Finite Group Databasebeta

← #11778253

Subgroups — #11778253

Order 1152.

633 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 633 conjugacy classes of subgroups — too many to draw. Only its 82 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#10596105C211yesmaximal, characteristic
2C3×#5050C211yesmaximal, characteristic, complemented
3#10591310C211yesmaximal, characteristic
4#10591186C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589154C211yesmaximal, characteristic, complemented
7#10589146C211yesmaximal, characteristic
8#70980—31nomaximal
9#68318—31nomaximal
10C22×C3×Dic6C2211yescharacteristic
11C32×C22⋊Q8C2211yescharacteristic
12#64155—21no—
13C2×#3752C2211yescharacteristic
14#64133C2211yescharacteristic
15#64106—21no—
16#64105—21no—
17#64105—21no—
18C22⋊C4×C3⋊D3—21no—
19#64087—21no—
20C2×C3×#216—21no—
21C2×#3722—21no—
22C2×#3719—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#810—21no—
27#63579—21no—
28#63566—21no—
29#5634—31no—
30#5634—31no—
31#5634—61no—
32C3×#451—31no—
33#5231—31no—
34#5228—31no—
35#5050D311yescharacteristic, complemented
36#4739—31no—
37#4673—31no—
38C3×#328—31no—
39#4538D311yescharacteristic, complemented
40#4468—31no—
41#4468—31no—
42#4467—31no—
43#4452—31no—
44C23×C3⋊D3D411yescharacteristic
45C2×C32×Q8D411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×#634—21no—
51C2×#634D411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4D411yescharacteristic
59C32×C22⋊C4—21no—
60#3757—21no—
61#3752—21no—
62#3752—21no—
63#3752—21no—
64#3752—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)D411yescharacteristic
67#3750—21no—
68#3750—21no—
69#3750—21no—
70C3×#216—42no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3722—42no—
74#3719—42no—
75#1602—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#946—62no—
83#946—61no—
84#946—61no—
85C2×#216—21no—
86C2×#216—61no—
87C2×(C2×D3)⋊C4—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92#924—31no—
93#924—31no—
94#924—61no—
95C2×Dic12—61no—
96#897—61no—
97#897—61no—
98#897—62no—
99#896—61no—
100#896—61no—
101#896—62no—
102#896—62no—
103#896—61no—
104#896—61no—
105D3×C22⋊C4—61no—
106D3×C22⋊C4—61no—
107D3×C22⋊C4—62no—
108#878—61no—
109#878—61no—
110#878—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—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3Q1612yescomplemented
129C32×Q8—41no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C4×C3⋊D3—81no—
140C4×C3⋊D3—81no—
141#634—41no—
142#634—81no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—41no—
152C3×Dic6—41no—
153C3×C3⋊C8—41no—
154C3×C3⋊C8—41no—
155#543—91no—
156#451—31no—
157#451—91no—
158#393—91no—
159#328—31no—
160#328—91no—
161#323—91no—
162C23×D3—31no—
163C23×D3—31no—
164C23×D3—61no—
165C2×C3×Q8—21no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—122no—
169C2×C3×Q8D1211yescharacteristic
170C2×C3×Q8#6711yescharacteristic
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181C2×C4×D3—62no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—62no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×Dic6—21no—
188C2×Dic6—21no—
189C2×Dic6—31no—
190C2×Dic6—31no—
191C2×Dic6—42no—
192C2×Dic6—61no—
193C2×Dic6—62no—
194C2×Dic6—61no—
195C2×Dic6—61no—
196C3×Q16—122no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4D1211yescharacteristic
204C3×C4⋊C4#6711yescharacteristic
205C3×C22⋊C4—22no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208#217—62no—
209#217—61no—
210#217—61no—
211#216—42no—
212#216—122no—
213(C2×D3)⋊C4—62no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—62no—
220(C2×D3)⋊C4—62no—
221(C2×D3)⋊C4—61no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—122no—
226(C2×D3)⋊C4—122no—
227C4⋊Dic3—31no—
228C4⋊Dic3—31no—
229C4⋊Dic3—61no—
230C4⋊Dic3—62no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233Dic3⋊C4—62no—
234Dic3⋊C4—61no—
235Dic3⋊C4—61no—
236Dic3⋊C4—62no—
237Dic3⋊C4—61no—
238Dic3⋊C4—61no—
239Dic3⋊C4—62no—
240Dic3⋊C4—61no—
241Dic3⋊C4—61no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244Dic12—122no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32#12011yescharacteristic
248C22×C32C2×Q1611yescharacteristic
249C22×C32#13711yescharacteristic
250C2×C3⋊D3—22no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—81no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—41no—
258C32×C4—41no—
259C3⋊Dic3—41no—
260C3⋊Dic3—41no—
261C3⋊Dic3—41no—
262C3×Dic3—42no—
263C3×Dic3—81no—
264C22×Q8—31no—
265C2×Q16—61no—
266C2×Q16—181no—
267C22⋊Q8—91no—
268C22⋊Q8—181no—
269C22⋊Q8—181no—
270C22⋊Q8—181no—
271C22⋊Q8—181no—
272C22⋊Q8—181no—
273C22⋊Q8D3211yescharacteristic
274C2×C22⋊C4—91no—
275C2×C22⋊C4—181no—
276C2×C22⋊C4—181no—
277#103—61no—
278#103—181no—
279C22⋊C8—31no—
280C22⋊C8—31no—
281#95—31no—
282#95—181no—
283C23×C3—21no—
284C23×C3D3×D411yescharacteristic
285C23×C3D3×D411yescharacteristic
286C22×D3—32no—
287C22×D3—32no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—62no—
293C22×D3—61no—
294C22×D3—61no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—241no—
300C22×D3—241no—
301C3×Q8—41no—
302C3×Q8—41no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—81no—
306C3×Q8—121no—
307C3×Q8—121no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—62no—
319C2×C3×C4—81no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×Dic3—22no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—241no—
347C4×D3—242no—
348C4×D3—242no—
349C4×D3—241no—
350C4×D3—241no—
351C4×D3—241no—
352C4×D3—241no—
353Dic6—22no—
354Dic6—22no—
355Dic6—41no—
356Dic6—41no—
357Dic6—121no—
358Dic6—121no—
359Dic6—241no—
360Dic6—242no—
361Dic6—241no—
362Dic6—241no—
363C3×C8—121no—
364C3×C8—121no—
365C3⋊C8—41no—
366C3⋊C8—41no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32#45111yescharacteristic
370C2×C32#45511yescharacteristic
371C2×C32B(4,𝔽2)11yescharacteristic
372C3⋊D3—42no—
373C24—91no—
374C2×Q8—61no—
375C2×Q8—61no—
376C2×Q8—91no—
377C2×Q8—122no—
378C2×Q8—181no—
379C2×Q8#62611yescharacteristic
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—91no—
383C22×C4—181no—
384C22×C4—181no—
385C22×C4C2×D3211yescharacteristic
386Q16—122no—
387Q16—362no—
388C2×C8—61no—
389C2×C8—61no—
390C4⋊C4—21no—
391C4⋊C4—91no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C4⋊C4#62611yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—362no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3#88211yescharacteristic
414C22×C3#91511yescharacteristic
415C22×C3D3×Q1611yescharacteristic
416C22×C3D3×Q1611yescharacteristic
417C22×C3#91811yescharacteristic
418C22×C3#93711yescharacteristic
419C2×D3—64no—
420C2×D3—62no—
421C2×D3—62no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—242no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—242no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—41no—
439C3×C4—41no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—41no—
446C3×C4—122no—
447C3×C4—241no—
448Dic3—42no—
449Dic3—81no—
450Dic3—122no—
451Dic3—122no—
452Dic3—122no—
453Dic3—121no—
454Dic3—121no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458Dic3—121no—
459C32#160211yescharacteristic, complemented, Sylow
460C23—92no—
461C23—181no—
462C23—181no—
463C23—361no—
464C23—361no—
465C23#381111yescharacteristic
466Q8—41no—
467Q8—62no—
468Q8—62no—
469Q8—121no—
470Q8—121no—
471Q8—361no—
472Q8—721no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—62no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—361no—
486C2×C4—721no—
487C2×C4—721no—
488C2×C4C2×#62611yescharacteristic
489C2×C4#381111yescharacteristic
490C8—121no—
491C8—121no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3#474111yescharacteristic
502C2×C3#480911yescharacteristic
503C2×C3#482511yescharacteristic
504C2×C3#503211yescharacteristic
505C2×C3#518611yescharacteristic
506C2×C3#520211yescharacteristic
507D3—124no—
508D3—122no—
509D3—122no—
510C22—21no—
511C22—21no—
512C22—182no—
513C22—362no—
514C22—361no—
515C22—361no—
516C22—721no—
517C22#6394411yescharacteristic
518C22#6395111yescharacteristic
519C22#6398111yescharacteristic
520C4—21no—
521C4—21no—
522C4—41no—
523C4—41no—
524C4—122no—
525C4—241no—
526C4—361no—
527C4—361no—
528C4—361no—
529C3—21no—
530C3#6831811yescharacteristic, complemented
531C3#7098011yescharacteristic, complemented
532C2—21no—
533C2—21no—
534C2—362no—
535C2#1059153211yescharacteristic
536C2#1059160311yescharacteristic
537C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32#120
prime radicalC23×C3⋊D3D4
hypercenterC22⋊Q8D32
hypocenterC32#1602
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
4. #10591186C2semidirect
5. C3×#4538C2semidirect
6. #10589154C2semidirect
35. #5050D3semidirect
39. #4538D3semidirect
128. C22×C3⋊D3Q16semidirect
459. C32#1602semidirect
530. C3#68318semidirect
531. C3#70980semidirect

Maximal subgroups

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

subgroupindex
#105961052
C3×#50502
#105913102
#105911862
C3×#45382
#105891542
#105891462
#709803
#683183