Finite Group Databasebeta

← #33103596

Subgroups — #33103596

Order 18688.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618585C211yesmaximal, characteristic
2#22618520C211yesmaximal, characteristic
3#22610681C211yesmaximal, characteristic, complemented
4#22610676C211yesmaximal, characteristic, complemented
5#22610530C211yesmaximal, characteristic, complemented
6#22610530C211yesmaximal, characteristic, complemented
7#22610527C211yesmaximal, characteristic, complemented
8#22610527C211yesmaximal, characteristic, complemented
9#22610030C211yesmaximal, characteristic
10#22610028C211yesmaximal, characteristic
11#22609971C211yesmaximal, characteristic
12#22609816C211yesmaximal, characteristic, complemented
13#22609811C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic
15C73×#2924C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C2×#14556550C2211yescharacteristic
18#17988645—21no—
19#17988645—21no—
20#17988641—21no—
21#17988637—21no—
22C2×#14556526C2211yescharacteristic
23C2×#14556526C2211yescharacteristic
24#17988630C411yescharacteristic, complemented
25#17988630C411yescharacteristic, complemented
26#17988630C411yescharacteristic, complemented
27#17988630C411yescharacteristic, complemented
28#17988627C411yescharacteristic, complemented
29#17988627C411yescharacteristic, complemented
30#17988627C411yescharacteristic, complemented
31#17988627C411yescharacteristic, complemented
32#17988623C2211yescharacteristic
33#17988623C2211yescharacteristic
34#17988623C2211yescharacteristic
35#17988623C2211yescharacteristic
36#17988613C2211yescharacteristic
37#17988613C2211yescharacteristic
38#17988551C2211yescharacteristic
39#17988542C2211yescharacteristic
40#17988542C2211yescharacteristic
41C2×#14556501C2211yescharacteristic
42C2×C8×Dic73C2211yescharacteristic
43C4×C22⋊Dic73C2211yescharacteristic
44#17988351C2211yescharacteristic
45#17988351C2211yescharacteristic
46#17988348C2211yescharacteristic
47#17988348C2211yescharacteristic
48#17988348C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988346C2211yescharacteristic
51#17988346C2211yescharacteristic
52#17988346C2211yescharacteristic
53#17988346C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C2×#117×C73C2211yescharacteristic
57#433×C73—21no—
58#433×C73—21no—
59#432×C73—21no—
60#431×C73—21no—
61#424×C73C2211yescharacteristic
62#424×C73C2211yescharacteristic
63#407×C73C2211yescharacteristic
64C2×C22⋊C8×C73C2211yescharacteristic
65#405×C73C2211yescharacteristic
66#405×C73C2211yescharacteristic
67C2×#11924012—22no—
68C2×#11924012—22no—
69C2×#11924012C2×C411yescharacteristic
70C2×#11924012C2×C411yescharacteristic
71C2×#11924012C2×C411yescharacteristic
72C2×#11924012C2×C411yescharacteristic
73C2×#11924012C2311yescharacteristic
74C2×#11924012C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77#14556550—21no—
78#14556550—21no—
79#14556550C2×C411yescharacteristic
80#14556550C2×C411yescharacteristic
81#14556550C2311yescharacteristic
82#14556550C2311yescharacteristic
83C2×C4⋊Dic73C2×C411yescharacteristic
84C2×C4⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73C2311yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90#14556526—22no—
91#14556526—22no—
92#14556524C2×C411yescharacteristic
93#14556524C2×C411yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556524C2×C411yescharacteristic
96#14556524C2×C411yescharacteristic
97#14556524C2×C411yescharacteristic
98#14556524C2×C411yescharacteristic
99#14556524C2×C411yescharacteristic
100#14556522C2×C411yescharacteristic
101#14556522C2×C411yescharacteristic
102#14556522C2×C411yescharacteristic
103#14556522C2×C411yescharacteristic
104#14556522C2×C411yescharacteristic
105#14556522C2×C411yescharacteristic
106#14556522C2×C411yescharacteristic
107#14556522C2×C411yescharacteristic
108#14556520—21no—
109#14556520—21no—
110#14556520—21no—
111#14556520—21no—
112C22⋊#10596831—21no—
113C22⋊#10596831—21no—
114#14556501—22no—
115#14556501—21no—
116#14556501—21no—
117C8×Dic73—22no—
118C8×Dic73—21no—
119C8×Dic73—21no—
120#14556498—21no—
121C23×C4×C73C2311yescharacteristic
122C2×M16×C73C2311yescharacteristic
123C2×M16×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126#117×C73—21no—
127#117×C73—21no—
128#117×C73C2×C411yescharacteristic
129#117×C73C2×C411yescharacteristic
130#117×C73C2311yescharacteristic
131#117×C73C2311yescharacteristic
132C2×C4⋊C4×C73C2×C411yescharacteristic
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C22⋊C4×C73—21no—
135C2×C42×C73—21no—
136C4⋊C8×C73—21no—
137C4⋊C8×C73—21no—
138C4⋊C8×C73—21no—
139C4⋊C8×C73—21no—
140C22⋊C8×C73—21no—
141C22⋊C8×C73—21no—
142C22⋊C8×C73D411yescharacteristic
143C22⋊C8×C73D411yescharacteristic
144C22⋊C8×C73D411yescharacteristic
145C22⋊C8×C73D411yescharacteristic
146#97×C73—21no—
147#97×C73—21no—
148C4×C8×C73—21no—
149C4×C8×C73—21no—
150C22×Dic73—21no—
151C22×Dic73—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154#11924012—22no—
155#11924012—22no—
156#11924012—22no—
157#11924012—22no—
158#11924012—21no—
159#11924012—21no—
160#11924012—21no—
161#11924012—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C2×#10596831C22×C411yescharacteristic
169C2×#10596831C22×C411yescharacteristic
170C2×#10596831#4112yes—
171C2×#10596831#4112yes—
172C4⋊Dic73—21no—
173C4⋊Dic73—21no—
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176C4⋊Dic73C22×C411yescharacteristic
177C4⋊Dic73C22×C411yescharacteristic
178C22⋊Dic73—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181C22⋊Dic73—21no—
182C22⋊Dic73—42no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C4×Dic73—21no—
188C4×Dic73—21no—
189C4×Dic73—21no—
190C4×Dic73—21no—
191C24×C73#4111yescharacteristic
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73C22×C411yescharacteristic
199C22×C4×C73C22×C411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73#4111yescharacteristic
203C22×C4×C73C2411yescharacteristic
204M16×C73—21no—
205M16×C73—21no—
206M16×C73—21no—
207M16×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73C2×D411yescharacteristic
215C2×C8×C73C2×D411yescharacteristic
216C2×C8×C73C2×D411yescharacteristic
217C2×C8×C73C2×D411yescharacteristic
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73C22×C411yescharacteristic
221C4⋊C4×C73C22×C411yescharacteristic
222C4⋊C4×C73C22×C411yescharacteristic
223C4⋊C4×C73C22×C411yescharacteristic
224C22⋊C4×C73—21no—
225C22⋊C4×C73—21no—
226C22⋊C4×C73—21no—
227C22⋊C4×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73C4×D411yescharacteristic
237C23×C73C4×D411yescharacteristic
238C23×C73C2×#4111yescharacteristic
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—42no—
254C2×C4×C73—81no—
255C2×C4×C73C4×D411yescharacteristic
256C2×C4×C73C4×D411yescharacteristic
257C2×C4×C73C23×C411yescharacteristic
258C2×C4×C73C22×D411yescharacteristic
259C2×C4×C73C2×#4111yescharacteristic
260C2×C4×C73C2×#4111yescharacteristic
261C2×C4×C732−1+411yescharacteristic
262C2×C4×C732−1+411yescharacteristic
263C2×Dic73—22no—
264C2×Dic73—21no—
265C2×Dic73—21no—
266C2×Dic73—21no—
267C2×Dic73—21no—
268C2×Dic73—41no—
269C2×Dic73—42no—
270C2×Dic73—41no—
271C2×Dic73—41no—
272C2×Dic73—41no—
273C2×Dic73—41no—
274C2×Dic73—81no—
275C8×C73—21no—
276C8×C73—21no—
277C8×C73—21no—
278C8×C73—21no—
279C8×C73—41no—
280C8×C73—41no—
281#10596831—21no—
282#10596831—21no—
283#10596831—41no—
284#10596831—41no—
285#10596831#11712yes—
286#10596831#11712yes—
287C22×C73—21no—
288C22×C73—21no—
289C22×C73—21no—
290C22×C73—21no—
291C22×C73—21no—
292C22×C73—21no—
293C22×C73—21no—
294C22×C73—21no—
295C22×C73—81no—
296C22×C73—81no—
297C22×C73C2×C4×D411yescharacteristic
298C22×C73#55211yescharacteristic
299C22×C73#55211yescharacteristic
300C4×C73—21no—
301C4×C73—21no—
302C4×C73—41no—
303C4×C73—41no—
304C4×C73—41no—
305C4×C73—41no—
306C4×C73C2×#11711yescharacteristic
307C4×C73#51911yescharacteristic
308C4×C73#54711yescharacteristic
309C4×C73#54711yescharacteristic
310Dic73—42no—
311Dic73—41no—
312Dic73—41no—
313Dic73—41no—
314Dic73—41no—
315Dic73—81no—
316#22608—731nomaximal, Sylow
317C2×C73—21no—
318C2×C73—21no—
319C2×C73—41no—
320C2×C73—41no—
321C2×C73#234411yescharacteristic
322C2×C73#295511yescharacteristic
323C2×C73#295611yescharacteristic
324#2924—731no—
325#2924D7311yescharacteristic
326#2911—731no—
327#1946—731no—
328#1945—731no—
329#1922—731no—
330#1922—731no—
331#1922—731no—
332#1922—731no—
333#1826—731no—
334#1826—731no—
335#1811—731no—
336#1773—731no—
337#1772—731no—
338#1753—731no—
339C73#2260811yescharacteristic, complemented, Sylow
340C22×M16—731no—
341C2×#117—731no—
342C2×#117C2×D7311yescharacteristic
343#433—21no—
344#433—21no—
345#433—1461no—
346#433—1461no—
347#432—21no—
348#432—1461no—
349#431—21no—
350#431—1461no—
351C2×#108—731no—
352C2×#108—731no—
353#428—731no—
354#428—731no—
355#428—731no—
356#428—731no—
357#428—731no—
358#428—731no—
359#428—731no—
360#428—731no—
361#427—731no—
362#427—731no—
363#427—731no—
364#427—731no—
365#424—731no—
366#424—731no—
367#424C2×D7311yescharacteristic
368#424C2×D7311yescharacteristic
369#407—731no—
370#407C2×D7311yescharacteristic
371C2×C22⋊C8C2×D7311yescharacteristic
372#405—731no—
373#405—731no—
374#405C2×D7311yescharacteristic
375#405C2×D7311yescharacteristic
376C2×#97—731no—
377C2×C4×C8—731no—
378C4×C22⋊C4—731no—
379#341—731no—
380#341—731no—
381#339—731no—
382#339—731no—
383#339—731no—
384#339—731no—
385#339—731no—
386#339—731no—
387#339—731no—
388#339—731no—
389#336—731no—
390#336—731no—
391C23×C4C22×D7311yescharacteristic
392C2×M16—731no—
393C2×M16—731no—
394C2×M16—731no—
395C2×M16—731no—
396C2×M16—731no—
397C2×M16—731no—
398C2×M16—1462no—
399C2×M16—1462no—
400C2×M16C22×D7311yescharacteristic
401C2×M16C22×D7311yescharacteristic
402C22×C8—731no—
403C22×C8—731no—
404C22×C8C22×D7311yescharacteristic
405C22×C8C22×D7311yescharacteristic
406#117—21no—
407#117—21no—
408#117—731no—
409#117—731no—
410#117—731no—
411#117—731no—
412#117—1461no—
413#117—1461no—
414#117C4×D7311yescharacteristic
415#117C4×D7311yescharacteristic
416#117C22×D7311yescharacteristic
417#117C22×D7311yescharacteristic
418C2×C4⋊C4—731no—
419C2×C4⋊C4—731no—
420C2×C4⋊C4C4×D7311yescharacteristic
421C2×C4⋊C4C4×D7311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—1461no—
424C2×C22⋊C4—1461no—
425C2×C42—21no—
426C2×C42—731no—
427C2×C42—731no—
428C2×C42—1461no—
429#108—1462no—
430#108—1462no—
431#107—731no—
432#107—731no—
433#107—731no—
434#107—731no—
435#107—731no—
436#107—731no—
437#107—731no—
438#107—731no—
439#106—731no—
440#106—731no—
441#106—731no—
442#106—731no—
443#106—731no—
444#106—731no—
445#106—731no—
446#106—731no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—1461no—
452C4⋊C8—1461no—
453C4⋊C8—1461no—
454C4⋊C8—1461no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—1461no—
458C22⋊C8—1461no—
459C22⋊C8C22⋊D7311yescharacteristic
460C22⋊C8C22⋊D7311yescharacteristic
461C22⋊C8C22⋊D7311yescharacteristic
462C22⋊C8C22⋊D7311yescharacteristic
463#97—21no—
464#97—21no—
465#97—1462no—
466#97—1461no—
467#97—1461no—
468C4×C8—21no—
469C4×C8—21no—
470C4×C8—1462no—
471C4×C8—1461no—
472C4×C8—1461no—
473#95—1461no—
474C24#1192402811yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—1461no—
482C22×C4—1461no—
483C22×C4—1461no—
484C22×C4—1461no—
485C22×C4C2×C4×D7311yescharacteristic
486C22×C4C2×C4×D7311yescharacteristic
487C22×C4C2×C22⋊D7311yescharacteristic
488C22×C4C2×C22⋊D7311yescharacteristic
489C22×C4#1192402811yescharacteristic
490C22×C4C23×D7311yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—1461no—
496M16—1461no—
497M16—1461no—
498M16—1461no—
499M16—1462no—
500M16—1462no—
501M16—1462no—
502M16—1462no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—731no—
510C2×C8—731no—
511C2×C8—732no—
512C2×C8—732no—
513C2×C8—731no—
514C2×C8—731no—
515C2×C8—1461no—
516C2×C8—1461no—
517C2×C8—1461no—
518C2×C8—1461no—
519C2×C8C2×C22⋊D7311yescharacteristic
520C2×C8C2×C22⋊D7311yescharacteristic
521C2×C8C2×C22⋊D7311yescharacteristic
522C2×C8C2×C22⋊D7311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—731no—
526C4⋊C4—731no—
527C4⋊C4—731no—
528C4⋊C4—731no—
529C4⋊C4—1461no—
530C4⋊C4—1461no—
531C4⋊C4C2×C4×D7311yescharacteristic
532C4⋊C4C2×C4×D7311yescharacteristic
533C4⋊C4C2×C4×D7311yescharacteristic
534C4⋊C4C2×C4×D7311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—2922no—
540C22⋊C4—1461no—
541C22⋊C4—1461no—
542C22⋊C4—1461no—
543C22⋊C4—1461no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—1461no—
549C42—1461no—
550C42—1461no—
551C42—1461no—
552C42—1461no—
553C42—1461no—
554C42—1461no—
555C42—1461no—
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23C4×C22⋊D7311yescharacteristic
561C23C4×C22⋊D7311yescharacteristic
562C23C2×#1192402811yescharacteristic
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—42no—
578C2×C4—81no—
579C2×C4—2921no—
580C2×C4—2922no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—2921no—
584C2×C4—2921no—
585C2×C4—5841no—
586C2×C4—1462no—
587C2×C4—1461no—
588C2×C4—1461no—
589C2×C4—1461no—
590C2×C4—1461no—
591C2×C4C4×C22⋊D7311yescharacteristic
592C2×C4C4×C22⋊D7311yescharacteristic
593C2×C4C22×C4×D7311yescharacteristic
594C2×C4C22×C22⋊D7311yescharacteristic
595C2×C4#41×D7311yescharacteristic
596C2×C4#41×D7311yescharacteristic
597C2×C4#1455663811yescharacteristic
598C2×C4#1455663811yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—2921no—
606C8—2921no—
607C8—732no—
608C8—732no—
609C8—1461no—
610C8—1461no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—81no—
620C22—81no—
621C22C2×C4×C22⋊D7311yescharacteristic
622C22#1798927011yescharacteristic
623C22#1798927011yescharacteristic
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—2922no—
631C4—2921no—
632C4—2921no—
633C4—2921no—
634C4—2921no—
635C4—5841no—
636C4#117×D7311yescharacteristic
637C4#1798906411yescharacteristic
638C4#1798923611yescharacteristic
639C4#1798923611yescharacteristic
640C2—21no—
641C2—21no—
642C2—41no—
643C2—41no—
644C2#2261280111yescharacteristic
645C2#2261883211yescharacteristic
646C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2924C2
socleC22×C73C2×C4×D4
prime radicalC24×C73#41
cosocleC22×C4×C73C24
hypercenter#2924D73
hypocenterC73#22608
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #22610681C2semidirect
4. #22610676C2semidirect
5. #22610530C2semidirect
6. #22610530C2semidirect
7. #22610527C2semidirect
8. #22610527C2semidirect
12. #22609816C2semidirect
13. #22609811C2semidirect
24. #17988630C4semidirect
25. #17988630C4semidirect
26. #17988630C4semidirect
27. #17988630C4semidirect
28. #17988627C4semidirect
29. #17988627C4semidirect
30. #17988627C4semidirect
31. #17988627C4semidirect
339. C73#22608semidirect

Maximal subgroups

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

subgroupindex
#226185852
#226185202
#226106812
#226106762
#226105302
#226105272
#226100302
#226100282
#226099712
#226098162
#226098112
#226097172
C73×#29242
#2260873