Finite Group Databasebeta

← #11778416

Subgroups — #11778416

Order 1152.

594 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#5644C211yesmaximal, characteristic
2#10592749C211yesmaximal, characteristic, complemented
3#10591322C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71885—31nomaximal
9#68319—31nomaximal
10C22×#634C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12C2×#3756—21no—
13C3×#947—21no—
14C3×#930C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4C2211yescharacteristic
16C3×#898—21no—
17C3×#895—21no—
18C3×#894—21no—
19C3×#882—21no—
20C3×#67⋊C4—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×#3716—21no—
23#63657C2211yescharacteristic
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29C3×#538—31no—
30#5644D311yescharacteristic
31#5050—31no—
32#5050—31no—
33#5050—61no—
34#5040—31no—
35#4947—31no—
36#4738—31no—
37#4673—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4525—31no—
42#4468—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—42no—
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4D411yescharacteristic
60C32×C22⋊C4—21no—
61#3756—42no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—42no—
74#3716—42no—
75#1606—91noSylow
76C22×Dic6—31no—
77C22×Dic6—31no—
78C22×Dic6—61no—
79C3×#126—61no—
80C3×#124—61no—
81C3×#123—61no—
82C3×C22⋊Q8—21no—
83C3×C22⋊Q8C2×D311yescharacteristic
84C3×C22⋊Q8C2×D311yescharacteristic
85C3×#121—31no—
86C3×#121—61no—
87C3×#120—61no—
88C3×C4×D4—61no—
89C2×C3×C22⋊C4—31no—
90C2×#217—61no—
91#947—21no—
92C2×#216—62no—
93C2×#216—61no—
94C2×#216—61no—
95C2×#214—61no—
96#930C2×D311yescharacteristic
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4C2×D311yescharacteristic
99C2×#204—61no—
100#898—21no—
101#895—21no—
102#894—21no—
103#882—21no—
104#67⋊C4—21no—
105C3×C22⋊C8—31no—
106C3×#95—31no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95C2×D311yescharacteristic
110#830—31no—
111#830—31no—
112#830—61no—
113#830C2×D311yescharacteristic
114#816—61no—
115#810—61no—
116#810—62no—
117#810—61no—
118#810—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C32×Q8—41no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135#634—22no—
136#634—22no—
137#634—41no—
138#634—41no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×D12—41no—
148C3×D12—81no—
149C3×D12—81no—
150C3×C4×D3—81no—
151C3⋊(C3⋊C8)—41no—
152C3×C3⋊C8—41no—
153#538—31no—
154#451—91no—
155#448—91no—
156#393—91no—
157#328—31no—
158#327—91no—
159#323—91no—
160C24×C3—31no—
161C23×D3#6711yescharacteristic
162C2×C3×Q8—21no—
163C2×C3×Q8D1211yescharacteristic
164C2×C3×Q8#6711yescharacteristic
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C22×Dic3—21no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—121no—
180C22×Dic3#6711yescharacteristic
181C2×D12—21no—
182C2×D12—21no—
183C2×D12#6711yescharacteristic
184C2×C4×D3—21no—
185C2×Dic6—62no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—121no—
191C2×Dic6—122no—
192C2×Dic6—122no—
193C2×Dic6—124no—
194C2×C3×C8—61no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—41no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4D1211yescharacteristic
202C3×C4⋊C4#6711yescharacteristic
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—41no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C42—61no—
213#217—122no—
214#216—122no—
215#216—122no—
216#216—124no—
217#214—122no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—122no—
225C4⋊Dic3#6711yescharacteristic
226Dic3⋊C4—21no—
227C4×Dic3—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232#204—122no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12011yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3×D3—42no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3—41no—
242C2×C3×D3—41no—
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—81no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—41no—
249C32×C4—41no—
250C3⋊Dic3—42no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—81no—
254C22×Q8—91no—
255C2×Q16—181no—
256C2×SD16—181no—
257#126—61no—
258#124—61no—
259#123—61no—
260C22⋊Q8D3211yescharacteristic
261#121—31no—
262#121—61no—
263#120—61no—
264C4×D4—61no—
265C2×C22⋊C4—31no—
266C2×C22⋊C4—181no—
267#103—181no—
268#103—181no—
269C22⋊C8—31no—
270C22⋊C8—91no—
271#95—31no—
272#95—181no—
273C23×C3—21no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—41no—
287C22×D3—41no—
288C3×Q8—41no—
289C3×Q8—41no—
290C3×Q8—42no—
291C3×D4—121no—
292C3×D4—121no—
293C3×D4—121no—
294C3×D4—241no—
295C3×D4—241no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—241no—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318#67—41no—
319#67—41no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335D12—41no—
336D12—81no—
337D12—81no—
338C4×D3—81no—
339Dic6—62no—
340Dic6—62no—
341Dic6—64no—
342Dic6—62no—
343Dic6—62no—
344Dic6—122no—
345Dic6—122no—
346Dic6—121no—
347Dic6—121no—
348Dic6—121no—
349Dic6—121no—
350Dic6—122no—
351C3×C8—121no—
352C3⋊C8—41no—
353C3⋊C8—122no—
354C3⋊C8—121no—
355C3⋊C8—121no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32#45211yescharacteristic
359C2×C32#45511yescharacteristic
360C2×C32B(4,𝔽2)11yescharacteristic
361C3×D3—81no—
362C3×D3—81no—
363C24—31no—
364C2×Q8—181no—
365C2×Q8—181no—
366C2×Q8—362no—
367C2×Q8#62611yescharacteristic
368C2×D4—31no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C22×C4—31no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—181no—
376C22×C4C2×D3211yescharacteristic
377Q16—362no—
378SD16—362no—
379C2×C8—61no—
380C2×C8—181no—
381C4⋊C4—21no—
382C4⋊C4—31no—
383C4⋊C4—61no—
384C4⋊C4#62611yescharacteristic
385C22⋊C4—21no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—362no—
393C42—61no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—122no—
404C22×C3—121no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3—121no—
408C22×C3—121no—
409C22×C3—121no—
410C22×C3—241no—
411C22×C3#88211yescharacteristic
412C22×C3#91611yescharacteristic
413C22×C3#91811yescharacteristic
414C22×C3#95011yescharacteristic
415C22×C3#95111yescharacteristic
416C22×C3#95311yescharacteristic
417C2×D3—42no—
418C2×D3—41no—
419C2×D3—41no—
420C2×D3—41no—
421C2×D3—41no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—81no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—41no—
431C3×C4—41no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—41no—
435C3×C4—81no—
436C3×C4—81no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—241no—
440Dic3—41no—
441Dic3—41no—
442Dic3—81no—
443Dic3—124no—
444Dic3—122no—
445Dic3—122no—
446C32#160611yescharacteristic, complemented, Sylow
447C23—61no—
448C23—61no—
449C23—61no—
450C23—61no—
451C23—121no—
452C23—121no—
453C23D3×#6711yescharacteristic
454Q8—41no—
455Q8—182no—
456Q8—182no—
457Q8—361no—
458Q8—361no—
459D4—121no—
460D4—121no—
461D4—121no—
462D4—241no—
463D4—241no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—182no—
474C2×C4—241no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4C2×#62611yescharacteristic
478C2×C4D3×#6711yescharacteristic
479C8—121no—
480C8—361no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—241no—
491C2×C3—241no—
492C2×C3#474111yescharacteristic
493C2×C3#480811yescharacteristic
494C2×C3#482511yescharacteristic
495C2×C3#523911yescharacteristic
496C2×C3#524211yescharacteristic
497C2×C3#524411yescharacteristic
498D3—81no—
499D3—81no—
500C22—21no—
501C22—21no—
502C22—122no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—241no—
510C22#6394311yescharacteristic
511C22#6394711yescharacteristic
512C22#6397711yescharacteristic
513C4—21no—
514C4—21no—
515C4—41no—
516C4—41no—
517C4—121no—
518C4—121no—
519C4—241no—
520C4—362no—
521C3—21no—
522C3#6831911yescharacteristic, complemented
523C3#7188511yescharacteristic, complemented
524C2—21no—
525C2—21no—
526C2—241no—
527C2—241no—
528C2#1059153111yescharacteristic
529C2#1059159911yescharacteristic
530C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC3×#5644C2
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. #10592749C2semidirect
3. #10591322C2semidirect
4. #10591181C2semidirect
5. C3×#4538C2semidirect
6. #10589149C2semidirect
7. #10589145C2semidirect
39. #4538D3semidirect
446. C32#1606semidirect
522. C3#68319semidirect
523. C3#71885semidirect

Maximal subgroups

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

subgroupindex
C3×#56442
#105927492
#105913222
#105911812
C3×#45382
#105891492
#105891452
#718853
#683193