Finite Group Databasebeta

← #33007484

Subgroups — #33007484

Order 18688.

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×D4×Dic73C211yesmaximal, characteristic
2C2×#17988467C211yesmaximal, characteristic
3C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
6C22×#14556498C211yesmaximal, characteristic, complemented
7#22608168C211yesmaximal, characteristic, complemented
8#22608168C211yesmaximal, characteristic, complemented
9#22608165C211yesmaximal, characteristic, complemented
10#22608165C211yesmaximal, characteristic, complemented
11#22608156C211yesmaximal, characteristic, complemented
12#22608153C211yesmaximal, characteristic, complemented
13#22608153C211yesmaximal, characteristic, complemented
14#95×Dic73C211yesmaximal, characteristic, complemented
15C2×#386×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C24×Dic73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C2×D4×Dic73—24no—
20C2×D4×Dic73—24no—
21C2×D4×Dic73C418yescomplemented
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C22⋊Dic73C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×C4×Dic73C2211yescharacteristic
29C22×C4×Dic73C2211yescharacteristic
30C22×C4×Dic73C2211yescharacteristic
31C22×C4×Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33#17988467C418yescomplemented
34C22⋊C4×Dic73—24no—
35C22⋊C4×Dic73—24no—
36C4×C22⋊Dic73—24no—
37C2×#14556498—24no—
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C2×#14556498C2211yescharacteristic
49C2×#14556498C2211yescharacteristic
50C2×#14556498C2211yescharacteristic
51C2×#14556498C2211yescharacteristic
52C23×D4×C73C2211yescharacteristic
53C24×C4×C73C2211yescharacteristic
54C22×C22⋊C4×C73C2211yescharacteristic
55C22×C22⋊C4×C73C2211yescharacteristic
56C22×C22⋊C4×C73C2211yescharacteristic
57#386×C73C418yescomplemented
58C2×#95×C73C2211yescharacteristic
59C2×#95×C73C2211yescharacteristic
60C23×Dic73—22no—
61C23×Dic73—22no—
62C23×Dic73—22no—
63C23×Dic73—22no—
64C23×Dic73—22no—
65C23×Dic73—22no—
66C23×Dic73—22no—
67C23×Dic73—22no—
68C23×Dic73—22no—
69C23×Dic73—22no—
70C23×Dic73—22no—
71C23×Dic73—22no—
72C23×Dic73—41no—
73C23×Dic73—41no—
74C23×Dic73—41no—
75C23×Dic73—41no—
76C23×Dic73—41no—
77C23×Dic73—41no—
78C23×Dic73C2×C414yes—
79C23×Dic73C2×C414yescomplemented
80C23×Dic73C2×C414yescomplemented
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2311yescharacteristic
84C23×Dic73C2311yescharacteristic
85C23×Dic73C2311yescharacteristic
86C23×Dic73C2311yescharacteristic
87C23×Dic73C2311yescharacteristic
88C23×Dic73C2311yescharacteristic
89D4×Dic73—232no—
90C2×C4⋊Dic73—22no—
91C2×C4⋊Dic73—22no—
92C2×C4⋊Dic73C2×C414yescomplemented
93C2×C22⋊Dic73—22no—
94C2×C22⋊Dic73—22no—
95C2×C22⋊Dic73—22no—
96C2×C22⋊Dic73—22no—
97C2×C22⋊Dic73—22no—
98C2×C22⋊Dic73—22no—
99C2×C22⋊Dic73—41no—
100C2×C22⋊Dic73—41no—
101C2×C22⋊Dic73C2×C414yes—
102C2×C22⋊Dic73C2×C414yescomplemented
103C2×C22⋊Dic73C2×C414yescomplemented
104C2×C22⋊Dic73C2×C414yescomplemented
105C2×C22⋊Dic73C2×C414yescomplemented
106C2×C22⋊Dic73D414yes—
107C2×C22⋊Dic73D414yes—
108C2×C4×Dic73—22no—
109C2×C4×Dic73—22no—
110C2×C4×Dic73—22no—
111C2×C4×Dic73—22no—
112C2×C4×Dic73—22no—
113C2×C4×Dic73—22no—
114C2×C4×Dic73—22no—
115C2×C4×Dic73—22no—
116C2×C4×Dic73—22no—
117C2×C4×Dic73—22no—
118C2×C4×Dic73—41no—
119C2×C4×Dic73—41no—
120C2×C4×Dic73—41no—
121C2×C4×Dic73—41no—
122C2×C4×Dic73C2×C414yescomplemented
123#14556498—22no—
124#14556498—22no—
125#14556498—22no—
126#14556498—22no—
127#14556498—22no—
128#14556498—22no—
129#14556498—22no—
130#14556498—22no—
131#14556498—22no—
132#14556498—41no—
133#14556498—41no—
134#14556498C2×C414yescomplemented
135#14556498C2×C414yescomplemented
136#14556498D414yescomplemented
137C25×C73C2311yescharacteristic
138C25×C73C2311yescharacteristic
139C22×D4×C73—22no—
140C22×D4×C73—22no—
141C22×D4×C73—22no—
142C22×D4×C73—22no—
143C22×D4×C73C2×C414yes—
144C22×D4×C73C2×C414yes—
145C22×D4×C73C2×C414yes—
146C23×C4×C73—22no—
147C23×C4×C73—22no—
148C23×C4×C73—22no—
149C23×C4×C73—22no—
150C23×C4×C73—41no—
151C23×C4×C73—41no—
152C23×C4×C73C2×C414yescomplemented
153C23×C4×C73C2311yescharacteristic
154C23×C4×C73C2311yescharacteristic
155C23×C4×C73C2311yescharacteristic
156C23×C4×C73C2311yescharacteristic
157C23×C4×C73C2311yescharacteristic
158C2×C22⋊C4×C73—22no—
159C2×C22⋊C4×C73—22no—
160C2×C22⋊C4×C73—22no—
161C2×C22⋊C4×C73—22no—
162C2×C22⋊C4×C73—41no—
163C2×C22⋊C4×C73—41no—
164C2×C22⋊C4×C73C2×C414yescomplemented
165C2×C22⋊C4×C73C2×C414yescomplemented
166C2×C22⋊C4×C73C2×C414yescomplemented
167#95×C73C2×C414yescomplemented
168#95×C73C2×C414yescomplemented
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—28no—
186C22×Dic73—28no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—21no—
202C22×Dic73—21no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73—21no—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—28no—
212C22×Dic73—28no—
213C22×Dic73—28no—
214C22×Dic73—28no—
215C22×Dic73—44no—
216C22×Dic73—44no—
217C22×Dic73—44no—
218C22×Dic73—44no—
219C22×Dic73—44no—
220C22×Dic73—44no—
221C22×Dic73—44no—
222C22×Dic73—44no—
223C22×Dic73—44no—
224C22×Dic73—44no—
225C22×Dic73—44no—
226C22×Dic73—44no—
227C22×Dic73—44no—
228C22×Dic73—44no—
229C22×Dic73—44no—
230C22×Dic73C22×C412yes—
231C22×Dic73C22×C412yes—
232C22×Dic73C22×C412yes—
233C22×Dic73C22×C412yes—
234C22×Dic73C22×C412yes—
235C22×Dic73C22×C412yes—
236C22×Dic73C22×C412yes—
237C22×Dic73C22×C412yes—
238C22×Dic73C2×D412yes—
239C22×Dic73C2×D412yes—
240C22×Dic73C2×D412yes—
241C22×Dic73C2×D412yes—
242C22×Dic73C2×D412yes—
243C22×Dic73C2×D412yes—
244C22×Dic73#4112yes—
245C22×Dic73#4112yes—
246C4⋊Dic73—28no—
247C22⋊Dic73—28no—
248C22⋊Dic73—28no—
249C22⋊Dic73—28no—
250C22⋊Dic73—44no—
251C22⋊Dic73C22⋊C4116yescomplemented
252C4×Dic73—28no—
253C4×Dic73—44no—
254C4×Dic73—44no—
255C4×Dic73—44no—
256C4×Dic73—44no—
257C24×C73—21no—
258C24×C73—21no—
259C24×C73—21no—
260C24×C73—21no—
261C24×C73—21no—
262C24×C73—21no—
263C24×C73—21no—
264C24×C73—21no—
265C24×C73—21no—
266C24×C73—21no—
267C24×C73—21no—
268C24×C73—21no—
269C24×C73—21no—
270C24×C73—21no—
271C24×C73—21no—
272C24×C73—21no—
273C24×C73—21no—
274C24×C73—21no—
275C24×C73—21no—
276C24×C73—21no—
277C24×C73C22×C412yes—
278C24×C73C22×C412yes—
279C24×C73C22×C412yes—
280C24×C73C22×C412yes—
281C24×C73C22×C412yes—
282C24×C73C22×C412yes—
283C24×C73C2×D412yes—
284C24×C73C2×D412yes—
285C24×C73#4112yes—
286C24×C73#4112yes—
287C24×C73C2411yescharacteristic
288C2×D4×C73—28no—
289C2×D4×C73—28no—
290C2×D4×C73—28no—
291C2×D4×C73—28no—
292C2×D4×C73—28no—
293C2×D4×C73—28no—
294C2×D4×C73C42116yescomplemented
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—21no—
298C22×C4×C73—21no—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73—21no—
303C22×C4×C73—28no—
304C22×C4×C73—21no—
305C22×C4×C73—21no—
306C22×C4×C73—21no—
307C22×C4×C73—21no—
308C22×C4×C73—21no—
309C22×C4×C73—21no—
310C22×C4×C73—21no—
311C22×C4×C73—21no—
312C22×C4×C73—21no—
313C22×C4×C73—21no—
314C22×C4×C73—21no—
315C22×C4×C73—21no—
316C22×C4×C73—21no—
317C22×C4×C73—21no—
318C22×C4×C73—21no—
319C22×C4×C73—21no—
320C22×C4×C73—21no—
321C22×C4×C73—21no—
322C22×C4×C73—28no—
323C22×C4×C73—44no—
324C22×C4×C73—44no—
325C22×C4×C73—44no—
326C22×C4×C73—44no—
327C22×C4×C73—44no—
328C22×C4×C73C22×C412yes—
329C22×C4×C73C22×C412yes—
330C22×C4×C73C22×C412yes—
331C22×C4×C73C22×C412yes—
332C22×C4×C73C22×C412yes—
333C22×C4×C73C22×C412yes—
334C22×C4×C73C22×C412yes—
335C22×C4×C73C2×D412yes—
336C22×C4×C73#4112yes—
337C22⋊C4×C73—28no—
338C22⋊C4×C73—28no—
339C22⋊C4×C73—44no—
340C23×C73—22no—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73—22no—
345C23×C73—22no—
346C23×C73—22no—
347C23×C73—22no—
348C23×C73—22no—
349C23×C73—22no—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—22no—
353C23×C73—22no—
354C23×C73—22no—
355C23×C73—22no—
356C23×C73—22no—
357C23×C73—22no—
358C23×C73—22no—
359C23×C73—22no—
360C23×C73—22no—
361C23×C73—22no—
362C23×C73—22no—
363C23×C73—22no—
364C23×C73—22no—
365C23×C73—22no—
366C23×C73—22no—
367C23×C73—22no—
368C23×C73—22no—
369C23×C73—22no—
370C23×C73—22no—
371C23×C73—22no—
372C23×C73—22no—
373C23×C73—22no—
374C23×C73—22no—
375C23×C73—22no—
376C23×C73—22no—
377C23×C73—22no—
378C23×C73—22no—
379C23×C73—22no—
380C23×C73—22no—
381C23×C73—22no—
382C23×C73—22no—
383C23×C73—22no—
384C23×C73—22no—
385C23×C73—22no—
386C23×C73—41no—
387C23×C73—41no—
388C23×C73—41no—
389C23×C73—41no—
390C23×C73—41no—
391C23×C73—41no—
392C23×C73—41no—
393C23×C73—41no—
394C23×C73—41no—
395C23×C73—41no—
396C23×C73—41no—
397C23×C73—41no—
398C23×C73—41no—
399C23×C73—41no—
400C23×C73—41no—
401C23×C73—41no—
402C23×C73C2×C4214yes—
403C23×C73C2×C4214yes—
404C23×C73C2×C22⋊C414yes—
405C23×C73#11714yes—
406C23×C73C4×D414yes—
407C23×C73C4×D414yes—
408C23×C73C4×D414yes—
409C23×C73C4×D414yes—
410C23×C73C23×C411yescharacteristic
411C23×C73C23×C411yescharacteristic
412C23×C73C23×C411yescharacteristic
413C23×C73C22×D411yescharacteristic
414C23×C73C22×D411yescharacteristic
415C23×C73C22×D411yescharacteristic
416C23×C73C2×#4111yescharacteristic
417C23×C73C2×#4111yescharacteristic
418C23×C73C2×#4111yescharacteristic
419C23×C73C2×#4111yescharacteristic
420C23×C73C2×#4111yescharacteristic
421C23×C73H(5,𝔽2)11yescharacteristic
422C23×C73H(5,𝔽2)11yescharacteristic
423C23×C73H(5,𝔽2)11yescharacteristic
424C23×C732−1+411yescharacteristic
425D4×C73—232no—
426C2×C4×C73—22no—
427C2×C4×C73—22no—
428C2×C4×C73—22no—
429C2×C4×C73—22no—
430C2×C4×C73—22no—
431C2×C4×C73—22no—
432C2×C4×C73—22no—
433C2×C4×C73—22no—
434C2×C4×C73—22no—
435C2×C4×C73—22no—
436C2×C4×C73—22no—
437C2×C4×C73—22no—
438C2×C4×C73—22no—
439C2×C4×C73—22no—
440C2×C4×C73—22no—
441C2×C4×C73—22no—
442C2×C4×C73—22no—
443C2×C4×C73—22no—
444C2×C4×C73—22no—
445C2×C4×C73—22no—
446C2×C4×C73—22no—
447C2×C4×C73—416no—
448C2×C4×C73—41no—
449C2×C4×C73—41no—
450C2×C4×C73—41no—
451C2×C4×C73—41no—
452C2×C4×C73—41no—
453C2×C4×C73—41no—
454C2×C4×C73—41no—
455C2×C4×C73—41no—
456C2×C4×C73—41no—
457C2×C4×C73—41no—
458C2×C4×C73—41no—
459C2×C4×C73—41no—
460C2×C4×C73C2×C4214yes—
461C2×C4×C73C4×D414yescomplemented
462C2×Dic73—22no—
463C2×Dic73—22no—
464C2×Dic73—22no—
465C2×Dic73—22no—
466C2×Dic73—22no—
467C2×Dic73—22no—
468C2×Dic73—22no—
469C2×Dic73—22no—
470C2×Dic73—22no—
471C2×Dic73—22no—
472C2×Dic73—22no—
473C2×Dic73—22no—
474C2×Dic73—22no—
475C2×Dic73—22no—
476C2×Dic73—22no—
477C2×Dic73—22no—
478C2×Dic73—22no—
479C2×Dic73—22no—
480C2×Dic73—22no—
481C2×Dic73—22no—
482C2×Dic73—22no—
483C2×Dic73—22no—
484C2×Dic73—22no—
485C2×Dic73—22no—
486C2×Dic73—22no—
487C2×Dic73—22no—
488C2×Dic73—22no—
489C2×Dic73—22no—
490C2×Dic73—22no—
491C2×Dic73—22no—
492C2×Dic73—22no—
493C2×Dic73—22no—
494C2×Dic73—22no—
495C2×Dic73—22no—
496C2×Dic73—22no—
497C2×Dic73—22no—
498C2×Dic73—416no—
499C2×Dic73—416no—
500C2×Dic73—416no—
501C2×Dic73—41no—
502C2×Dic73—41no—
503C2×Dic73—41no—
504C2×Dic73—41no—
505C2×Dic73—41no—
506C2×Dic73—41no—
507C2×Dic73—41no—
508C2×Dic73—41no—
509C2×Dic73—41no—
510C2×Dic73—41no—
511C2×Dic73—41no—
512C2×Dic73—41no—
513C2×Dic73—41no—
514C2×Dic73—41no—
515C2×Dic73—41no—
516C2×Dic73—41no—
517C2×Dic73C2×C22⋊C414yes—
518C2×Dic73C2×C22⋊C414yes—
519C2×Dic73C4×D414yes—
520C2×Dic73C4×D414yescomplemented
521C22×C73—24no—
522C22×C73—24no—
523C22×C73—24no—
524C22×C73—24no—
525C22×C73—24no—
526C22×C73—24no—
527C22×C73—24no—
528C22×C73—24no—
529C22×C73—24no—
530C22×C73—24no—
531C22×C73—24no—
532C22×C73—24no—
533C22×C73—24no—
534C22×C73—24no—
535C22×C73—24no—
536C22×C73—24no—
537C22×C73—24no—
538C22×C73—42no—
539C22×C73—42no—
540C22×C73—42no—
541C22×C73—42no—
542C22×C73—42no—
543C22×C73—42no—
544C22×C73—42no—
545C22×C73—42no—
546C22×C73—42no—
547C22×C73—42no—
548C22×C73—42no—
549C22×C73—42no—
550C22×C73C4×C22⋊C418yescomplemented
551C22×C73C22×C4211yescharacteristic
552C22×C73C22×C22⋊C411yescharacteristic
553C22×C73C2×#11711yescharacteristic
554C22×C73C2×C4×D411yescharacteristic
555C22×C73C2×C4×D411yescharacteristic
556C22×C73C2×C4×D411yescharacteristic
557C22×C73C2×C4×D411yescharacteristic
558C22×C73C2×C4×D411yescharacteristic
559C22×C73C2×C4×D411yescharacteristic
560C22×C73C2×C4×D411yescharacteristic
561C22×C73C4×#4111yescharacteristic
562C22×C73C4×#4111yescharacteristic
563C22×C73C4×#4111yescharacteristic
564C22×C73#51811yescharacteristic
565C22×C73#51811yescharacteristic
566C22×C73#51811yescharacteristic
567C22×C73#52011yescharacteristic
568C22×C73#52011yescharacteristic
569C22×C73#52011yescharacteristic
570C22×C73D4211yescharacteristic
571C22×C73D4211yescharacteristic
572C22×C73#54611yescharacteristic
573C22×C73#54611yescharacteristic
574C22×C73#54611yescharacteristic
575C22×C73#54611yescharacteristic
576C22×C73#54611yescharacteristic
577C22×C73#54711yescharacteristic
578C22×C73#54711yescharacteristic
579C22×C73#54811yescharacteristic
580C22×C73#55111yescharacteristic
581C22×C73#55111yescharacteristic
582C22×C73#55211yescharacteristic
583C22×C73#55311yescharacteristic
584C22×C73#55311yescharacteristic
585C22×C73#55311yescharacteristic
586C4×C73—24no—
587C4×C73—24no—
588C4×C73—42no—
589C4×C73—42no—
590C4×C73—42no—
591Dic73—24no—
592Dic73—24no—
593Dic73—24no—
594Dic73—24no—
595Dic73—42no—
596Dic73—42no—
597Dic73—42no—
598Dic73—42no—
599#13813—731nomaximal, Sylow
600C2×C73—28no—
601C2×C73—44no—
602C2×C73C2×C4×C22⋊C411yescharacteristic
603C2×C73C42×D411yescharacteristic
604C2×C73#227511yescharacteristic
605C2×C73D4×C22⋊C411yescharacteristic
606C2×C73#233911yescharacteristic
607C2×C73#235211yescharacteristic
608C2×C73#235311yescharacteristic
609C2×C73#235811yescharacteristic
610C2×C73#235811yescharacteristic
611C2×C73#235911yescharacteristic
612C2×C73#235911yescharacteristic
613C2×C73#236111yescharacteristic
614C2×C73#236111yescharacteristic
615C2×C73#236411yescharacteristic
616C2×C73#236411yescharacteristic
617C22×C4×D4—731no—
618C2×#386—731no—
619C2×#386D7311yescharacteristic
620C2×C4×C22⋊C4—731no—
621C2×C4×C22⋊C4—731no—
622C2×C4×C22⋊C4—731no—
623C22×#95—731no—
624#1437—731no—
625#1437—731no—
626#1436—731no—
627#1436—731no—
628#1434—731no—
629C22⋊#95—731no—
630C22⋊#95—731no—
631C4×#95—731no—
632C73#1381311yescharacteristic, complemented, Sylow
633C23×D4C2×D7311yescharacteristic
634C24×C4—731no—
635C24×C4—731no—
636C24×C4—731no—
637C24×C4C2×D7311yescharacteristic
638C2×C4×D4—738no—
639C2×C4×D4—1464no—
640C2×C4×D4—1464no—
641C22×C4⋊C4—731no—
642C22×C22⋊C4—731no—
643C22×C22⋊C4—731no—
644C22×C22⋊C4—731no—
645C22×C22⋊C4—731no—
646C22×C22⋊C4—731no—
647C22×C22⋊C4C2×D7311yescharacteristic
648C22×C22⋊C4C2×D7311yescharacteristic
649C22×C22⋊C4C2×D7311yescharacteristic
650C22×C42—731no—
651C22×C42—731no—
652C22×C42—731no—
653C22×C42—731no—
654C22×C42—731no—
655#386—738no—
656#386Dic7318yescomplemented
657C4×C22⋊C4—1464no—
658C4×C22⋊C4—1464no—
659C4×C22⋊C4—1464no—
660C2×#95—731no—
661C2×#95—731no—
662C2×#95—731no—
663C2×#95—731no—
664C2×#95—731no—
665C2×#95—731no—
666C2×#95—731no—
667C2×#95—731no—
668C2×#95—731no—
669C2×#95—731no—
670C2×#95—731no—
671C2×#95—731no—
672C2×#95—731no—
673C2×#95—731no—
674C2×#95—1464no—
675C2×#95C2×D7311yescharacteristic
676C2×#95C2×D7311yescharacteristic
677C25C22×D7311yescharacteristic
678C25C22×D7311yescharacteristic
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—22no—
682C22×D4—22no—
683C22×D4C4×D7314yes—
684C22×D4C4×D7314yes—
685C22×D4C2×Dic7314yes—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—22no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—2921no—
693C23×C4—2921no—
694C23×C4—2921no—
695C23×C4—2921no—
696C23×C4—2921no—
697C23×C4—2921no—
698C23×C4—734no—
699C23×C4—734no—
700C23×C4—734no—
701C23×C4—731no—
702C23×C4—731no—
703C23×C4—731no—
704C23×C4—731no—
705C23×C4—731no—
706C23×C4—731no—
707C23×C4—731no—
708C23×C4—731no—
709C23×C4—1462no—
710C23×C4—1462no—
711C23×C4—1462no—
712C23×C4—1462no—
713C23×C4—1462no—
714C23×C4—1462no—
715C23×C4—1462no—
716C23×C4—1462no—
717C23×C4—1462no—
718C23×C4—1462no—
719C23×C4—1462no—
720C23×C4—1462no—
721C23×C4C2×Dic7314yescomplemented
722C23×C4C22×D7311yescharacteristic
723C23×C4C22×D7311yescharacteristic
724C23×C4C22×D7311yescharacteristic
725C23×C4C22×D7311yescharacteristic
726C23×C4C22×D7311yescharacteristic
727C4×D4—14632no—
728C2×C4⋊C4—734no—
729C2×C4⋊C4—1462no—
730C2×C4⋊C4—1462no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—41no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—2921no—
738C2×C22⋊C4—2921no—
739C2×C22⋊C4—734no—
740C2×C22⋊C4—734no—
741C2×C22⋊C4—734no—
742C2×C22⋊C4—734no—
743C2×C22⋊C4—734no—
744C2×C22⋊C4—734no—
745C2×C22⋊C4—734no—
746C2×C22⋊C4—1462no—
747C2×C22⋊C4—1462no—
748C2×C22⋊C4—1462no—
749C2×C22⋊C4—1462no—
750C2×C22⋊C4—1462no—
751C2×C22⋊C4—1462no—
752C2×C22⋊C4C2×Dic7314yescomplemented
753C2×C22⋊C4C2×Dic7314yescomplemented
754C2×C22⋊C4C2×Dic7314yescomplemented
755C2×C42—2921no—
756C2×C42—2921no—
757C2×C42—2921no—
758C2×C42—2921no—
759C2×C42—734no—
760C2×C42—1462no—
761C2×C42—1462no—
762C2×C42—1462no—
763C2×C42—1462no—
764C2×C42—1462no—
765C2×C42—1462no—
766C2×C42—1462no—
767C2×C42—1462no—
768C2×C42—1462no—
769C2×C42—1462no—
770#95—2921no—
771#95—2921no—
772#95—734no—
773#95—734no—
774#95—734no—
775#95—1462no—
776#95—1462no—
777#95—1462no—
778#95—1462no—
779#95—1462no—
780#95—1462no—
781#95—1462no—
782#95—1462no—
783#95—1462no—
784#95C2×Dic7314yescomplemented
785#95C2×Dic7314yescomplemented
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24C2×C4×D7312yes—
807C24C2×C4×D7312yes—
808C24C2×C4×D7312yes—
809C24C2×C4×D7312yes—
810C24C22×Dic7312yes—
811C24C22×Dic7312yes—
812C24D4×D7312yes—
813C24D4×D7312yes—
814C24#1192402712yes—
815C24#1192402712yes—
816C24C23×D7311yescharacteristic
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4C4×Dic73116yescomplemented
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—28no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
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—28no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—2924no—
858C22×C4—2924no—
859C22×C4—2924no—
860C22×C4—2924no—
861C22×C4—2924no—
862C22×C4—2924no—
863C22×C4—2924no—
864C22×C4—2924no—
865C22×C4—2924no—
866C22×C4—2924no—
867C22×C4—2924no—
868C22×C4—2924no—
869C22×C4—2924no—
870C22×C4—2924no—
871C22×C4—2924no—
872C22×C4—732no—
873C22×C4—732no—
874C22×C4—732no—
875C22×C4—732no—
876C22×C4—732no—
877C22×C4—732no—
878C22×C4—732no—
879C22×C4—732no—
880C22×C4—732no—
881C22×C4—732no—
882C22×C4—732no—
883C22×C4—732no—
884C22×C4—732no—
885C22×C4—732no—
886C22×C4—732no—
887C22×C4—732no—
888C22×C4—1468no—
889C22×C4—1468no—
890C22×C4—1468no—
891C22×C4—1468no—
892C22×C4—1468no—
893C22×C4—1468no—
894C22×C4—1461no—
895C22×C4—1461no—
896C22×C4—1461no—
897C22×C4—1461no—
898C22×C4—1461no—
899C22×C4—1461no—
900C22×C4—1461no—
901C22×C4—1461no—
902C22×C4—1461no—
903C22×C4—1461no—
904C22×C4—1461no—
905C22×C4—1461no—
906C22×C4—1461no—
907C22×C4—1461no—
908C22×C4—1461no—
909C22×C4—1461no—
910C22×C4—1461no—
911C22×C4—1461no—
912C22×C4—1461no—
913C22×C4—1461no—
914C22×C4—1461no—
915C22×C4—1461no—
916C22×C4—1461no—
917C22×C4—1461no—
918C22×C4—1461no—
919C22×C4—1461no—
920C22×C4—1461no—
921C22×C4—1461no—
922C22×C4—1461no—
923C22×C4—1461no—
924C22×C4—1461no—
925C22×C4—1461no—
926C22×C4—1461no—
927C22×C4—1461no—
928C22×C4—1461no—
929C22×C4—1461no—
930C22×C4—1461no—
931C22×C4—1461no—
932C22×C4—1461no—
933C22×C4—1461no—
934C22×C4C2×C4×D7312yes—
935C22×C4C2×C4×D7312yes—
936C22×C4C22×Dic7312yes—
937C22×C4C22×Dic7312yes—
938C22×C4C22×Dic7312yes—
939C22×C4C22×Dic7312yes—
940C22×C4C22×Dic7312yes—
941C22×C4D4×D7312yes—
942C22×C4#1192402712yes—
943C4⋊C4—1468no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—44no—
947C22⋊C4—2924no—
948C22⋊C4—7316no—
949C22⋊C4—1468no—
950C22⋊C4—1468no—
951C22⋊C4—1468no—
952C42—2924no—
953C42—2924no—
954C42—2924no—
955C42—2924no—
956C42—1468no—
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—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×C4×Dic7314yes—
1020C23C2×C4×Dic7314yes—
1021C23C22⋊C4×D7314yes—
1022C23#1455654714yes—
1023C23#1455655114yes—
1024C23#1455655114yes—
1025C23D4×Dic7314yes—
1026C23D4×Dic7314yes—
1027C23C22×C4×D7311yescharacteristic
1028C23C22×C4×D7311yescharacteristic
1029C23C23×Dic7311yescharacteristic
1030C23C2×D4×D7311yescharacteristic
1031C23C2×D4×D7311yescharacteristic
1032C23C2×D4×D7311yescharacteristic
1033C23#41×D7311yescharacteristic
1034C23#41×D7311yescharacteristic
1035C23C2×#1192402711yescharacteristic
1036C23C2×#1192402711yescharacteristic
1037C23C2×#1192402711yescharacteristic
1038C23#1455663611yescharacteristic
1039C23#1455663611yescharacteristic
1040C23#1455663711yescharacteristic
1041C23#1455663811yescharacteristic
1042D4—232no—
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—416no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—2921no—
1078C2×C4—2921no—
1079C2×C4—2921no—
1080C2×C4—2921no—
1081C2×C4—2921no—
1082C2×C4—2921no—
1083C2×C4—2921no—
1084C2×C4—2921no—
1085C2×C4—2921no—
1086C2×C4—2921no—
1087C2×C4—2921no—
1088C2×C4—2921no—
1089C2×C4—2921no—
1090C2×C4—2921no—
1091C2×C4—2921no—
1092C2×C4—2921no—
1093C2×C4—29216no—
1094C2×C4—29216no—
1095C2×C4—29216no—
1096C2×C4—734no—
1097C2×C4—734no—
1098C2×C4—734no—
1099C2×C4—734no—
1100C2×C4—1462no—
1101C2×C4—1462no—
1102C2×C4—1462no—
1103C2×C4—1462no—
1104C2×C4—1462no—
1105C2×C4—1462no—
1106C2×C4—1462no—
1107C2×C4—1462no—
1108C2×C4—1462no—
1109C2×C4—1462no—
1110C2×C4—1462no—
1111C2×C4—1462no—
1112C2×C4—1462no—
1113C2×C4—1462no—
1114C2×C4—1462no—
1115C2×C4—1462no—
1116C2×C4—1462no—
1117C2×C4—1462no—
1118C2×C4—1462no—
1119C2×C4—1462no—
1120C2×C4—1462no—
1121C2×C4—1462no—
1122C2×C4—1462no—
1123C2×C4—1462no—
1124C2×C4—1462no—
1125C2×C4—1462no—
1126C2×C4—1462no—
1127C2×C4—1462no—
1128C2×C4—1462no—
1129C2×C4—1462no—
1130C2×C4—1462no—
1131C2×C4—1462no—
1132C2×C4—1462no—
1133C2×C4—1462no—
1134C2×C4—1462no—
1135C2×C4—1462no—
1136C2×C4C2×C4×Dic7314yes—
1137C2×C4D4×Dic7314yescomplemented
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—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22C22⋊C4×Dic7318yescomplemented
1168C22C22×C4×Dic7311yescharacteristic
1169C22C2×C22⋊C4×D7311yescharacteristic
1170C22C2×#1455654711yescharacteristic
1171C22C4×D4×D7311yescharacteristic
1172C22C4×D4×D7311yescharacteristic
1173C22C2×#1455655111yescharacteristic
1174C22C2×#1455655111yescharacteristic
1175C22C2×D4×Dic7311yescharacteristic
1176C22C2×D4×Dic7311yescharacteristic
1177C22C2×D4×Dic7311yescharacteristic
1178C22C4×#1192402711yescharacteristic
1179C22C4×#1192402711yescharacteristic
1180C22#41×Dic7311yescharacteristic
1181C22#1798905911yescharacteristic
1182C22#1798905911yescharacteristic
1183C22#1798906211yescharacteristic
1184C22#1798906611yescharacteristic
1185C22#1798906611yescharacteristic
1186C22#1798907011yescharacteristic
1187C22#1798921911yescharacteristic
1188C22#1798922111yescharacteristic
1189C22#1798922411yescharacteristic
1190C22#1798922411yescharacteristic
1191C22#1798922611yescharacteristic
1192C22#1798922611yescharacteristic
1193C22#1798922911yescharacteristic
1194C22#1798923511yescharacteristic
1195C22#1798923711yescharacteristic
1196C22#1798924311yescharacteristic
1197C22#1798926011yescharacteristic
1198C22#1798926811yescharacteristic
1199C22#1798927411yescharacteristic
1200C22#1798928011yescharacteristic
1201C22#1798928011yescharacteristic
1202C22#1798928911yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—2922no—
1209C4—2922no—
1210C4—2922no—
1211C4—2922no—
1212C4—1464no—
1213C4—1464no—
1214C4—1464no—
1215C4—1464no—
1216C2—28no—
1217C2—44no—
1218C2C2×C22⋊C4×Dic7311yescharacteristic
1219C2C4×D4×Dic7311yescharacteristic
1220C2#2261229211yescharacteristic
1221C2#2261274911yescharacteristic
1222C2#2261275711yescharacteristic
1223C2#2261285811yescharacteristic
1224C2#2261286911yescharacteristic
1225C2#2261291111yescharacteristic
1226C2#2261291511yescharacteristic
1227C2#2261292711yescharacteristic
1228C2#2261292911yescharacteristic
1229C2#2261294211yescharacteristic
1230C2#2261295111yescharacteristic
1231C2#2261297911yescharacteristic
1232C2#2261298311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC2×#386×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC2×#386D73
hypocenterC73#13813
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic73C2semidirect
4. C2×C22⋊C4×Dic73C2semidirect
5. C2×C4×C22⋊Dic73C2semidirect
6. C22×#14556498C2semidirect
7. #22608168C2semidirect
8. #22608168C2semidirect
9. #22608165C2semidirect
10. #22608165C2semidirect
11. #22608156C2semidirect
12. #22608153C2semidirect
13. #22608153C2semidirect
14. #95×Dic73C2semidirect
21. C2×D4×Dic73C4semidirect
33. #17988467C4semidirect
57. #386×C73C4semidirect
79. C23×Dic73C2×C4semidirect
80. C23×Dic73C2×C4semidirect
92. C2×C4⋊Dic73C2×C4semidirect
102. C2×C22⋊Dic73C2×C4semidirect
103. C2×C22⋊Dic73C2×C4semidirect
104. C2×C22⋊Dic73C2×C4semidirect
105. C2×C22⋊Dic73C2×C4semidirect
122. C2×C4×Dic73C2×C4semidirect
134. #14556498C2×C4semidirect
135. #14556498C2×C4semidirect
136. #14556498D4semidirect
152. C23×C4×C73C2×C4semidirect
164. C2×C22⋊C4×C73C2×C4semidirect
165. C2×C22⋊C4×C73C2×C4semidirect
166. C2×C22⋊C4×C73C2×C4semidirect
167. #95×C73C2×C4semidirect
168. #95×C73C2×C4semidirect
251. C22⋊Dic73C22⋊C4semidirect
294. C2×D4×C73C42semidirect
461. C2×C4×C73C4×D4semidirect
520. C2×Dic73C4×D4semidirect
550. C22×C73C4×C22⋊C4semidirect
632. C73#13813semidirect
656. #386Dic73semidirect
721. C23×C4C2×Dic73semidirect
752. C2×C22⋊C4C2×Dic73semidirect
753. C2×C22⋊C4C2×Dic73semidirect
754. C2×C22⋊C4C2×Dic73semidirect
784. #95C2×Dic73semidirect
785. #95C2×Dic73semidirect
823. C2×D4C4×Dic73semidirect
1137. C2×C4D4×Dic73semidirect
1167. C22C22⋊C4×Dic73semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic732
C2×#179884672
C2×C22⋊C4×Dic732
C2×C4×C22⋊Dic732
C22×#145564982
#226081682
#226081652
#226081562
#226081532
#95×Dic732
C2×#386×C732
#1381373