Finite Group Databasebeta

← #33098313

Subgroups — #33098313

Order 18688.

628 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619719C211yesmaximal, characteristic
2#22618871C211yesmaximal, characteristic, complemented
3#22610875C211yesmaximal, characteristic, complemented
4#22610706C211yesmaximal, characteristic, complemented
5#22610681C211yesmaximal, characteristic, complemented
6#22610676C211yesmaximal, characteristic, complemented
7#22610645C211yesmaximal, characteristic
8#22610638C211yesmaximal, characteristic
9#22610576C211yesmaximal, characteristic
10#22610576C211yesmaximal, characteristic
11#22610527C211yesmaximal, characteristic, complemented
12#22610527C211yesmaximal, characteristic, complemented
13#22609951C211yesmaximal, characteristic
14#22609803C211yesmaximal, characteristic, complemented
15C73×#2923C211yesmaximal, characteristic
16#17989144C2211yescharacteristic
17#17988894C411yescharacteristic, complemented
18#17988894C411yescharacteristic, complemented
19#17988887C411yescharacteristic, complemented
20#17988887C411yescharacteristic, complemented
21#17988882C411yescharacteristic, complemented
22#17988877C411yescharacteristic, complemented
23#17988872C411yescharacteristic, complemented
24#17988867C411yescharacteristic, complemented
25#17988715—21no—
26#17988715—21no—
27#17988715—21no—
28#17988715—21no—
29C2×#14556526C2211yescharacteristic
30C2×#14556526C2211yescharacteristic
31#17988623C2211yescharacteristic
32#17988623C2211yescharacteristic
33#17988613C2211yescharacteristic
34#17988613C2211yescharacteristic
35#17988611C2211yescharacteristic
36C2×C4⋊#10596831C2211yescharacteristic
37C2×#14556518C2211yescharacteristic
38C2×#14556518C2211yescharacteristic
39#17988583C2211yescharacteristic
40#17988583C2211yescharacteristic
41#17988542C2211yescharacteristic
42#17988542C2211yescharacteristic
43C2×#14556501C2211yescharacteristic
44C2×C8×Dic73C2211yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46#17988351C2211yescharacteristic
47#17988351C2211yescharacteristic
48#17988348C2211yescharacteristic
49#17988348C2211yescharacteristic
50#17988348C2211yescharacteristic
51#17988348C2211yescharacteristic
52#17988346C2211yescharacteristic
53#17988346C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C4×#41×C73C2211yescharacteristic
57#433×C73—21no—
58#433×C73—21no—
59#432×C73—21no—
60#432×C73—21no—
61#424×C73C2211yescharacteristic
62#424×C73C2211yescharacteristic
63#408×C73C2211yescharacteristic
64#408×C73C2211yescharacteristic
65C4×M16×C73C2211yescharacteristic
66C2×#97×C73C2211yescharacteristic
67C2×#11924012C2311yescharacteristic
68C2×#11924012C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556591C2×C411yescharacteristic
72#14556591C2×C411yescharacteristic
73#14556583C2×C411yescharacteristic
74#14556583C2×C411yescharacteristic
75#14556570—21no—
76#14556570—21no—
77C4×Dic146—21no—
78C4×Dic146—21no—
79#14556550C2311yescharacteristic
80#14556550C2311yescharacteristic
81C2×C4⋊Dic73—21no—
82C2×C4×Dic73C2311yescharacteristic
83C2×C4×Dic73C2311yescharacteristic
84#14556526—41no—
85#14556526—41no—
86#14556524C2×C411yescharacteristic
87#14556524C2×C411yescharacteristic
88#14556524C2×C411yescharacteristic
89#14556524C2×C411yescharacteristic
90#14556522C2×C411yescharacteristic
91#14556522C2×C411yescharacteristic
92#14556522C2×C411yescharacteristic
93#14556522C2×C411yescharacteristic
94C4⋊#10596831—21no—
95C4⋊#10596831—21no—
96C4⋊#10596831C2×C411yescharacteristic
97C4⋊#10596831C2×C411yescharacteristic
98C4⋊#10596831C2×C411yescharacteristic
99C4⋊#10596831C2×C411yescharacteristic
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556518—41no—
105#14556518—41no—
106#14556515C2×C411yescharacteristic
107#14556515C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556515C2×C411yescharacteristic
110#14556512C2×C411yescharacteristic
111#14556512C2×C411yescharacteristic
112#14556512C2×C411yescharacteristic
113#14556512C2×C411yescharacteristic
114#14556501—21no—
115#14556501—21no—
116#14556501—41no—
117C8×Dic73—21no—
118C8×Dic73—21no—
119C8×Dic73—41no—
120#14556498—21no—
121C2×#41×C73C2311yescharacteristic
122C2×M16×C73C2311yescharacteristic
123C2×M16×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C4×Q8×C73C2×C411yescharacteristic
127C4×Q8×C73C2×C411yescharacteristic
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73C2×C411yescharacteristic
131C4×D4×C73C2×C411yescharacteristic
132#117×C73—21no—
133#117×C73C2311yescharacteristic
134C2×C42×C73—21no—
135C2×C42×C73C2311yescharacteristic
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×C73—21no—
143C22⋊C8×C73—21no—
144#97×C73—21no—
145#97×C73D411yescharacteristic
146#97×C73D411yescharacteristic
147#97×C73D411yescharacteristic
148#97×C73D411yescharacteristic
149C4×C8×C73—21no—
150C2×Dic146—21no—
151C2×Dic146—21no—
152C22×Dic73—21no—
153C22×Dic73—21no—
154#11924012—21no—
155#11924012—21no—
156#11924012—21no—
157#11924012—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831C22×C411yescharacteristic
165C2×#10596831C22×C411yescharacteristic
166C2×#10596831C22×C411yescharacteristic
167C2×#10596831C22×C411yescharacteristic
168C4⋊Dic73—21no—
169C4⋊Dic73—21no—
170C4⋊Dic73—42no—
171C4⋊Dic73C22×C411yescharacteristic
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175#11924007—21no—
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179C22⋊Dic73—21no—
180C22⋊Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187#41×C73—21no—
188#41×C73—21no—
189#41×C73—21no—
190#41×C73—21no—
191C2×Q8×C73C22×C411yescharacteristic
192C2×D4×C73—21no—
193C2×D4×C73C22×C411yescharacteristic
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73#4111yescharacteristic
198C22×C4×C73#4111yescharacteristic
199C22×C4×C73C2411yescharacteristic
200M16×C73—21no—
201M16×C73—21no—
202M16×C73—21no—
203M16×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73C2×D411yescharacteristic
211C2×C8×C73C2×D411yescharacteristic
212C2×C8×C73C2×D411yescharacteristic
213C2×C8×C73C2×D411yescharacteristic
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73C22×C411yescharacteristic
217C4⋊C4×C73C22×C411yescharacteristic
218C22⋊C4×C73—21no—
219C22⋊C4×C73—21no—
220C22⋊C4×C73—21no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73C22×C411yescharacteristic
225C42×C73C22×C411yescharacteristic
226C42×C73C2×D411yescharacteristic
227C42×C73C2×D411yescharacteristic
228C23×C73—21no—
229C23×C73C2×#4111yescharacteristic
230Q8×C73—21no—
231Q8×C73—21no—
232D4×C73—21no—
233D4×C73—21no—
234D4×C73—41no—
235D4×C73—41no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—81no—
244C2×C4×C73—81no—
245C2×C4×C73C4×D411yescharacteristic
246C2×C4×C73C4×D411yescharacteristic
247C2×C4×C73C4×D411yescharacteristic
248C2×C4×C73C4×D411yescharacteristic
249C2×C4×C73C23×C411yescharacteristic
250C2×C4×C73C22×D411yescharacteristic
251C2×C4×C73H(5,𝔽2)11yescharacteristic
252C2×C4×C732−1+411yescharacteristic
253C2×C4×C732−1+411yescharacteristic
254C2×C4×C732−1+411yescharacteristic
255C2×Dic73—22no—
256C2×Dic73—21no—
257C2×Dic73—21no—
258C2×Dic73—21no—
259C2×Dic73—21no—
260C2×Dic73—41no—
261C2×Dic73—41no—
262C2×Dic73—41no—
263C2×Dic73—41no—
264C2×Dic73—41no—
265Dic146—81no—
266Dic146—81no—
267C8×C73—21no—
268C8×C73—21no—
269C8×C73—21no—
270C8×C73—21no—
271C8×C73—41no—
272C8×C73—41no—
273#10596831—21no—
274#10596831—21no—
275#10596831—21no—
276#10596831—21no—
277#10596831—41no—
278#10596831—41no—
279C22×C73—21no—
280C22×C73—21no—
281C22×C73—41no—
282C22×C73—41no—
283C22×C73—41no—
284C22×C73C2×C4×D411yescharacteristic
285C22×C73#54111yescharacteristic
286C22×C73#54211yescharacteristic
287C4×C73—21no—
288C4×C73—21no—
289C4×C73—21no—
290C4×C73—21no—
291C4×C73—41no—
292C4×C73—41no—
293C4×C73—41no—
294C4×C73#51911yescharacteristic
295C4×C73#52011yescharacteristic
296C4×C73#53611yescharacteristic
297C4×C73#53711yescharacteristic
298Dic73—42no—
299Dic73—41no—
300Dic73—41no—
301Dic73—41no—
302Dic73—41no—
303Dic73—81no—
304#22132—731nomaximal, Sylow
305C2×C73—21no—
306C2×C73—21no—
307C2×C73—81no—
308C2×C73#232311yescharacteristic
309C2×C73#295611yescharacteristic
310C2×C73#295711yescharacteristic
311#3076—731no—
312#2961—731no—
313#2923D7311yescharacteristic
314#1986—731no—
315#1950—731no—
316#1946—731no—
317#1945—731no—
318#1938—731no—
319#1937—731no—
320#1929—731no—
321#1929—731no—
322#1922—731no—
323#1922—731no—
324#1806—731no—
325#1771—731no—
326C73#2213211yescharacteristic, complemented, Sylow
327#533—731no—
328C4×#41C2×D7311yescharacteristic
329#479—731no—
330#479—731no—
331#478—731no—
332#478—731no—
333#477—731no—
334#476—731no—
335#475—731no—
336#474—731no—
337#446—1461no—
338#446—1461no—
339#446—1461no—
340#446—1461no—
341#433—21no—
342#433—21no—
343#432—21no—
344#432—21no—
345C2×#108—731no—
346C2×#108—731no—
347#427—731no—
348#427—731no—
349#424—731no—
350#424—731no—
351#424C2×D7311yescharacteristic
352#424C2×D7311yescharacteristic
353#423—731no—
354C2×C4⋊C8—731no—
355C2×#104—731no—
356C2×#104—731no—
357#416—731no—
358#416—731no—
359#408C2×D7311yescharacteristic
360#408C2×D7311yescharacteristic
361#405—731no—
362#405—731no—
363C4×M16C2×D7311yescharacteristic
364C2×#97—731no—
365C2×#97C2×D7311yescharacteristic
366C2×C4×C8—731no—
367C4×C4⋊C4—731no—
368#341—731no—
369#341—731no—
370#339—731no—
371#339—731no—
372#339—731no—
373#339—731no—
374#339—731no—
375#339—731no—
376#336—731no—
377#336—731no—
378C2×#41C22×D7311yescharacteristic
379C2×M16—731no—
380C2×M16—731no—
381C2×M16C22×D7311yescharacteristic
382C2×M16C22×D7311yescharacteristic
383C22×C8—731no—
384C22×C8—731no—
385C22×C8C22×D7311yescharacteristic
386C22×C8C22×D7311yescharacteristic
387C4⋊Q8—731no—
388C4⋊Q8—731no—
389#125—731no—
390#125—731no—
391C22⋊Q8—1461no—
392C22⋊Q8—1461no—
393C4×Q8—1461no—
394C4×Q8—1461no—
395C4×Q8C4×D7311yescharacteristic
396C4×Q8C4×D7311yescharacteristic
397C4×D4—21no—
398C4×D4—21no—
399C4×D4C4×D7311yescharacteristic
400C4×D4C4×D7311yescharacteristic
401#117—21no—
402#117—731no—
403#117—731no—
404#117C22×D7311yescharacteristic
405C2×C4⋊C4—1461no—
406C2×C42—21no—
407C2×C42—731no—
408C2×C42—731no—
409C2×C42C22×D7311yescharacteristic
410#108—2921no—
411#108—2921no—
412#107—731no—
413#107—731no—
414#107—731no—
415#107—731no—
416#106—731no—
417#106—731no—
418#106—731no—
419#106—731no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—731no—
425C4⋊C8—731no—
426C4⋊C8—731no—
427C4⋊C8—731no—
428C4⋊C8—1461no—
429C4⋊C8—1461no—
430C4⋊C8—1461no—
431C4⋊C8—1461no—
432C4⋊C8—1461no—
433C4⋊C8—1461no—
434#104—2921no—
435#104—2921no—
436#103—731no—
437#103—731no—
438#103—731no—
439#103—731no—
440#102—731no—
441#102—731no—
442#102—731no—
443#102—731no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448#97—21no—
449#97—2921no—
450#97—1461no—
451#97—1461no—
452#97C22⋊D7311yescharacteristic
453#97C22⋊D7311yescharacteristic
454#97C22⋊D7311yescharacteristic
455#97C22⋊D7311yescharacteristic
456C4×C8—21no—
457C4×C8—2921no—
458C4×C8—1461no—
459C4×C8—1461no—
460#95—1461no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465C2×Q8—1461no—
466C2×Q8—1461no—
467C2×Q8C2×C4×D7311yescharacteristic
468C2×D4—21no—
469C2×D4C2×C4×D7311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4#1192402811yescharacteristic
476C22×C4#1192402811yescharacteristic
477C22×C4C23×D7311yescharacteristic
478M16—21no—
479M16—21no—
480M16—21no—
481M16—21no—
482M16—1461no—
483M16—1461no—
484M16—1461no—
485M16—1461no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—731no—
493C2×C8—731no—
494C2×C8—731no—
495C2×C8—731no—
496C2×C8—1461no—
497C2×C8—1461no—
498C2×C8—1461no—
499C2×C8—1461no—
500C2×C8—1461no—
501C2×C8—1461no—
502C2×C8C2×C22⋊D7311yescharacteristic
503C2×C8C2×C22⋊D7311yescharacteristic
504C2×C8C2×C22⋊D7311yescharacteristic
505C2×C8C2×C22⋊D7311yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—2922no—
509C4⋊C4—731no—
510C4⋊C4—731no—
511C4⋊C4—731no—
512C4⋊C4—731no—
513C4⋊C4—1461no—
514C4⋊C4—1461no—
515C4⋊C4—1461no—
516C4⋊C4—1461no—
517C4⋊C4—1461no—
518C4⋊C4—1461no—
519C4⋊C4C2×C4×D7311yescharacteristic
520C4⋊C4C2×C4×D7311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—1461no—
530C42—1461no—
531C42—1461no—
532C42—1461no—
533C42—1461no—
534C42—1461no—
535C42C2×C4×D7311yescharacteristic
536C42C2×C4×D7311yescharacteristic
537C42C2×C22⋊D7311yescharacteristic
538C42C2×C22⋊D7311yescharacteristic
539C23—21no—
540C23C2×#1192402811yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—5841no—
544Q8—5841no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—1462no—
564C2×C4—1461no—
565C2×C4—1461no—
566C2×C4—1461no—
567C2×C4—1461no—
568C2×C4C4×C22⋊D7311yescharacteristic
569C2×C4C4×C22⋊D7311yescharacteristic
570C2×C4C4×C22⋊D7311yescharacteristic
571C2×C4C4×C22⋊D7311yescharacteristic
572C2×C4C22×C4×D7311yescharacteristic
573C2×C4C22×C22⋊D7311yescharacteristic
574C2×C4#1455663711yescharacteristic
575C2×C4#1455663811yescharacteristic
576C2×C4#1455663811yescharacteristic
577C2×C4#1455663811yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—2921no—
585C8—2921no—
586C8—1461no—
587C8—1461no—
588C8—1461no—
589C8—1461no—
590C22—21no—
591C22—21no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×C4×C22⋊D7311yescharacteristic
596C22#1798919911yescharacteristic
597C22#1798920811yescharacteristic
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—2922no—
606C4—2921no—
607C4—2921no—
608C4—2921no—
609C4—2921no—
610C4—5841no—
611C4#1798906411yescharacteristic
612C4#1798906711yescharacteristic
613C4#1798915811yescharacteristic
614C4#1798916511yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2#2261261311yescharacteristic
619C2#2261883811yescharacteristic
620C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2923C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×C73C23
cosocleC22×C4×C73C24
hypercenter#2923D73
hypocenterC73#22132
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #22618871C2semidirect
3. #22610875C2semidirect
4. #22610706C2semidirect
5. #22610681C2semidirect
6. #22610676C2semidirect
11. #22610527C2semidirect
12. #22610527C2semidirect
14. #22609803C2semidirect
17. #17988894C4semidirect
18. #17988894C4semidirect
19. #17988887C4semidirect
20. #17988887C4semidirect
21. #17988882C4semidirect
22. #17988877C4semidirect
23. #17988872C4semidirect
24. #17988867C4semidirect
326. C73#22132semidirect

Maximal subgroups

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

subgroupindex
#226197192
#226188712
#226108752
#226107062
#226106812
#226106762
#226106452
#226106382
#226105762
#226105272
#226099512
#226098032
C73×#29232
#2213273