Finite Group Databasebeta

← #11778408

Subgroups — #11778408

Order 1152.

645 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 80 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#10595965C211yesmaximal, characteristic
2C3×#4947C211yesmaximal, characteristic, complemented
3#10591186C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic, complemented
8#69700—31nomaximal
9#68109—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12#64162—21no—
13#64139C2211yescharacteristic
14C4×#638—21no—
15#64133C2211yescharacteristic
16#64094—21no—
17#64093—21no—
18#64092—21no—
19#64088—21no—
20C2×C3×#217—21no—
21C2×#3719—21no—
22C2×#3717—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63566—21no—
28#63566—21no—
29#5494—31no—
30#5494—31no—
31#5494—61no—
32C3×#393—31no—
33#5228—31no—
34#5227—31no—
35#4947D311yescharacteristic, complemented
36#4739—31no—
37#4738—31no—
38C3×#323—31no—
39#4525D311yescharacteristic, complemented
40#4470—31no—
41#4467—31no—
42#4452—31no—
43#4451—31no—
44C24×C32D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—42no—
58C32×C22⋊C4—21no—
59C32×C22⋊C4—21no—
60#3757—21no—
61#3757—21no—
62#3757—21no—
63#3752—21no—
64#3752—21no—
65C4⋊(C3⋊Dic3)D411yescharacteristic
66C4⋊(C3⋊Dic3)D411yescharacteristic
67#3750—21no—
68#3750—21no—
69C4×C3⋊Dic3—21no—
70C3×#217—42no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3719—42no—
74#3717—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—61no—
80C2×C3×C22⋊C4C2×D311yescharacteristic
81C2×C3×C22⋊C4C2×D311yescharacteristic
82#953—62no—
83#953—61no—
84#953—61no—
85C2×#217—21no—
86C2×#216—61no—
87C2×#215—61no—
88#930—31no—
89#930—31no—
90#930—61no—
91C4×#67—62no—
92C4×#67—61no—
93C4×#67—61no—
94#924—31no—
95#924—31no—
96#924—61no—
97C2×Dic12—61no—
98C2×#204—61no—
99#885—61no—
100#885—61no—
101#885—62no—
102#884—61no—
103#884—61no—
104#884—62no—
105#883—61no—
106#883—61no—
107#883—62no—
108#879—61no—
109#879—61no—
110#879—62no—
111C3×C22⋊C8—31no—
112C3×C22⋊C8—31no—
113C3×#95—31no—
114C3×#95—61no—
115#835—61no—
116#835—61no—
117C3⋊#95—21no—
118C3⋊#95C2×D311yescharacteristic
119#830C2×D311yescharacteristic
120#830C2×D311yescharacteristic
121#816—61no—
122#816—61no—
123C23×C32—21no—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—21no—
130C2×C32×C4—21no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135#638—41no—
136#638—41no—
137#638—81no—
138#638—81no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C4⋊(C3⋊D3)—41no—
143C4×C3⋊D3—81no—
144#634—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C3×C3⋊C8—41no—
156C3×C3⋊C8—41no—
157#538—91no—
158#451—91no—
159#448—91no—
160#393—31no—
161#328—91no—
162#327—91no—
163#323—31no—
164C24×C3—21no—
165C24×C3D1211yescharacteristic
166C24×C3#6711yescharacteristic
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—122no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4D1211yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—62no—
179C2×#67—61no—
180C2×#67—61no—
181C2×#67—62no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—62no—
185C2×#67—61no—
186C2×#67—61no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C2×D12—31no—
190C2×D12—31no—
191C2×D12—61no—
192C2×C4×D3—62no—
193C2×C4×D3—61no—
194C2×C4×D3—61no—
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6—31no—
198C2×Dic6—31no—
199C2×Dic6—42no—
200C2×Dic6—61no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C3×C22⋊C4—22no—
204C3×C22⋊C4—22no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—122no—
210#217—42no—
211#217—62no—
212#217—61no—
213#217—61no—
214#217—62no—
215#217—61no—
216#217—61no—
217#217—62no—
218#217—61no—
219#217—61no—
220#216—122no—
221#215—122no—
222(C2×D3)⋊C4—62no—
223(C2×D3)⋊C4—62no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—61no—
228C4⋊Dic3—31no—
229C4⋊Dic3—31no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234Dic3⋊C4—62no—
235Dic3⋊C4—61no—
236Dic3⋊C4—61no—
237Dic3⋊C4—62no—
238Dic3⋊C4—61no—
239Dic3⋊C4—61no—
240C4×Dic3—62no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245Dic12—122no—
246#204—122no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—41no—
250C22×C32—41no—
251C22×C32—41no—
252C22×C32—42no—
253C22×C32—81no—
254C22×C32#12011yescharacteristic
255C22×C32#13511yescharacteristic
256C22×C32#13711yescharacteristic
257C2×C3⋊D3—41no—
258C2×C3⋊D3—41no—
259C2×C3⋊D3—41no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—41no—
263C3⋊Dic3—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3×Dic3—42no—
267C3×Dic3—81no—
268C22×Q8—31no—
269C2×Q16—181no—
270C2×SD16—181no—
271#126—181no—
272#124—181no—
273#123—181no—
274C22⋊Q8—91no—
275#121—91no—
276#121—181no—
277#120—181no—
278C4×D4—181no—
279C2×C22⋊C4—61no—
280C2×C22⋊C4D3211yescharacteristic
281#103—181no—
282#103—181no—
283C22⋊C8—31no—
284C22⋊C8—31no—
285#95—31no—
286#95—61no—
287C23×C3—22no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—81no—
302C23×C3—81no—
303C23×C3C2×D1211yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—62no—
306C22×D3—61no—
307C22×D3—61no—
308C3×Q8—62no—
309C3×Q8—62no—
310C3×Q8—121no—
311C3×Q8—121no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—62no—
322C2×C3×C4—81no—
323C2×C3×C4—81no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333#67—122no—
334#67—122no—
335#67—121no—
336#67—121no—
337#67—121no—
338#67—121no—
339#67—242no—
340#67—242no—
341#67—241no—
342#67—241no—
343#67—241no—
344#67—241no—
345C2×Dic3—22no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360D12—121no—
361D12—121no—
362D12—241no—
363C4×D3—242no—
364C4×D3—241no—
365C4×D3—241no—
366Dic6—22no—
367Dic6—22no—
368Dic6—41no—
369Dic6—41no—
370Dic6—121no—
371Dic6—121no—
372Dic6—241no—
373C3×C8—121no—
374C3×C8—121no—
375C3⋊C8—41no—
376C3⋊C8—41no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32—81no—
380C2×C32#45211yescharacteristic
381C2×C32#45511yescharacteristic
382C2×C32B(4,𝔽2)11yescharacteristic
383C3⋊D3—81no—
384C24#62611yescharacteristic
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—91no—
388C2×Q8—122no—
389C2×D4—91no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—181no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—181no—
396C22×C4#62611yescharacteristic
397C22×C4C2×D3211yescharacteristic
398Q16—362no—
399SD16—362no—
400C2×C8—61no—
401C2×C8—61no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—122no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C22⋊C4—181no—
413C22⋊C4—181no—
414C42—181no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—82no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—82no—
439C22×C3#88211yescharacteristic
440C22×C3#90411yescharacteristic
441C22×C3#90911yescharacteristic
442C22×C3#93711yescharacteristic
443C22×C3#94211yescharacteristic
444C22×C3#95011yescharacteristic
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—121no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—42no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—122no—
464C3×C4—241no—
465Dic3—42no—
466Dic3—81no—
467Dic3—122no—
468Dic3—122no—
469Dic3—122no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476C32#160611yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—41no—
481C23—41no—
482C23—181no—
483C23C2×#62611yescharacteristic
484Q8—62no—
485Q8—62no—
486Q8—121no—
487Q8—121no—
488Q8—361no—
489D4—361no—
490D4—361no—
491D4—361no—
492D4—721no—
493D4—721no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—62no—
498C2×C4—121no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—721no—
507C2×C4#381111yescharacteristic
508C2×C4#381111yescharacteristic
509C8—121no—
510C8—121no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—41no—
519C2×C3—41no—
520C2×C3—82no—
521C2×C3—81no—
522C2×C3—81no—
523C2×C3#473311yescharacteristic
524C2×C3#474111yescharacteristic
525C2×C3#474611yescharacteristic
526C2×C3#503211yescharacteristic
527C2×C3#504711yescharacteristic
528C2×C3#506111yescharacteristic
529D3—242no—
530D3—241no—
531D3—241no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—81no—
539C22—361no—
540C22—361no—
541C22—361no—
542C22#6382911yescharacteristic
543C22#6383311yescharacteristic
544C22#6398111yescharacteristic
545C4—21no—
546C4—21no—
547C4—41no—
548C4—122no—
549C4—241no—
550C4—361no—
551C4—361no—
552C4—361no—
553C3—21no—
554C3#6810911yescharacteristic, complemented
555C3#6970011yescharacteristic, complemented
556C2—21no—
557C2—21no—
558C2—81no—
559C2—721no—
560C2#1059118411yescharacteristic
561C2#1059151411yescharacteristic
562C2#1059153211yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radical#10595965C2
hypercenterC2×C22⋊C4D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4947C2semidirect
3. #10591186C2semidirect
4. #10591174C2semidirect
5. C3×#4525C2semidirect
6. #10589154C2semidirect
7. #10589151C2semidirect
35. #4947D3semidirect
39. #4525D3semidirect
476. C32#1606semidirect
554. C3#68109semidirect
555. C3#69700semidirect

Maximal subgroups

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

subgroupindex
#105959652
C3×#49472
#105911862
#105911742
C3×#45252
#105891542
#105891512
#697003
#681093