Finite Group Databasebeta

← #33130468

Subgroups — #33130468

Order 18688.

776 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22614248C211yesmaximal, characteristic
2#22611498C211yesmaximal, characteristic, complemented
3#22611413C211yesmaximal, characteristic, complemented
4#22611368C211yesmaximal, characteristic, complemented
5#22611357C211yesmaximal, characteristic, complemented
6#22610509C211yesmaximal, characteristic, complemented
7#22610502C211yesmaximal, characteristic, complemented
8#22610224C211yesmaximal, characteristic
9#22610130C211yesmaximal, characteristic, complemented
10#22610119C211yesmaximal, characteristic, complemented
11#22610026C211yesmaximal, characteristic, complemented
12#22610019C211yesmaximal, characteristic, complemented
13#22609954C211yesmaximal, characteristic, complemented
14C2×#17988349C211yesmaximal, characteristic, complemented
15C73×#2352C211yesmaximal, characteristic
16C23×#10596831C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C2×#14556524C2211yescharacteristic
19C2×#14556524C2211yescharacteristic
20C2×#14556522C2211yescharacteristic
21C2×#14556522C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25#17988526—21no—
26#17988523—21no—
27#17988485C2211yescharacteristic
28#17988485C2211yescharacteristic
29#17988467—21no—
30#17988459—21no—
31#17988447C2211yescharacteristic
32#17988447C2211yescharacteristic
33#17988447C2211yescharacteristic
34#17988349C2211yescharacteristic
35#17988349C2211yescharacteristic
36#17988349C2211yescharacteristic
37#17988349C2211yescharacteristic
38#17988349C2211yescharacteristic
39#17988349C2211yescharacteristic
40#17988349C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48C2×C4×D4×C73C2211yescharacteristic
49C2×#117×C73C2211yescharacteristic
50C22×C4⋊C4×C73C2211yescharacteristic
51#388×C73—21no—
52#387×C73—21no—
53#386×C73—21no—
54#382×C73C2211yescharacteristic
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73—21no—
59C23×Dic73—21no—
60C22×#10596831—22no—
61C22×#10596831—22no—
62C22×#10596831—41no—
63C22×#10596831C2311yescharacteristic
64C22×#10596831C2311yescharacteristic
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C2×C4⋊Dic73—21no—
68C2×C4⋊Dic73—22no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×C22⋊Dic73—21no—
77C2×C22⋊Dic73—21no—
78C2×C22⋊Dic73—21no—
79#14556524—22no—
80#14556524—41no—
81#14556522—22no—
82#14556522—41no—
83C22⋊#10596831—22no—
84C22⋊#10596831—22no—
85C22⋊#10596831—41no—
86#14556498—21no—
87#14556498—21no—
88#14556498—21no—
89#14556498—21no—
90#14556498—21no—
91C22×D4×C73D411yescharacteristic
92C23×C4×C73—21no—
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C4×D4×C73—22no—
96C4×D4×C73—22no—
97#117×C73—22no—
98#117×C73—41no—
99C2×C4⋊C4×C73—22no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—41no—
102C2×C4⋊C4×C73D411yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73D411yescharacteristic
111C2×C22⋊C4×C73D411yescharacteristic
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2311yescharacteristic
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120C22×Dic73—21no—
121C22×Dic73—21no—
122C22×Dic73—21no—
123C22×Dic73—21no—
124C22×Dic73—42no—
125C22×Dic73—81no—
126C22×Dic73—81no—
127C2×#10596831—21no—
128C2×#10596831—21no—
129C2×#10596831—21no—
130C2×#10596831—21no—
131C2×#10596831—21no—
132C2×#10596831—21no—
133C2×#10596831—21no—
134C2×#10596831—21no—
135C2×#10596831—21no—
136C2×#10596831—21no—
137C2×#10596831—21no—
138C2×#10596831—44no—
139C2×#10596831#4112yes—
140C4⋊Dic73—21no—
141C4⋊Dic73—21no—
142C4⋊Dic73—21no—
143C4⋊Dic73—21no—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—42no—
149#11924007—81no—
150#11924007—81no—
151C22⋊Dic73—42no—
152C22⋊Dic73—81no—
153C22⋊Dic73—81no—
154C24×C73C2×D411yescharacteristic
155C24×C73C2×D411yescharacteristic
156C2×D4×C73—22no—
157C2×D4×C73—22no—
158C2×D4×C73—22no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—42no—
174C22×C4×C73—42no—
175C22×C4×C73—81no—
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73#4112yes—
181C22×C4×C73#4112yes—
182C22×C4×C73C2411yescharacteristic
183C4⋊C4×C73—22no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—42no—
192C4⋊C4×C73#4112yes—
193C22⋊C4×C73—22no—
194C22⋊C4×C73—22no—
195C22⋊C4×C73—42no—
196C22⋊C4×C73—42no—
197C22⋊C4×C73—81no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—42no—
201C42×C73—81no—
202C23×C73—21no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73—21no—
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73#12312yes—
214C23×C73#13512yes—
215C23×C73#13712yes—
216C23×C73C22×D411yescharacteristic
217D4×C73—44no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—22no—
223C2×C4×C73—22no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—22no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—84no—
250C2×C4×C73#12312yes—
251C2×C4×C73C2×#4111yescharacteristic
252C2×C4×C73C2×#4111yescharacteristic
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73H(5,𝔽2)11yescharacteristic
256C2×C4×C732−1+411yescharacteristic
257C2×Dic73—41no—
258C2×Dic73—41no—
259C2×Dic73—41no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265C2×Dic73—41no—
266C2×Dic73—41no—
267C2×Dic73—41no—
268C2×Dic73—41no—
269C2×Dic73—84no—
270#10596831—22no—
271#10596831—41no—
272#10596831—41no—
273#10596831—41no—
274C22×C73—22no—
275C22×C73—22no—
276C22×C73—22no—
277C22×C73—22no—
278C22×C73—22no—
279C22×C73—22no—
280C22×C73—41no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73—41no—
285C22×C73—41no—
286C22×C73—41no—
287C22×C73#48514yes—
288C22×C73C2×#12311yescharacteristic
289C22×C73#54611yescharacteristic
290C22×C73#54711yescharacteristic
291C22×C73C2×#13511yescharacteristic
292C22×C73C2×#13711yescharacteristic
293C22×C73#57611yescharacteristic
294C22×C73#57711yescharacteristic
295C4×C73—22no—
296C4×C73—41no—
297C4×C73—41no—
298C4×C73—41no—
299C4×C73—42no—
300C4×C73—81no—
301C4×C73—81no—
302C4×C73—81no—
303C4×C73#52911yescharacteristic
304C4×C73#53911yescharacteristic
305C4×C73#55111yescharacteristic
306C4×C73#55211yescharacteristic
307Dic73—81no—
308Dic73—81no—
309Dic73—81no—
310Dic73—81no—
311#24943—731nomaximal, Sylow
312C2×C73—24no—
313C2×C73—81no—
314C2×C73#241911yescharacteristic
315C2×C73C2×#48511yescharacteristic
316C2×C73#309611yescharacteristic
317C2×C73#329711yescharacteristic
318C2×C73#331611yescharacteristic
319C2×C73#333711yescharacteristic
320C2×C73#334611yescharacteristic
321#2487—731no—
322#2352D7311yescharacteristic
323#2101—731no—
324#2085—731no—
325#2077—731no—
326#2075—731no—
327#1919—731no—
328#1918—731no—
329#1869—731no—
330#1854—731no—
331#1852—731no—
332#1825—731no—
333#1824—731no—
334#1807—731no—
335C2×#340—731no—
336C73#2494311yescharacteristic, complemented, Sylow
337C23×C8—731no—
338C2×C4×D4C2×D7311yescharacteristic
339C2×#117C2×D7311yescharacteristic
340C22×C4⋊C4—731no—
341C22×C4⋊C4C2×D7311yescharacteristic
342C2×#107—731no—
343C2×#107—731no—
344C2×#106—731no—
345C2×#106—731no—
346C2×C22⋊C8—731no—
347C2×C22⋊C8—731no—
348C2×C22⋊C8—731no—
349#400—1461no—
350#399—1461no—
351#389—731no—
352#389—731no—
353#388—21no—
354#387—21no—
355#386—21no—
356#386—1461no—
357#385—1461no—
358#382C2×D7311yescharacteristic
359#380—731no—
360#380—731no—
361#380—731no—
362#380C2×D7311yescharacteristic
363#380C2×D7311yescharacteristic
364C4×C4⋊C4C2×D7311yescharacteristic
365C4×C22⋊C4—21no—
366#340—731no—
367#340—731no—
368#340—731no—
369#340—731no—
370#340—731no—
371#340—731no—
372#340—731no—
373#340—731no—
374#340—731no—
375#340—731no—
376#340—731no—
377#340—731no—
378#336—731no—
379#336—731no—
380C22×D4C22⋊D7311yescharacteristic
381C23×C4—21no—
382C23×C4—1461no—
383C23×C4C22×D7311yescharacteristic
384C23×C4C22×D7311yescharacteristic
385C22×C8—2921no—
386C22×C8—731no—
387C22×C8—731no—
388C22×C8—731no—
389C22×C8—731no—
390C22×C8—1462no—
391C22×C8—1462no—
392C4×D4—22no—
393C4×D4—22no—
394#117—22no—
395#117—41no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—731no—
400C2×C4⋊C4—731no—
401C2×C4⋊C4—731no—
402C2×C4⋊C4—731no—
403C2×C4⋊C4—1461no—
404C2×C4⋊C4—1462no—
405C2×C4⋊C4—1462no—
406C2×C4⋊C4—1461no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4C22⋊D7311yescharacteristic
409C2×C4⋊C4C22×D7311yescharacteristic
410C2×C4⋊C4C22×D7311yescharacteristic
411C2×C4⋊C4C22×D7311yescharacteristic
412C2×C4⋊C4C22×D7311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—1461no—
417C2×C22⋊C4—1461no—
418C2×C22⋊C4—1461no—
419C2×C22⋊C4C22⋊D7311yescharacteristic
420C2×C22⋊C4C22⋊D7311yescharacteristic
421C2×C42—21no—
422C2×C42—21no—
423C2×C42C22×D7311yescharacteristic
424#107—2921no—
425#107—1462no—
426#106—2921no—
427#106—1462no—
428C22⋊C8—2921no—
429C22⋊C8—1462no—
430C22⋊C8—1462no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—1461no—
437#95—1461no—
438#95—1461no—
439#95—1461no—
440#95—1461no—
441C24C2×C22⋊D7311yescharacteristic
442C24C2×C22⋊D7311yescharacteristic
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4—2922no—
464C22×C4—5841no—
465C22×C4—5841no—
466C22×C4—1461no—
467C22×C4—1461no—
468C22×C4—1461no—
469C22×C4—1461no—
470C22×C4C2×C22⋊D7311yescharacteristic
471C22×C4C2×C22⋊D7311yescharacteristic
472C22×C4C2×C22⋊D7311yescharacteristic
473C22×C4C2×C22⋊D7311yescharacteristic
474C22×C4#1192402812yes—
475C22×C4#1192402812yes—
476C22×C4C23×D7311yescharacteristic
477C2×C8—2924no—
478C2×C8—732no—
479C2×C8—1461no—
480C2×C8—1461no—
481C2×C8—1461no—
482C2×C8—1461no—
483C2×C8—1461no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—2922no—
500C4⋊C4—5841no—
501C4⋊C4—5841no—
502C4⋊C4—1461no—
503C4⋊C4—1461no—
504C4⋊C4—1461no—
505C4⋊C4—1461no—
506C4⋊C4—1461no—
507C4⋊C4—1461no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4#1192402712yes—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—2922no—
517C22⋊C4—5841no—
518C22⋊C4—5841no—
519C42—21no—
520C42—21no—
521C42—42no—
522C42—81no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23#1455657412yes—
535C23#1455661112yes—
536C23#1455662112yes—
537C23C22×C22⋊D7311yescharacteristic
538D4—44no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—2921no—
572C2×C4—2921no—
573C2×C4—2921no—
574C2×C4—2921no—
575C2×C4—2921no—
576C2×C4—2921no—
577C2×C4—2921no—
578C2×C4—2921no—
579C2×C4—2921no—
580C2×C4—2921no—
581C2×C4—2921no—
582C2×C4—2921no—
583C2×C4—5844no—
584C2×C4#1455657412yes—
585C2×C4#41×D7311yescharacteristic
586C2×C4C2×#1192402711yescharacteristic
587C2×C4C2×#1192402811yescharacteristic
588C2×C4C2×#1192402811yescharacteristic
589C2×C4#1455663611yescharacteristic
590C2×C4#1455663811yescharacteristic
591C8—2921no—
592C8—2921no—
593C8—2921no—
594C8—1462no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22#1798892814yes—
609C22C2×#1455657411yescharacteristic
610C22#1798923111yescharacteristic
611C22#1798923611yescharacteristic
612C22C2×#1455661111yescharacteristic
613C22C2×#1455662111yescharacteristic
614C22#1798939011yescharacteristic
615C22#1798939511yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—5841no—
625C4—5841no—
626C4—5841no—
627C4—5841no—
628C4#1798911711yescharacteristic
629C4#1798917911yescharacteristic
630C4#1798926611yescharacteristic
631C4#1798927711yescharacteristic
632C2—24no—
633C2—81no—
634C2#2261340211yescharacteristic
635C2C2×#1798892811yescharacteristic
636C2#2261988911yescharacteristic
637C2#2262178111yescharacteristic
638C2#2262204211yescharacteristic
639C2#2262231011yescharacteristic
640C2#2262241611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutator, cosocleC22×C4×C73C24
FrattiniC22×C4C23×D73
FittingC73×#2352C2
socleC23×C73C22×D4
prime radicalC22×D4×C73D4
hypercenter#2352D73
hypocenterC73#24943
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #22611498C2semidirect
3. #22611413C2semidirect
4. #22611368C2semidirect
5. #22611357C2semidirect
6. #22610509C2semidirect
7. #22610502C2semidirect
9. #22610130C2semidirect
10. #22610119C2semidirect
11. #22610026C2semidirect
12. #22610019C2semidirect
13. #22609954C2semidirect
14. C2×#17988349C2semidirect
336. C73#24943semidirect

Maximal subgroups

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

subgroupindex
#226142482
#226114982
#226114132
#226113682
#226113572
#226105092
#226105022
#226102242
#226101302
#226101192
#226100262
#226100192
#226099542
C2×#179883492
C73×#23522
#2494373