22×Dic43—21no—
309C22×Dic43—21no—
310C22×Dic43—21no—
311C22×Dic43—21no—
312C22×Dic43—21no—
313C22×Dic43—21no—
314C22×Dic43—21no—
315C22×Dic43—21no—
316C22×Dic43—21no—
317C22×Dic43—21no—
318C22×Dic43—21no—
319C22×Dic43—21no—
320C22×Dic43—21no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—21no—
324C22×Dic43—21no—
325C22×Dic43—21no—
326C22×Dic43—21no—
327C22×Dic43—21no—
328C22×Dic43—44no—
329C22×Dic43—44no—
330C22×Dic43—44no—
331C22×Dic43—44no—
332C22×Dic43—44no—
333C22×Dic43—44no—
334C22×Dic43—44no—
335C22×Dic43—44no—
336C22×Dic43—44no—
337C22×Dic43—44no—
338C22×Dic43—44no—
339C22×Dic43C22×C412yes—
340C22×Dic43C22×C412yes—
341C22×Dic43C2×D412yes—
342C22×Dic43C2×D412yes—
343C22×Dic43C2×D412yes—
344C22×Dic43C2×D412yes—
345C22×Dic43C2×D412yes—
346C22×Dic43C2×D412yes—
347C22×Dic43#4112yes—
348C22×Dic43#4112yes—
349C2×D172—28no—
350C2×D172—28no—
351C2×D172—44no—
352C2×D172—44no—
353C2×D172—44no—
354C2×D172—44no—
355C2×D172—44no—
356C2×C4×D43—28no—
357C2×C4×D43—44no—
358C2×C4×D43—44no—
359C2×C4×D43—44no—
360C2×C4×D43—44no—
361C2×C4×D43—44no—
362C2×C4×D43—44no—
363C22⋊C4×C43—28no—
364C22⋊C4×C43—44no—
365(C2×D43)⋊C4—28no—
366(C2×D43)⋊C4—28no—
367(C2×D43)⋊C4—28no—
368(C2×D43)⋊C4—44no—
369(C2×D43)⋊C4—44no—
370(C2×D43)⋊C4—44no—
371(C2×D43)⋊C4—44no—
372(C2×D43)⋊C4—44no—
373(C2×D43)⋊C4—44no—
374C4⋊Dic43—28no—
375Dic43⋊C4—28no—
376C4×Dic43—28no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43—22no—
385C23×C43—22no—
386C23×C43—22no—
387C23×C43—22no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—22no—
391C23×C43—22no—
392C23×C43—22no—
393C23×C43—22no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—22no—
397C23×C43—22no—
398C23×C43—22no—
399C23×C43—22no—
400C23×C43—22no—
401C23×C43—22no—
402C23×C43—22no—
403C23×C43—22no—
404C23×C43—22no—
405C23×C43C2×C22⋊C414yes—
406C23×C43C4×D414yes—
407C23×C43C4×D414yes—
408C23×C43#12014yes—
409C23×C43#12114yes—
410C23×C43#12114yes—
411C23×C43#12314yes—
412C23×C43C23×C411yescharacteristic
413C23×C43C22×D411yescharacteristic
414C23×C43C22×D411yescharacteristic
415C23×C43C22×D411yescharacteristic
416C23×C43C22×D411yescharacteristic
417C23×C43C22×D411yescharacteristic
418C23×C43C2×#4111yescharacteristic
419C23×C43C2×#4111yescharacteristic
420C23×C43C2×#4111yescharacteristic
421C23×C43C2×#4111yescharacteristic
422C23×C43C2×#4111yescharacteristic
423C23×C43H(5,𝔽2)11yescharacteristic
424C23×C43H(5,𝔽2)11yescharacteristic
425C23×C43H(5,𝔽2)11yescharacteristic
426C23×C432−1+411yescharacteristic
427C22×D43—22no—
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—22no—
433C22×D43—22no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43—22no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—22no—
444C22×D43—22no—
445C22×D43—22no—
446C22×D43—22no—
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—41no—
453C22×D43—41no—
454C22×D43—41no—
455C22×D43—41no—
456C22×D43—41no—
457C22×D43—41no—
458C22×D43—41no—
459C22×D43—41no—
460C22×D43—41no—
461C22×D43—41no—
462C22×D43—41no—
463C22×D43—41no—
464C22×D43—41no—
465C22×D43—41no—
466C22×D43—41no—
467C22×D43—41no—
468C22×D43—41no—
469C22×D43—41no—
470C22×D43—41no—
471C22×D43—41no—
472C22×D43—41no—
473C22×D43—41no—
474C22×D43—41no—
475C22×D43—41no—
476C22×D43—41no—
477C22×D43—41no—
478C22×D43—41no—
479C22×D43—41no—
480C22×D43—41no—
481C22×D43—41no—
482C22×D43—41no—
483C22×D43—41no—
484C22×D43—41no—
485C22×D43—41no—
486C22×D43—41no—
487C22×D43—41no—
488C22×D43—41no—
489C22×D43—41no—
490C22×D43—41no—
491C22×D43—41no—
492C22×D43—41no—
493C22×D43—41no—
494C22×D43—41no—
495C22×D43—41no—
496C22×D43C2×C22⋊C414yes—
497C2×C4×C43—22no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—22no—
503C2×C4×C43—22no—
504C2×C4×C43—22no—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—22no—
508C2×C4×C43—22no—
509C2×C4×C43—22no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—416no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43—41no—
519C2×C4×C43—41no—
520C2×C4×C43—41no—
521C2×C4×C43—41no—
522C2×C4×C43—41no—
523C2×C4×C43—41no—
524C2×C4×C43—41no—
525C2×C4×C43—41no—
526C2×C4×C43—41no—
527C2×C4×C43—41no—
528C2×C4×C43—41no—
529C2×C4×C43—41no—
530C2×C4×C43—41no—
531C2×C4×C43—41no—
532C2×C4×C43—41no—
533C2×C4×C43—41no—
534C2×C4×C43—41no—
535C2×C4×C43—41no—
536C2×C4×C43—41no—
537C2×C4×C43—41no—
538C2×C4×C43—41no—
539C2×C4×C43C4×D414yescomplemented
540C22⋊D43—232no—
541C22⋊D43—416no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—22no—
545C2×Dic43—22no—
546C2×Dic43—22no—
547C2×Dic43—22no—
548C2×Dic43—22no—
549C2×Dic43—22no—
550C2×Dic43—22no—
551C2×Dic43—22no—
552C2×Dic43—22no—
553C2×Dic43—22no—
554C2×Dic43—22no—
555C2×Dic43—22no—
556C2×Dic43—22no—
557C2×Dic43—22no—
558C2×Dic43—22no—
559C2×Dic43—22no—
560C2×Dic43—22no—
561C2×Dic43—22no—
562C2×Dic43—22no—
563C2×Dic43—22no—
564C2×Dic43—22no—
565C2×Dic43—22no—
566C2×Dic43—416no—
567C2×Dic43—416no—
568C2×Dic43—41no—
569C2×Dic43—41no—
570C2×Dic43—41no—
571C2×Dic43—41no—
572C2×Dic43—41no—
573C2×Dic43—41no—
574C2×Dic43—41no—
575C2×Dic43—41no—
576C2×Dic43—41no—
577C2×Dic43—41no—
578C2×Dic43—41no—
579C2×Dic43—41no—
580C2×Dic43—41no—
581C2×Dic43—41no—
582C2×Dic43—41no—
583C2×Dic43—41no—
584C2×Dic43C2×C22⋊C414yes—
585C2×Dic43#12114yescomplemented
586D172—416no—
587C4×D43—416no—
588#14023—431nomaximal, Sylow
589C22×C43—24no—
590C22×C43—24no—
591C22×C43—24no—
592C22×C43—24no—
593C22×C43—24no—
594C22×C43—24no—
595C22×C43—24no—
596C22×C43—24no—
597C22×C43—24no—
598C22×C43—24no—
599C22×C43—24no—
600C22×C43—24no—
601C22×C43—24no—
602C22×C43—24no—
603C22×C43#38618yescomplemented
604C22×C43C22×C22⋊C411yescharacteristic
605C22×C43C2×C4×D411yescharacteristic
606C22×C43C2×C4×D411yescharacteristic
607C22×C43C2×C4×D411yescharacteristic
608C22×C43C4×#4111yescharacteristic
609C22×C43#51811yescharacteristic
610C22×C43#52011yescharacteristic
611C22×C43C2×#12011yescharacteristic
612C22×C43C2×#12111yescharacteristic
613C22×C43C2×#12111yescharacteristic
614C22×C43C2×#12111yescharacteristic
615C22×C43C2×#12311yescharacteristic
616C22×C43#52511yescharacteristic
617C22×C43#52911yescharacteristic
618C22×C43#53211yescharacteristic
619C22×C43#53411yescharacteristic
620C22×C43#53711yescharacteristic
621C22×C43#53811yescharacteristic
622C22×C43#53911yescharacteristic
623C22×C43D4211yescharacteristic
624C22×C43D4211yescharacteristic
625C22×C43D4211yescharacteristic
626C22×C43#54611yescharacteristic
627C22×C43#54611yescharacteristic
628C22×C43#54611yescharacteristic
629C22×C43#54611yescharacteristic
630C22×C43#54611yescharacteristic
631C22×C43#54611yescharacteristic
632C22×C43#54711yescharacteristic
633C22×C43#54711yescharacteristic
634C22×C43#54711yescharacteristic
635C22×C43#54811yescharacteristic
636C22×C43#55311yescharacteristic
637C22×C43#55311yescharacteristic
638C22×C43#55311yescharacteristic
639C2×D43—24no—
640C2×D43—24no—
641C2×D43—24no—
642C2×D43—42no—
643C2×D43—42no—
644C2×D43—42no—
645C2×D43—42no—
646C2×D43—42no—
647C2×D43—42no—
648C2×D43—42no—
649C2×D43—42no—
650C2×D43—42no—
651C2×D43—42no—
652C2×D43—42no—
653C2×D43—42no—
654C2×D43—42no—
655C2×D43—42no—
656C2×D43—42no—
657C2×D43—42no—
658C2×D43—42no—
659C2×D43—42no—
660C2×D43—42no—
661C2×D43—81no—
662C2×D43—81no—
663C2×D43—81no—
664C2×D43—81no—
665C2×D43—81no—
666C2×D43—81no—
667C2×D43—81no—
668C2×D43—81no—
669C4×C43—24no—
670C4×C43—42no—
671C4×C43—42no—
672C4×C43—42no—
673C4×C43—81no—
674C4×C43—81no—
675Dic43—24no—
676Dic43—24no—
677Dic43—42no—
678Dic43—42no—
679Dic43—42no—
680Dic43—42no—
681C22×#121—431no—
682C22×C4×D4—431no—
683C2×#386—431no—
684C2×#386—431no—
685C2×#386—431no—
686C2×#386—431no—
687C22×#95—431no—
688#1441—431no—
689#1440—431no—
690#1439—431no—
691#1438—431no—
692#1437—431no—
693#1436—431no—
694C22⋊#95—431no—
695C22⋊#95D4311yescharacteristic, complemented
696C2×C43—28no—
697C2×C43C2×#38611yescharacteristic
698C2×C43C4×#12111yescharacteristic
699C2×C43#232511yescharacteristic
700C2×C43D4×C22⋊C411yescharacteristic
701C2×C43#233911yescharacteristic
702C2×C43#236111yescharacteristic
703C2×C43#236411yescharacteristic
704C2×C43#241011yescharacteristic
705C2×C43#241611yescharacteristic
706C2×C43#242411yescharacteristic
707C2×C43#242511yescharacteristic
708C2×C43#243011yescharacteristic
709C2×C43#244311yescharacteristic
710C2×C43#244411yescharacteristic
711C2×C43#254311yescharacteristic
712D43—44no—
713D43—82no—
714C23×D4—431no—
715C23×D4—431no—
716C23×D4—431no—
717C24×C4—431no—
718C24×C4—431no—
719C24×C4—431no—
720C24×C4C2×D4311yescharacteristic
721C2×#121—438no—
722C2×#121—864no—
723C2×#121—864no—
724C2×C4×D4—864no—
725C2×C4×D4—864no—
726C2×C4×D4—864no—
727C22×C4⋊C4—431no—
728C22×C4⋊C4—431no—
729C22×C22⋊C4—431no—
730C22×C22⋊C4—431no—
731C22×C22⋊C4—431no—
732C22×C22⋊C4—431no—
733C22×C22⋊C4—431no—
734C22×C22⋊C4—431no—
735C22×C22⋊C4—431no—
736C22×C22⋊C4—431no—
737C22×C22⋊C4—431no—
738C22×C22⋊C4C2×D4311yescharacteristic
739C22×C22⋊C4C2×D4311yescharacteristic
740C22×C42—431no—
741#386—864no—
742#386—864no—
743#386—864no—
744#386—864no—
745C2×#95—431no—
746C2×#95—431no—
747C2×#95—431no—
748C2×#95—431no—
749C2×#95—431no—
750C2×#95—431no—
751C2×#95—431no—
752C2×#95—431no—
753C2×#95—431no—
754C2×#95—431no—
755C2×#95—864no—
756C2×#95C2×D4311yescharacteristic
757C2×#95C2×D4311yescharacteristic
758C2×#95C2×D4311yescharacteristic
759C2×#95C2×D4311yescharacteristic
760C43#1402311yescharacteristic, complemented, Sylow
761C25—431no—
762C25—431no—
763C25C22×D4311yescharacteristic
764C22×D4—434no—
765C22×D4—434no—
766C22×D4—434no—
767C22×D4—434no—
768C22×D4—434no—
769C22×D4—862no—
770C22×D4—862no—
771C22×D4—862no—
772C22×D4—862no—
773C22×D4—862no—
774C22×D4—862no—
775C22×D4—862no—
776C22×D4—862no—
777C22×D4—862no—
778C22×D4—862no—
779C22×D4—862no—
780C22×D4—862no—
781C22×D4—862no—
782C22×D4—862no—
783C22×D4—1721no—
784C22×D4—1721no—
785C23×C4—22no—
786C23×C4—22no—
787C23×C4—22no—
788C23×C4—22no—
789C23×C4—41no—
790C23×C4—41no—
791C23×C4—431no—
792C23×C4—431no—
793C23×C4—431no—
794C23×C4—431no—
795C23×C4—431no—
796C23×C4—431no—
797C23×C4—434no—
798C23×C4—862no—
799C23×C4—862no—
800C23×C4—862no—
801C23×C4—862no—
802C23×C4—862no—
803C23×C4—862no—
804C23×C4—862no—
805C23×C4—862no—
806C23×C4—862no—
807C23×C4—862no—
808C23×C4—862no—
809C23×C4—862no—
810C23×C4—862no—
811C23×C4—862no—
812C23×C4—1721no—
813C23×C4—1721no—
814C23×C4—1721no—
815C23×C4—1721no—
816C23×C4—1721no—
817C23×C4—1721no—
818C23×C4C4×D4314yescomplemented
819C23×C4C22×D4311yescharacteristic
820C23×C4C22×D4311yescharacteristic
821C23×C4C22×D4311yescharacteristic
822C23×C4C22×D4311yescharacteristic
823C23×C4C22×D4311yescharacteristic
824C23×C4C22×D4311yescharacteristic
825#121—8632no—
826C4×D4—8632no—
827C2×C4⋊C4—434no—
828C2×C4⋊C4—862no—
829C2×C4⋊C4—862no—
830C2×C4⋊C4—862no—
831C2×C4⋊C4—862no—
832C2×C4⋊C4—862no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—434no—
839C2×C22⋊C4—434no—
840C2×C22⋊C4—862no—
841C2×C22⋊C4—862no—
842C2×C22⋊C4—862no—
843C2×C22⋊C4—862no—
844C2×C22⋊C4—862no—
845C2×C22⋊C4—862no—
846C2×C22⋊C4—862no—
847C2×C22⋊C4—862no—
848C2×C22⋊C4—862no—
849C2×C22⋊C4—862no—
850C2×C22⋊C4—862no—
851C2×C22⋊C4—862no—
852C2×C22⋊C4—862no—
853C2×C22⋊C4—862no—
854C2×C22⋊C4—862no—
855C2×C22⋊C4—862no—
856C2×C22⋊C4—862no—
857C2×C22⋊C4—862no—
858C2×C22⋊C4—862no—
859C2×C22⋊C4—1721no—
860C2×C22⋊C4—1721no—
861C2×C22⋊C4—1721no—
862C2×C22⋊C4—1721no—
863C2×C22⋊C4—1721no—
864C2×C22⋊C4—1721no—
865C2×C22⋊C4D17214yescomplemented
866C2×C42—862no—
867C2×C42—862no—
868C2×C42—862no—
869#95—22no—
870#95—22no—
871#95—41no—
872#95—41no—
873#95—434no—
874#95—862no—
875#95—862no—
876#95—862no—
877#95—862no—
878#95—862no—
879#95—862no—
880#95—862no—
881#95—862no—
882#95—862no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—432no—
892C24—432no—
893C24—432no—
894C24—432no—
895C24—861no—
896C24—861no—
897C24—861no—
898C24—861no—
899C24—861no—
900C24—861no—
901C24—861no—
902C24—861no—
903C24—861no—
904C24—861no—
905C24—861no—
906C24—861no—
907C24—861no—
908C24—861no—
909C24—861no—
910C24—861no—
911C24—861no—
912C24—861no—
913C24—861no—
914C24—861no—
915C24—861no—
916C24—861no—
917C24—861no—
918C24—861no—
919C24—861no—
920C24—861no—
921C24C2×C4×D4312yes—
922C24C2×D17212yes—
923C24#1062189812yes—
924C24D4×D4312yes—
925C24D4×D4312yes—
926C24D4×D4312yes—
927C24#1062190212yes—
928C24C23×D4311yescharacteristic
929C2×D4—4316no—
930C2×D4—868no—
931C2×D4—868no—
932C2×D4—868no—
933C2×D4—868no—
934C2×D4—868no—
935C2×D4—868no—
936C2×D4—868no—
937C2×D4—868no—
938C2×D4—868no—
939C2×D4—868no—
940C2×D4—868no—
941C2×D4—1724no—
942C2×D4—1724no—
943C2×D4—1724no—
944C2×D4—1724no—
945C2×D4—1724no—
946C2×D4—1724no—
947C2×D4—1724no—
948C2×D4—1724no—
949C2×D4—1724no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—28no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—28no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—432no—
994C22×C4—432no—
995C22×C4—432no—
996C22×C4—432no—
997C22×C4—432no—
998C22×C4—432no—
999C22×C4—432no—
1000C22×C4—432no—
1001C22×C4—432no—
1002C22×C4—432no—
1003C22×C4—868no—
1004C22×C4—868no—
1005C22×C4—861no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—868no—
1014C22×C4—868no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4—861no—
1018C22×C4—861no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—861no—
1023C22×C4—861no—
1024C22×C4—861no—
1025C22×C4—861no—
1026C22×C4—861no—
1027C22×C4—861no—
1028C22×C4—861no—
1029C22×C4—861no—
1030C22×C4—861no—
1031C22×C4—861no—
1032C22×C4—861no—
1033C22×C4—861no—
1034C22×C4—861no—
1035C22×C4—861no—
1036C22×C4—861no—
1037C22×C4—861no—
1038C22×C4—861no—
1039C22×C4—1724no—
1040C22×C4—1724no—
1041C22×C4—1724no—
1042C22×C4—1724no—
1043C22×C4—1724no—
1044C22×C4—1724no—
1045C22×C4—1724no—
1046C22×C4—1724no—
1047C22×C4—1724no—
1048C22×C4—1724no—
1049C22×C4—1724no—
1050C22×C4—1724no—
1051C22×C4—1724no—
1052C22×C4—1724no—
1053C22×C4—1724no—
1054C22×C4—1724no—
1055C22×C4—1724no—
1056C22×C4C2×C4×D4312yes—
1057C22×C4C2×C4×D4312yes—
1058C22×C4C2×D17212yes—
1059C22×C4C2×D17212yes—
1060C22×C4D4×D4312yes—
1061C22×C4#1062190012yes—
1062C4⋊C4—868no—
1063C4⋊C4—868no—
1064C22⋊C4—28no—
1065C22⋊C4—44no—
1066C22⋊C4—868no—
1067C22⋊C4—868no—
1068C22⋊C4—868no—
1069C22⋊C4—1724no—
1070C22⋊C4—1724no—
1071C22⋊C4—1724no—
1072C22⋊C4—1724no—
1073C22⋊C4—1724no—
1074C22⋊C4—1724no—
1075C42—868no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—434no—
1105C23—862no—
1106C23—862no—
1107C23—862no—
1108C23—862no—
1109C23—862no—
1110C23—862no—
1111C23—862no—
1112C23—862no—
1113C23—862no—
1114C23—862no—
1115C23—862no—
1116C23—862no—
1117C23—862no—
1118C23—862no—
1119C23—862no—
1120C23—862no—
1121C23—862no—
1122C23—862no—
1123C23—862no—
1124C23—862no—
1125C23—862no—
1126C23—862no—
1127C23—862no—
1128C23—862no—
1129C23—862no—
1130C23—1721no—
1131C23—1721no—
1132C23—1721no—
1133C23—1721no—
1134C23—1721no—
1135C23—1721no—
1136C23—1721no—
1137C23—1721no—
1138C23—1721no—
1139C23—1721no—
1140C23—1721no—
1141C23—1721no—
1142C23—1721no—
1143C23—1721no—
1144C23—1721no—
1145C23—1721no—
1146C23—1721no—
1147C23—1721no—
1148C23—1721no—
1149C23—1721no—
1150C23—1721no—
1151C23—1721no—
1152C23—1721no—
1153C23—1721no—
1154C23—1721no—
1155C23—1721no—
1156C23—1721no—
1157C23—1721no—
1158C23—1721no—
1159C23—1721no—
1160C23—1721no—
1161C23—1721no—
1162C23—1721no—
1163C23—1721no—
1164C23—1721no—
1165C23—1721no—
1166C23—1721no—
1167C23—1721no—
1168C23—1721no—
1169C23—1721no—
1170C23—1721no—
1171C23—1721no—
1172C23—1721no—
1173C23—1721no—
1174C23C22⋊C4×D4314yes—
1175C23#1306328714yes—
1176C23C4×D17214yes—
1177C23#1306329514yes—
1178C23#1306329814yes—
1179C23#1306330014yes—
1180C23#1306331014yes—
1181C23C22×C4×D4311yescharacteristic
1182C23C2×D4×D4311yescharacteristic
1183C23C2×D4×D4311yescharacteristic
1184C23C2×D4×D4311yescharacteristic
1185C23C2×D4×D4311yescharacteristic
1186C23C22×D17211yescharacteristic
1187C23#41×D4311yescharacteristic
1188C23#41×D4311yescharacteristic
1189C23C2×#1062190011yescharacteristic
1190C23C2×#1062189811yescharacteristic
1191C23C2×#1062190211yescharacteristic
1192C23#1306337011yescharacteristic
1193C23#1306337011yescharacteristic
1194C23#1306337111yescharacteristic
1195C23#1306337211yescharacteristic
1196D4—8632no—
1197D4—17216no—
1198D4—17216no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—416no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—434no—
1242C2×C4—434no—
1243C2×C4—862no—
1244C2×C4—862no—
1245C2×C4—862no—
1246C2×C4—862no—
1247C2×C4—862no—
1248C2×C4—862no—
1249C2×C4—862no—
1250C2×C4—862no—
1251C2×C4—862no—
1252C2×C4—862no—
1253C2×C4—862no—
1254C2×C4—862no—
1255C2×C4—862no—
1256C2×C4—862no—
1257C2×C4—862no—
1258C2×C4—862no—
1259C2×C4—862no—
1260C2×C4—862no—
1261C2×C4—862no—
1262C2×C4—862no—
1263C2×C4—862no—
1264C2×C4—862no—
1265C2×C4—862no—
1266C2×C4—862no—
1267C2×C4—17216no—
1268C2×C4—17216no—
1269C2×C4—17216no—
1270C2×C4—1721no—
1271C2×C4—1721no—
1272C2×C4—1721no—
1273C2×C4—1721no—
1274C2×C4—1721no—
1275C2×C4—1721no—
1276C2×C4—1721no—
1277C2×C4—1721no—
1278C2×C4—1721no—
1279C2×C4—1721no—
1280C2×C4—1721no—
1281C2×C4—1721no—
1282C2×C4—1721no—
1283C2×C4—1721no—
1284C2×C4—1721no—
1285C2×C4—1721no—
1286C2×C4(C22⋊D43)⋊C414yescomplemented
1287C22—24no—
1288C22—24no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—24no—
1298C22—24no—
1299C22—24no—
1300C22—24no—
1301C22—864no—
1302C22—864no—
1303C22—864no—
1304C22—3441no—
1305C22—3441no—
1306C22—3441no—
1307C22—3441no—
1308C22—3441no—
1309C22—3441no—
1310C22—3441no—
1311C22—3441no—
1312C22—1722no—
1313C22—1722no—
1314C22—1722no—
1315C22—1722no—
1316C22—1722no—
1317C22—1722no—
1318C22—1722no—
1319C22—1722no—
1320C22—1722no—
1321C22—1722no—
1322C22—1722no—
1323C22—1722no—
1324C22—1722no—
1325C22—1722no—
1326C22—1722no—
1327C22—1722no—
1328C22—1722no—
1329C22—1722no—
1330C22—1722no—
1331C22#1458277718yescomplemented
1332C22C2×C22⋊C4×D4311yescharacteristic
1333C22C2×(C22⋊D43)⋊C411yescharacteristic
1334C22C2×#1306328711yescharacteristic
1335C22C2×C4×D17211yescharacteristic
1336C22#1458336711yescharacteristic
1337C22#1458337211yescharacteristic
1338C22#1458337911yescharacteristic
1339C22C2×#1306329511yescharacteristic
1340C22#121×D4311yescharacteristic
1341C22C2×#1306329811yescharacteristic
1342C22C2×#1306330011yescharacteristic
1343C22C2×#1306331011yescharacteristic
1344C22#1458341211yescharacteristic
1345C22#1458343511yescharacteristic
1346C22#1458344411yescharacteristic
1347C22#1458345711yescharacteristic
1348C22#1458347611yescharacteristic
1349C22#1458348911yescharacteristic
1350C22#1458349811yescharacteristic
1351C22#1458353111yescharacteristic
1352C22#1458353111yescharacteristic
1353C22D4×D17211yescharacteristic
1354C22#1458353611yescharacteristic
1355C22#1458353611yescharacteristic
1356C22#1458354111yescharacteristic
1357C22#1458354111yescharacteristic
1358C22#1458354411yescharacteristic
1359C22#1458354411yescharacteristic
1360C22#1458354711yescharacteristic
1361C22#1458354711yescharacteristic
1362C22#1458355311yescharacteristic
1363C22#1458355811yescharacteristic
1364C22#1458359511yescharacteristic
1365C22#1458359811yescharacteristic
1366C22#1458359811yescharacteristic
1367C4—24no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—81no—
1372C4—81no—
1373C4—864no—
1374C4—864no—
1375C4—1722no—
1376C4—1722no—
1377C4—1722no—
1378C4—1722no—
1379C2—28no—
1380C2—3442no—
1381C2—1724no—
1382C2C2×#1458277711yescharacteristic
1383C2#1913710111yescharacteristic
1384C2#1913729511yescharacteristic
1385C2#1913741111yescharacteristic
1386C2#1913741911yescharacteristic
1387C2#1913760911yescharacteristic
1388C2#1913764511yescharacteristic
1389C2#1913796811yescharacteristic
1390C2#1913803411yescharacteristic
1391C2#1913812911yescharacteristic
1392C2#1913814411yescharacteristic
1393C2#1913820311yescharacteristic
1394C2#1913833411yescharacteristic
1395C2#1913834911yescharacteristic
1396C2#1913955911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC22×#13063299C2
hypercenterC22⋊#95D43
hypocenterC43#14023
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×(C22⋊D43)⋊C4C2semidirect
3. C2×#14582777C2semidirect
4. C2×#14582776C2semidirect
5. C2×#14582776C2semidirect
6. C2×#14582776C2semidirect
7. C22×C43⋊#95C2semidirect
8. #19132847C2semidirect
9. #19132843C2semidirect
10. #19132839C2semidirect
11. #19132835C2semidirect
12. #19132831C2semidirect
13. #19132829C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×C22⋊#95C2semidirect
24. C2×#13063299C4semidirect
70. C22×D172C2×C4semidirect
82. C22×C22⋊D43C2×C4semidirect
98. C23×Dic43D4semidirect
116. C2×C4⋊Dic43C2×C4semidirect
145. C2×(C2×D43)⋊C4C2×C4semidirect
146. C2×(C2×D43)⋊C4C2×C4semidirect
159. C43⋊#95D4semidirect
167. C23×C4×C43C2×C4semidirect
179. C2×C22⋊C4×C43D4semidirect
292. C2×C22⋊D43C22⋊C4semidirect
539. C2×C4×C43C4×D4semidirect
585. C2×Dic43#121semidirect
603. C22×C43#386semidirect
695. C22⋊#95D43semidirect
760. C43#14023semidirect
818. C23×C4C4×D43semidirect
865. C2×C22⋊C4D172semidirect
1286. C2×C4(C22⋊D43)⋊C4semidirect
1331. C22#14582777semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130632992
C22×(C22⋊D43)⋊C42
C2×#145827772
C2×#145827762
C22×C43⋊#952
#191328472
#191328432
#191328392
#191328352
#191328312
#191328292
(C2×D43)⋊#952
C43×C22⋊#952
#1402343