Finite Group Databasebeta

← #11778417

Subgroups — #11778417

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#10596115C211yesmaximal, characteristic
2C3×#5050C211yesmaximal, characteristic, complemented
3#10591310C211yesmaximal, characteristic, complemented
4#10591174C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic, complemented
8#70981—31nomaximal
9#68319—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12#64156—21no—
13#64139C2211yescharacteristic
14C2×#3752C2211yescharacteristic
15#64107—21no—
16#64104—21no—
17#64103—21no—
18#64091—21no—
19#64090—21no—
20C2×C3×#216—21no—
21C2×#3722—21no—
22C2×#3717—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63566—21no—
29#5644—31no—
30#5644—31no—
31#5644—61no—
32C3×#451—31no—
33#5231—31no—
34#5227—31no—
35#5050D311yescharacteristic, complemented
36#4738—31no—
37#4673—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4470—31no—
41#4468—31no—
42#4468—31no—
43#4451—31no—
44C23×C3⋊D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)D411yescharacteristic
52C2×C4×C3⋊D3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—42no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4D411yescharacteristic
60C32×C22⋊C4—21no—
61#3752—21no—
62#3752—21no—
63#3752—21no—
64#3752—21no—
65#3752—21no—
66#3752—21no—
67C4⋊(C3⋊Dic3)D411yescharacteristic
68#3750—21no—
69C4×C3⋊Dic3—21no—
70C3×#216—42no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3722—42no—
74#3717—42no—
75#1606—91noSylow
76C22×C3×Q8—31no—
77C22×Dic6C2×D311yescharacteristic
78C2×C3×Q16—61no—
79C3×C22⋊Q8—21no—
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×C22⋊Q8C2×D311yescharacteristic
82#947—62no—
83#947—61no—
84#947—61no—
85C2×#216—21no—
86C2×#215—61no—
87#930—31no—
88#930—31no—
89#930—61no—
90C2×(C2×D3)⋊C4—31no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×#204—61no—
96#898—61no—
97#898—61no—
98#898—62no—
99#895—61no—
100#895—61no—
101#895—62no—
102#894—62no—
103#894—61no—
104#894—61no—
105#882—61no—
106#882—61no—
107#882—62no—
108#67⋊C4—61no—
109#67⋊C4—61no—
110#67⋊C4—62no—
111C3×#103—61no—
112C3×C22⋊C8—31no—
113C3×C22⋊C8—31no—
114C3×#95—31no—
115#835—61no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95C2×D311yescharacteristic
119#830C2×D311yescharacteristic
120#830C2×D311yescharacteristic
121#816—61no—
122#810—21no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C32×Q8—41no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136#638—41no—
137#638—41no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—41no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—81no—
143C4⋊(C3⋊D3)—81no—
144C4×C3⋊D3—81no—
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—31no—
159#448—91no—
160#393—91no—
161#328—31no—
162#327—91no—
163#323—91no—
164C23×D3—31no—
165C23×D3—31no—
166C23×D3—61no—
167C2×C3×Q8—21no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—122no—
171C2×C3×Q8D1211yescharacteristic
172C2×C3×Q8#6711yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—62no—
179C2×#67—61no—
180C2×#67—61no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—61no—
186C2×D12—31no—
187C2×D12—31no—
188C2×D12—61no—
189C2×D12—62no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—62no—
193C2×D12—61no—
194C2×D12—61no—
195C2×C4×D3—62no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6—42no—
201C3×Q16—122no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4D1211yescharacteristic
209C3×C4⋊C4#6711yescharacteristic
210C3×C22⋊C4—22no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—21no—
213#216—42no—
214#215—122no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—61no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221(C2×D3)⋊C4—62no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—62no—
225(C2×D3)⋊C4—62no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—61no—
228(C2×D3)⋊C4—61no—
229(C2×D3)⋊C4—61no—
230(C2×D3)⋊C4—61no—
231(C2×D3)⋊C4—61no—
232(C2×D3)⋊C4—61no—
233(C2×D3)⋊C4—122no—
234(C2×D3)⋊C4—122no—
235C4⋊Dic3—31no—
236C4⋊Dic3—31no—
237C4⋊Dic3—61no—
238Dic3⋊C4—62no—
239Dic3⋊C4—61no—
240Dic3⋊C4—61no—
241C4×Dic3—62no—
242C4×Dic3—61no—
243C4×Dic3—61no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246#204—122no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32#12011yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32#13711yescharacteristic
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C2×C3⋊D3—41no—
255C2×C3⋊D3—41no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—81no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—41no—
263C32×C4—41no—
264C3⋊Dic3—41no—
265C3⋊Dic3—41no—
266C3×Dic3—42no—
267C3×Dic3—81no—
268C22×Q8—31no—
269C2×Q16—61no—
270C2×SD16—181no—
271#126—181no—
272#124—181no—
273#123—181no—
274C22⋊Q8D3211yescharacteristic
275#121—91no—
276#121—181no—
277#120—181no—
278C4×D4—181no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—181no—
281#103—61no—
282#103—181no—
283C22⋊C8—31no—
284C22⋊C8—31no—
285#95—31no—
286#95—181no—
287C23×C3—21no—
288C23×C3D3×D411yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—61no—
293C22×D3—61no—
294C22×D3—61no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—241no—
307C22×D3—241no—
308C3×Q8—41no—
309C3×Q8—41no—
310C3×Q8—62no—
311C3×Q8—62no—
312C3×Q8—81no—
313C3×Q8—121no—
314C3×Q8—121no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—62no—
326C2×C3×C4—81no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336#67—122no—
337#67—122no—
338#67—121no—
339#67—121no—
340#67—121no—
341#67—121no—
342C2×Dic3—22no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—241no—
357D12—121no—
358D12—121no—
359D12—241no—
360D12—242no—
361D12—242no—
362D12—241no—
363D12—241no—
364D12—241no—
365D12—241no—
366C4×D3—242no—
367C4×D3—241no—
368C4×D3—241no—
369Dic6—22no—
370Dic6—22no—
371Dic6—41no—
372Dic6—41no—
373C3×C8—121no—
374C3×C8—121no—
375C3⋊C8—41no—
376C3⋊C8—41no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32#45211yescharacteristic
380C2×C32#45511yescharacteristic
381C2×C32B(4,𝔽2)11yescharacteristic
382C3⋊D3—81no—
383C3⋊D3—81no—
384C24—91no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—122no—
388C2×Q8#62611yescharacteristic
389C2×D4—91no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—181no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—91no—
396C22×C4—181no—
397C22×C4C2×D3211yescharacteristic
398Q16—122no—
399SD16—362no—
400C2×C8—61no—
401C2×C8—61no—
402C4⋊C4—21no—
403C4⋊C4—91no—
404C4⋊C4—181no—
405C4⋊C4#62611yescharacteristic
406C22⋊C4—21no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C22⋊C4—181no—
412C22⋊C4—181no—
413C22⋊C4—362no—
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#88211yescharacteristic
425C22×C3#91611yescharacteristic
426C22×C3#91811yescharacteristic
427C22×C3#91811yescharacteristic
428C22×C3#91911yescharacteristic
429C22×C3#93711yescharacteristic
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—242no—
451C2×D3—242no—
452C2×D3—241no—
453C2×D3—241no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—42no—
461C3×C4—42no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—122no—
467C3×C4—241no—
468Dic3—42no—
469Dic3—81no—
470Dic3—122no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—121no—
476C32#160611yescharacteristic, complemented, Sylow
477C23—181no—
478C23—181no—
479C23—181no—
480C23—181no—
481C23—361no—
482C23—361no—
483C23#381111yescharacteristic
484Q8—41no—
485Q8—62no—
486Q8—62no—
487Q8—121no—
488Q8—121no—
489D4—361no—
490D4—361no—
491D4—361no—
492D4—721no—
493D4—721no—
494C2×C4—21no—
495C2×C4—21no—
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—361no—
506C2×C4—721no—
507C2×C4C2×#62611yescharacteristic
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#474111yescharacteristic
521C2×C3#480811yescharacteristic
522C2×C3#482511yescharacteristic
523C2×C3#503211yescharacteristic
524C2×C3#518711yescharacteristic
525C2×C3#520211yescharacteristic
526D3—242no—
527D3—242no—
528D3—241no—
529D3—241no—
530D3—241no—
531D3—241no—
532C22—21no—
533C22—21no—
534C22—362no—
535C22—361no—
536C22—361no—
537C22—361no—
538C22—361no—
539C22—361no—
540C22—361no—
541C22—721no—
542C22#6394511yescharacteristic
543C22#6395011yescharacteristic
544C22#6398111yescharacteristic
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—122no—
550C4—241no—
551C4—361no—
552C4—361no—
553C3—21no—
554C3#6831911yescharacteristic, complemented
555C3#7098111yescharacteristic, complemented
556C2—21no—
557C2—21no—
558C2—721no—
559C2—721no—
560C2#1059153211yescharacteristic
561C2#1059160211yescharacteristic
562C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radical#10596115C2
hypercenterC22⋊Q8D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5050C2semidirect
3. #10591310C2semidirect
4. #10591174C2semidirect
5. C3×#4538C2semidirect
6. #10589151C2semidirect
7. #10589146C2semidirect
35. #5050D3semidirect
39. #4538D3semidirect
476. C32#1606semidirect
554. C3#68319semidirect
555. C3#70981semidirect

Maximal subgroups

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

subgroupindex
#105961152
C3×#50502
#105913102
#105911742
C3×#45382
#105891512
#105891462
#709813
#683193