Finite Group Databasebeta

← #11775128

Subgroups — #11775128

Order 1152.

763 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 763 conjugacy classes of subgroups — too many to draw. Only its 94 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#10591370C211yesmaximal, characteristic, complemented
4C3×#4470C211yesmaximal, characteristic, complemented
5C3×#4467C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#68334—31nomaximal
9#68302—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#624—21no—
12C2×#3796C411yescharacteristic, complemented
13C2×#3743—21no—
14C3×#930C2211yescharacteristic
15C3×#924C2211yescharacteristic
16#63981—21no—
17#67⋊Dic3—21no—
18#63916C411yescharacteristic, complemented
19#63881—21no—
20#63871C411yescharacteristic, complemented
21#63853—21no—
22#63849C411yescharacteristic, complemented
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25#63647—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×C3⋊#95C2211yescharacteristic
28#63579—21no—
29#5627—31no—
30#5606—31no—
31#4726—31no—
32#4726—31no—
33#4726—61no—
34D3×#95—31no—
35D3×#95—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, complemented
56C2×C3×Dic6C2×C411yescharacteristic, complemented
57C2×#626—21no—
58C2×#626—21no—
59C2×#624—24no—
60C2×#624—42no—
61C2×#624—42no—
62C2×D3×Dic3—21no—
63#3796—42no—
64C2×C32×C8—21no—
65C2×C3⋊(C3⋊C8)—21no—
66#3743—42no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic, complemented
70C3×C4⋊Dic3C2×C411yescharacteristic, complemented
71C3×Dic3⋊C4—21no—
72Dic3⋊Dic3—21no—
73#3722—21no—
74#3722—21no—
75(C2×D3)⋊Dic3—21no—
76Dic32—21no—
77#1504—91noSylow
78C2×#239—31no—
79C2×#237—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C22×C4×D3—61no—
85C3×C22⋊Q8—31no—
86C3×#121—31no—
87#946—31no—
88#938—31no—
89#937—61no—
90D4×Dic3—61no—
91#930C2×D311yescharacteristic
92#924C2×D311yescharacteristic
93C2×ΓL(1,𝔽25)—61no—
94C2×ΓL(1,𝔽25)—61no—
95C2×ΓL(1,𝔽25)—62no—
96#897—31no—
97#895—31no—
98#894—61no—
99#893—61no—
100#892—31no—
101#892—31no—
102#883—61no—
103#882—61no—
104#67⋊C4—61no—
105#67⋊C4—61no—
106C3×C22⋊C8—21no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109C3×#95—31no—
110C3×#95—31no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113C3⋊#95C2×D311yescharacteristic
114C3⋊#95C2×D311yescharacteristic
115#830—31no—
116#830—31no—
117#830—61no—
118(C2×D3)⋊C8—61no—
119(C2×D3)⋊C8—61no—
120(C2×D3)⋊C8—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3C22⋊C411yescharacteristic
127C22×C3⋊D3C22⋊C411yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3C22⋊C411yescharacteristic
134C2×C3⋊Dic3C22⋊C411yescharacteristic
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C4×C3⋊D3—41no—
138C4×C3⋊D3—41no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C3×D12—41no—
151C3×Dic6—41no—
152#626—42no—
153#626—42no—
154#624—48no—
155D3×Dic3—42no—
156C32×C8—41no—
157C3⋊(C3⋊C8)—41no—
158#525—91no—
159#407—91no—
160C2×#95—91no—
161#328—31no—
162#328—91no—
163#327—31no—
164#327—91no—
165C23×D3—31no—
166C23×D3—31no—
167C23×D3—61no—
168C2×C3×Q8—31no—
169C2×C3×D4—31no—
170C2×C3×D4—61no—
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—21no—
177C2×#67—61no—
178C2×#67—61no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185#239—122no—
186#237—122no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12C4×D311yescharacteristic, complemented
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—31no—
197C2×C4×D3—31no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—61no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×C4×D3—124no—
208C2×C4×D3—122no—
209C2×C4×D3—122no—
210C2×C4×D3—122no—
211C2×C4×D3—122no—
212C2×Dic6C4×D311yescharacteristic, complemented
213C2×C3×C8—22no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C3×C4⋊C4—31no—
217C3×C4⋊C4—31no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221#217—21no—
222#217—61no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3C4×D311yescharacteristic, complemented
231C4⋊Dic3C4×D311yescharacteristic, complemented
232Dic3⋊C4—21no—
233Dic3⋊C4—61no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239ΓL(1,𝔽25)—122no—
240ΓL(1,𝔽25)—122no—
241ΓL(1,𝔽25)—124no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32C2×C22⋊C411yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C22×C32#13711yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—24no—
249C2×C3⋊D3—21no—
250C2×C3⋊D3—21no—
251C2×C3⋊D3—21no—
252C2×C3⋊D3—21no—
253C2×C3⋊D3#9912yes—
254C2×C3⋊D3#10412yes—
255C2×C3×D3—41no—
256C2×C3×D3—41no—
257C2×C3×D3—41no—
258C32×C4—21no—
259C32×C4—21no—
260C3⋊Dic3—21no—
261C3⋊Dic3—21no—
262C3×Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3—41no—
265C3×Dic3—41no—
266C3×Dic3—41no—
267C2×#41—91no—
268C23×C4—91no—
269C23×C4—181no—
270C2×M16—181no—
271#123—181no—
272C22⋊Q8—31no—
273C22⋊Q8—91no—
274#121—31no—
275#121—91no—
276#120—181no—
277C4×D4—181no—
278C4×D4—181no—
279#117—91no—
280C22⋊C8—91no—
281C22⋊C8—181no—
282C22⋊C8D3211yescharacteristic
283#95—31no—
284#95—31no—
285#95—181no—
286C23×C3—21no—
287C23×C3—61no—
288C23×C3D3×D411yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—21no—
291C22×D3—31no—
292C22×D3—31no—
293C22×D3—31no—
294C22×D3—31no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—61no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—121no—
308C22×D3—121no—
309C3×Q8—121no—
310C3×D4—121no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—42no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331#67—41no—
332#67—41no—
333#67—122no—
334#67—122no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—31no—
341C2×Dic3—31no—
342C2×Dic3—31no—
343C2×Dic3—31no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—122no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—122no—
354D12—41no—
355D12—122no—
356D12—122no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—62no—
360C4×D3—62no—
361C4×D3—64no—
362C4×D3—122no—
363C4×D3—128no—
364C4×D3—128no—
365C4×D3—121no—
366C4×D3—121no—
367C4×D3—121no—
368C4×D3—121no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—122no—
372Dic6—41no—
373C3×C8—42no—
374C3×C8—41no—
375C3×C8—41no—
376C3⋊C8—122no—
377C3⋊C8—121no—
378C3⋊C8—121no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32C2×#9911yescharacteristic
382C2×C32#41711yescharacteristic
383C2×C32C2×#10411yescharacteristic
384C3⋊D3—22no—
385C3⋊D3—22no—
386C3×D3—81no—
387C24—91no—
388#41—362no—
389C2×Q8—31no—
390C2×D4—31no—
391C2×D4—61no—
392C2×D4—181no—
393C2×D4—181no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—184no—
402C22×C4—181no—
403C22×C4—362no—
404C22×C4—362no—
405C22×C4—362no—
406C22×C4C2×D3211yescharacteristic
407M16—362no—
408C2×C8—21no—
409C2×C8—181no—
410C4⋊C4—31no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—181no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—181no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3D3×C22⋊C411yescharacteristic
433C22×C3D3×C22⋊C411yescharacteristic
434C22×C3#91111yescharacteristic
435C22×C3#91411yescharacteristic
436C22×C3#91511yescharacteristic
437C22×C3#91811yescharacteristic
438C2×D3—32no—
439C2×D3—32no—
440C2×D3—32no—
441C2×D3—32no—
442C2×D3—41no—
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—64no—
451C2×D3—61no—
452C2×D3—61no—
453C2×D3—61no—
454C2×D3—61no—
455C2×D3—61no—
456C2×D3—61no—
457C2×D3—61no—
458C2×D3—61no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—121no—
463C2×D3—124no—
464C2×D3—124no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—41no—
471C3×C4—122no—
472C3×C4—122no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—121no—
476Dic3—42no—
477Dic3—42no—
478Dic3—41no—
479Dic3—41no—
480Dic3—41no—
481Dic3—62no—
482Dic3—61no—
483Dic3—61no—
484Dic3—61no—
485Dic3—61no—
486Dic3—121no—
487C32#150411yescharacteristic, complemented, Sylow
488C23—61no—
489C23—91no—
490C23—91no—
491C23—182no—
492C23—182no—
493C23—181no—
494C23—181no—
495C23#380211yescharacteristic
496Q8—121no—
497D4—121no—
498D4—121no—
499D4—121no—
500D4—362no—
501D4—362no—
502C2×C4—41no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—91no—
509C2×C4—91no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—361no—
517C2×C4—361no—
518C2×C4—368no—
519C2×C4—362no—
520C2×C4—361no—
521C2×C4C4×D3211yescharacteristic
522C2×C4#381111yescharacteristic
523C8—41no—
524C8—361no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—41no—
533C2×C3—41no—
534C2×C3—241no—
535C2×C3D3×#9911yescharacteristic
536C2×C3D3×#9911yescharacteristic
537C2×C3#477111yescharacteristic
538C2×C3#480311yescharacteristic
539C2×C3D3×#10411yescharacteristic
540C2×C3D3×#10411yescharacteristic
541D3—62no—
542D3—62no—
543D3—62no—
544D3—62no—
545D3—81no—
546D3—122no—
547D3—122no—
548C22—21no—
549C22—21no—
550C22—92no—
551C22—92no—
552C22—121no—
553C22—121no—
554C22—121no—
555C22—184no—
556C22—184no—
557C22—181no—
558C22—181no—
559C22—181no—
560C22—181no—
561C22#6379811yescharacteristic
562C22#6381111yescharacteristic
563C22#6392111yescharacteristic
564C4—21no—
565C4—21no—
566C4—122no—
567C4—122no—
568C4—121no—
569C4—121no—
570C4—121no—
571C4—181no—
572C4—181no—
573C3—21no—
574C3#6830211yescharacteristic, complemented
575C3#6833411yescharacteristic, complemented
576C2—21no—
577C2—21no—
578C2—182no—
579C2—182no—
580C2—241no—
581C2#1059040411yescharacteristic
582C2#1059095711yescharacteristic
583C2#1059100811yescharacteristic
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#1504
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. #10591370C2semidirect
4. C3×#4470C2semidirect
5. C3×#4467C2semidirect
6. #10589153C2semidirect
7. #10589149C2semidirect
12. C2×#3796C4semidirect
18. #63916C4semidirect
20. #63871C4semidirect
22. #63849C4semidirect
40. #4470D3semidirect
41. #4467D3semidirect
55. C2×C3×D12C2×C4semidirect
56. C2×C3×Dic6C2×C4semidirect
69. C3×C4⋊Dic3C2×C4semidirect
70. C3×C4⋊Dic3C2×C4semidirect
189. C2×D12C4×D3semidirect
212. C2×Dic6C4×D3semidirect
230. C4⋊Dic3C4×D3semidirect
231. C4⋊Dic3C4×D3semidirect
487. C32#1504semidirect
574. C3#68302semidirect
575. C3#68334semidirect

Maximal subgroups

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

subgroupindex
#105949222
#105924252
#105913702
C3×#44702
C3×#44672
#105891532
#105891492
#683343
#683023