Finite Group Databasebeta

← #11775404

Subgroups — #11775404

Order 1152.

667 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 667 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594922C211yesmaximal, characteristic
2#10592425C211yesmaximal, characteristic, complemented
3#10591355C211yesmaximal, characteristic, complemented
4C3×#4470C211yesmaximal, characteristic, complemented
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#68337—31nomaximal
9#68305—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3796C411yescharacteristic, complemented
12C2×#3743—21no—
13C3×#930C2211yescharacteristic
14C3×#924C2211yescharacteristic
15#63981—21no—
16#67⋊Dic3—21no—
17C2×#3724—21no—
18C2×#3722—21no—
19#63916C411yescharacteristic, complemented
20#63881—21no—
21#63871C411yescharacteristic, complemented
22#63853—21no—
23#63849C411yescharacteristic, complemented
24C32×C22⋊C8C2211yescharacteristic
25#63657C2211yescharacteristic
26#63647—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×C3⋊#95C2211yescharacteristic
29#5627—31no—
30#5606—31no—
31#4726—31no—
32#4726—31no—
33#4726—61no—
34#4667—31no—
35#4667—31no—
36C3×#328—31no—
37C3×#327—31no—
38#4538—31no—
39#4537—31no—
40#4470D311yescharacteristic, complemented
41#4467D311yescharacteristic, complemented
42#4452—31no—
43#4451—31no—
44C23×C3⋊D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C2×C4×C3⋊D3—42no—
48C2×C4×C3⋊D3C2×C411yescharacteristic
49C2×C4×C3⋊D3C2×C411yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C3×#67—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×Dic6C2×C411yescharacteristic
57C2×#626—21no—
58C2×#626—21no—
59C2×D3×Dic3—21no—
60#3796—42no—
61C2×C32×C8—21no—
62C2×C3⋊(C3⋊C8)—21no—
63#3743—42no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×C4⋊Dic3C2×C411yescharacteristic
68C3×Dic3⋊C4—21no—
69#3724—42no—
70Dic3⋊Dic3—21no—
71#3722—21no—
72#3722—21no—
73#3722—42no—
74(C2×D3)⋊Dic3—21no—
75Dic32—21no—
76#1513—91noSylow
77C2×#239—31no—
78C2×#237—31no—
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—61no—
82C3×C22⋊Q8—31no—
83C3×#121—31no—
84#946—31no—
85#938—31no—
86#937—61no—
87D4×Dic3—61no—
88#930C2×D311yescharacteristic
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94C2×ΓL(1,𝔽25)—61no—
95C2×ΓL(1,𝔽25)—61no—
96C2×ΓL(1,𝔽25)—62no—
97#897—31no—
98#895—31no—
99#894—61no—
100#893—61no—
101#892—31no—
102#892—31no—
103#883—61no—
104#882—61no—
105#67⋊C4—61no—
106#67⋊C4—61no—
107C3×C22⋊C8—21no—
108C3×C22⋊C8C2×D311yescharacteristic
109C3×C22⋊C8C2×D311yescharacteristic
110C3×#95—31no—
111C3×#95—31no—
112C3⋊#95C2×D311yescharacteristic
113C3⋊#95C2×D311yescharacteristic
114#830—31no—
115#830—31no—
116#830—61no—
117(C2×D3)⋊C8—61no—
118(C2×D3)⋊C8—61no—
119(C2×D3)⋊C8—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3C22⋊C411yescharacteristic
126C22×C3⋊D3C22⋊C411yescharacteristic
127C22×C3×D3—21no—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C22⋊C411yescharacteristic
133C2×C3⋊Dic3C22⋊C411yescharacteristic
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—41no—
137C4×C3⋊D3—41no—
138C3×#67—41no—
139C3×#67—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—41no—
150C3×Dic6—41no—
151#626—42no—
152#626—42no—
153D3×Dic3—42no—
154C32×C8—41no—
155C3⋊(C3⋊C8)—41no—
156#525—91no—
157#407—91no—
158#380—91no—
159#328—31no—
160#328—91no—
161#327—31no—
162#327—91no—
163C23×D3—31no—
164C23×D3—31no—
165C23×D3—61no—
166C2×C3×Q8—31no—
167C2×C3×D4—31no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—21no—
175C2×#67—61no—
176C2×#67—61no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183#239—122no—
184#237—122no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12C4×D311yescharacteristic
188C2×C4×D3—31no—
189C2×C4×D3—31no—
190C2×C4×D3—31no—
191C2×C4×D3—31no—
192C2×C4×D3—31no—
193C2×C4×D3—31no—
194C2×C4×D3—31no—
195C2×C4×D3—31no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—122no—
202C2×C4×D3—122no—
203C2×C4×D3—124no—
204C2×Dic6C4×D311yescharacteristic
205C2×C3×C8—22no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C3×C4⋊C4—31no—
209C3×C4⋊C4—31no—
210C3×C4⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213#217—21no—
214#217—61no—
215(C2×D3)⋊C4—21no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—122no—
222(C2×D3)⋊C4—122no—
223C4⋊Dic3—61no—
224C4⋊Dic3C4×D311yescharacteristic
225C4⋊Dic3C4×D311yescharacteristic
226Dic3⋊C4—21no—
227Dic3⋊C4—61no—
228Dic3⋊C4—122no—
229Dic3⋊C4—122no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235ΓL(1,𝔽25)—122no—
236ΓL(1,𝔽25)—122no—
237ΓL(1,𝔽25)—124no—
238C22×C32—21no—
239C22×C32—21no—
240C22×C32C2×C22⋊C411yescharacteristic
241C22×C32AGL(1,ℤ/8)11yescharacteristic
242C22×C32#13711yescharacteristic
243C2×C3⋊D3—21no—
244C2×C3⋊D3—21no—
245C2×C3⋊D3—21no—
246C2×C3⋊D3—21no—
247C2×C3⋊D3—21no—
248C2×C3⋊D3—21no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C32×C4—21no—
255C32×C4—21no—
256C3⋊Dic3—21no—
257C3⋊Dic3#9912yes—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C3×Dic3—41no—
261C3×Dic3—81no—
262C3×Dic3—81no—
263C2×#41—91no—
264C23×C4—91no—
265C2×M16—181no—
266#123—181no—
267C22⋊Q8—31no—
268C22⋊Q8—91no—
269#121—31no—
270#121—91no—
271#120—181no—
272C4×D4—181no—
273C4×D4—181no—
274#117—91no—
275C2×C4⋊C4—181no—
276C2×C22⋊C4—181no—
277C22⋊C8—91no—
278C22⋊C8—181no—
279C22⋊C8D3211yescharacteristic
280#95—31no—
281#95—31no—
282C23×C3—21no—
283C23×C3—61no—
284C23×C3D3×D411yescharacteristic
285C23×C3D3×D411yescharacteristic
286C22×D3—21no—
287C22×D3—31no—
288C22×D3—31no—
289C22×D3—31no—
290C22×D3—31no—
291C22×D3—61no—
292C22×D3—61no—
293C22×D3—61no—
294C22×D3—61no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—122no—
304C22×D3—122no—
305C3×Q8—121no—
306C3×D4—121no—
307C3×D4—121no—
308C3×D4—121no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—42no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327#67—41no—
328#67—41no—
329#67—122no—
330#67—122no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—41no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350D12—41no—
351D12—122no—
352D12—122no—
353C4×D3—62no—
354C4×D3—62no—
355C4×D3—62no—
356C4×D3—62no—
357C4×D3—64no—
358C4×D3—122no—
359C4×D3—122no—
360C4×D3—121no—
361C4×D3—121no—
362C4×D3—121no—
363C4×D3—121no—
364C4×D3—122no—
365C4×D3—122no—
366Dic6—41no—
367C3×C8—42no—
368C3×C8—41no—
369C3×C8—41no—
370C3⋊C8—122no—
371C3⋊C8—121no—
372C3⋊C8—121no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32C2×#9911yescharacteristic
376C2×C32#41711yescharacteristic
377C2×C32#42111yescharacteristic
378C3⋊D3—41no—
379C3⋊D3—41no—
380C3×D3—81no—
381C24—91no—
382#41—362no—
383C2×Q8—31no—
384C2×D4—31no—
385C2×D4—61no—
386C2×D4—181no—
387C2×D4—181no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—181no—
396C22×C4—362no—
397C22×C4C2×D3211yescharacteristic
398M16—362no—
399C2×C8—21no—
400C2×C8—181no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—61no—
404C4⋊C4—181no—
405C4⋊C4—362no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—362no—
412C42—181no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3D3×C22⋊C411yescharacteristic
426C22×C3D3×C22⋊C411yescharacteristic
427C22×C3#91111yescharacteristic
428C22×C3#91411yescharacteristic
429C22×C3#91511yescharacteristic
430C22×C3#91811yescharacteristic
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—41no—
434C2×D3—62no—
435C2×D3—62no—
436C2×D3—61no—
437C2×D3—61no—
438C2×D3—61no—
439C2×D3—61no—
440C2×D3—61no—
441C2×D3—61no—
442C2×D3—61no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—61no—
447C2×D3—61no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—124no—
457C2×D3—124no—
458C3×C4—22no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—41no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4—121no—
467C3×C4—241no—
468C3×C4—241no—
469Dic3—32no—
470Dic3—32no—
471Dic3—41no—
472Dic3—41no—
473Dic3—41no—
474Dic3—62no—
475Dic3—61no—
476Dic3—61no—
477Dic3—81no—
478Dic3—81no—
479Dic3—121no—
480C32#151311yescharacteristic, complemented, Sylow
481C23—61no—
482C23—91no—
483C23—91no—
484C23—181no—
485C23—181no—
486C23—361no—
487C23—361no—
488C23#380211yescharacteristic
489Q8—121no—
490D4—121no—
491D4—121no—
492D4—121no—
493D4—362no—
494D4—362no—
495C2×C4—41no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4—362no—
513C2×C4C4×D3211yescharacteristic
514C2×C4#381111yescharacteristic
515C8—41no—
516C8—361no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—241no—
527C2×C3D3×#9911yescharacteristic
528C2×C3D3×#9911yescharacteristic
529C2×C3#477111yescharacteristic
530C2×C3#480311yescharacteristic
531C2×C3#482111yescharacteristic
532C2×C3#482111yescharacteristic
533D3—81no—
534D3—122no—
535D3—122no—
536D3—121no—
537D3—121no—
538D3—121no—
539D3—121no—
540C22—21no—
541C22—21no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22—181no—
546C22—181no—
547C22—181no—
548C22—181no—
549C22—181no—
550C22—181no—
551C22—362no—
552C22—362no—
553C22#6379811yescharacteristic
554C22#6381111yescharacteristic
555C22#6392111yescharacteristic
556C4—21no—
557C4—21no—
558C4—92no—
559C4—121no—
560C4—121no—
561C4—121no—
562C4—181no—
563C4—241no—
564C4—241no—
565C3—21no—
566C3#6830511yescharacteristic, complemented
567C3#6833711yescharacteristic, complemented
568C2—21no—
569C2—21no—
570C2—241no—
571C2—361no—
572C2—361no—
573C2#1059040411yescharacteristic
574C2#1059095711yescharacteristic
575C2#1059100911yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#10594922C2
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1513
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592425C2semidirect
3. #10591355C2semidirect
4. C3×#4470C2semidirect
5. C3×#4467C2semidirect
6. #10589153C2semidirect
7. #10589149C2semidirect
11. C2×#3796C4semidirect
19. #63916C4semidirect
21. #63871C4semidirect
23. #63849C4semidirect
40. #4470D3semidirect
41. #4467D3semidirect
480. C32#1513semidirect
566. C3#68305semidirect
567. C3#68337semidirect

Maximal subgroups

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

subgroupindex
#105949222
#105924252
#105913552
C3×#44702
C3×#44672
#105891532
#105891492
#683373
#683053