Finite Group Databasebeta

← #33008848

Subgroups — #33008848

Order 18688.

2690 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×#17988462C211yesmaximal, characteristic, complemented
4C2×#17988462C211yesmaximal, characteristic, complemented
5C2×#17988447C211yesmaximal, characteristic, complemented
6C22×#14556498C211yesmaximal, characteristic, complemented
7#22608196C211yesmaximal, characteristic, complemented
8#22608188C211yesmaximal, characteristic, complemented
9#22608176C211yesmaximal, characteristic, complemented
10#22608176C211yesmaximal, characteristic, complemented
11#22608165C211yesmaximal, characteristic, complemented
12#22608165C211yesmaximal, characteristic, complemented
13#22608153C211yesmaximal, characteristic, complemented
14#22608153C211yesmaximal, characteristic, complemented
15C2×#386×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C24×Dic73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C2×D4×Dic73—24no—
20C2×D4×Dic73—24no—
21C2×D4×Dic73—24no—
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C4⋊Dic73C2211yescharacteristic
25C22×C4⋊Dic73C2211yescharacteristic
26C22×C4⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×C22⋊Dic73C2211yescharacteristic
29C22×C22⋊Dic73C2211yescharacteristic
30C22×C22⋊Dic73C2211yescharacteristic
31C22×C22⋊Dic73C2211yescharacteristic
32C22×C4×Dic73C2211yescharacteristic
33#17988467—24no—
34#17988462—24no—
35#17988462—24no—
36#17988447—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—22no—
73C23×Dic73—22no—
74C23×Dic73—41no—
75C23×Dic73—41no—
76C23×Dic73—41no—
77C23×Dic73—41no—
78C23×Dic73—41no—
79C23×Dic73—41no—
80C23×Dic73D414yes—
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⋊Dic73—22no—
93C2×C4⋊Dic73—22no—
94C2×C4⋊Dic73—22no—
95C2×C4⋊Dic73—22no—
96C2×C4⋊Dic73—22no—
97C2×C4⋊Dic73—22no—
98C2×C4⋊Dic73—22no—
99C2×C4⋊Dic73—22no—
100C2×C4⋊Dic73—22no—
101C2×C4⋊Dic73—41no—
102C2×C4⋊Dic73—41no—
103C2×C4⋊Dic73—41no—
104C2×C4⋊Dic73—41no—
105C2×C22⋊Dic73—22no—
106C2×C22⋊Dic73—22no—
107C2×C22⋊Dic73—22no—
108C2×C22⋊Dic73—22no—
109C2×C22⋊Dic73—22no—
110C2×C22⋊Dic73—22no—
111C2×C22⋊Dic73—22no—
112C2×C22⋊Dic73—22no—
113C2×C22⋊Dic73—22no—
114C2×C22⋊Dic73—22no—
115C2×C22⋊Dic73—22no—
116C2×C22⋊Dic73—22no—
117C2×C22⋊Dic73—41no—
118C2×C22⋊Dic73—41no—
119C2×C22⋊Dic73D414yes—
120C2×C4×Dic73—22no—
121C2×C4×Dic73—22no—
122C2×C4×Dic73—22no—
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—22no—
133#14556498—22no—
134#14556498—41no—
135#14556498—41no—
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×C73D414yes—
145C22×D4×C73Q814yes—
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—28no—
174C22×Dic73—28no—
175C22×Dic73—28no—
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—21no—
186C22×Dic73—21no—
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—28no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73—21no—
210C22×Dic73—21no—
211C22×Dic73—21no—
212C22×Dic73—21no—
213C22×Dic73—21no—
214C22×Dic73—21no—
215C22×Dic73—21no—
216C22×Dic73—21no—
217C22×Dic73—21no—
218C22×Dic73—21no—
219C22×Dic73—21no—
220C22×Dic73—21no—
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×Dic73—44no—
231C22×Dic73—44no—
232C22×Dic73—44no—
233C22×Dic73—44no—
234C22×Dic73—44no—
235C22×Dic73—44no—
236C22×Dic73—44no—
237C22×Dic73—44no—
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—
247C4⋊Dic73—44no—
248C4⋊Dic73—44no—
249C4⋊Dic73—44no—
250C4⋊Dic73—44no—
251C22⋊Dic73—28no—
252C22⋊Dic73—28no—
253C22⋊Dic73—44no—
254C22⋊Dic73—44no—
255C22⋊Dic73—44no—
256C4×Dic73—28no—
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×C73C2×D412yes—
280C24×C73C2×D412yes—
281C24×C73C2×D412yes—
282C24×C73C2×D412yes—
283C24×C73C2×Q812yes—
284C24×C73C2×Q812yes—
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×C73C4⋊C4116yescomplemented
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×C73C2×D412yes—
334C22×C4×C73C2×D412yes—
335C22×C4×C73C2×Q812yes—
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×C4⋊C414yes—
403C23×C73C2×C4⋊C414yes—
404C23×C73C4×D414yes—
405C23×C73C4×D414yes—
406C23×C73#12014yes—
407C23×C73C22⋊Q814yes—
408C23×C73C22⋊Q814yes—
409C23×C73#12314yes—
410C23×C73C23×C411yescharacteristic
411C23×C73C22×D411yescharacteristic
412C23×C73C22×D411yescharacteristic
413C23×C73C22×D411yescharacteristic
414C23×C73C22×D411yescharacteristic
415C23×C73C22×Q811yescharacteristic
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×C4⋊C414yes—
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—416no—
484C2×Dic73—416no—
485C2×Dic73—416no—
486C2×Dic73—41no—
487C2×Dic73—41no—
488C2×Dic73—41no—
489C2×Dic73—41no—
490C2×Dic73—41no—
491C2×Dic73—41no—
492C2×Dic73—41no—
493C2×Dic73—41no—
494C2×Dic73—41no—
495C2×Dic73—41no—
496C2×Dic73—41no—
497C2×Dic73—41no—
498C2×Dic73—41no—
499C2×Dic73—41no—
500C2×Dic73—41no—
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×Dic73—41no—
518C2×Dic73—41no—
519C2×Dic73—41no—
520C2×Dic73#12114yes—
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×C73#38518yescomplemented
551C22×C73C22×C4⋊C411yescharacteristic
552C22×C73C2×C4×D411yescharacteristic
553C22×C73C2×C4×D411yescharacteristic
554C22×C73C2×C4×D411yescharacteristic
555C22×C73C4×#4111yescharacteristic
556C22×C73#51811yescharacteristic
557C22×C73#52011yescharacteristic
558C22×C73C2×#12011yescharacteristic
559C22×C73C2×#12111yescharacteristic
560C22×C73C2×C22⋊Q811yescharacteristic
561C22×C73C2×C22⋊Q811yescharacteristic
562C22×C73C2×#12311yescharacteristic
563C22×C73#52511yescharacteristic
564C22×C73#52911yescharacteristic
565C22×C73#53211yescharacteristic
566C22×C73#53411yescharacteristic
567C22×C73#53711yescharacteristic
568C22×C73#53811yescharacteristic
569C22×C73#53911yescharacteristic
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×C73D4×Q811yescharacteristic
580C22×C73#55111yescharacteristic
581C22×C73#55111yescharacteristic
582C22×C73#55211yescharacteristic
583C22×C73#55411yescharacteristic
584C22×C73#55411yescharacteristic
585C22×C73#55411yescharacteristic
586C4×C73—24no—
587C4×C73—24no—
588C4×C73—42no—
589C4×C73—42no—
590C4×C73—42no—
591Dic73—24no—
592Dic73—42no—
593Dic73—42no—
594Dic73—42no—
595Dic73—42no—
596Dic73—42no—
597Dic73—81no—
598Dic73—81no—
599#13975—731nomaximal, Sylow
600C2×C73—28no—
601C2×C73—44no—
602C2×C73C2×#38511yescharacteristic
603C2×C73C4×#12111yescharacteristic
604C2×C73#232511yescharacteristic
605C2×C73D4×C4⋊C411yescharacteristic
606C2×C73#234911yescharacteristic
607C2×C73#235811yescharacteristic
608C2×C73#235911yescharacteristic
609C2×C73#241011yescharacteristic
610C2×C73#241711yescharacteristic
611C2×C73#241811yescharacteristic
612C2×C73#241911yescharacteristic
613C2×C73#243011yescharacteristic
614C2×C73#244911yescharacteristic
615C2×C73#245011yescharacteristic
616C2×C73#256411yescharacteristic
617C22×C4×D4—731no—
618C2×#386—731no—
619C2×#386D7311yescharacteristic
620C2×#385—731no—
621C2×#385—731no—
622C2×#380—731no—
623C22×#95—731no—
624#1444—731no—
625#1442—731no—
626#1439—731no—
627#1439—731no—
628#1436—731no—
629#1436—731no—
630C22⋊#95—731no—
631C22⋊#95—731no—
632C73#1397511yescharacteristic, complemented, Sylow
633C23×D4C2×D7311yescharacteristic
634C24×C4—731no—
635C24×C4—731no—
636C24×C4—731no—
637C24×C4C2×D7311yescharacteristic
638C2×C4×D4—1464no—
639C2×C4×D4—1464no—
640C2×C4×D4—1464no—
641C22×C4⋊C4—731no—
642C22×C4⋊C4—731no—
643C22×C4⋊C4—731no—
644C22×C4⋊C4—731no—
645C22×C4⋊C4—731no—
646C22×C22⋊C4—731no—
647C22×C22⋊C4—731no—
648C22×C22⋊C4—731no—
649C22×C22⋊C4—731no—
650C22×C22⋊C4—731no—
651C22×C22⋊C4C2×D7311yescharacteristic
652C22×C22⋊C4C2×D7311yescharacteristic
653C22×C22⋊C4C2×D7311yescharacteristic
654C22×C42—731no—
655#386—1464no—
656#386Dic7318yescomplemented
657#385—1464no—
658#385—1464no—
659#380—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×D4Dic14614yes—
684C22×D4D29214yes—
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—731no—
700C23×C4—731no—
701C23×C4—731no—
702C23×C4—731no—
703C23×C4—731no—
704C23×C4—731no—
705C23×C4—731no—
706C23×C4—731no—
707C23×C4—1462no—
708C23×C4—1462no—
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—2921no—
729C2×C4⋊C4—2921no—
730C2×C4⋊C4—2921no—
731C2×C4⋊C4—2921no—
732C2×C4⋊C4—1462no—
733C2×C4⋊C4—1462no—
734C2×C4⋊C4—1462no—
735C2×C4⋊C4—1462no—
736C2×C4⋊C4—1462no—
737C2×C4⋊C4—1462no—
738C2×C4⋊C4—1462no—
739C2×C4⋊C4—1462no—
740C2×C4⋊C4—1462no—
741C2×C4⋊C4—1462no—
742C2×C4⋊C4—1462no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—2921no—
750C2×C22⋊C4—2921no—
751C2×C22⋊C4—734no—
752C2×C22⋊C4—1462no—
753C2×C22⋊C4—1462no—
754C2×C22⋊C4—1462no—
755C2×C22⋊C4—1462no—
756C2×C22⋊C4—1462no—
757C2×C22⋊C4—1462no—
758C2×C22⋊C4—1462no—
759C2×C22⋊C4—1462no—
760C2×C22⋊C4—1462no—
761C2×C22⋊C4—1462no—
762C2×C22⋊C4—1462no—
763C2×C22⋊C4—1462no—
764C2×C22⋊C4C2×Dic7314yescomplemented
765C2×C22⋊C4C2×Dic7314yescomplemented
766C2×C22⋊C4C2×Dic7314yescomplemented
767C2×C42—1462no—
768C2×C42—1462no—
769C2×C42—1462no—
770#95—2921no—
771#95—2921no—
772#95—734no—
773#95—1462no—
774#95—1462no—
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—
806C24C22×Dic7312yes—
807C24C22×Dic7312yes—
808C24D4×D7312yes—
809C24D4×D7312yes—
810C24C2×D29212yes—
811C24C2×D29212yes—
812C24C2×Dic14612yes—
813C24C2×Dic14612yes—
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—2924no—
873C22×C4—2924no—
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—1461no—
883C22×C4—1461no—
884C22×C4—1461no—
885C22×C4—1461no—
886C22×C4—1461no—
887C22×C4—1461no—
888C22×C4—1461no—
889C22×C4—1461no—
890C22×C4—1461no—
891C22×C4—1461no—
892C22×C4—1461no—
893C22×C4—1461no—
894C22×C4—1461no—
895C22×C4—1461no—
896C22×C4—1468no—
897C22×C4—1468no—
898C22×C4—1468no—
899C22×C4—1468no—
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×C4C22×Dic7312yes—
935C22×C4C22×Dic7312yes—
936C22×C4C22×Dic7312yes—
937C22×C4C22×Dic7312yes—
938C22×C4C22×Dic7312yes—
939C22×C4D4×D7312yes—
940C22×C4C2×D29212yes—
941C22×C4C2×Dic14612yes—
942C22×C4#1192402712yes—
943C4⋊C4—2924no—
944C4⋊C4—2924no—
945C4⋊C4—2924no—
946C4⋊C4—2924no—
947C4⋊C4—1468no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—2924no—
952C22⋊C4—2924no—
953C22⋊C4—2924no—
954C22⋊C4—1468no—
955C22⋊C4—1468no—
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—
1021C23D4×Dic7314yes—
1022C23D4×Dic7314yes—
1023C23#1455656114yes—
1024C23#1455656814yes—
1025C23#1455656814yes—
1026C23#1455657514yes—
1027C23C23×Dic7311yescharacteristic
1028C23C2×D4×D7311yescharacteristic
1029C23C2×D4×D7311yescharacteristic
1030C23C2×D4×D7311yescharacteristic
1031C23C22×D29211yescharacteristic
1032C23C22×Dic14611yescharacteristic
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—29216no—
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—2921no—
1094C2×C4—2921no—
1095C2×C4—2921no—
1096C2×C4—2921no—
1097C2×C4—2921no—
1098C2×C4—29216no—
1099C2×C4—29216no—
1100C2×C4—2921no—
1101C2×C4—2921no—
1102C2×C4—2921no—
1103C2×C4—2921no—
1104C2×C4—2921no—
1105C2×C4—2921no—
1106C2×C4—2921no—
1107C2×C4—2921no—
1108C2×C4—2921no—
1109C2×C4—2921no—
1110C2×C4—2921no—
1111C2×C4—2921no—
1112C2×C4—2921no—
1113C2×C4—2921no—
1114C2×C4—734no—
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—
1167C22#1798846218yescomplemented
1168C22C22×C4⋊Dic7311yescharacteristic
1169C22C2×D4×Dic7311yescharacteristic
1170C22C2×D4×Dic7311yescharacteristic
1171C22C2×D4×Dic7311yescharacteristic
1172C22#41×Dic7311yescharacteristic
1173C22#1798906211yescharacteristic
1174C22#1798907011yescharacteristic
1175C22C2×#1455656111yescharacteristic
1176C22#121×D7311yescharacteristic
1177C22C2×#1455656811yescharacteristic
1178C22C2×#1455656811yescharacteristic
1179C22C2×#1455657511yescharacteristic
1180C22#1798909711yescharacteristic
1181C22#1798911811yescharacteristic
1182C22#1798913211yescharacteristic
1183C22#1798914511yescharacteristic
1184C22#1798916411yescharacteristic
1185C22#1798917411yescharacteristic
1186C22#1798918211yescharacteristic
1187C22#1798921911yescharacteristic
1188C22D4×D29211yescharacteristic
1189C22#1798922411yescharacteristic
1190C22#1798922411yescharacteristic
1191C22#1798922911yescharacteristic
1192C22#1798923211yescharacteristic
1193C22#1798923211yescharacteristic
1194C22#1798923511yescharacteristic
1195C22#1798924111yescharacteristic
1196C22D4×Dic14611yescharacteristic
1197C22#1798926011yescharacteristic
1198C22#1798926811yescharacteristic
1199C22#1798927411yescharacteristic
1200C22#1798929411yescharacteristic
1201C22#1798929611yescharacteristic
1202C22#1798929611yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—2922no—
1209C4—2922no—
1210C4—2922no—
1211C4—2922no—
1212C4—2922no—
1213C4—5841no—
1214C4—5841no—
1215C4—1464no—
1216C2—28no—
1217C2—44no—
1218C2C2×#1798846211yescharacteristic
1219C2#121×Dic7311yescharacteristic
1220C2#2261263611yescharacteristic
1221C2D4×C4⋊Dic7311yescharacteristic
1222C2#2261284111yescharacteristic
1223C2#2261291511yescharacteristic
1224C2#2261292711yescharacteristic
1225C2#2261330411yescharacteristic
1226C2#2261337911yescharacteristic
1227C2#2261339111yescharacteristic
1228C2#2261340611yescharacteristic
1229C2#2261353911yescharacteristic
1230C2#2261374411yescharacteristic
1231C2#2261375911yescharacteristic
1232C2#2261511511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#386×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC2×#386D73
hypocenterC73#13975
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#17988462C2semidirect
4. C2×#17988462C2semidirect
5. C2×#17988447C2semidirect
6. C22×#14556498C2semidirect
7. #22608196C2semidirect
8. #22608188C2semidirect
9. #22608176C2semidirect
10. #22608176C2semidirect
11. #22608165C2semidirect
12. #22608165C2semidirect
13. #22608153C2semidirect
14. #22608153C2semidirect
57. #386×C73C4semidirect
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
294. C2×D4×C73C4⋊C4semidirect
461. C2×C4×C73C4×D4semidirect
550. C22×C73#385semidirect
632. C73#13975semidirect
656. #386Dic73semidirect
721. C23×C4C2×Dic73semidirect
764. C2×C22⋊C4C2×Dic73semidirect
765. C2×C22⋊C4C2×Dic73semidirect
766. C2×C22⋊C4C2×Dic73semidirect
784. #95C2×Dic73semidirect
785. #95C2×Dic73semidirect
823. C2×D4C4⋊Dic73semidirect
1137. C2×C4D4×Dic73semidirect
1167. C22#17988462semidirect

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×#179884622
C2×#179884472
C22×#145564982
#226081962
#226081882
#226081762
#226081652
#226081532
C2×#386×C732
#1397573