Finite Group Databasebeta

← #33101539

Subgroups — #33101539

Order 18688.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic, complemented
2C2×#17988592C211yesmaximal, characteristic, complemented
3C2×#17988583C211yesmaximal, characteristic, complemented
4#22612880C211yesmaximal, characteristic, complemented
5#22610864C211yesmaximal, characteristic, complemented
6#22610748C211yesmaximal, characteristic, complemented
7#22610365C211yesmaximal, characteristic, complemented
8#22610360C211yesmaximal, characteristic, complemented
9#22610254C211yesmaximal, characteristic, complemented
10#22610244C211yesmaximal, characteristic, complemented
11#22609931C211yesmaximal, characteristic, complemented
12#22609871C211yesmaximal, characteristic, complemented
13#22609862C211yesmaximal, characteristic, complemented
14#22609756C211yesmaximal, characteristic, complemented
15C2×#546×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic, complemented
18C2×#14556550C2211yescharacteristic
19C2×#14556550C2211yescharacteristic, complemented
20#17988659—24no—
21C2×C4⋊#10596831C2211yescharacteristic, complemented
22#17988592—24no—
23#17988583—24no—
24C2×#14556515C2211yescharacteristic, complemented
25C2×#14556515C2211yescharacteristic, complemented
26C2×#14556515C2211yescharacteristic, complemented
27C2×#14556515C2211yescharacteristic, complemented
28C2×#14556512C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×#14556512C2211yescharacteristic
34C2×#14556512C2211yescharacteristic
35C2×#14556512C2211yescharacteristic
36C2×C22⋊#10596831C2211yescharacteristic
37C2×C22⋊#10596831C2211yescharacteristic, complemented
38C2×#14556502C2211yescharacteristic, complemented
39#17988490—21no—
40#17988480—21no—
41#17988480—21no—
42#17988457C2211yescharacteristic, complemented
43#17988447C2211yescharacteristic
44#17988447C2211yescharacteristic, complemented
45C4⋊C4×Dic73—21no—
46C4×C4⋊Dic73C2211yescharacteristic, complemented
47#17988349C2211yescharacteristic, complemented
48#17988349C2211yescharacteristic, complemented
49#17988349C2211yescharacteristic, complemented
50#17988349C2211yescharacteristic, complemented
51C22×#41×C73C2211yescharacteristic
52C23×D4×C73C2211yescharacteristic
53#546×C73—24no—
54#546×C73C418yescomplemented
55C2×#124×C73C2211yescharacteristic
56C2×#123×C73—21no—
57C2×C22⋊Q8×C73C2211yescharacteristic
58C2×#121×C73—21no—
59C2×#121×C73C2211yescharacteristic
60C2×#120×C73—21no—
61C2×C4×D4×C73C2211yescharacteristic
62C2×C4×D4×C73C2211yescharacteristic
63C22×C22⋊C4×C73—21no—
64C2×#11924012—22no—
65C2×#11924012—22no—
66C2×#11924012—41no—
67C22×#10596831—22no—
68C22×#10596831—22no—
69C22×#10596831—41no—
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74#14556550—22no—
75#14556550—22no—
76#14556550—41no—
77#14556550—41no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73—21no—
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C4⋊Dic73C2311yescharacteristic
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C4×Dic73—21no—
89C2×C4×Dic73—21no—
90C2×C4×Dic73—21no—
91C4⋊#10596831—22no—
92#14556515—22no—
93#14556515—22no—
94#14556515—41no—
95#14556515—41no—
96#14556512—22no—
97#14556512—22no—
98#14556512—22no—
99#14556512—22no—
100#14556512—22no—
101#14556512—41no—
102#14556512—41no—
103#14556512D414yescomplemented
104C22⋊#10596831—22no—
105C22⋊#10596831—22no—
106#14556502—22no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C25×C73—21no—
111C2×#41×C73—22no—
112C2×#41×C73—22no—
113C2×#41×C73—22no—
114C2×#41×C73—41no—
115C2×#41×C73—41no—
116C2×#41×C73C2×C414yes—
117C22×Q8×C73C2311yescharacteristic
118C22×D4×C73—22no—
119C22×D4×C73—22no—
120C22×D4×C73—21no—
121C22×D4×C73—21no—
122C22×D4×C73—21no—
123C22×D4×C73—22no—
124C22×D4×C73—41no—
125C22×D4×C73—41no—
126C22×D4×C73C2×C414yes—
127C22×D4×C73D411yescharacteristic
128C22×D4×C73C2311yescharacteristic
129C22×D4×C73C2311yescharacteristic
130C23×C4×C73—21no—
131C23×C4×C73—21no—
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134#124×C73—22no—
135#124×C73C2×C414yes—
136#123×C73—28no—
137C22⋊Q8×C73—22no—
138C22⋊Q8×C73C2×C414yes—
139#121×C73—22no—
140#121×C73—28no—
141#121×C73C2×C414yes—
142#120×C73—28no—
143C4×D4×C73—22no—
144C4×D4×C73C2×C414yes—
145C4×D4×C73C2×C414yes—
146C4×D4×C73D414yes—
147C2×C4⋊C4×C73—21no—
148C2×C4⋊C4×C73D411yescharacteristic
149C2×C4⋊C4×C73C2311yescharacteristic
150C2×C22⋊C4×C73—21no—
151C2×C22⋊C4×C73—21no—
152C2×C22⋊C4×C73—21no—
153C2×C22⋊C4×C73—21no—
154C2×C22⋊C4×C73—21no—
155C2×C22⋊C4×C73—28no—
156C2×C22⋊C4×C73D411yescharacteristic
157C2×C22⋊C4×C73D411yescharacteristic
158C2×C42×C73C2311yescharacteristic
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163#11924012—44no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831—44no—
176C2×#10596831C2×D412yes—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73—21no—
183C4⋊Dic73—21no—
184C4⋊Dic73—42no—
185C4⋊Dic73—81no—
186C4⋊Dic73C2×D412yes—
187C22⋊Dic73—42no—
188C22⋊Dic73—42no—
189C22⋊Dic73—81no—
190C22⋊Dic73—81no—
191C4×Dic73—42no—
192C4×Dic73—42no—
193C4×Dic73—42no—
194C24×C73—21no—
195C24×C73—21no—
196C24×C73—24no—
197C24×C73—42no—
198C24×C73—42no—
199C24×C73—42no—
200C24×C73—42no—
201C24×C73—81no—
202C24×C73—81no—
203C24×C73C2×D411yescharacteristic
204C24×C73C2×D411yescharacteristic
205#41×C73—28no—
206#41×C73—44no—
207#41×C73—44no—
208#41×C73—44no—
209C2×Q8×C73—21no—
210C2×Q8×C73—21no—
211C2×Q8×C73—21no—
212C2×Q8×C73—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73C22×C412yes—
215C2×D4×C73—28no—
216C2×D4×C73—24no—
217C2×D4×C73—24no—
218C2×D4×C73—24no—
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73—21no—
226C2×D4×C73—21no—
227C2×D4×C73—44no—
228C2×D4×C73—44no—
229C2×D4×C73—44no—
230C2×D4×C73—41no—
231C2×D4×C73—41no—
232C2×D4×C73—42no—
233C2×D4×C73—42no—
234C2×D4×C73—42no—
235C2×D4×C73—42no—
236C2×D4×C73—81no—
237C2×D4×C73—81no—
238C2×D4×C73C22⋊C414yes—
239C2×D4×C73C22×C412yes—
240C2×D4×C73C22×C412yes—
241C2×D4×C73C2×D412yes—
242C2×D4×C73#4112yes—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—24no—
254C22×C4×C73—24no—
255C22×C4×C73—42no—
256C22×C4×C73—42no—
257C22×C4×C73—81no—
258C22×C4×C73—81no—
259C22×C4×C73C22×C412yes—
260C22×C4×C73C22×C412yes—
261C22×C4×C73C2×D411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2×D412yes—
267C22×C4×C73C2411yescharacteristic
268C4⋊C4×C73—24no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73C22⋊C414yes—
271C4⋊C4×C73C22×C412yes—
272C22⋊C4×C73—24no—
273C22⋊C4×C73—24no—
274C22⋊C4×C73—24no—
275C22⋊C4×C73—24no—
276C22⋊C4×C73—24no—
277C22⋊C4×C73C22⋊C414yes—
278C22⋊C4×C73C22⋊C414yes—
279C42×C73C22×C412yes—
280C42×C73C2×D412yes—
281C23×C73—22no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—22no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—22no—
288C23×C73—21no—
289C23×C73—21no—
290C23×C73—21no—
291C23×C73—21no—
292C23×C73—21no—
293C23×C73—21no—
294C23×C73—21no—
295C23×C73—21no—
296C23×C73—22no—
297C23×C73—48no—
298C23×C73—48no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73—84no—
310C23×C73—84no—
311C23×C73—84no—
312C23×C73—84no—
313C23×C73—84no—
314C23×C73C2×C22⋊C412yes—
315C23×C73C2×C22⋊C412yes—
316C23×C73C22×D411yescharacteristic
317Q8×C73—22no—
318Q8×C73—22no—
319Q8×C73—41no—
320Q8×C73—41no—
321D4×C73—22no—
322D4×C73—22no—
323D4×C73—22no—
324D4×C73—22no—
325D4×C73—22no—
326D4×C73—44no—
327D4×C73—48no—
328D4×C73—48no—
329D4×C73—41no—
330D4×C73—41no—
331D4×C73—84no—
332D4×C73C4×D414yes—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—48no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—84no—
357C2×C4×C73C2×C22⋊C412yes—
358C2×C4×C73C2×C22⋊C412yes—
359C2×C4×C73C2×C22⋊C412yes—
360C2×C4×C73C2×C22⋊C412yes—
361C2×C4×C73C23×C411yescharacteristic
362C2×C4×C73C22×D411yescharacteristic
363C2×C4×C73C22×D411yescharacteristic
364C2×C4×C73C2×#4111yescharacteristic
365C2×C4×C73H(5,𝔽2)11yescharacteristic
366C2×C4×C73H(5,𝔽2)11yescharacteristic
367C2×Dic73—22no—
368C2×Dic73—41no—
369C2×Dic73—41no—
370C2×Dic73—41no—
371C2×Dic73—41no—
372C2×Dic73—41no—
373C2×Dic73—41no—
374C2×Dic73—41no—
375C2×Dic73—41no—
376C2×Dic73—41no—
377C2×Dic73—41no—
378C2×Dic73—41no—
379#10596831—22no—
380#10596831—41no—
381#10596831—41no—
382#10596831—41no—
383C22×C73—22no—
384C22×C73—22no—
385C22×C73—24no—
386C22×C73—22no—
387C22×C73—22no—
388C22×C73—22no—
389C22×C73—22no—
390C22×C73—42no—
391C22×C73—42no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—42no—
395C22×C73—41no—
396C22×C73—41no—
397C22×C73—42no—
398C22×C73—41no—
399C22×C73—41no—
400C22×C73—42no—
401C22×C73—41no—
402C22×C73—41no—
403C22×C73—42no—
404C22×C73—42no—
405C22×C73—42no—
406C22×C73—42no—
407C22×C73—816no—
408C22×C73—81no—
409C22×C73—81no—
410C22×C73—81no—
411C22×C73—81no—
412C22×C73C22×C22⋊C411yescharacteristic
413C22×C73D4211yescharacteristic
414C22×C73#54611yescharacteristic
415C22×C73#57511yescharacteristic
416C22×C73#57511yescharacteristic
417C22×C73#57611yescharacteristic
418C22×C73#57711yescharacteristic
419C4×C73—22no—
420C4×C73—22no—
421C4×C73—22no—
422C4×C73—22no—
423C4×C73—42no—
424C4×C73—42no—
425C4×C73C2×C4×D411yescharacteristic
426C4×C73#51811yescharacteristic
427C4×C73D4211yescharacteristic
428C4×C73#54611yescharacteristic
429Dic73—42no—
430Dic73—81no—
431Dic73—81no—
432Dic73—81no—
433#22424—731nomaximal, Sylow
434C2×C73—42no—
435C2×C73—42no—
436C2×C73—44no—
437C2×C73—82no—
438C2×C73D4×C22⋊C411yescharacteristic
439C2×C73#289611yescharacteristic
440C2×C73#289711yescharacteristic
441C2×C73#326711yescharacteristic
442C2×C73#326811yescharacteristic
443C2×C73#331111yescharacteristic
444C2×C73#331911yescharacteristic
445C2×#546D7311yescharacteristic
446C2×#435—731no—
447C2×#418—731no—
448C2×#416—731no—
449#2354—731no—
450#1983—731no—
451#1959—731no—
452#1894—731no—
453#1893—731no—
454#1875—731no—
455#1873—731no—
456#1802—731no—
457#1788—731no—
458#1786—731no—
459#1762—731no—
460C73#2242411yescharacteristic, complemented, Sylow
461C22×#41C2×D7311yescharacteristic
462C23×D4C2×D7311yescharacteristic
463C22×M16—731no—
464C23×C8—731no—
465#546—24no—
466#546Dic7318yescomplemented
467C2×#124C2×D7311yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C2×D7311yescharacteristic
470C2×#121—21no—
471C2×#121C2×D7311yescharacteristic
472C2×#120—21no—
473C2×C4×D4C2×D7311yescharacteristic
474C2×C4×D4C2×D7311yescharacteristic
475C2×#117—731no—
476C2×#117—731no—
477C22×C22⋊C4—21no—
478#435—1464no—
479C2×C4⋊C8—731no—
480#418—1464no—
481#416—1464no—
482C2×#103—731no—
483C2×#103—731no—
484C2×#103—731no—
485C2×#103—731no—
486C2×#102—731no—
487C2×#102—731no—
488C2×#102—731no—
489C2×#102—731no—
490C2×#102—731no—
491C2×#102—731no—
492C2×#102—731no—
493C2×#102—731no—
494C2×C22⋊C8—731no—
495C2×C22⋊C8—731no—
496C2×#97—731no—
497#390—1461no—
498#388—1461no—
499#388—1461no—
500#384—731no—
501#380—731no—
502#380—731no—
503C4×C4⋊C4—731no—
504C4×C4⋊C4—1461no—
505#340—731no—
506#340—731no—
507#340—731no—
508#340—731no—
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×Dic7314yes—
516C22×Q8C22×D7311yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×Dic7314yes—
526C22×D4C22⋊D7311yescharacteristic
527C22×D4C22×D7311yescharacteristic
528C22×D4C22×D7311yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D7311yescharacteristic
532C23×C4C22×D7311yescharacteristic
533C2×M16—2921no—
534C2×M16—1462no—
535C2×M16—1462no—
536C22×C8—2921no—
537C22×C8—731no—
538C22×C8—731no—
539C22×C8—731no—
540C22×C8—731no—
541C22×C8—1462no—
542C22×C8—1462no—
543#124—22no—
544#124C2×Dic7314yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×Dic7314yes—
548#121—22no—
549#121—28no—
550#121C2×Dic7314yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×Dic7314yes—
554C4×D4C2×Dic7314yes—
555C4×D4C22⋊D7314yes—
556#117—2921no—
557#117—2921no—
558#117—1462no—
559#117—1462no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—731no—
562C2×C4⋊C4—731no—
563C2×C4⋊C4—731no—
564C2×C4⋊C4—731no—
565C2×C4⋊C4—1461no—
566C2×C4⋊C4—1461no—
567C2×C4⋊C4C22⋊D7311yescharacteristic
568C2×C4⋊C4C22×D7311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—1461no—
576C2×C22⋊C4—1461no—
577C2×C22⋊C4—1461no—
578C2×C22⋊C4—1461no—
579C2×C22⋊C4C22⋊D7311yescharacteristic
580C2×C22⋊C4C22⋊D7311yescharacteristic
581C2×C42—1461no—
582C2×C42—1461no—
583C2×C42—1461no—
584C2×C42C22×D7311yescharacteristic
585C4⋊C8—1462no—
586#103—2921no—
587#103—2921no—
588#103—1462no—
589#103—1462no—
590#102—2921no—
591#102—2921no—
592#102—734no—
593#102—1462no—
594#102—1462no—
595#102—1462no—
596#102—1462no—
597#102—1462no—
598C22⋊C8—1462no—
599C22⋊C8—1462no—
600#97—1462no—
601#95—1461no—
602#95—1461no—
603#95—1461no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×C22⋊D7311yescharacteristic
614C24C2×C22⋊D7311yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×Dic7312yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊Dic7314yes—
649C2×D4C22×Dic7312yes—
650C2×D4C22×Dic7312yes—
651C2×D4D4×D7312yes—
652C2×D4#1192402712yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—81no—
668C22×C4—81no—
669C22×C4—1461no—
670C22×C4—1461no—
671C22×C4—1461no—
672C22×C4—1461no—
673C22×C4C22×Dic7312yes—
674C22×C4C22×Dic7312yes—
675C22×C4C2×C22⋊D7311yescharacteristic
676C22×C4C2×C22⋊D7311yescharacteristic
677C22×C4C2×C22⋊D7311yescharacteristic
678C22×C4C2×C22⋊D7311yescharacteristic
679C22×C4C2×C22⋊D7312yes—
680C22×C4C2×C22⋊D7312yes—
681C22×C4C23×D7311yescharacteristic
682M16—2924no—
683C2×C8—2924no—
684C2×C8—732no—
685C2×C8—1461no—
686C2×C8—1461no—
687C2×C8—1461no—
688C2×C8—1461no—
689C2×C8—1461no—
690C2×C8—1461no—
691C2×C8—1461no—
692C2×C8—1461no—
693C2×C8—1461no—
694C2×C8—1461no—
695C2×C8—1461no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—2922no—
699C4⋊C4—5841no—
700C4⋊C4—732no—
701C4⋊C4—1461no—
702C4⋊C4—1461no—
703C4⋊C4—1461no—
704C4⋊C4—1461no—
705C4⋊C4—1461no—
706C4⋊C4—1461no—
707C4⋊C4—1461no—
708C4⋊C4C22⋊Dic7314yes—
709C4⋊C4C22×Dic7312yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—2922no—
716C22⋊C4—2922no—
717C22⋊C4—5841no—
718C22⋊C4—5841no—
719C22⋊C4C22⋊Dic7314yes—
720C22⋊C4C22⋊Dic7314yes—
721C42—2922no—
722C42—2922no—
723C42—2922no—
724C42C22×Dic7312yes—
725C42C2×C22⋊D7312yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊Dic7312yes—
760C23C2×C22⋊Dic7312yes—
761C23C22×C22⋊D7311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4D4×Dic7314yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—2921no—
803C2×C4—2921no—
804C2×C4—2921no—
805C2×C4—2921no—
806C2×C4—2921no—
807C2×C4—2921no—
808C2×C4—2921no—
809C2×C4—2921no—
810C2×C4—2921no—
811C2×C4—2921no—
812C2×C4—2921no—
813C2×C4—1462no—
814C2×C4C2×C22⋊Dic7312yes—
815C2×C4C2×C22⋊Dic7312yes—
816C2×C4C2×C22⋊Dic7312yes—
817C2×C4C2×C22⋊Dic7312yes—
818C2×C4C23×Dic7311yescharacteristic
819C2×C4C2×D4×D7311yescharacteristic
820C2×C4C22×C22⋊D7311yescharacteristic
821C2×C4C2×#1192402711yescharacteristic
822C2×C4#1455663611yescharacteristic
823C2×C4#1455663611yescharacteristic
824C8—2921no—
825C8—2921no—
826C8—2921no—
827C8—1462no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊Dic7311yescharacteristic
858C22D4×C22⋊D7311yescharacteristic
859C22#1798923111yescharacteristic
860C22#1798938511yescharacteristic
861C22#1798938511yescharacteristic
862C22#1798939011yescharacteristic
863C22#1798939811yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—2922no—
871C4—5841no—
872C4—5841no—
873C4—5841no—
874C4C2×D4×Dic7311yescharacteristic
875C4#1798906211yescharacteristic
876C4D4×C22⋊D7311yescharacteristic
877C4#1798923111yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊Dic7311yescharacteristic
883C2#2261845011yescharacteristic
884C2#2261845711yescharacteristic
885C2#2262145211yescharacteristic
886C2#2262146711yescharacteristic
887C2#2262196711yescharacteristic
888C2#2262208711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
Fitting, prime radicalC2×#546×C73C2
socleC23×C73C22×D4
cosocleC22×C4×C73C24
hypercenterC2×#546D73
hypocenterC73#22424
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#17988659C2semidirect
2. C2×#17988592C2semidirect
3. C2×#17988583C2semidirect
4. #22612880C2semidirect
5. #22610864C2semidirect
6. #22610748C2semidirect
7. #22610365C2semidirect
8. #22610360C2semidirect
9. #22610254C2semidirect
10. #22610244C2semidirect
11. #22609931C2semidirect
12. #22609871C2semidirect
13. #22609862C2semidirect
14. #22609756C2semidirect
17. C23×#10596831C22semidirect
19. C2×#14556550C22semidirect
21. C2×C4⋊#10596831C22semidirect
24. C2×#14556515C22semidirect
25. C2×#14556515C22semidirect
26. C2×#14556515C22semidirect
27. C2×#14556515C22semidirect
37. C2×C22⋊#10596831C22semidirect
38. C2×#14556502C22semidirect
42. #17988457C22semidirect
44. #17988447C22semidirect
46. C4×C4⋊Dic73C22semidirect
47. #17988349C22semidirect
48. #17988349C22semidirect
49. #17988349C22semidirect
50. #17988349C22semidirect
54. #546×C73C4semidirect
103. #14556512D4semidirect
460. C73#22424semidirect
466. #546Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
C2×#179885922
C2×#179885832
#226128802
#226108642
#226107482
#226103652
#226103602
#226102542
#226102442
#226099312
#226098712
#226098622
#226097562
C2×#546×C732
#2242473