Finite Group Databasebeta

← #11778407

Subgroups — #11778407

Order 1152.

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

normal subgroups only

This group has 621 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×#5494C211yesmaximal, characteristic
2#10592646C211yesmaximal, characteristic, complemented
3#10591190C211yesmaximal, characteristic, complemented
4#10591181C211yesmaximal, characteristic, complemented
5C3×#4525C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#71885—31nomaximal
9#68109—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757—21no—
13C3×#953—21no—
14C3×#930C2211yescharacteristic
15C3×C4×#67—21no—
16C3×#924C2211yescharacteristic
17C3×#885—21no—
18C3×#884—21no—
19C3×#883—21no—
20C3×#879—21no—
21C2×#3719—21no—
22C2×#3716—21no—
23#63658—21no—
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63567—21no—
28#63567—21no—
29C3×#538—31no—
30#5494D311yescharacteristic
31#5050—31no—
32#5040—31no—
33#4947—31no—
34#4947—31no—
35#4947—61no—
36#4739—31no—
37#4738—31no—
38C3×#323—31no—
39#4538—31no—
40#4537—31no—
41#4525D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C24×C32D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—42no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C2×C3×#67—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×Dic6D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C22⋊C4—21no—
60#3757—42no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3D411yescharacteristic
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3719—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—31no—
83C3×#121—31no—
84C3×#121—61no—
85C3×#120—61no—
86C3×C4×D4—61no—
87C2×C3×C22⋊C4—21no—
88C2×C3×C22⋊C4C2×D311yescharacteristic
89C2×C3×C22⋊C4C2×D311yescharacteristic
90#953—21no—
91C2×#217—62no—
92C2×#217—61no—
93C2×#217—61no—
94C2×#216—61no—
95C2×#214—61no—
96#930C2×D311yescharacteristic
97C4×#67—21no—
98#924C2×D311yescharacteristic
99C2×Dic12—61no—
100C2×#204—61no—
101#885—21no—
102#884—21no—
103#883—21no—
104#879—21no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—61no—
110C3⋊#95—62no—
111C3⋊#95—61no—
112C3⋊#95—61no—
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#816—61no—
116#816—61no—
117#810—61no—
118#810—61no—
119C23×C32—21no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—21no—
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137#634—22no—
138#634—22no—
139#634—41no—
140#634—41no—
141C3×#67—41no—
142C3×#67—41no—
143C3×#67—81no—
144C3×#67—81no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C3×D12—41no—
149C3×C4×D3—81no—
150C3×Dic6—41no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153#538—31no—
154#451—91no—
155#448—91no—
156#393—91no—
157#328—91no—
158#327—91no—
159#323—31no—
160C24×C3—21no—
161C24×C3D1211yescharacteristic
162C24×C3#6711yescharacteristic
163C2×C3×Q8—31no—
164C2×C3×D4—31no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4D1211yescharacteristic
172C22×C3×C4#6711yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C2×#67—21no—
176C2×#67—21no—
177C2×#67—21no—
178C22×Dic3—62no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—62no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C2×D12#6711yescharacteristic
185C2×C4×D3—21no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—121no—
191C2×Dic6—121no—
192C2×Dic6—122no—
193C2×Dic6—122no—
194C2×Dic6—124no—
195C2×Dic6#6711yescharacteristic
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—41no—
207C3×C22⋊C4—41no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C42—61no—
214#217—21no—
215#217—21no—
216#217—21no—
217#217—122no—
218#217—122no—
219#217—124no—
220#216—122no—
221#214—122no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—21no—
224C4⋊Dic3#6711yescharacteristic
225C4⋊Dic3#6711yescharacteristic
226Dic3⋊C4—21no—
227Dic3⋊C4—21no—
228C4×Dic3—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231Dic12—122no—
232#204—122no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—42no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32—81no—
240C22×C32#12011yescharacteristic
241C22×C32#13511yescharacteristic
242C22×C32#13711yescharacteristic
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4—21no—
247C32×C4—21no—
248C32×C4—41no—
249C3⋊Dic3—42no—
250C3⋊Dic3—81no—
251C3×Dic3—41no—
252C3×Dic3—41no—
253C3×Dic3—41no—
254C22×Q8—91no—
255C2×Q16—181no—
256C2×SD16—181no—
257#126—61no—
258#124—61no—
259#123—61no—
260C22⋊Q8—31no—
261#121—31no—
262#121—61no—
263#120—61no—
264C4×D4—61no—
265C2×C22⋊C4—181no—
266C2×C22⋊C4D3211yescharacteristic
267#103—181no—
268#103—181no—
269C22⋊C8—31no—
270C22⋊C8—31no—
271#95—91no—
272#95—181no—
273C23×C3—22no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—61no—
290C23×C3C2×D1211yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C22×D3—21no—
293C3×Q8—121no—
294C3×D4—121no—
295C3×D4—121no—
296C3×D4—121no—
297C3×D4—241no—
298C3×D4—241no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—241no—
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318#67—41no—
319#67—41no—
320#67—81no—
321#67—81no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—64no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—122no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—122no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—122no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—122no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343D12—41no—
344C4×D3—81no—
345Dic6—41no—
346Dic6—62no—
347Dic6—62no—
348Dic6—62no—
349Dic6—62no—
350Dic6—122no—
351Dic6—122no—
352Dic6—121no—
353Dic6—121no—
354Dic6—121no—
355Dic6—121no—
356Dic6—122no—
357Dic6—122no—
358C3×C8—121no—
359C3×C8—121no—
360C3⋊C8—41no—
361C3⋊C8—41no—
362C2×C32—21no—
363C2×C32—21no—
364C2×C32—81no—
365C2×C32#45211yescharacteristic
366C2×C32#45511yescharacteristic
367C2×C32B(4,𝔽2)11yescharacteristic
368C3×D3—81no—
369C24#62611yescharacteristic
370C2×Q8—31no—
371C2×Q8—181no—
372C2×Q8—181no—
373C2×Q8—362no—
374C2×D4—31no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C22×C4—61no—
379C22×C4—181no—
380C22×C4—181no—
381C22×C4#62611yescharacteristic
382C22×C4C2×D3211yescharacteristic
383Q16—362no—
384SD16—362no—
385C2×C8—61no—
386C2×C8—61no—
387C4⋊C4—31no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—61no—
396C22⋊C4—61no—
397C22⋊C4—61no—
398C22⋊C4—362no—
399C42—61no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—44no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—81no—
420C22×C3—81no—
421C22×C3—81no—
422C22×C3—81no—
423C22×C3—82no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3#88211yescharacteristic
428C22×C3#90411yescharacteristic
429C22×C3#90911yescharacteristic
430C22×C3#95011yescharacteristic
431C22×C3#95111yescharacteristic
432C22×C3#95311yescharacteristic
433C2×D3—41no—
434C2×D3—41no—
435C2×D3—41no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—81no—
445C3×C4—121no—
446C3×C4—121no—
447C3×C4—121no—
448Dic3—41no—
449Dic3—41no—
450Dic3—41no—
451Dic3—124no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455Dic3—241no—
456Dic3—241no—
457C32#160611yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—21no—
461C23—41no—
462C23—41no—
463C23—61no—
464C23C2×#62611yescharacteristic
465Q8—121no—
466Q8—182no—
467Q8—182no—
468Q8—361no—
469Q8—361no—
470D4—121no—
471D4—121no—
472D4—121no—
473D4—241no—
474D4—241no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—182no—
482C2×C4—241no—
483C2×C4—361no—
484C2×C4—361no—
485C2×C4—361no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4D3×#6711yescharacteristic
489C2×C4D3×#6711yescharacteristic
490C8—121no—
491C8—121no—
492C2×C3—22no—
493C2×C3—22no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—82no—
502C2×C3—81no—
503C2×C3—81no—
504C2×C3—241no—
505C2×C3#473311yescharacteristic
506C2×C3#474111yescharacteristic
507C2×C3#474611yescharacteristic
508C2×C3#523911yescharacteristic
509C2×C3#524211yescharacteristic
510C2×C3#524411yescharacteristic
511D3—81no—
512C22—21no—
513C22—21no—
514C22—42no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—81no—
519C22—121no—
520C22—121no—
521C22—121no—
522C22#6382911yescharacteristic
523C22#6383111yescharacteristic
524C22#6397711yescharacteristic
525C4—21no—
526C4—21no—
527C4—41no—
528C4—121no—
529C4—121no—
530C4—121no—
531C4—362no—
532C4—721no—
533C3—21no—
534C3#6810911yescharacteristic, complemented
535C3#7188511yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—81no—
539C2—241no—
540C2#1059117311yescharacteristic
541C2#1059151311yescharacteristic
542C2#1059153111yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC3×#5494C2
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. #10592646C2semidirect
3. #10591190C2semidirect
4. #10591181C2semidirect
5. C3×#4525C2semidirect
6. #10589152C2semidirect
7. #10589150C2semidirect
41. #4525D3semidirect
457. C32#1606semidirect
534. C3#68109semidirect
535. C3#71885semidirect

Maximal subgroups

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

subgroupindex
C3×#54942
#105926462
#105911902
#105911812
C3×#45252
#105891522
#105891502
#718853
#681093