Finite Group Databasebeta

← #33098286

Subgroups — #33098286

Order 18688.

648 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#22619717C211yesmaximal, characteristic
2#22618864C211yesmaximal, characteristic, complemented
3#22618574C211yesmaximal, characteristic
4#22610873C211yesmaximal, characteristic, complemented
5#22610703C211yesmaximal, characteristic, complemented
6#22610676C211yesmaximal, characteristic, complemented
7#22610635C211yesmaximal, characteristic
8#22610634C211yesmaximal, characteristic
9#22610578C211yesmaximal, characteristic
10#22610577C211yesmaximal, characteristic
11#22610533C211yesmaximal, characteristic, complemented
12#22610532C211yesmaximal, characteristic, complemented
13#22609950C211yesmaximal, characteristic
14C8×#11924007C211yesmaximal, characteristic, complemented
15C73×#1945C211yesmaximal, characteristic, complemented
16#17989140C2211yescharacteristic
17#17989055C2211yescharacteristic
18#17988897C411yescharacteristic, complemented
19#17988893C411yescharacteristic, complemented
20#17988890C411yescharacteristic, complemented
21#17988886C411yescharacteristic, complemented
22#17988881C411yescharacteristic, complemented
23#17988876C411yescharacteristic, complemented
24#17988871C411yescharacteristic, complemented
25#17988866C411yescharacteristic, complemented
26#17988716—21no—
27#17988716—21no—
28#17988711—21no—
29#17988711—21no—
30#17988647—21no—
31#17988647—21no—
32#17988639—21no—
33#17988639—21no—
34C2×#14556526C2211yescharacteristic
35#17988623C2211yescharacteristic
36#17988614C2211yescharacteristic
37#17988613C2211yescharacteristic
38#17988610C2211yescharacteristic
39C2×#14556520C2211yescharacteristic
40C2×#14556519C2211yescharacteristic
41C2×#14556517C2211yescharacteristic
42#17988584C2211yescharacteristic
43#17988581C2211yescharacteristic
44#17988555C2211yescharacteristic
45#17988553C2211yescharacteristic
46#17988545C2211yescharacteristic
47#17988543C2211yescharacteristic
48M16×Dic73C2211yescharacteristic
49C2×C8×Dic73C2211yescharacteristic
50C2×C8×Dic73C2211yescharacteristic
51C4×#11924007C2211yescharacteristic
52#17988352C2211yescharacteristic
53#17988351C2211yescharacteristic
54#17988348C2211yescharacteristic
55#17988347C2211yescharacteristic
56#17988346C2211yescharacteristic
57#17988346C2211yescharacteristic
58#17988342C2211yescharacteristic
59#17988341C2211yescharacteristic
60C2×#108×C73C2211yescharacteristic
61#427×C73C2211yescharacteristic
62#424×C73C2211yescharacteristic
63#424×C73C2211yescharacteristic
64C2×C4×C8×C73C2211yescharacteristic
65#339×C73C2211yescharacteristic
66#339×C73C2211yescharacteristic
67C2×#11924028C2311yescharacteristic
68C2×#11924012C2311yescharacteristic
69C2×#11924012C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72#14556590C2×C411yescharacteristic
73#14556590C2×C411yescharacteristic
74#14556582C2×C411yescharacteristic
75#14556582C2×C411yescharacteristic
76#14556568—21no—
77#14556568—21no—
78C4×Dic146—21no—
79C4×Dic146—21no—
80#14556556C2×C411yescharacteristic
81#14556556C2×C411yescharacteristic
82#14556553C2×C411yescharacteristic
83#14556553C2×C411yescharacteristic
84#14556551—21no—
85#14556551—21no—
86#14556550C2311yescharacteristic
87#14556548—21no—
88C2×#11924007—21no—
89C2×C4×Dic73C2311yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91C42×D73—21no—
92#14556526—41no—
93#14556524C2×C411yescharacteristic
94#14556524C2×C411yescharacteristic
95#14556522C2×C411yescharacteristic
96#14556522C2×C411yescharacteristic
97C4⋊#10596831—21no—
98C4⋊#10596831—21no—
99#14556520—21no—
100#14556520—21no—
101#14556520—21no—
102#14556520—21no—
103#14556520C2×C411yescharacteristic
104#14556520C2×C411yescharacteristic
105#14556520C2×C411yescharacteristic
106#14556520C2×C411yescharacteristic
107#14556519—41no—
108#14556517—41no—
109#14556516C2×C411yescharacteristic
110#14556516C2×C411yescharacteristic
111#14556514C2×C411yescharacteristic
112#14556514C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114#14556513C2×C411yescharacteristic
115#14556511C2×C411yescharacteristic
116#14556511C2×C411yescharacteristic
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503—21no—
121#14556502—21no—
122#14556501—21no—
123#14556501—21no—
124C4×#10596831—21no—
125C8×Dic73—21no—
126C8×Dic73—21no—
127C8×Dic73—41no—
128C8×Dic73D411yescharacteristic
129C8×Dic73D411yescharacteristic
130C8×Dic73D411yescharacteristic
131C8×Dic73D411yescharacteristic
132#14556498—21no—
133C2×M16×C73C2311yescharacteristic
134C2×M16×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137#117×C73C2311yescharacteristic
138#117×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140#108×C73—41no—
141#107×C73C2×C411yescharacteristic
142#107×C73C2×C411yescharacteristic
143#106×C73C2×C411yescharacteristic
144#106×C73C2×C411yescharacteristic
145C4⋊C8×C73—21no—
146C4⋊C8×C73—21no—
147C4⋊C8×C73—21no—
148C4⋊C8×C73—21no—
149C4×C8×C73—41no—
150#11924028—21no—
151#11924028—21no—
152#11924028—21no—
153#11924028—21no—
154C2×Dic146—21no—
155C2×Dic146—21no—
156C2×Dic146C22×C411yescharacteristic
157C2×D292C22×C411yescharacteristic
158C2×C22⋊D73—21no—
159C22×Dic73—21no—
160C22×Dic73#4111yescharacteristic
161C22×Dic73#4111yescharacteristic
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165#11924012—21no—
166#11924012—21no—
167#11924012—21no—
168#11924012—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C22×C411yescharacteristic
177C2×#10596831C2×D411yescharacteristic
178C2×#10596831C2×D411yescharacteristic
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73C22×C411yescharacteristic
182C4⋊Dic73C22×C411yescharacteristic
183#11924007—24no—
184#11924007—21no—
185#11924007—21no—
186#11924007—21no—
187#11924007—21no—
188#11924007—21no—
189#11924007—21no—
190C22⋊Dic73—21no—
191#11924005—21no—
192#11924005—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73—21no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73C22×C411yescharacteristic
199C4×Dic73C22×C411yescharacteristic
200C4×Dic73C2×D411yescharacteristic
201C4×Dic73C2×D411yescharacteristic
202C22×C4×C73—21no—
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×C73C22×C411yescharacteristic
215C2×C8×C73C22×C411yescharacteristic
216C2×C8×C73C2×D411yescharacteristic
217C2×C8×C73C2×D411yescharacteristic
218C4⋊C4×C73C22×C411yescharacteristic
219C4⋊C4×C73C22×C411yescharacteristic
220C4⋊C4×C73C22×C411yescharacteristic
221C4⋊C4×C73C22×C411yescharacteristic
222C22⋊C4×C73—21no—
223C22⋊C4×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C23×C73C2×#4111yescharacteristic
229C22×D73—21no—
230C2×C4×C73—22no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73C23×C411yescharacteristic
238C2×C4×C73C22×D411yescharacteristic
239C2×C4×C73H(5,𝔽2)11yescharacteristic
240C2×C4×C732−1+411yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C22⋊D73—41no—
244C22⋊D73—41no—
245C2×Dic73—22no—
246C2×Dic73—22no—
247C2×Dic73—21no—
248C2×Dic73—21no—
249C2×Dic73—21no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73C4×D411yescharacteristic
254C2×Dic73C4×D411yescharacteristic
255C2×Dic73C4×D411yescharacteristic
256C2×Dic73C4×D411yescharacteristic
257D292—21no—
258D292—21no—
259C4×D73—42no—
260C4×D73—41no—
261C4×D73—41no—
262C4×D73—42no—
263Dic146—21no—
264Dic146—21no—
265Dic146—42no—
266Dic146—42no—
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×C73C2×C4×D411yescharacteristic
282C22×C73#54111yescharacteristic
283C22×C73#54211yescharacteristic
284C2×D73—41no—
285C2×D73—41no—
286C2×D73—41no—
287C4×C73—42no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—41no—
291C4×C73—41no—
292C4×C73#51911yescharacteristic
293C4×C73#52011yescharacteristic
294C4×C73#53611yescharacteristic
295C4×C73#53711yescharacteristic
296Dic73—21no—
297Dic73—21no—
298Dic73—21no—
299Dic73—42no—
300Dic73—41no—
301Dic73—41no—
302Dic73—41no—
303Dic73#44312yes—
304#22130—731nomaximal, Sylow
305C2×C73—21no—
306C2×C73—21no—
307C2×C73#232311yescharacteristic
308C2×C73C2×#44311yescharacteristic
309C2×C73#295511yescharacteristic
310D73—81no—
311#3076—731no—
312#2960—731no—
313#2922—731no—
314#1986—731no—
315#1950—731no—
316#1945—731no—
317#1945D7311yescharacteristic, complemented
318#1937—731no—
319#1937—731no—
320#1929—731no—
321#1929—731no—
322#1922—731no—
323#1922—731no—
324#1806—731no—
325C8×C4⋊C4—731no—
326C73#2213011yescharacteristic, complemented, Sylow
327#533—731no—
328C4×#41—731no—
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—
339C8×Q8—1461no—
340C8×Q8—1461no—
341#433—1461no—
342#433—1461no—
343#431—1461no—
344#431—1461no—
345C2×#108—731no—
346C2×#108C2×D7311yescharacteristic
347#427—731no—
348#427C2×D7311yescharacteristic
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#408—731no—
360#408—731no—
361#405—731no—
362#405—731no—
363C4×M16—731no—
364C2×C4×C8—731no—
365C2×C4×C8—731no—
366C2×C4×C8C2×D7311yescharacteristic
367C4×C4⋊C4—731no—
368#341—731no—
369#341—731no—
370#339—731no—
371#339—731no—
372#339—731no—
373#339—731no—
374#339C2×D7311yescharacteristic
375#339C2×D7311yescharacteristic
376#336—731no—
377#336—731no—
378C2×#41—731no—
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—731no—
394C4×Q8—731no—
395C4×Q8—1461no—
396C4×Q8—1461no—
397C4×D4—731no—
398C4×D4—731no—
399C4×D4—1461no—
400C4×D4—1461no—
401#117—731no—
402#117—1461no—
403#117C22×D7311yescharacteristic
404#117C22×D7311yescharacteristic
405C2×C4⋊C4—1461no—
406C2×C42—731no—
407C2×C42—731no—
408C2×C42—1461no—
409C2×C42C22×D7311yescharacteristic
410#108—41no—
411#108—2921no—
412#107—731no—
413#107—731no—
414#107C4×D7311yescharacteristic
415#107C4×D7311yescharacteristic
416#106—731no—
417#106—731no—
418#106C4×D7311yescharacteristic
419#106C4×D7311yescharacteristic
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—1461no—
445C22⋊C8—1461no—
446C22⋊C8—1461no—
447C22⋊C8—1461no—
448#97—1461no—
449#97—1461no—
450#97—1461no—
451C4×C8—41no—
452C4×C8—2921no—
453C4×C8—731no—
454C4×C8—731no—
455C4×C8—731no—
456C4×C8—731no—
457C4×C8—1461no—
458C4×C8—1461no—
459C4×C8—1461no—
460#95—1461no—
461#41—1461no—
462#41—1461no—
463#41—1461no—
464#41—1461no—
465C2×Q8—731no—
466C2×Q8—1461no—
467C2×Q8—1461no—
468C2×D4—731no—
469C2×D4—1461no—
470C22×C4—21no—
471C22×C4—731no—
472C22×C4—731no—
473C22×C4—1461no—
474C22×C4—1461no—
475C22×C4—1461no—
476C22×C4—1461no—
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×C4×D7311yescharacteristic
503C2×C8C2×C4×D7311yescharacteristic
504C2×C8D4×D7311yescharacteristic
505C2×C8D4×D7311yescharacteristic
506C4⋊C4—731no—
507C4⋊C4—731no—
508C4⋊C4—1461no—
509C4⋊C4—1461no—
510C4⋊C4—1461no—
511C4⋊C4—1461no—
512C4⋊C4—1461no—
513C4⋊C4—1461no—
514C4⋊C4—1461no—
515C4⋊C4—1461no—
516C4⋊C4—1464no—
517C4⋊C4C2×C4×D7311yescharacteristic
518C4⋊C4C2×C4×D7311yescharacteristic
519C4⋊C4C2×C4×D7311yescharacteristic
520C4⋊C4C2×C4×D7311yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—1461no—
524C22⋊C4—1461no—
525C22⋊C4—1461no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—731no—
531C42—731no—
532C42—731no—
533C42—731no—
534C42—1461no—
535C42—1461no—
536C42—1461no—
537C42—1461no—
538C42—1461no—
539C23—1461no—
540C23#41×D7311yescharacteristic
541Q8—2922no—
542Q8—2922no—
543Q8—1461no—
544Q8—1461no—
545D4—2921no—
546D4—2921no—
547D4—1461no—
548D4—1461no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—2922no—
557C2×C4—2922no—
558C2×C4—2921no—
559C2×C4—2921no—
560C2×C4—2921no—
561C2×C4—2921no—
562C2×C4—2921no—
563C2×C4—731no—
564C2×C4—731no—
565C2×C4—731no—
566C2×C4—731no—
567C2×C4—1462no—
568C2×C4—1461no—
569C2×C4—1461no—
570C2×C4—1461no—
571C2×C4—1462no—
572C2×C4C22×C4×D7311yescharacteristic
573C2×C4C2×D4×D7311yescharacteristic
574C2×C4#1455663611yescharacteristic
575C2×C4#1455663811yescharacteristic
576C2×C4#1455663911yescharacteristic
577C2×C4#1455663911yescharacteristic
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—2921no—
593C22—2921no—
594C22—2921no—
595C22C4×D4×D7311yescharacteristic
596C22#1798919611yescharacteristic
597C22#1798920711yescharacteristic
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—2922no—
604C4—2921no—
605C4—2921no—
606C4—2921no—
607C4—732no—
608C4—1461no—
609C4—1461no—
610C4—1461no—
611C4#1798906311yescharacteristic
612C4#1798906811yescharacteristic
613C4#1798916211yescharacteristic
614C4#1798916411yescharacteristic
615C2—21no—
616C2—21no—
617C2—5841no—
618C2#2261260811yescharacteristic
619C2#443×D7311yescharacteristic
620C2#2261882911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1945C2
socleC22×C73C2×C4×D4
prime radicalC2×#11924028C23
cosocleC22×C4×C73C24
hypercenter#1945D73
hypocenterC73#22130
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
2. #22618864C2semidirect
4. #22610873C2semidirect
5. #22610703C2semidirect
6. #22610676C2semidirect
11. #22610533C2semidirect
12. #22610532C2semidirect
14. C8×#11924007C2semidirect
15. C73×#1945C2semidirect
18. #17988897C4semidirect
19. #17988893C4semidirect
20. #17988890C4semidirect
21. #17988886C4semidirect
22. #17988881C4semidirect
23. #17988876C4semidirect
24. #17988871C4semidirect
25. #17988866C4semidirect
317. #1945D73semidirect
326. C73#22130semidirect

Maximal subgroups

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

subgroupindex
#226197172
#226188642
#226185742
#226108732
#226107032
#226106762
#226106352
#226106342
#226105782
#226105772
#226105332
#226105322
#226099502
C8×#119240072
C73×#19452
#2213073