Finite Group Databasebeta

← #46839978

Subgroups — #46839978

Order 34688.

952 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#16864653C211yesmaximal, characteristic, complemented
2C2×#22576156C211yesmaximal, characteristic, complemented
3C2×#22576146C211yesmaximal, characteristic, complemented
4C2×#22576132C211yesmaximal, characteristic, complemented
5#31773806C211yesmaximal, characteristic, complemented
6#31773805C211yesmaximal, characteristic, complemented
7#31773805C211yesmaximal, characteristic, complemented
8#31773801C211yesmaximal, characteristic, complemented
9#31773797C211yesmaximal, characteristic, complemented
10#31773777C211yesmaximal, characteristic, complemented
11#31773775C211yesmaximal, characteristic, complemented
12#31773774C211yesmaximal, characteristic, complemented
13#31773773C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic271C211yesmaximal, characteristic, complemented
15#392×C271C211yesmaximal, characteristic, complemented
16C2×#16864653—24no—
17C2×#16864653—24no—
18C2×#16864653—24no—
19C22×Dic542C2211yescharacteristic
20C22×D1084C2211yescharacteristic
21C22×C22⋊D271C2211yescharacteristic
22C22×C22⋊D271C2211yescharacteristic
23C22×C22⋊D271C2211yescharacteristic
24C22×C22⋊D271C2211yescharacteristic
25C22×C22⋊D271C2211yescharacteristic
26C22×C22⋊D271C2211yescharacteristic
27C23×Dic271C2211yescharacteristic
28C23×Dic271C2211yescharacteristic
29C22×C4×D271C2211yescharacteristic
30#22576156—24no—
31#22576146—24no—
32#22576132—24no—
33C2×Dic271⋊C4C2211yescharacteristic
34C2×C22⋊Dic271C2211yescharacteristic
35C2×C22⋊Dic271C2211yescharacteristic
36C2×C22⋊Dic271C2211yescharacteristic
37C2×C22⋊Dic271C2211yescharacteristic
38C2×(C2×D271)⋊C4C2211yescharacteristic
39C2×(C2×D271)⋊C4C2211yescharacteristic
40C2×(C2×D271)⋊C4C2211yescharacteristic
41C2×(C2×D271)⋊C4C2211yescharacteristic
42C2×(C2×D271)⋊C4C2211yescharacteristic
43C2×C4×Dic271C2211yescharacteristic
44C2×C4×Dic271C2211yescharacteristic
45C271⋊#95C2211yescharacteristic
46C271⋊#95C2211yescharacteristic
47C271⋊#95C2211yescharacteristic
48C271⋊#95C2211yescharacteristic
49C271⋊#95C2211yescharacteristic
50C22×D4×C271C2211yescharacteristic
51C22×D4×C271C2211yescharacteristic
52C22×D4×C271C2211yescharacteristic
53C2×C22⋊C4×C271C2211yescharacteristic
54C2×C22⋊C4×C271C2211yescharacteristic
55C2×C22⋊C4×C271C2211yescharacteristic
56#95×C271C2211yescharacteristic
57C23×D271C2311yescharacteristic
58C23×D271C2311yescharacteristic
59#16864653—232no—
60C2×Dic542—22no—
61C2×Dic542—22no—
62C2×Dic542D414yescomplemented
63C2×D1084—22no—
64C2×D1084—22no—
65C2×D1084—41no—
66C2×C22⋊D271—22no—
67C2×C22⋊D271—22no—
68C2×C22⋊D271—22no—
69C2×C22⋊D271—22no—
70C2×C22⋊D271—22no—
71C2×C22⋊D271—22no—
72C2×C22⋊D271—22no—
73C2×C22⋊D271—22no—
74C2×C22⋊D271—22no—
75C2×C22⋊D271—22no—
76C2×C22⋊D271—22no—
77C2×C22⋊D271—22no—
78C2×C22⋊D271—22no—
79C2×C22⋊D271—41no—
80C2×C22⋊D271—41no—
81C2×C22⋊D271—41no—
82C2×C22⋊D271—41no—
83C2×C22⋊D271D414yescomplemented
84C22×Dic271—22no—
85C22×Dic271—22no—
86C22×Dic271—22no—
87C22×Dic271—22no—
88C22×Dic271—22no—
89C22×Dic271D414yescomplemented
90C22×Dic271C2311yescharacteristic
91C22×Dic271C2311yescharacteristic
92C22×Dic271C2311yescharacteristic
93C22×Dic271C2311yescharacteristic
94C22×Dic271C2311yescharacteristic
95C22×Dic271C2311yescharacteristic
96C2×C4×D271—22no—
97C2×C4×D271—22no—
98C2×C4×D271—22no—
99Dic271⋊C4—22no—
100C22⋊Dic271—22no—
101C22⋊Dic271—22no—
102C22⋊Dic271—22no—
103C22⋊Dic271—41no—
104(C2×D271)⋊C4—22no—
105(C2×D271)⋊C4—22no—
106(C2×D271)⋊C4—22no—
107(C2×D271)⋊C4—41no—
108(C2×D271)⋊C4—41no—
109C4×Dic271—22no—
110C4×Dic271—22no—
111C24×C271C2311yescharacteristic
112C24×C271C2311yescharacteristic
113C24×C271C2311yescharacteristic
114C2×D4×C271—22no—
115C2×D4×C271—22no—
116C2×D4×C271—22no—
117C2×D4×C271—22no—
118C2×D4×C271—22no—
119C2×D4×C271—22no—
120C2×D4×C271—41no—
121C2×D4×C271—41no—
122C2×D4×C271—41no—
123C22×C4×C271C2311yescharacteristic
124C22×C4×C271C2311yescharacteristic
125C22×C4×C271C2311yescharacteristic
126C22×C4×C271C2311yescharacteristic
127C22⋊C4×C271—22no—
128C22⋊C4×C271—22no—
129C22⋊C4×C271—41no—
130C22×D271—21no—
131C22×D271—21no—
132C22×D271—21no—
133C22×D271—21no—
134C22×D271—21no—
135C22×D271—21no—
136C22×D271—21no—
137C22×D271—21no—
138C22×D271—21no—
139C22×D271—21no—
140C22×D271—21no—
141C22×D271—21no—
142C22×D271—21no—
143C22×D271C2×D412yes—
144Dic542—28no—
145D1084—44no—
146C22⋊D271—28no—
147C22⋊D271—28no—
148C22⋊D271—44no—
149C22⋊D271—44no—
150C22⋊D271—44no—
151C22⋊D271—44no—
152C2×Dic271—28no—
153C2×Dic271—21no—
154C2×Dic271—21no—
155C2×Dic271—21no—
156C2×Dic271—21no—
157C2×Dic271—21no—
158C2×Dic271—21no—
159C2×Dic271—28no—
160C2×Dic271—21no—
161C2×Dic271—21no—
162C2×Dic271—21no—
163C2×Dic271—21no—
164C2×Dic271—21no—
165C2×Dic271—21no—
166C2×Dic271C2×D412yes—
167C2×Dic271C2×D412yes—
168C2×Dic271C2×D412yes—
169C2×Dic271C2×D412yes—
170C2×Dic271C2×D412yes—
171C2×Dic271#4112yescomplemented
172C4×D271—28no—
173C23×C271—21no—
174C23×C271—21no—
175C23×C271—21no—
176C23×C271—21no—
177C23×C271—21no—
178C23×C271—21no—
179C23×C271—21no—
180C23×C271—21no—
181C23×C271—21no—
182C23×C271—21no—
183C23×C271—21no—
184C23×C271—21no—
185C23×C271—21no—
186C23×C271—21no—
187C23×C271—21no—
188C23×C271—21no—
189C23×C271—21no—
190C23×C271—21no—
191C23×C271—21no—
192C23×C271C2×D412yes—
193C23×C271C2×D412yes—
194C23×C271C2411yescharacteristic
195D4×C271—28no—
196D4×C271—44no—
197D4×C271—44no—
198C2×C4×C271—21no—
199C2×C4×C271—21no—
200C2×C4×C271—21no—
201C2×C4×C271—21no—
202C2×C4×C271—21no—
203C2×C4×C271—21no—
204C2×C4×C271—21no—
205C2×C4×C271—21no—
206C2×C4×C271—21no—
207C2×C4×C271—21no—
208C2×C4×C271C2×D412yes—
209C2×C4×C271#4112yescomplemented
210C22×C271—22no—
211C22×C271—22no—
212C22×C271—22no—
213C22×C271—22no—
214C22×C271—22no—
215C22×C271—22no—
216C22×C271—41no—
217C22×C271—41no—
218C22×C271—41no—
219C22×C271—41no—
220C22×C271—41no—
221C22×C271—41no—
222C22×C271—41no—
223C22×C271—41no—
224C22×C271—41no—
225C22×C271—41no—
226C22×C271—41no—
227C22×C271—41no—
228C22×C271—41no—
229C22×C271—41no—
230C22×C271—41no—
231C22×C271C22×D411yescharacteristic
232C22×C271C22×D411yescharacteristic
233C22×C271C22×D411yescharacteristic
234C22×C271C2×#4111yescharacteristic
235C22×C271C2×#4111yescharacteristic
236C22×C271H(5,𝔽2)11yescharacteristic
237C22×C271H(5,𝔽2)11yescharacteristic
238C2×D271—22no—
239C2×D271—22no—
240C2×D271—22no—
241C2×D271—41no—
242C2×D271—41no—
243C2×D271—41no—
244C2×D271—41no—
245C2×D271—41no—
246C2×D271—41no—
247C2×D271—41no—
248C2×D271—41no—
249C2×D271—41no—
250C2×D271—41no—
251C2×D271—41no—
252C4×C271—22no—
253C4×C271—22no—
254C4×C271—41no—
255C4×C271—41no—
256Dic271—22no—
257Dic271—22no—
258Dic271—22no—
259Dic271—41no—
260Dic271—41no—
261Dic271#12014yes—
262C2×C271—42no—
263C2×C271—42no—
264C2×C271—81no—
265C2×C271C2×#12011yescharacteristic
266C2×C271#53211yescharacteristic
267C2×C271#53511yescharacteristic
268C2×C271#54611yescharacteristic
269C2×C271#54611yescharacteristic
270C2×C271#55011yescharacteristic
271C2×C271#55011yescharacteristic
272D271—42no—
273D271—81no—
274C271#243111yescharacteristic, complemented, Sylow
275#2431—2711nomaximal, Sylow
276C22×#41—2711no—
277C2×#127—2711no—
278C2×#124—2711no—
279C2×#121—2711no—
280#392—2711no—
281#392—2711no—
282#392—2711no—
283#392D27111yescharacteristic, complemented
284#391—2711no—
285#390—2711no—
286#386—2711no—
287#386—2711no—
288#386—2711no—
289#386—2711no—
290C4×C22⋊C4—2711no—
291C2×#41—5424no—
292C2×#41—5424no—
293C2×#41—5424no—
294C22×Q8—2711no—
295C22×D4—2711no—
296C22×D4—2711no—
297C22×D4—2711no—
298C22×D4—2711no—
299C22×D4—2711no—
300C22×D4—2711no—
301C22×D4—2711no—
302C22×D4C2×D27111yescharacteristic
303C22×D4C2×D27111yescharacteristic
304C22×D4C2×D27111yescharacteristic
305C23×C4—2711no—
306C23×C4—2711no—
307C23×C4—2711no—
308#127—5424no—
309#124—5424no—
310#121—5424no—
311C2×C4⋊C4—2711no—
312C2×C22⋊C4—2711no—
313C2×C22⋊C4—2711no—
314C2×C22⋊C4—2711no—
315C2×C22⋊C4—2711no—
316C2×C22⋊C4—2711no—
317C2×C22⋊C4—2711no—
318C2×C22⋊C4—2711no—
319C2×C22⋊C4—2711no—
320C2×C22⋊C4—2711no—
321C2×C22⋊C4C2×D27111yescharacteristic
322C2×C22⋊C4C2×D27111yescharacteristic
323C2×C22⋊C4C2×D27111yescharacteristic
324C2×C42—2711no—
325C2×C42—2711no—
326#95—2711no—
327#95—2711no—
328#95—2711no—
329#95—2711no—
330#95—2711no—
331#95C2×D27111yescharacteristic
332C24—2711no—
333C24—2711no—
334C24C22×D27111yescharacteristic
335C24C22×D27111yescharacteristic
336C24C22×D27111yescharacteristic
337#41—54232no—
338C2×Q8—2714no—
339C2×Q8—5422no—
340C2×Q8—5422no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—2714no—
351C2×D4—5422no—
352C2×D4—5422no—
353C2×D4—5422no—
354C2×D4—5422no—
355C2×D4—5422no—
356C2×D4—5422no—
357C2×D4—5422no—
358C2×D4—5422no—
359C2×D4—5422no—
360C2×D4—5422no—
361C2×D4—5422no—
362C2×D4—5422no—
363C2×D4—5422no—
364C2×D4—5422no—
365C2×D4—5422no—
366C2×D4—10841no—
367C2×D4—10841no—
368C2×D4—10841no—
369C2×D4—10841no—
370C2×D4—10841no—
371C22×C4—2711no—
372C22×C4—2714no—
373C22×C4—2711no—
374C22×C4—2711no—
375C22×C4—2711no—
376C22×C4—2711no—
377C22×C4—2711no—
378C22×C4—5422no—
379C22×C4—5422no—
380C22×C4—5422no—
381C22×C4—5422no—
382C22×C4—5422no—
383C22×C4—5422no—
384C22×C4—5422no—
385C22×C4—5422no—
386C22×C4C22×D27111yescharacteristic
387C22×C4C22×D27111yescharacteristic
388C22×C4C22×D27111yescharacteristic
389C22×C4C22×D27111yescharacteristic
390C4⋊C4—5422no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—41no—
394C22⋊C4—5422no—
395C22⋊C4—5422no—
396C22⋊C4—5422no—
397C22⋊C4—5422no—
398C22⋊C4—5422no—
399C22⋊C4—5422no—
400C22⋊C4—10841no—
401C22⋊C4—10841no—
402C22⋊C4—10841no—
403C42—5422no—
404C42—5422no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—2712no—
425C23—5421no—
426C23—5421no—
427C23—5421no—
428C23—5421no—
429C23—5421no—
430C23—5421no—
431C23—5421no—
432C23—5421no—
433C23—5421no—
434C23—5421no—
435C23—5421no—
436C23—5421no—
437C23—5421no—
438C23D4×D27112yes—
439C23D4×D27112yes—
440C23C23×D27111yescharacteristic
441Q8—5428no—
442D4—28no—
443D4—44no—
444D4—44no—
445D4—5428no—
446D4—5428no—
447D4—10844no—
448D4—10844no—
449D4—10844no—
450D4—10844no—
451D4—10844no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—2712no—
463C2×C4—2712no—
464C2×C4—2712no—
465C2×C4—2712no—
466C2×C4—2712no—
467C2×C4—2712no—
468C2×C4—5428no—
469C2×C4—5428no—
470C2×C4—5428no—
471C2×C4—5421no—
472C2×C4—5421no—
473C2×C4—5421no—
474C2×C4—5421no—
475C2×C4—5421no—
476C2×C4—5421no—
477C2×C4—5421no—
478C2×C4—5421no—
479C2×C4—5421no—
480C2×C4—5421no—
481C2×C4—5421no—
482C2×C4—5421no—
483C2×C4D4×D27112yes—
484C2×C4#1686465312yescomplemented
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—5422no—
507C22—5422no—
508C22—5422no—
509C22—10841no—
510C22—10841no—
511C22—10841no—
512C22—10841no—
513C22—10841no—
514C22—10841no—
515C22—10841no—
516C22—10841no—
517C22—10841no—
518C22—10841no—
519C22—10841no—
520C22C2×D4×D27111yescharacteristic
521C22C2×D4×D27111yescharacteristic
522C22C2×D4×D27111yescharacteristic
523C22#41×D27111yescharacteristic
524C22C2×#1686465311yescharacteristic
525C22#2257620511yescharacteristic
526C22#2257620511yescharacteristic
527C4—22no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—2714no—
532C4—5422no—
533C4—5422no—
534C4—5422no—
535C4—10841no—
536C4—10841no—
537C2—42no—
538C2—42no—
539C2—81no—
540C2—10842no—
541C2—21681no—
542C2#120×D27111yescharacteristic
543C2#3177444211yescharacteristic
544C2#3177446211yescharacteristic
545C2#3177453411yescharacteristic
546C2#3177453611yescharacteristic
547C2#3177456511yescharacteristic
548C2#3177456711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, cosocleC23×C271C24
Fitting#392×C271C2
hypercenter#392D271
hypocenterC271#2431
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#16864653C2semidirect
2. C2×#22576156C2semidirect
3. C2×#22576146C2semidirect
4. C2×#22576132C2semidirect
5. #31773806C2semidirect
6. #31773805C2semidirect
7. #31773805C2semidirect
8. #31773801C2semidirect
9. #31773797C2semidirect
10. #31773777C2semidirect
11. #31773775C2semidirect
12. #31773774C2semidirect
13. #31773773C2semidirect
14. C22⋊C4×Dic271C2semidirect
15. #392×C271C2semidirect
62. C2×Dic542D4semidirect
83. C2×C22⋊D271D4semidirect
89. C22×Dic271D4semidirect
171. C2×Dic271#41semidirect
209. C2×C4×C271#41semidirect
274. C271#2431semidirect
283. #392D271semidirect
484. C2×C4#16864653semidirect

Maximal subgroups

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

subgroupindex
C22×#168646532
C2×#225761562
C2×#225761462
C2×#225761322
#317738062
#317738052
#317738012
#317737972
#317737772
#317737752
#317737742
#317737732
C22⋊C4×Dic2712
#392×C2712
#2431271