Finite Group Databasebeta

← #25019750

Subgroups — #25019750

Order 11008.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582775C211yesmaximal, characteristic
2C2×#14582775C211yesmaximal, characteristic
3C2×#14582775C211yesmaximal, characteristic
4C2×#14582756C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6C2×#95×D43C211yesmaximal, characteristic, complemented
7#19132856C211yesmaximal, characteristic, complemented
8#19132854C211yesmaximal, characteristic, complemented
9#19132842C211yesmaximal, characteristic, complemented
10#19132840C211yesmaximal, characteristic, complemented
11#19132832C211yesmaximal, characteristic, complemented
12#19132829C211yesmaximal, characteristic, complemented
13#19132822C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28#14582775—24no—
29#14582775—24no—
30#14582775C418yescomplemented
31#14582756—24no—
32C4×(C2×D43)⋊C4—24no—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49#95×D43—24no—
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#388—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43C2×C414yes—
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
76C22×C4×D43—22no—
77C22×C4×D43—22no—
78C22×C4×D43—22no—
79C22×C4×D43—22no—
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—22no—
85C22×C4×D43—22no—
86C22×C4×D43—41no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89C22×C4×D43—41no—
90C22×C4×D43—41no—
91C22×C4×D43—41no—
92C22×C4×D43C2×C414yes—
93C22×C4×D43D414yes—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43—22no—
96C2×C4⋊Dic43—41no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43—41no—
101C2×C22⋊Dic43—41no—
102C2×C22⋊Dic43—41no—
103C2×C22⋊Dic43—41no—
104C2×C22⋊Dic43—41no—
105C2×C22⋊Dic43C2×C414yescomplemented
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112C2×(C2×D43)⋊C4—22no—
113C2×(C2×D43)⋊C4C2×C414yes—
114C2×(C2×D43)⋊C4D414yes—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—41no—
117C2×C4×Dic43—41no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95C2×C414yescomplemented
133C43⋊#95C2×C414yescomplemented
134C25×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—41no—
144C2×C22⋊C4×C43—22no—
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43—22no—
151C2×C22⋊C4×C43—41no—
152C2×C22⋊C4×C43C2×C414yescomplemented
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—22no—
156#95×C43—22no—
157#95×C43D414yescomplemented
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43C22×C412yes—
173C24×C43C2411yescharacteristic
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43C22×C412yes—
183C23×D43C2×D412yes—
184C23×D43C2×D412yes—
185C23×D43#4112yes—
186C23×D43#4112yes—
187C23×D43#4112yes—
188C23×D43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43C22×C412yes—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C2×D412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43#4112yes—
230C22×C4×C43#4112yes—
231C2×C22⋊D43—28no—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—28no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—44no—
236C2×C22⋊D43—44no—
237C2×C22⋊D43—44no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43—21no—
281C22×Dic43C22×C412yes—
282C22×Dic43C22×C412yes—
283C22×Dic43C22×C412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43C2×D412yes—
286C22×Dic43#4112yes—
287C2×C4×D43—28no—
288C2×C4×D43—28no—
289C2×C4×D43—28no—
290C2×C4×D43—28no—
291C2×C4×D43—28no—
292C2×C4×D43—44no—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C2×C4×D43—44no—
303C2×C4×D43—44no—
304C2×C4×D43—44no—
305C2×C4×D43—44no—
306C2×C4×D43—44no—
307C2×C4×D43—44no—
308C4⋊C4×C43—44no—
309C22⋊C4×C43—28no—
310C22⋊C4×C43—44no—
311C22⋊C4×C43—44no—
312C42×C43—44no—
313C22⋊Dic43—44no—
314C22⋊Dic43—44no—
315C22⋊Dic43—44no—
316(C2×D43)⋊C4—28no—
317(C2×D43)⋊C4—28no—
318(C2×D43)⋊C4—44no—
319C4⋊Dic43—44no—
320C4×Dic43—44no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43—41no—
351C23×C43—41no—
352C23×C43—41no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—41no—
356C23×C43C23×C411yescharacteristic
357C23×C43C22×D411yescharacteristic
358C23×C43C22×D411yescharacteristic
359C23×C43C22×D411yescharacteristic
360C23×C43C2×#4111yescharacteristic
361C23×C43C2×#4111yescharacteristic
362C23×C43C2×#4111yescharacteristic
363C23×C43C2×#4111yescharacteristic
364C23×C43C2×#4111yescharacteristic
365C23×C43C2×#4111yescharacteristic
366C23×C43C2×#4111yescharacteristic
367C23×C43H(5,𝔽2)11yescharacteristic
368C23×C43H(5,𝔽2)11yescharacteristic
369C23×C43H(5,𝔽2)11yescharacteristic
370C23×C432−1+411yescharacteristic
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
381C22×D43—22no—
382C22×D43—22no—
383C22×D43—22no—
384C22×D43—22no—
385C22×D43—22no—
386C22×D43—22no—
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—22no—
394C22×D43—22no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43#11714yes—
400C22×D43C4×D414yes—
401C22×D43C4×D414yes—
402C22×D43#12114yes—
403C22×D43#12314yes—
404C22×D43#12414yes—
405C22×D43#12614yes—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43—41no—
440C2×C4×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43C4×D414yes—
447C2×C4×C43#12114yes—
448C22⋊D43—416no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—22no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43—41no—
491C2×Dic43—41no—
492C2×Dic43—41no—
493C2×Dic43—41no—
494C2×Dic43—41no—
495C2×Dic43—41no—
496C2×Dic43—41no—
497C2×Dic43—41no—
498C4×D43—416no—
499C4×D43—416no—
500C4×D43—416no—
501#13999—431nomaximal, Sylow
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43—42no—
509C22×C43—81no—
510C22×C43—81no—
511C22×C43—81no—
512C22×C43—81no—
513C22×C43—81no—
514C22×C43—81no—
515C22×C43—81no—
516C22×C43—81no—
517C22×C43C2×#11711yescharacteristic
518C22×C43C2×C4×D411yescharacteristic
519C22×C43C2×C4×D411yescharacteristic
520C22×C43C2×C4×D411yescharacteristic
521C22×C43C4×#4111yescharacteristic
522C22×C43#51811yescharacteristic
523C22×C43#52011yescharacteristic
524C22×C43C2×#12111yescharacteristic
525C22×C43C2×#12111yescharacteristic
526C22×C43C2×#12311yescharacteristic
527C22×C43#52511yescharacteristic
528C22×C43C2×#12411yescharacteristic
529C22×C43C2×#12611yescharacteristic
530C22×C43#52911yescharacteristic
531C22×C43#53211yescharacteristic
532C22×C43#53411yescharacteristic
533C22×C43#53711yescharacteristic
534C22×C43#53811yescharacteristic
535C22×C43#53911yescharacteristic
536C22×C43D4211yescharacteristic
537C22×C43#54611yescharacteristic
538C22×C43#54611yescharacteristic
539C22×C43#54611yescharacteristic
540C22×C43#54611yescharacteristic
541C22×C43#54711yescharacteristic
542C22×C43#54811yescharacteristic
543C22×C43#55111yescharacteristic
544C22×C43#55111yescharacteristic
545C22×C43#55111yescharacteristic
546C22×C43#55111yescharacteristic
547C22×C43#55211yescharacteristic
548C22×C43#55211yescharacteristic
549C22×C43#55311yescharacteristic
550C22×C43#55311yescharacteristic
551C22×C43#55311yescharacteristic
552C2×D43—24no—
553C2×D43—24no—
554C2×D43—24no—
555C2×D43—24no—
556C2×D43—24no—
557C2×D43—24no—
558C2×D43—24no—
559C2×D43—24no—
560C2×D43—24no—
561C2×D43—24no—
562C2×D43—24no—
563C2×D43—24no—
564C2×D43—24no—
565C2×D43—24no—
566C2×D43#38818yescomplemented
567C4×C43—24no—
568C4×C43—24no—
569C4×C43—42no—
570C4×C43—42no—
571C4×C43—42no—
572C4×C43—81no—
573Dic43—42no—
574Dic43—42no—
575Dic43—42no—
576Dic43—42no—
577Dic43—42no—
578Dic43—42no—
579Dic43—81no—
580C2×#388D4311yescharacteristic, complemented
581C2×#386—431no—
582C2×#386—431no—
583C2×#386—431no—
584C2×#380—431no—
585C2×C4×C22⋊C4—431no—
586C22×#95—431no—
587#1443—431no—
588#1442—431no—
589#1440—431no—
590#1439—431no—
591#1437—431no—
592#1436—431no—
593#1434—431no—
594C22⋊#95—431no—
595C2×C43—82no—
596C2×C43C2×#38811yescharacteristic
597C2×C43C4×#12111yescharacteristic
598C2×C43#232511yescharacteristic
599C2×C43#235211yescharacteristic
600C2×C43#235311yescharacteristic
601C2×C43#235811yescharacteristic
602C2×C43#235911yescharacteristic
603C2×C43#241211yescharacteristic
604C2×C43#241611yescharacteristic
605C2×C43#247211yescharacteristic
606C2×C43#248111yescharacteristic
607C2×C43#248811yescharacteristic
608C2×C43#249811yescharacteristic
609C2×C43#251011yescharacteristic
610C2×C43#254311yescharacteristic
611D43—28no—
612C23×D4—431no—
613C24×C4—431no—
614C24×C4—431no—
615C24×C4—431no—
616C22×C4⋊C4—431no—
617C22×C4⋊C4C2×D4311yescharacteristic
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C22⋊C4—431no—
624C22×C22⋊C4C2×D4311yescharacteristic
625C22×C22⋊C4C2×D4311yescharacteristic
626C22×C22⋊C4C2×D4311yescharacteristic
627C22×C42—431no—
628C22×C42C2×D4311yescharacteristic
629#388—24no—
630#386—438no—
631#386—864no—
632#386—864no—
633#380—864no—
634C4×C22⋊C4—864no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—431no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—431no—
646C2×#95—431no—
647C2×#95—431no—
648C2×#95—431no—
649C2×#95—431no—
650C2×#95—431no—
651C2×#95—864no—
652C2×#95C2×D4311yescharacteristic
653C2×#95C2×D4311yescharacteristic
654C43#1399911yescharacteristic, complemented, Sylow
655C25—431no—
656C25C22×D4311yescharacteristic
657C22×D4—434no—
658C22×D4—862no—
659C22×D4—862no—
660C22×D4—862no—
661C22×D4—862no—
662C22×D4—862no—
663C22×D4—862no—
664C23×C4—431no—
665C23×C4—431no—
666C23×C4—431no—
667C23×C4—431no—
668C23×C4—431no—
669C23×C4—431no—
670C23×C4—434no—
671C23×C4—434no—
672C23×C4—431no—
673C23×C4—862no—
674C23×C4—862no—
675C23×C4—862no—
676C23×C4—862no—
677C23×C4—862no—
678C23×C4—862no—
679C23×C4—862no—
680C23×C4—862no—
681C23×C4—862no—
682C23×C4—862no—
683C23×C4—862no—
684C23×C4—862no—
685C23×C4—862no—
686C23×C4—1721no—
687C23×C4—1721no—
688C23×C4—1721no—
689C23×C4—1721no—
690C23×C4—1721no—
691C23×C4—1721no—
692C23×C4C22×D4311yescharacteristic
693C23×C4C22×D4311yescharacteristic
694C23×C4C22×D4311yescharacteristic
695C23×C4C22×D4311yescharacteristic
696C23×C4C22×D4311yescharacteristic
697C23×C4C22×D4311yescharacteristic
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—862no—
703C2×C4⋊C4—1721no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—434no—
713C2×C22⋊C4—434no—
714C2×C22⋊C4—434no—
715C2×C22⋊C4—862no—
716C2×C22⋊C4—862no—
717C2×C22⋊C4—862no—
718C2×C22⋊C4—862no—
719C2×C22⋊C4—862no—
720C2×C22⋊C4—862no—
721C2×C22⋊C4—862no—
722C2×C22⋊C4—862no—
723C2×C22⋊C4—862no—
724C2×C22⋊C4—862no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C22⋊C4—1721no—
728C2×C22⋊C4—1721no—
729C2×C22⋊C4—1721no—
730C2×C22⋊C4C4×D4314yescomplemented
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—862no—
735C2×C42—1721no—
736C2×C42—1721no—
737#95—22no—
738#95—434no—
739#95—434no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—862no—
745#95—862no—
746#95—862no—
747#95—862no—
748#95—862no—
749#95—862no—
750#95—862no—
751#95—862no—
752#95—1721no—
753#95—1721no—
754#95C22⋊D4314yescomplemented
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—432no—
770C24—432no—
771C24—432no—
772C24—432no—
773C24—432no—
774C24—432no—
775C24—432no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24—861no—
780C24—861no—
781C24—861no—
782C24—861no—
783C24—861no—
784C24C2×C4×D4312yes—
785C24C23×D4311yescharacteristic
786C2×D4—868no—
787C2×D4—868no—
788C2×D4—868no—
789C2×D4—1724no—
790C2×D4—1724no—
791C2×D4—1724no—
792C2×D4—1724no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—868no—
833C22×C4—868no—
834C22×C4—868no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—861no—
870C22×C4—861no—
871C22×C4—868no—
872C22×C4—868no—
873C22×C4—861no—
874C22×C4—861no—
875C22×C4—861no—
876C22×C4—861no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—1724no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4—1724no—
887C22×C4—1724no—
888C22×C4—1724no—
889C22×C4—1724no—
890C22×C4—1724no—
891C22×C4—1724no—
892C22×C4—1724no—
893C22×C4—1724no—
894C22×C4—1724no—
895C22×C4—1724no—
896C22×C4C2×C4×D4312yes—
897C22×C4C2×C4×D4312yes—
898C22×C4#1062189812yes—
899C22×C4D4×D4312yes—
900C22×C4D4×D4312yes—
901C22×C4#1062190012yes—
902C22×C4C2×C22⋊D4312yes—
903C22×C4C2×C22⋊D4312yes—
904C22×C4C2×C22⋊D4312yes—
905C4⋊C4—44no—
906C4⋊C4—1724no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—868no—
911C22⋊C4—868no—
912C22⋊C4—1724no—
913C22⋊C4—1724no—
914C22⋊C4—1724no—
915C22⋊C4—1724no—
916C42—44no—
917C42—1724no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—434no—
954C23—434no—
955C23—434no—
956C23—434no—
957C23—434no—
958C23—434no—
959C23—434no—
960C23—862no—
961C23—862no—
962C23—862no—
963C23—862no—
964C23—862no—
965C23—862no—
966C23—862no—
967C23—862no—
968C23—862no—
969C23—862no—
970C23—862no—
971C23—862no—
972C23—862no—
973C23—862no—
974C23—862no—
975C23—862no—
976C23—862no—
977C23—862no—
978C23—862no—
979C23—862no—
980C23—862no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—862no—
985C23—862no—
986C23—862no—
987C23—862no—
988C23C22×C4×D4311yescharacteristic
989C23C2×D4×D4311yescharacteristic
990C23C2×D4×D4311yescharacteristic
991C23C22×C22⋊D4311yescharacteristic
992C23#41×D4311yescharacteristic
993C23#41×D4311yescharacteristic
994C23#41×D4311yescharacteristic
995C23#41×D4311yescharacteristic
996C23#41×D4311yescharacteristic
997C23C2×#1062190011yescharacteristic
998C23C2×#1062189811yescharacteristic
999C23#1306337011yescharacteristic
1000C23#1306337111yescharacteristic
1001C23#1306337111yescharacteristic
1002C23#1306337211yescharacteristic
1003D4—17216no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—862no—
1059C2×C4—862no—
1060C2×C4—862no—
1061C2×C4—862no—
1062C2×C4—17216no—
1063C2×C4—17216no—
1064C2×C4—17216no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4—1721no—
1084C2×C4—1721no—
1085C2×C4—1721no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4—1721no—
1089C2×C4—1721no—
1090C2×C4—1721no—
1091C2×C4—1721no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4C4×C22⋊D4314yes—
1097C2×C4#1306329614yes—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—438no—
1114C22—864no—
1115C22—864no—
1116C22—864no—
1117C22—864no—
1118C22—864no—
1119C22—864no—
1120C22—864no—
1121C22—864no—
1122C22—864no—
1123C22—864no—
1124C22—864no—
1125C22—864no—
1126C22—864no—
1127C22—864no—
1128C22#117×D4311yescharacteristic
1129C22C4×D4×D4311yescharacteristic
1130C22C4×D4×D4311yescharacteristic
1131C22C2×C4×C22⋊D4311yescharacteristic
1132C22C4×#1062190011yescharacteristic
1133C22#1458337111yescharacteristic
1134C22#1458337911yescharacteristic
1135C22#121×D4311yescharacteristic
1136C22C2×#1306329611yescharacteristic
1137C22#123×D4311yescharacteristic
1138C22#1458340611yescharacteristic
1139C22#124×D4311yescharacteristic
1140C22#126×D4311yescharacteristic
1141C22#1458343111yescharacteristic
1142C22#1458344611yescharacteristic
1143C22#1458346011yescharacteristic
1144C22#1458347811yescharacteristic
1145C22#1458348311yescharacteristic
1146C22#1458349011yescharacteristic
1147C22D4×C22⋊D4311yescharacteristic
1148C22#1458353711yescharacteristic
1149C22#1458353711yescharacteristic
1150C22#1458354211yescharacteristic
1151C22#1458354511yescharacteristic
1152C22#1458354911yescharacteristic
1153C22#1458355611yescharacteristic
1154C22#1458357211yescharacteristic
1155C22#1458357211yescharacteristic
1156C22#1458357811yescharacteristic
1157C22#1458357911yescharacteristic
1158C22#1458358511yescharacteristic
1159C22#1458358811yescharacteristic
1160C22#1458359311yescharacteristic
1161C22#1458359611yescharacteristic
1162C22#1458360011yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—81no—
1169C4—3441no—
1170C4—1722no—
1171C4—1722no—
1172C4—1722no—
1173C4—1722no—
1174C4—1722no—
1175C4—1722no—
1176C2—82no—
1177C2—868no—
1178C2#388×D4311yescharacteristic
1179C2C4×#1306329611yescharacteristic
1180C2#1913729911yescharacteristic
1181C2#1913752511yescharacteristic
1182C2#1913753011yescharacteristic
1183C2#1913757211yescharacteristic
1184C2#1913758611yescharacteristic
1185C2#1913798711yescharacteristic
1186C2#1913803111yescharacteristic
1187C2#1913871711yescharacteristic
1188C2#1913885211yescharacteristic
1189C2#1913892011yescharacteristic
1190C2#1913903811yescharacteristic
1191C2#1913916011yescharacteristic
1192C2#1913956011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#13999
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#14582756C2semidirect
5. C2×C4×(C2×D43)⋊C4C2semidirect
6. C2×#95×D43C2semidirect
7. #19132856C2semidirect
8. #19132854C2semidirect
9. #19132842C2semidirect
10. #19132840C2semidirect
11. #19132832C2semidirect
12. #19132829C2semidirect
13. #19132822C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C2×C43×#388C2semidirect
30. #14582775C4semidirect
105. C2×C22⋊Dic43C2×C4semidirect
132. C43⋊#95C2×C4semidirect
133. C43⋊#95C2×C4semidirect
152. C2×C22⋊C4×C43C2×C4semidirect
157. #95×C43D4semidirect
566. C2×D43#388semidirect
580. C2×#388D43semidirect
654. C43#13999semidirect
730. C2×C22⋊C4C4×D43semidirect
754. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827752
C2×#145827562
C2×C4×(C2×D43)⋊C42
C2×#95×D432
#191328562
#191328542
#191328422
#191328402
#191328322
#191328292
#191328222
(C2×D43)⋊#952
C2×C43×#3882
#1399943