Finite Group Databasebeta

← #11778075

Subgroups — #11778075

Order 1152.

663 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 663 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594974C211yesmaximal, characteristic, complemented
2#10592371C211yesmaximal, characteristic, complemented
3#10591183C211yesmaximal, characteristic, complemented
4#10591168C211yesmaximal, characteristic
5C3×#4452C211yesmaximal, characteristic, complemented
6C3×#4451C211yesmaximal, characteristic, complemented
7#10589148C211yesmaximal, characteristic, complemented
8#68324—31nomaximal
9#68292—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×#3752—21no—
12C2×#3752—21no—
13C2×#3750C2211yescharacteristic
14C3×#930C2211yescharacteristic
15C3×#924C2211yescharacteristic
16#67⋊Dic3—21no—
17#63962—21no—
18#63887—21no—
19#63884—21no—
20#63858—21no—
21#63846—21no—
22C2×#3717—21no—
23C2×#3714—21no—
24C32×#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63564—21no—
28#63564—21no—
29#5645—31no—
30#5602—31no—
31#5046—31no—
32#5036—31no—
33#4732—31no—
34#4731—31no—
35#4672—31no—
36#4672—31no—
37#4672—61no—
38C3×#328—31no—
39C3×#327—31no—
40#4469—31no—
41#4469—31no—
42#4452D311yescharacteristic, complemented
43#4451D311yescharacteristic, complemented
44C23×C3⋊D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—42no—
52C2×C3×#67—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×Dic6D411yescharacteristic
55C2×D3×Dic3—21no—
56#3752—42no—
57#3752—42no—
58#3750—21no—
59#3750—21no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73Dic32—21no—
74#3717—42no—
75#3714—42no—
76#1597—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C3×C22⋊Q8—31no—
81C3×#121—31no—
82#946—61no—
83C2×#215—61no—
84#935—61no—
85#935—61no—
86D4×Dic3—61no—
87C2×#213—61no—
88#930C2×D311yescharacteristic
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—62no—
94C2×(C2×D3)⋊C4—62no—
95#924C2×D311yescharacteristic
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—61no—
99C2×D24—61no—
100C2×#204—61no—
101#898—61no—
102#894—61no—
103#890—61no—
104#889—61no—
105#886—61no—
106#67⋊C4—61no—
107#879—61no—
108#878—61no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8—31no—
111C3×#95—21no—
112C3×#95C2×D311yescharacteristic
113C3×#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#830C2×D311yescharacteristic
116#821—61no—
117#821—61no—
118#809—61no—
119#809—61no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3×D3—21no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
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—21no—
139C2×C3⋊Dic3—41no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—41no—
143C4⋊(C3⋊D3)—41no—
144C3×#67—41no—
145C3×#67—41no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C3×D12—41no—
150C3×Dic6—41no—
151D3×Dic3—81no—
152C3×C3⋊C8—41no—
153C3×C3⋊C8—41no—
154#539—91no—
155#450—91no—
156#447—91no—
157#394—91no—
158#328—31no—
159#327—31no—
160#324—91no—
161C23×D3—62no—
162C23×D3—61no—
163C23×D3—61no—
164C2×C3×Q8—31no—
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—21no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—121no—
186C2×D12—121no—
187C2×D12—122no—
188C2×D12—122no—
189C2×D12—124no—
190C2×D12D1211yescharacteristic
191C2×C4×D3—61no—
192C2×Dic6D1211yescharacteristic
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—31no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200#217—21no—
201#217—61no—
202#217—61no—
203#217—61no—
204#215—122no—
205#213—122no—
206(C2×D3)⋊C4—21no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—124no—
211(C2×D3)⋊C4—122no—
212(C2×D3)⋊C4—122no—
213(C2×D3)⋊C4—122no—
214(C2×D3)⋊C4—122no—
215(C2×D3)⋊C4—124no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3D1211yescharacteristic
220C4⋊Dic3D1211yescharacteristic
221Dic3⋊C4—21no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—61no—
229Dic3⋊C4—121no—
230Dic3⋊C4—121no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235D24—122no—
236#204—122no—
237C22×C32—21no—
238C22×C32—21no—
239C22×C32#12011yescharacteristic
240C22×C32#13511yescharacteristic
241C22×C32AGL(1,ℤ/8)11yescharacteristic
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—42no—
245C2×C3⋊D3—81no—
246C2×C3⋊D3—81no—
247C2×C3⋊D3—81no—
248C2×C3⋊D3—81no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—81no—
255C3⋊Dic3—41no—
256C3⋊Dic3—41no—
257C3×Dic3—41no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C22×D4—91no—
261C2×SD16—181no—
262C2×D8—181no—
263#126—181no—
264#125—181no—
265#123—181no—
266#123—181no—
267C22⋊Q8—31no—
268C22⋊Q8—181no—
269#121—31no—
270C4×D4—181no—
271C2×C4⋊C4—91no—
272C2×C22⋊C4—181no—
273C2×C22⋊C4—181no—
274#102—181no—
275#102—181no—
276C22⋊C8—31no—
277C22⋊C8—31no—
278#95D3211yescharacteristic
279C23×C3—21no—
280C23×C3—61no—
281C23×C3D3×D411yescharacteristic
282C23×C3D3×D411yescharacteristic
283C22×D3—21no—
284C22×D3—64no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—122no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C3×Q8—121no—
306C3×D4—121no—
307C3×D4—121no—
308C3×D4—121no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330#67—41no—
331#67—41no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—62no—
336C2×Dic3—61no—
337C2×Dic3—61no—
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—121no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—122no—
350C2×Dic3—241no—
351D12—41no—
352D12—62no—
353D12—62no—
354D12—62no—
355D12—62no—
356D12—122no—
357D12—122no—
358D12—121no—
359D12—121no—
360D12—121no—
361D12—121no—
362D12—122no—
363D12—122no—
364C4×D3—241no—
365Dic6—41no—
366C3×C8—121no—
367C3×C8—121no—
368C3⋊C8—41no—
369C3⋊C8—41no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32#44911yescharacteristic
373C2×C32#45411yescharacteristic
374C2×C32B(4,𝔽2)11yescharacteristic
375C3⋊D3—82no—
376C3×D3—81no—
377C24—181no—
378C2×Q8—31no—
379C2×D4—31no—
380C2×D4—61no—
381C2×D4—181no—
382C2×D4—181no—
383C2×D4—362no—
384C22×C4—21no—
385C22×C4—91no—
386C22×C4—91no—
387C22×C4—181no—
388C22×C4C2×D3211yescharacteristic
389SD16—362no—
390D8—362no—
391C2×C8—61no—
392C2×C8—61no—
393C4⋊C4—31no—
394C4⋊C4—31no—
395C4⋊C4—61no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—181no—
401C22⋊C4—61no—
402C22⋊C4—61no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C22⋊C4—181no—
406C22⋊C4—362no—
407C22⋊C4—362no—
408C42—181no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3#88211yescharacteristic
422C22×C3#88211yescharacteristic
423C22×C3#91111yescharacteristic
424C22×C3#91411yescharacteristic
425C22×C3#91611yescharacteristic
426C22×C3#91911yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—124no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—242no—
440C2×D3—242no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—241no—
444C2×D3—241no—
445C2×D3—242no—
446C2×D3—242no—
447C2×D3—241no—
448C2×D3—241no—
449C2×D3—241no—
450C2×D3—241no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—82no—
458C3×C4—81no—
459C3×C4—81no—
460C3×C4—121no—
461C3×C4—121no—
462C3×C4—121no—
463Dic3—41no—
464Dic3—41no—
465Dic3—41no—
466Dic3—122no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—241no—
472C32#159711yescharacteristic, complemented, Sylow
473C23—61no—
474C23—182no—
475C23—361no—
476C23—361no—
477C23—361no—
478C23—361no—
479C23—361no—
480C23—361no—
481C23#381111yescharacteristic
482Q8—121no—
483D4—121no—
484D4—121no—
485D4—121no—
486D4—182no—
487D4—182no—
488D4—361no—
489D4—361no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—361no—
502C2×C4—721no—
503C2×C4D3×D1211yescharacteristic
504C2×C4D3×D1211yescharacteristic
505C8—121no—
506C8—121no—
507C2×C3—22no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—241no—
517C2×C3#474111yescharacteristic
518C2×C3#474111yescharacteristic
519C2×C3#478111yescharacteristic
520C2×C3#481011yescharacteristic
521C2×C3#482711yescharacteristic
522C2×C3#482711yescharacteristic
523D3—81no—
524D3—244no—
525D3—242no—
526D3—242no—
527C22—21no—
528C22—21no—
529C22—121no—
530C22—121no—
531C22—121no—
532C22—362no—
533C22—362no—
534C22—362no—
535C22—721no—
536C22—721no—
537C22—721no—
538C22—721no—
539C22#6392311yescharacteristic
540C22#6393711yescharacteristic
541C22#6395011yescharacteristic
542C4—21no—
543C4—21no—
544C4—81no—
545C4—121no—
546C4—121no—
547C4—121no—
548C4—361no—
549C4—361no—
550C3—21no—
551C3#6829211yescharacteristic, complemented
552C3#6832411yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—241no—
556C2—722no—
557C2#1059040211yescharacteristic
558C2#1059041011yescharacteristic
559C2#1059061711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10591168C2
hypercenter#95D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #10594974C2semidirect
2. #10592371C2semidirect
3. #10591183C2semidirect
5. C3×#4452C2semidirect
6. C3×#4451C2semidirect
7. #10589148C2semidirect
42. #4452D3semidirect
43. #4451D3semidirect
472. C32#1597semidirect
551. C3#68292semidirect
552. C3#68324semidirect

Maximal subgroups

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

subgroupindex
#105949742
#105923712
#105911832
#105911682
C3×#44522
C3×#44512
#105891482
#683243
#682923