Finite Group Databasebeta

← #25018095

Subgroups — #25018095

Order 11008.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C2×#14582778C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6C22×C43⋊#95C211yesmaximal, characteristic, complemented
7#19132833C211yesmaximal, characteristic, complemented
8#19132831C211yesmaximal, characteristic, complemented
9#19132830C211yesmaximal, characteristic, complemented
10#19132828C211yesmaximal, characteristic, complemented
11#19132819C211yesmaximal, characteristic, complemented
12#19132817C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14C4×C43⋊#95C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—24no—
21C2×(C22⋊D43)⋊C4—24no—
22C2×(C22⋊D43)⋊C4C418yescomplemented
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582778C418yescomplemented
34#14582776C418yescomplemented
35C22⋊C4×Dic43—24no—
36C4×(C2×D43)⋊C4—24no—
37C2×C43⋊#95—24no—
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
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C24×C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C22×C42×C43C2211yescharacteristic
56C22×C42×C43C2211yescharacteristic
57C4×C22⋊C4×C43—24no—
58C2×#95×C43C2211yescharacteristic
59C2×#95×C43C2211yescharacteristic
60C24×D43C2311yescharacteristic
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—22no—
64C22×C22⋊D43—22no—
65C22×C22⋊D43C2×C414yes—
66C22×C22⋊D43C2×C414yes—
67C22×C22⋊D43C2×C414yes—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—22no—
71C23×Dic43—22no—
72C23×Dic43—22no—
73C23×Dic43—22no—
74C23×Dic43—22no—
75C23×Dic43—22no—
76C23×Dic43—41no—
77C23×Dic43—41no—
78C23×Dic43—41no—
79C23×Dic43—41no—
80C23×Dic43C2×C414yes—
81C23×Dic43C2×C414yescomplemented
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C22×C4×D43—22no—
90C22×C4×D43—22no—
91C22×C4×D43—22no—
92C22×C4×D43—22no—
93C22×C4×D43—41no—
94C22×C4×D43—41no—
95C22×C4×D43C2×C414yescomplemented
96(C22⋊D43)⋊C4—232no—
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4C2×C414yescomplemented
100C2×C22⋊Dic43—22no—
101C2×C22⋊Dic43—22no—
102C2×C22⋊Dic43C2×C414yescomplemented
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4C2×C414yescomplemented
114C2×(C2×D43)⋊C4C2×C414yescomplemented
115C2×(C2×D43)⋊C4C2×C414yescomplemented
116C2×(C2×D43)⋊C4C2×C414yescomplemented
117C2×(C2×D43)⋊C4C2×C414yescomplemented
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—22no—
124C2×C4×Dic43—41no—
125C2×C4×Dic43—41no—
126C2×C4×Dic43C2×C414yescomplemented
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C43⋊#95C2×C414yescomplemented
137C43⋊#95C2×C414yescomplemented
138C43⋊#95C2×C414yescomplemented
139C43⋊#95C2×C414yescomplemented
140C43⋊#95D414yescomplemented
141C25×C43C2311yescharacteristic
142C23×C4×C43—22no—
143C23×C4×C43—22no—
144C23×C4×C43—22no—
145C23×C4×C43—22no—
146C23×C4×C43—41no—
147C23×C4×C43—41no—
148C23×C4×C43C2×C414yescomplemented
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C2×C22⋊C4×C43—22no—
156C2×C22⋊C4×C43—22no—
157C2×C22⋊C4×C43C2×C414yes—
158C2×C22⋊C4×C43C2×C414yescomplemented
159C2×C22⋊C4×C43D414yes—
160C2×C22⋊C4×C43D414yes—
161C2×C42×C43—22no—
162C2×C42×C43—22no—
163C2×C42×C43—22no—
164C2×C42×C43—22no—
165C2×C42×C43—41no—
166C2×C42×C43—41no—
167#95×C43—22no—
168#95×C43—22no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43C22×C412yes—
178C24×C43C22×C412yes—
179C24×C43C22×C412yes—
180C24×C43C2×D412yes—
181C24×C43C2×D412yes—
182C24×C43#4112yes—
183C24×C43#4112yes—
184C24×C43C2411yescharacteristic
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—21no—
195C23×D43—21no—
196C23×D43—21no—
197C23×D43C22×C412yes—
198C23×D43C22×C412yes—
199C23×D43C22×C412yes—
200C22×C4×C43—28no—
201C22×C4×C43—28no—
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×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—44no—
233C22×C4×C43—44no—
234C22×C4×C43—44no—
235C22×C4×C43—44no—
236C22×C4×C43—44no—
237C22×C4×C43C22×C412yes—
238C22×C4×C43C22×C412yes—
239C22×C4×C43C22×C412yes—
240C22×C4×C43C22×C412yes—
241C22×C4×C43C22×C412yes—
242C22×C4×C43C22×C412yes—
243C22×C4×C43C2×D412yes—
244C22×C4×C43C2×D412yes—
245C22×C4×C43C2×D412yes—
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D412yes—
248C22×C4×C43#4112yes—
249C2×C22⋊D43—28no—
250C2×C22⋊D43—28no—
251C2×C22⋊D43—28no—
252C2×C22⋊D43—28no—
253C2×C22⋊D43—28no—
254C2×C22⋊D43—28no—
255C2×C22⋊D43C42116yescomplemented
256C22×Dic43—28no—
257C22×Dic43—28no—
258C22×Dic43—28no—
259C22×Dic43—28no—
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×Dic43—21no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43—21no—
286C22×Dic43—21no—
287C22×Dic43—21no—
288C22×Dic43—21no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—44no—
297C22×Dic43—44no—
298C22×Dic43—44no—
299C22×Dic43—44no—
300C22×Dic43—44no—
301C22×Dic43—44no—
302C22×Dic43—44no—
303C22×Dic43—44no—
304C22×Dic43—44no—
305C22×Dic43—44no—
306C22×Dic43C22×C412yes—
307C22×Dic43C22×C412yes—
308C22×Dic43C22×C412yes—
309C22×Dic43C22×C412yes—
310C22×Dic43C22×C412yes—
311C22×Dic43C22×C412yes—
312C22×Dic43C22×C412yes—
313C22×Dic43C22×C412yes—
314C22×Dic43C22×C412yes—
315C22×Dic43C2×D412yes—
316C22×Dic43C2×D412yes—
317C22×Dic43#4112yes—
318C22×Dic43#4112yes—
319C2×C4×D43—28no—
320C2×C4×D43—28no—
321C2×C4×D43—44no—
322C2×C4×D43—44no—
323C2×C4×D43—44no—
324C2×C4×D43—44no—
325C2×C4×D43—44no—
326C22⋊C4×C43—28no—
327C22⋊C4×C43C22⋊C4116yescomplemented
328C42×C43—44no—
329C42×C43—44no—
330C22⋊Dic43—28no—
331(C2×D43)⋊C4—28no—
332(C2×D43)⋊C4—28no—
333(C2×D43)⋊C4—28no—
334(C2×D43)⋊C4—44no—
335(C2×D43)⋊C4—44no—
336Dic43⋊C4—28no—
337C4×Dic43—28no—
338C4×Dic43—44no—
339C4×Dic43—44no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—22no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—22no—
366C23×C43—22no—
367C23×C43—22no—
368C23×C43C2×C4214yes—
369C23×C43C2×C22⋊C414yes—
370C23×C43#11714yes—
371C23×C43C4×D414yes—
372C23×C43C4×D414yes—
373C23×C43C4×D414yes—
374C23×C43C4×D414yes—
375C23×C43C23×C411yescharacteristic
376C23×C43C23×C411yescharacteristic
377C23×C43C23×C411yescharacteristic
378C23×C43C22×D411yescharacteristic
379C23×C43C22×D411yescharacteristic
380C23×C43C22×D411yescharacteristic
381C23×C43C2×#4111yescharacteristic
382C23×C43C2×#4111yescharacteristic
383C23×C43C2×#4111yescharacteristic
384C23×C43C2×#4111yescharacteristic
385C23×C43C2×#4111yescharacteristic
386C23×C43H(5,𝔽2)11yescharacteristic
387C23×C43H(5,𝔽2)11yescharacteristic
388C23×C43H(5,𝔽2)11yescharacteristic
389C23×C432−1+411yescharacteristic
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—22no—
400C22×D43—22no—
401C22×D43—22no—
402C22×D43—22no—
403C22×D43—22no—
404C22×D43—22no—
405C22×D43—22no—
406C22×D43—22no—
407C22×D43—22no—
408C22×D43—41no—
409C22×D43—41no—
410C22×D43—41no—
411C22×D43—41no—
412C22×D43—41no—
413C22×D43—41no—
414C22×D43—41no—
415C22×D43—41no—
416C22×D43—41no—
417C22×D43—41no—
418C22×D43—41no—
419C22×D43—41no—
420C22×D43—41no—
421C22×D43—41no—
422C22×D43—41no—
423C22×D43—41no—
424C22×D43C2×C4214yes—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—22no—
436C2×C4×C43—22no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—22no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—22no—
444C2×C4×C43—22no—
445C2×C4×C43—22no—
446C2×C4×C43—22no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—416no—
453C2×C4×C43—41no—
454C2×C4×C43—41no—
455C2×C4×C43—41no—
456C2×C4×C43—41no—
457C2×C4×C43—41no—
458C2×C4×C43—41no—
459C2×C4×C43—41no—
460C2×C4×C43—41no—
461C2×C4×C43—41no—
462C2×C4×C43—41no—
463C2×C4×C43—41no—
464C2×C4×C43—41no—
465C2×C4×C43C2×C22⋊C414yes—
466C2×C4×C43C2×C22⋊C414yes—
467C2×C4×C43C4×D414yescomplemented
468C22⋊D43—232no—
469C2×Dic43—22no—
470C2×Dic43—22no—
471C2×Dic43—22no—
472C2×Dic43—22no—
473C2×Dic43—22no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—22no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—22no—
483C2×Dic43—22no—
484C2×Dic43—22no—
485C2×Dic43—22no—
486C2×Dic43—22no—
487C2×Dic43—22no—
488C2×Dic43—22no—
489C2×Dic43—22no—
490C2×Dic43—22no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—22no—
495C2×Dic43—22no—
496C2×Dic43—22no—
497C2×Dic43—22no—
498C2×Dic43—22no—
499C2×Dic43—416no—
500C2×Dic43—416no—
501C2×Dic43—41no—
502C2×Dic43—41no—
503C2×Dic43—41no—
504C2×Dic43—41no—
505C2×Dic43—41no—
506C2×Dic43—41no—
507C2×Dic43—41no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510C2×Dic43—41no—
511C2×Dic43—41no—
512C2×Dic43—41no—
513C2×Dic43—41no—
514C2×Dic43—41no—
515C2×Dic43—41no—
516C2×Dic43—41no—
517C2×Dic43C2×C4214yes—
518C2×Dic43C4×D414yes—
519C2×Dic43C4×D414yescomplemented
520C4×D43—416no—
521#13813—431nomaximal, Sylow
522C22×C43—24no—
523C22×C43—24no—
524C22×C43—24no—
525C22×C43—24no—
526C22×C43—24no—
527C22×C43—24no—
528C22×C43—24no—
529C22×C43—24no—
530C22×C43—24no—
531C22×C43—24no—
532C22×C43—24no—
533C22×C43—24no—
534C22×C43—24no—
535C22×C43—24no—
536C22×C43C4×C22⋊C418yescomplemented
537C22×C43C22×C4211yescharacteristic
538C22×C43C22×C22⋊C411yescharacteristic
539C22×C43C2×#11711yescharacteristic
540C22×C43C2×C4×D411yescharacteristic
541C22×C43C2×C4×D411yescharacteristic
542C22×C43C2×C4×D411yescharacteristic
543C22×C43C2×C4×D411yescharacteristic
544C22×C43C2×C4×D411yescharacteristic
545C22×C43C2×C4×D411yescharacteristic
546C22×C43C2×C4×D411yescharacteristic
547C22×C43C4×#4111yescharacteristic
548C22×C43C4×#4111yescharacteristic
549C22×C43C4×#4111yescharacteristic
550C22×C43#51811yescharacteristic
551C22×C43#51811yescharacteristic
552C22×C43#51811yescharacteristic
553C22×C43#52011yescharacteristic
554C22×C43#52011yescharacteristic
555C22×C43#52011yescharacteristic
556C22×C43D4211yescharacteristic
557C22×C43D4211yescharacteristic
558C22×C43#54611yescharacteristic
559C22×C43#54611yescharacteristic
560C22×C43#54611yescharacteristic
561C22×C43#54611yescharacteristic
562C22×C43#54611yescharacteristic
563C22×C43#54711yescharacteristic
564C22×C43#54711yescharacteristic
565C22×C43#54811yescharacteristic
566C22×C43#55111yescharacteristic
567C22×C43#55111yescharacteristic
568C22×C43#55211yescharacteristic
569C22×C43#55311yescharacteristic
570C22×C43#55311yescharacteristic
571C22×C43#55311yescharacteristic
572C2×D43—24no—
573C2×D43—24no—
574C2×D43—24no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—42no—
581C2×D43—42no—
582C2×D43—42no—
583C2×D43—42no—
584C2×D43—42no—
585C2×D43—42no—
586C2×D43—42no—
587C4×C43—24no—
588C4×C43—24no—
589C4×C43—24no—
590C4×C43—42no—
591C4×C43—42no—
592C4×C43—42no—
593Dic43—24no—
594Dic43—24no—
595Dic43—24no—
596Dic43—42no—
597Dic43—42no—
598Dic43—42no—
599Dic43—42no—
600C22×C4×D4—431no—
601C2×#386—431no—
602C2×#386—431no—
603C2×C4×C22⋊C4—431no—
604C2×C4×C22⋊C4—431no—
605C2×C4×C22⋊C4D4311yescharacteristic, complemented
606C22×#95—431no—
607#1437—431no—
608#1437—431no—
609#1436—431no—
610#1436—431no—
611#1434—431no—
612C22⋊#95—431no—
613C22⋊#95—431no—
614C4×#95—431no—
615C2×C43—28no—
616C2×C43C2×C4×C22⋊C411yescharacteristic
617C2×C43C42×D411yescharacteristic
618C2×C43#227511yescharacteristic
619C2×C43D4×C22⋊C411yescharacteristic
620C2×C43#233911yescharacteristic
621C2×C43#235211yescharacteristic
622C2×C43#235311yescharacteristic
623C2×C43#235811yescharacteristic
624C2×C43#235811yescharacteristic
625C2×C43#235911yescharacteristic
626C2×C43#235911yescharacteristic
627C2×C43#236111yescharacteristic
628C2×C43#236111yescharacteristic
629C2×C43#236411yescharacteristic
630C2×C43#236411yescharacteristic
631D43—44no—
632C23×D4—431no—
633C24×C4—431no—
634C24×C4—431no—
635C24×C4—431no—
636C24×C4C2×D4311yescharacteristic
637C2×C4×D4—438no—
638C2×C4×D4—864no—
639C2×C4×D4—864no—
640C22×C4⋊C4—431no—
641C22×C22⋊C4—431no—
642C22×C22⋊C4—431no—
643C22×C22⋊C4—431no—
644C22×C22⋊C4—431no—
645C22×C22⋊C4—431no—
646C22×C22⋊C4—431no—
647C22×C22⋊C4C2×D4311yescharacteristic
648C22×C22⋊C4C2×D4311yescharacteristic
649C22×C42—431no—
650C22×C42—431no—
651C22×C42—431no—
652C22×C42C2×D4311yescharacteristic
653C22×C42C2×D4311yescharacteristic
654#386—438no—
655#386—438no—
656C4×C22⋊C4—24no—
657C4×C22⋊C4—864no—
658C4×C22⋊C4—864no—
659C2×#95—431no—
660C2×#95—431no—
661C2×#95—431no—
662C2×#95—431no—
663C2×#95—431no—
664C2×#95—431no—
665C2×#95—431no—
666C2×#95—431no—
667C2×#95—431no—
668C2×#95—431no—
669C2×#95—431no—
670C2×#95—431no—
671C2×#95—431no—
672C2×#95—431no—
673C2×#95—864no—
674C2×#95C2×D4311yescharacteristic
675C2×#95C2×D4311yescharacteristic
676C43#1381311yescharacteristic, complemented, Sylow
677C25—431no—
678C25C22×D4311yescharacteristic
679C22×D4—434no—
680C22×D4—434no—
681C22×D4—434no—
682C22×D4—862no—
683C22×D4—862no—
684C22×D4—862no—
685C22×D4—862no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—431no—
693C23×C4—431no—
694C23×C4—431no—
695C23×C4—431no—
696C23×C4—431no—
697C23×C4—431no—
698C23×C4—431no—
699C23×C4—434no—
700C23×C4—434no—
701C23×C4—434no—
702C23×C4—862no—
703C23×C4—862no—
704C23×C4—862no—
705C23×C4—862no—
706C23×C4—862no—
707C23×C4—862no—
708C23×C4—862no—
709C23×C4—862no—
710C23×C4—862no—
711C23×C4—862no—
712C23×C4—862no—
713C23×C4—862no—
714C23×C4—1721no—
715C23×C4—1721no—
716C23×C4—1721no—
717C23×C4—1721no—
718C23×C4—1721no—
719C23×C4—1721no—
720C23×C4C4×D4314yescomplemented
721C23×C4C22×D4311yescharacteristic
722C23×C4C22×D4311yescharacteristic
723C23×C4C22×D4311yescharacteristic
724C23×C4C22×D4311yescharacteristic
725C23×C4C22×D4311yescharacteristic
726C23×C4C22×D4311yescharacteristic
727C4×D4—8632no—
728C2×C4⋊C4—434no—
729C2×C4⋊C4—862no—
730C2×C4⋊C4—862no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—434no—
734C2×C22⋊C4—434no—
735C2×C22⋊C4—434no—
736C2×C22⋊C4—434no—
737C2×C22⋊C4—434no—
738C2×C22⋊C4—434no—
739C2×C22⋊C4—862no—
740C2×C22⋊C4—862no—
741C2×C22⋊C4—862no—
742C2×C22⋊C4—862no—
743C2×C22⋊C4—862no—
744C2×C22⋊C4—862no—
745C2×C22⋊C4—862no—
746C2×C22⋊C4—862no—
747C2×C22⋊C4—1721no—
748C2×C22⋊C4—1721no—
749C2×C22⋊C4—1721no—
750C2×C22⋊C4—1721no—
751C2×C22⋊C4C4×D4314yes—
752C2×C22⋊C4C4×D4314yescomplemented
753C2×C22⋊C4D17214yes—
754C2×C22⋊C4C22⋊D4314yes—
755C2×C42—22no—
756C2×C42—22no—
757C2×C42—22no—
758C2×C42—22no—
759C2×C42—41no—
760C2×C42—41no—
761C2×C42—434no—
762C2×C42—862no—
763C2×C42—862no—
764C2×C42—862no—
765C2×C42—862no—
766C2×C42—862no—
767C2×C42—862no—
768C2×C42—1721no—
769C2×C42—1721no—
770#95—22no—
771#95—22no—
772#95—434no—
773#95—434no—
774#95—434no—
775#95—434no—
776#95—434no—
777#95—862no—
778#95—862no—
779#95—862no—
780#95—862no—
781#95—862no—
782#95—862no—
783#95—862no—
784#95—1721no—
785#95—1721no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—432no—
795C24—432no—
796C24—432no—
797C24—861no—
798C24—861no—
799C24—861no—
800C24—861no—
801C24—861no—
802C24—861no—
803C24—861no—
804C24—861no—
805C24—861no—
806C24—861no—
807C24—861no—
808C24—861no—
809C24C2×C4×D4312yes—
810C24C2×C4×D4312yes—
811C24C2×C4×D4312yes—
812C24C2×D17212yes—
813C24#1062189812yes—
814C24#1062189812yes—
815C24C2×C22⋊D4312yes—
816C24C23×D4311yescharacteristic
817C2×D4—4316no—
818C2×D4—868no—
819C2×D4—868no—
820C2×D4—868no—
821C2×D4—868no—
822C2×D4—868no—
823C2×D4—868no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—28no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—28no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—432no—
862C22×C4—432no—
863C22×C4—432no—
864C22×C4—432no—
865C22×C4—432no—
866C22×C4—432no—
867C22×C4—432no—
868C22×C4—432no—
869C22×C4—432no—
870C22×C4—432no—
871C22×C4—432no—
872C22×C4—432no—
873C22×C4—432no—
874C22×C4—868no—
875C22×C4—868no—
876C22×C4—868no—
877C22×C4—861no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—861no—
882C22×C4—861no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—868no—
890C22×C4—868no—
891C22×C4—861no—
892C22×C4—861no—
893C22×C4—861no—
894C22×C4—861no—
895C22×C4—861no—
896C22×C4—861no—
897C22×C4—861no—
898C22×C4—861no—
899C22×C4—861no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—861no—
905C22×C4—861no—
906C22×C4—861no—
907C22×C4—861no—
908C22×C4—861no—
909C22×C4—861no—
910C22×C4—861no—
911C22×C4—861no—
912C22×C4—861no—
913C22×C4—861no—
914C22×C4—861no—
915C22×C4—868no—
916C22×C4—1724no—
917C22×C4—1724no—
918C22×C4—1724no—
919C22×C4—1724no—
920C22×C4—1724no—
921C22×C4—1724no—
922C22×C4—1724no—
923C22×C4—1724no—
924C22×C4—1724no—
925C22×C4—1724no—
926C22×C4—1724no—
927C22×C4—1724no—
928C22×C4—1724no—
929C22×C4—1724no—
930C22×C4—1724no—
931C22×C4C2×C4×D4312yes—
932C22×C4C2×C4×D4312yes—
933C22×C4C2×C4×D4312yes—
934C22×C4C2×C4×D4312yes—
935C22×C4C2×C4×D4312yes—
936C22×C4C2×C4×D4312yes—
937C22×C4C2×D17212yes—
938C22×C4C2×D17212yes—
939C22×C4D4×D4312yes—
940C22×C4#1062190012yes—
941C22×C4C2×C22⋊D4312yes—
942C22×C4C2×C22⋊D4312yes—
943C4⋊C4—868no—
944C22⋊C4—28no—
945C22⋊C4—868no—
946C22⋊C4—868no—
947C22⋊C4—868no—
948C22⋊C4—868no—
949C22⋊C4—1724no—
950C22⋊C4—1724no—
951C22⋊C4(C2×D43)⋊C4116yescomplemented
952C42—44no—
953C42—44no—
954C42—868no—
955C42—1724no—
956C42—1724no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—434no—
986C23—862no—
987C23—862no—
988C23—862no—
989C23—862no—
990C23—862no—
991C23—862no—
992C23—862no—
993C23—862no—
994C23—862no—
995C23—862no—
996C23—862no—
997C23—862no—
998C23—862no—
999C23—862no—
1000C23—862no—
1001C23—862no—
1002C23—862no—
1003C23—862no—
1004C23—1721no—
1005C23—1721no—
1006C23—1721no—
1007C23—1721no—
1008C23—1721no—
1009C23—1721no—
1010C23—1721no—
1011C23—1721no—
1012C23—1721no—
1013C23—1721no—
1014C23—1721no—
1015C23—1721no—
1016C23—1721no—
1017C23—1721no—
1018C23—1721no—
1019C23—1721no—
1020C23C42×D4314yes—
1021C23C2×(C2×D43)⋊C414yes—
1022C23#1306328214yes—
1023C23C4×C22⋊D4314yes—
1024C23C4×C22⋊D4314yes—
1025C23C4×D17214yes—
1026C23C4×D17214yes—
1027C23C22×C4×D4311yescharacteristic
1028C23C22×C4×D4311yescharacteristic
1029C23C22×C4×D4311yescharacteristic
1030C23C2×D4×D4311yescharacteristic
1031C23C22×C22⋊D4311yescharacteristic
1032C23C22×D17211yescharacteristic
1033C23#41×D4311yescharacteristic
1034C23#41×D4311yescharacteristic
1035C23C2×#1062190011yescharacteristic
1036C23C2×#1062189811yescharacteristic
1037C23C2×#1062189811yescharacteristic
1038C23#1306337011yescharacteristic
1039C23#1306337011yescharacteristic
1040C23#1306337111yescharacteristic
1041C23#1306337211yescharacteristic
1042D4—8632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—434no—
1084C2×C4—434no—
1085C2×C4—434no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—862no—
1093C2×C4—862no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—862no—
1099C2×C4—862no—
1100C2×C4—862no—
1101C2×C4—862no—
1102C2×C4—862no—
1103C2×C4—862no—
1104C2×C4—862no—
1105C2×C4—862no—
1106C2×C4—862no—
1107C2×C4—862no—
1108C2×C4—862no—
1109C2×C4—862no—
1110C2×C4—862no—
1111C2×C4—862no—
1112C2×C4—862no—
1113C2×C4—862no—
1114C2×C4—862no—
1115C2×C4—862no—
1116C2×C4—17216no—
1117C2×C4—17216no—
1118C2×C4—17216no—
1119C2×C4—1721no—
1120C2×C4—1721no—
1121C2×C4—1721no—
1122C2×C4—1721no—
1123C2×C4—1721no—
1124C2×C4—1721no—
1125C2×C4—1721no—
1126C2×C4—1721no—
1127C2×C4—1721no—
1128C2×C4—1721no—
1129C2×C4—1721no—
1130C2×C4—1721no—
1131C2×C4—1721no—
1132C2×C4—1721no—
1133C2×C4—1721no—
1134C2×C4—1721no—
1135C2×C4C2×(C2×D43)⋊C414yes—
1136C2×C4C2×(C2×D43)⋊C414yes—
1137C2×C4(C22⋊D43)⋊C414yescomplemented
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—864no—
1153C22—864no—
1154C22—864no—
1155C22—1722no—
1156C22—1722no—
1157C22—1722no—
1158C22—1722no—
1159C22—1722no—
1160C22—1722no—
1161C22—1722no—
1162C22—1722no—
1163C22—1722no—
1164C22—1722no—
1165C22—1722no—
1166C22—1722no—
1167C22C4×(C2×D43)⋊C418yescomplemented
1168C22C2×C42×D4311yescharacteristic
1169C22C22×(C2×D43)⋊C411yescharacteristic
1170C22C2×#1306328211yescharacteristic
1171C22C4×D4×D4311yescharacteristic
1172C22C4×D4×D4311yescharacteristic
1173C22C2×(C22⋊D43)⋊C411yescharacteristic
1174C22C2×C4×C22⋊D4311yescharacteristic
1175C22C2×C4×C22⋊D4311yescharacteristic
1176C22C2×C4×D17211yescharacteristic
1177C22C2×C4×D17211yescharacteristic
1178C22C4×#1062190011yescharacteristic
1179C22C4×#1062190011yescharacteristic
1180C22#1458336711yescharacteristic
1181C22#1458337111yescharacteristic
1182C22#1458337111yescharacteristic
1183C22#1458337211yescharacteristic
1184C22#1458337811yescharacteristic
1185C22#1458337811yescharacteristic
1186C22#1458337911yescharacteristic
1187C22D4×C22⋊D4311yescharacteristic
1188C22D4×D17211yescharacteristic
1189C22#1458353711yescharacteristic
1190C22#1458353911yescharacteristic
1191C22#1458354311yescharacteristic
1192C22#1458354411yescharacteristic
1193C22#1458354411yescharacteristic
1194C22#1458354811yescharacteristic
1195C22#1458355311yescharacteristic
1196C22#1458355811yescharacteristic
1197C22#1458357311yescharacteristic
1198C22#1458357511yescharacteristic
1199C22#1458358211yescharacteristic
1200C22#1458359511yescharacteristic
1201C22#1458359811yescharacteristic
1202C22#1458359811yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—864no—
1210C4—864no—
1211C4—864no—
1212C4—1722no—
1213C4—1722no—
1214C4—1722no—
1215C4—1722no—
1216C2—28no—
1217C2—1724no—
1218C2C2×C4×(C2×D43)⋊C411yescharacteristic
1219C2C4×(C22⋊D43)⋊C411yescharacteristic
1220C2#1913695411yescharacteristic
1221C2D4×(C2×D43)⋊C411yescharacteristic
1222C2#1913742011yescharacteristic
1223C2#1913751811yescharacteristic
1224C2#1913752911yescharacteristic
1225C2#1913757411yescharacteristic
1226C2#1913757711yescharacteristic
1227C2#1913758711yescharacteristic
1228C2#1913758911yescharacteristic
1229C2#1913760911yescharacteristic
1230C2#1913761211yescharacteristic
1231C2#1913764011yescharacteristic
1232C2#1913764511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13813
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic43C2semidirect
5. C2×C4×(C2×D43)⋊C4C2semidirect
6. C22×C43⋊#95C2semidirect
7. #19132833C2semidirect
8. #19132831C2semidirect
9. #19132830C2semidirect
10. #19132828C2semidirect
11. #19132819C2semidirect
12. #19132817C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. C4×C43⋊#95C2semidirect
15. C2×C4×C22⋊C4×C43C2semidirect
22. C2×(C22⋊D43)⋊C4C4semidirect
33. #14582778C4semidirect
34. #14582776C4semidirect
81. C23×Dic43C2×C4semidirect
95. C22×C4×D43C2×C4semidirect
99. C2×Dic43⋊C4C2×C4semidirect
102. C2×C22⋊Dic43C2×C4semidirect
113. C2×(C2×D43)⋊C4C2×C4semidirect
114. C2×(C2×D43)⋊C4C2×C4semidirect
115. C2×(C2×D43)⋊C4C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
126. C2×C4×Dic43C2×C4semidirect
136. C43⋊#95C2×C4semidirect
137. C43⋊#95C2×C4semidirect
138. C43⋊#95C2×C4semidirect
139. C43⋊#95C2×C4semidirect
140. C43⋊#95D4semidirect
148. C23×C4×C43C2×C4semidirect
158. C2×C22⋊C4×C43C2×C4semidirect
255. C2×C22⋊D43C42semidirect
327. C22⋊C4×C43C22⋊C4semidirect
467. C2×C4×C43C4×D4semidirect
519. C2×Dic43C4×D4semidirect
536. C22×C43C4×C22⋊C4semidirect
605. C2×C4×C22⋊C4D43semidirect
676. C43#13813semidirect
720. C23×C4C4×D43semidirect
752. C2×C22⋊C4C4×D43semidirect
951. C22⋊C4(C2×D43)⋊C4semidirect
1137. C2×C4(C22⋊D43)⋊C4semidirect
1167. C22C4×(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C2×#145827782
C2×#145827762
C2×C22⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
C22×C43⋊#952
#191328332
#191328312
#191328302
#191328282
#191328192
#191328172
(C2×D43)⋊#952
C4×C43⋊#952
C2×C4×C22⋊C4×C432
#1381343