Finite Group Databasebeta

← #11778404

Subgroups — #11778404

Order 1152.

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

normal subgroups only

This group has 599 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×#5617C211yesmaximal, characteristic
2#10592739C211yesmaximal, characteristic, complemented
3#10591322C211yesmaximal, characteristic, complemented
4#10591190C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#71885—31nomaximal
9#68287—31nomaximal
10C22×#634C2211yescharacteristic
11C32×#121C2211yescharacteristic
12C2×#3754—21no—
13C3×#939—21no—
14C3×#937—21no—
15C3×D4×Dic3—21no—
16C2×C3×(C2×D3)⋊C4C2211yescharacteristic
17C3×#924C2211yescharacteristic
18C3×#898—21no—
19C3×#886—21no—
20C3×#885—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C2×#3719—21no—
23#63657C2211yescharacteristic
24#63637—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28#63567—21no—
29C3×#538—31no—
30#5617D311yescharacteristic
31#5050—31no—
32#5040—31no—
33#5040—31no—
34#5040—61no—
35#4947—31no—
36#4739—31no—
37#4673—31no—
38C3×#327—31no—
39#4538—31no—
40#4537D311yescharacteristic, complemented
41#4525—31no—
42#4468—31no—
43#4452—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×D4—21no—
46C2×C32×D4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—42no—
52C2×C3×#67—21no—
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×Dic6D411yescharacteristic
58C32×C4⋊C4D411yescharacteristic
59C32×C22⋊C4—21no—
60#3754—42no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—42no—
74#3719—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—21no—
84C3×#121—61no—
85C3×#121C2×D311yescharacteristic
86C3×#121C2×D311yescharacteristic
87C3×#120—61no—
88C3×C4×D4—61no—
89C2×C3×C22⋊C4—31no—
90C2×#217—61no—
91C2×#216—61no—
92#939—21no—
93#937—21no—
94D4×Dic3—21no—
95C2×#214—62no—
96C2×#214—61no—
97C2×#214—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4C2×D311yescharacteristic
100#924C2×D311yescharacteristic
101C2×Dic12—61no—
102#898—21no—
103#886—21no—
104#885—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×C32—21no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C32×D4—41no—
127C32×D4—41no—
128C32×D4—41no—
129C2×C32×C4—21no—
130C2×C32×C4—41no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136#634—22no—
137#634—22no—
138#634—41no—
139#634—41no—
140C3×#67—81no—
141C3×#67—81no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—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—31no—
159#323—91no—
160C24×C3—31no—
161C23×D3#6711yescharacteristic
162C2×C3×Q8—31no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—41no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C2×C3×D4D1211yescharacteristic
170C2×C3×D4#6711yescharacteristic
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C2×#67—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—121no—
184C22×Dic3#6711yescharacteristic
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×Dic6#6711yescharacteristic
195C2×C3×C8—61no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4D1211yescharacteristic
201C3×C4⋊C4#6711yescharacteristic
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—41no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C22⋊C4—61no—
211C3×C42—61no—
212#217—21no—
213#217—21no—
214#217—122no—
215#216—122no—
216#214—122no—
217#214—122no—
218#214—124no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—21no—
223(C2×D3)⋊C4—122no—
224C4⋊Dic3—21no—
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—
232Dic12—122no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32#12011yescharacteristic
239C22×C32#13511yescharacteristic
240C22×C32#13711yescharacteristic
241C2×C3×D3—42no—
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—
249C3⋊Dic3—42no—
250C3×Dic3—41no—
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⋊Q8—31no—
261#121—61no—
262#121D3211yescharacteristic
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—21no—
275C23×C3—21no—
276C23×C3—41no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3D3×D411yescharacteristic
283C23×C3C2×#6711yescharacteristic
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—21no—
287C22×D3—41no—
288C22×D3—41no—
289C3×Q8—121no—
290C3×D4—41no—
291C3×D4—41no—
292C3×D4—42no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—81no—
298C3×D4—81no—
299C3×D4—241no—
300C3×D4—241no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—42no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—241no—
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321#67—81no—
322#67—81no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—81no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340Dic6—41no—
341Dic6—62no—
342Dic6—64no—
343Dic6—62no—
344Dic6—62no—
345Dic6—62no—
346Dic6—122no—
347Dic6—122no—
348Dic6—121no—
349Dic6—121no—
350Dic6—121no—
351Dic6—121no—
352Dic6—122no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—81no—
361C2×C32#45211yescharacteristic
362C2×C32#45511yescharacteristic
363C2×C32B(4,𝔽2)11yescharacteristic
364C3×D3—81no—
365C24—31no—
366C2×Q8—31no—
367C2×Q8—181no—
368C2×Q8—181no—
369C2×Q8—362no—
370C2×D4—21no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4#62611yescharacteristic
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—181no—
378C22×C4C2×D3211yescharacteristic
379Q16—362no—
380SD16—362no—
381C2×C8—61no—
382C2×C8—181no—
383C4⋊C4—31no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4#62611yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—362no—
395C42—61no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—122no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3—241no—
419C22×C3#88211yescharacteristic
420C22×C3#91211yescharacteristic
421C22×C3#91511yescharacteristic
422C22×C3#95011yescharacteristic
423C22×C3#95111yescharacteristic
424C22×C3#95311yescharacteristic
425C2×D3—42no—
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—81no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—41no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—81no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4—121no—
442C3×C4—241no—
443Dic3—41no—
444Dic3—41no—
445Dic3—41no—
446Dic3—81no—
447Dic3—124no—
448Dic3—122no—
449Dic3—122no—
450C32#160611yescharacteristic, complemented, Sylow
451C23—21no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—121no—
456C23—121no—
457C23D3×#6711yescharacteristic
458Q8—121no—
459Q8—182no—
460Q8—182no—
461Q8—361no—
462Q8—361no—
463D4—41no—
464D4—41no—
465D4—41no—
466D4—241no—
467D4—241no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—182no—
478C2×C4—241no—
479C2×C4—361no—
480C2×C4—361no—
481C2×C4C2×#62611yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C8—121no—
484C8—361no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—81no—
495C2×C3—81no—
496C2×C3—161no—
497C2×C3—241no—
498C2×C3#474111yescharacteristic
499C2×C3#478311yescharacteristic
500C2×C3#482511yescharacteristic
501C2×C3#523911yescharacteristic
502C2×C3#524211yescharacteristic
503C2×C3#524411yescharacteristic
504D3—81no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—122no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—241no—
515C22#6392911yescharacteristic
516C22#6393311yescharacteristic
517C22#6397711yescharacteristic
518C4—21no—
519C4—21no—
520C4—41no—
521C4—121no—
522C4—121no—
523C4—121no—
524C4—241no—
525C4—362no—
526C3—21no—
527C3#6828711yescharacteristic, complemented
528C3#7188511yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—81no—
532C2—241no—
533C2#1059146311yescharacteristic
534C2#1059153111yescharacteristic
535C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radicalC3×#5617C2
hypercenter#121D32
hypocenterC32#1606
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10592739C2semidirect
3. #10591322C2semidirect
4. #10591190C2semidirect
5. C3×#4537C2semidirect
6. #10589153C2semidirect
7. #10589145C2semidirect
40. #4537D3semidirect
450. C32#1606semidirect
527. C3#68287semidirect
528. C3#71885semidirect

Maximal subgroups

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

subgroupindex
C3×#56172
#105927392
#105913222
#105911902
C3×#45372
#105891532
#105891452
#718853
#682873