Finite Group Databasebeta

← #33056032

Subgroups — #33056032

Order 18688.

692 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619989C211yesmaximal, characteristic
2C8×#11924029C211yesmaximal, characteristic, complemented
3#22618640C211yesmaximal, characteristic, complemented
4#22608774C211yesmaximal, characteristic, complemented
5#22608762C211yesmaximal, characteristic, complemented
6#22608758C211yesmaximal, characteristic, complemented
7#22608754C211yesmaximal, characteristic, complemented
8#22608752C211yesmaximal, characteristic, complemented
9#22608746C211yesmaximal, characteristic, complemented
10SD16⋊#10596831C211yesmaximal, characteristic, complemented
11#22608718C211yesmaximal, characteristic, complemented
12#22608369C211yesmaximal, characteristic, complemented
13#22608346C211yesmaximal, characteristic, complemented
14#22608217C211yesmaximal, characteristic, complemented
15C73×#1583C211yesmaximal, characteristic, complemented
16C2×#14556599—21no—
17#17989134C2211yescharacteristic
18C4×#11924029C2211yescharacteristic
19#17988913C411yescharacteristic
20#17988909C411yescharacteristic
21#17988880C411yescharacteristic
22#17988876C411yescharacteristic
23#17988785C411yescharacteristic
24#17988781C411yescharacteristic
25#17988735C411yescharacteristic
26#17988731C411yescharacteristic
27Q8×#10596831C2211yescharacteristic
28C4×#11924015C2211yescharacteristic
29C4×D584C2211yescharacteristic
30C4×#11924013C2211yescharacteristic
31#17988666C2211yescharacteristic
32#17988663—21no—
33C8×D292—21no—
34C8×D292C2211yescharacteristic
35D4×#10596831C2211yescharacteristic
36#17988652—21no—
37#17988652C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988650—21no—
40#17988639—21no—
41#17988639C2211yescharacteristic
42#17988638C2211yescharacteristic
43#17988609C2211yescharacteristic
44#17988552—21no—
45C4×#11924011C2211yescharacteristic
46C4×C8×D73—21no—
47C4×C8×D73C2211yescharacteristic
48#17988340C2211yescharacteristic
49#17988339C2211yescharacteristic
50#17988337C2211yescharacteristic
51Q8⋊#10596831C2211yescharacteristic
52#17988316C2211yescharacteristic
53#17988316C2211yescharacteristic
54D4⋊#10596831C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60C8×Q8×C73C2211yescharacteristic
61C4×SD16×C73C2211yescharacteristic
62#436×C73C2211yescharacteristic
63#334×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66#322×C73C2211yescharacteristic
67C2×#11924029C2×C411yescharacteristic
68C2×#11924028—21no—
69C2×#11924015C2×C411yescharacteristic
70C2×D584C2×C411yescharacteristic
71C2×#11924013C2×C411yescharacteristic
72#14556599—44no—
73C2×#11924011—21no—
74C2×#11924011—21no—
75C2×#11924011—21no—
76C22×#10596831—21no—
77C2×C8×D73—21no—
78C2×C8×D73—21no—
79C2×C8×D73—21no—
80C2×C8×D73D411yescharacteristic
81C2×C8×D73D411yescharacteristic
82#14556590C2×C411yescharacteristic
83#14556587C2×C411yescharacteristic
84#14556577—21no—
85#14556566C2×C411yescharacteristic
86#14556564—21no—
87#14556562C2×C411yescharacteristic
88Q8×Dic73C2×C411yescharacteristic
89C4×D292—21no—
90C4×D292C2311yescharacteristic
91C4×D292C2311yescharacteristic
92#14556553—21no—
93#14556553C2×C411yescharacteristic
94C4×C22⋊D73—21no—
95#14556549—21no—
96#14556549C2×C411yescharacteristic
97C42×D73—21no—
98C42×D73C2311yescharacteristic
99#14556525C2×C411yescharacteristic
100#14556524C2×C411yescharacteristic
101#14556522C2×C411yescharacteristic
102C4⋊#10596831—21no—
103C4⋊#10596831C2311yescharacteristic
104C4⋊#10596831C2311yescharacteristic
105#14556520—21no—
106#14556520C2×C411yescharacteristic
107#14556520C2×C411yescharacteristic
108#14556515C2×C411yescharacteristic
109#14556513C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556512C2×C411yescharacteristic
112#14556511C2×C411yescharacteristic
113#14556511C2×C411yescharacteristic
114C22⋊#10596831—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556503—21no—
120#14556503C2×C411yescharacteristic
121#14556503C2×C411yescharacteristic
122#14556501—21no—
123C4×#10596831—21no—
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C4×#10596831C2311yescharacteristic
127C8×Dic73—21no—
128C8×Dic73D411yescharacteristic
129C8×Dic73D411yescharacteristic
130C2×SD16×C73C2×C411yescharacteristic
131C2×M16×C73—21no—
132C4×Q8×C73C2311yescharacteristic
133C4×D4×C73C2311yescharacteristic
134#106×C73C2×C411yescharacteristic
135C4⋊C8×C73—21no—
136C4⋊C8×C73C2311yescharacteristic
137C4⋊C8×C73C2311yescharacteristic
138#103×C73C2×C411yescharacteristic
139#102×C73C2×C411yescharacteristic
140C22⋊C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C4×C8×C73C2311yescharacteristic
145#11924029—22no—
146#11924029—22no—
147#11924028—42no—
148#11924028—42no—
149C2×Dic146—21no—
150C2×D292—21no—
151C2×D292—21no—
152C2×D292C22×C411yescharacteristic
153C2×D292C22×C411yescharacteristic
154C2×C22⋊D73—21no—
155C2×C22⋊D73—21no—
156C2×C22⋊D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—21no—
161C2×C4×D73C22×C411yescharacteristic
162C2×C4×D73C2×D411yescharacteristic
163C2×C4×D73#4111yescharacteristic
164#11924015—22no—
165D584—22no—
166#11924013—22no—
167#11924011—42no—
168#11924011—42no—
169#11924011—42no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—42no—
174C2×#10596831C22×C411yescharacteristic
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C2×D411yescharacteristic
177C2×#10596831C2×D411yescharacteristic
178C8×D73—22no—
179C8×D73—41no—
180C8×D73—42no—
181C8×D73—42no—
182C8×D73—42no—
183C4⋊Dic73—21no—
184C4⋊Dic73C22×C411yescharacteristic
185C4⋊Dic73C22×C411yescharacteristic
186#11924007—21no—
187C22⋊Dic73—21no—
188#11924005—21no—
189#11924005—21no—
190#11924005—21no—
191#11924005—21no—
192#11924005—21no—
193C4×Dic73—21no—
194C4×Dic73—21no—
195C4×Dic73C22×C411yescharacteristic
196C4×Dic73C2×D411yescharacteristic
197C4×Dic73#4111yescharacteristic
198C2×Q8×C73C22×C411yescharacteristic
199C2×D4×C73C22×C411yescharacteristic
200C22×C4×C73—21no—
201SD16×C73—22no—
202M16×C73—42no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73C22×C411yescharacteristic
207C2×C8×C73C22×C411yescharacteristic
208C2×C8×C73C2×D411yescharacteristic
209C2×C8×C73C2×D411yescharacteristic
210C4⋊C4×C73—21no—
211C4⋊C4×C73C22×C411yescharacteristic
212C4⋊C4×C73C22×C411yescharacteristic
213C22⋊C4×C73—21no—
214C42×C73—21no—
215C42×C73C2411yescharacteristic
216C23×C73—21no—
217C22×D73—21no—
218C22×D73—21no—
219C22×D73C4×D411yescharacteristic
220Q8×C73—21no—
221Q8×C73#13112yescomplemented
222D4×C73—21no—
223D4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73C23×C411yescharacteristic
230C2×C4×C73C22×D411yescharacteristic
231C2×C4×C73C2×#4111yescharacteristic
232C22⋊D73—42no—
233C22⋊D73—42no—
234C22⋊D73—42no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73C4×D411yescharacteristic
238C2×Dic73C4×D411yescharacteristic
239C2×Dic73C4×D411yescharacteristic
240D292—24no—
241D292—21no—
242D292—21no—
243D292—21no—
244D292—42no—
245D292#13112yescomplemented
246C4×D73—24no—
247C4×D73—21no—
248C4×D73—21no—
249C4×D73—21no—
250C4×D73—21no—
251C4×D73—22no—
252C4×D73—41no—
253C4×D73—41no—
254C4×D73—41no—
255C4×D73—41no—
256C4×D73—42no—
257Dic146—42no—
258C8×C73—21no—
259C8×C73—21no—
260C8×C73—21no—
261C8×C73—41no—
262C8×C73—41no—
263C8×C73—41no—
264C8×C73AGL(1,ℤ/8)12yes—
265#10596831—21no—
266#10596831—21no—
267#10596831—21no—
268#10596831—21no—
269#10596831—41no—
270#10596831—41no—
271#10596831—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73C2×C4×D411yescharacteristic
276C2×D73—21no—
277C2×D73—22no—
278C2×D73—21no—
279C2×D73—21no—
280C2×D73—41no—
281C2×D73—41no—
282C2×D73—41no—
283C2×D73—41no—
284C2×D73—41no—
285C4×C73—22no—
286C4×C73—21no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73C2×#13111yescharacteristic
290C4×C73C2×#13111yescharacteristic
291C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C73#57511yescharacteristic
293Dic73—21no—
294Dic73—21no—
295Dic73—41no—
296Dic73—41no—
297Dic73#44412yes—
298#17917—731nomaximal, Sylow
299C2×C73—81no—
300C2×C73#292911yescharacteristic
301C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
302C2×C73C2×#44411yescharacteristic
303D73—41no—
304D73—42no—
305D73—81no—
306#3106—731no—
307C8×#41—731no—
308#2931—731no—
309#1583—731no—
310#1583D7311yescharacteristic, complemented
311#1581—731no—
312#1581—731no—
313#1580—731no—
314#1580—731no—
315SD16⋊C8—731no—
316SD16⋊C8—731no—
317#1574—731no—
318#1489—731no—
319#1484—731no—
320#1451—731no—
321C73#1791711yescharacteristic, complemented, Sylow
322C2×#131—1461no—
323#532—731no—
324C4×#41—731no—
325#482—731no—
326#482—731no—
327#477—731no—
328#476—731no—
329#460—731no—
330#459—731no—
331#449—731no—
332#449—731no—
333C8×Q8—731no—
334C8×Q8C2×D7311yescharacteristic
335C4×SD16—731no—
336C4×SD16C2×D7311yescharacteristic
337C4×D8—731no—
338C4×D8—731no—
339#436—731no—
340#436—1461no—
341#436C2×D7311yescharacteristic
342C8×D4—731no—
343C8×D4—731no—
344C8×D4—731no—
345C8×D4—731no—
346C8×D4—1461no—
347C8×D4—1461no—
348C8×D4—1461no—
349#431—731no—
350#431—731no—
351#431—1461no—
352#423—731no—
353#408—1461no—
354C4×M16—731no—
355C2×C4×C8—731no—
356C2×C4×C8—1461no—
357#335—731no—
358#335—731no—
359#334—731no—
360#334C2×D7311yescharacteristic
361Q8⋊C8—731no—
362Q8⋊C8C2×D7311yescharacteristic
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366D4⋊C8—731no—
367D4⋊C8—731no—
368D4⋊C8C2×D7311yescharacteristic
369#322—731no—
370#322—731no—
371#322—731no—
372#322C2×D7311yescharacteristic
373C2×#41—731no—
374C2×#41—1461no—
375C2×SD16—731no—
376C2×SD16C4×D7311yescharacteristic
377C2×D8—731no—
378C2×D8—731no—
379#131—2924no—
380C2×M16—21no—
381C2×M16—1461no—
382C2×M16—1461no—
383C2×M16—1461no—
384C22×C8—731no—
385C22×C8—731no—
386C22×C8—1461no—
387C22×C8—1461no—
388C22×C8—1461no—
389C22×C8—1461no—
390C4⋊Q8—731no—
391#127—731no—
392#124—1461no—
393#121—731no—
394#121—731no—
395#121—1461no—
396C4×Q8—731no—
397C4×Q8C22×D7311yescharacteristic
398C4×D4—731no—
399C4×D4—731no—
400C4×D4—731no—
401C4×D4—1461no—
402C4×D4—1461no—
403C4×D4—1461no—
404C4×D4C22×D7311yescharacteristic
405#117—731no—
406#117—1461no—
407C2×C42—731no—
408C2×C42—1461no—
409#107—731no—
410#107—731no—
411#106—731no—
412#106C4×D7311yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—731no—
415C4⋊C8—731no—
416C4⋊C8—731no—
417C4⋊C8—731no—
418C4⋊C8—1461no—
419C4⋊C8—1461no—
420C4⋊C8C22×D7311yescharacteristic
421C4⋊C8C22×D7311yescharacteristic
422#103—731no—
423#103C4×D7311yescharacteristic
424#102—731no—
425#102—731no—
426#102—731no—
427#102—731no—
428#102—731no—
429#102C4×D7311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—731no—
432C22⋊C8—731no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437C22⋊C8—1461no—
438C22⋊C8—1461no—
439#97—1461no—
440C4×C8—21no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—731no—
445C4×C8—731no—
446C4×C8—1461no—
447C4×C8—1461no—
448C4×C8C22×D7311yescharacteristic
449C4×C8C22×D7311yescharacteristic
450C4×C8C22×D7311yescharacteristic
451#41—2922no—
452#41—2922no—
453#41—1462no—
454#41—1462no—
455C2×Q8—1461no—
456C2×Q8C2×C4×D7311yescharacteristic
457C2×D4—731no—
458C2×D4—731no—
459C2×D4—1461no—
460C2×D4—1461no—
461C2×D4—1461no—
462C2×D4—1461no—
463C2×D4—1461no—
464C2×D4C2×C4×D7311yescharacteristic
465C22×C4—21no—
466C22×C4—731no—
467C22×C4—731no—
468C22×C4—731no—
469C22×C4—1461no—
470C22×C4—1461no—
471C22×C4—1461no—
472C22×C4—1461no—
473SD16—22no—
474SD16—1462no—
475D8—1462no—
476D8—1462no—
477M16—42no—
478M16—2922no—
479M16—2922no—
480M16—2922no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—2921no—
485C2×C8—2922no—
486C2×C8—2922no—
487C2×C8—2922no—
488C2×C8—2922no—
489C2×C8—731no—
490C2×C8—731no—
491C2×C8—731no—
492C2×C8—731no—
493C2×C8—1461no—
494C2×C8—1461no—
495C2×C8—1461no—
496C2×C8—1462no—
497C2×C8C2×C4×D7311yescharacteristic
498C2×C8C2×C4×D7311yescharacteristic
499C2×C8D4×D7311yescharacteristic
500C2×C8D4×D7311yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—731no—
503C4⋊C4—731no—
504C4⋊C4—1461no—
505C4⋊C4—1461no—
506C4⋊C4C2×C4×D7311yescharacteristic
507C4⋊C4C2×C4×D7311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C22⋊C4—1461no—
513C22⋊C4—1461no—
514C22⋊C4—1461no—
515C42—21no—
516C42—731no—
517C42—731no—
518C42—731no—
519C42—1461no—
520C42—1461no—
521C42C23×D7311yescharacteristic
522C23—21no—
523C23—731no—
524C23—1461no—
525C23—1461no—
526Q8—21no—
527Q8—2922no—
528Q8#1455659912yescomplemented
529D4—21no—
530D4—21no—
531D4—2922no—
532D4—2922no—
533D4—2922no—
534D4—2922no—
535D4—732no—
536D4—1464no—
537D4—1461no—
538D4—1461no—
539D4—1461no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—2922no—
546C2×C4—2921no—
547C2×C4—2921no—
548C2×C4—2921no—
549C2×C4—2921no—
550C2×C4—731no—
551C2×C4—731no—
552C2×C4—731no—
553C2×C4—1462no—
554C2×C4—1464no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4—1461no—
558C2×C4—1461no—
559C2×C4—1461no—
560C2×C4—1461no—
561C2×C4C22×C4×D7311yescharacteristic
562C2×C4C2×D4×D7311yescharacteristic
563C2×C4#41×D7311yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—2921no—
571C8—2921no—
572C8—2921no—
573C8—1461no—
574C8—1461no—
575C8—1461no—
576C8—1461no—
577C8#1455661812yes—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—2921no—
582C22—2921no—
583C22—2921no—
584C22—2921no—
585C22—2921no—
586C22—1461no—
587C22—1461no—
588C22—1462no—
589C22—1461no—
590C22C4×D4×D7311yescharacteristic
591C4—21no—
592C4—22no—
593C4—41no—
594C4—41no—
595C4—2921no—
596C4—2921no—
597C4—732no—
598C4—1461no—
599C4—1461no—
600C4#131×D7311yescharacteristic
601C4C2×#1455659911yescharacteristic
602C4C2×#1455661811yescharacteristic
603C4#1798938411yescharacteristic
604C2—81no—
605C2—2922no—
606C2—2921no—
607C2—5841no—
608C2#2261862211yescharacteristic
609C2C4×#1455661811yescharacteristic
610C2#444×D7311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1583C2
socleC22×C73C2×C4×D4
prime radical#22619989C2
cosocleC42×C73C24
hypercenter#1583D73
hypocenterC73#17917
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. C8×#11924029C2semidirect
3. #22618640C2semidirect
4. #22608774C2semidirect
5. #22608762C2semidirect
6. #22608758C2semidirect
7. #22608754C2semidirect
8. #22608752C2semidirect
9. #22608746C2semidirect
10. SD16⋊#10596831C2semidirect
11. #22608718C2semidirect
12. #22608369C2semidirect
13. #22608346C2semidirect
14. #22608217C2semidirect
15. C73×#1583C2semidirect
221. Q8×C73#131semidirect
245. D292#131semidirect
310. #1583D73semidirect
321. C73#17917semidirect
528. Q8#14556599semidirect

Maximal subgroups

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

subgroupindex
#226199892
C8×#119240292
#226186402
#226087742
#226087622
#226087582
#226087542
#226087522
#226087462
SD16⋊#105968312
#226087182
#226083692
#226083462
#226082172
C73×#15832
#1791773