Finite Group Databasebeta

← #11778068

Subgroups — #11778068

Order 1152.

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

normal subgroups only

This group has 663 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×#5515C211yesmaximal, characteristic, complemented
2#10592690C211yesmaximal, characteristic, complemented
3#10591183C211yesmaximal, characteristic, complemented
4#10591168C211yesmaximal, characteristic
5C3×#4528C211yesmaximal, characteristic, complemented
6#10589152C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic, complemented
8#71888—31nomaximal
9#68130—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×#3752—21no—
14C3×#930C2211yescharacteristic
15C3×#929—21no—
16C3×C4×#67—21no—
17C3×#924C2211yescharacteristic
18C3×#898—21no—
19C3×#896—21no—
20C3×#894—21no—
21C3×#889—21no—
22C2×#3717—21no—
23C2×#3714—21no—
24#63658C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63564—21no—
28#63564—21no—
29C3×#539—31no—
30#5515D311yescharacteristic, complemented
31#5046—31no—
32#5036—31no—
33#4991—31no—
34#4991—31no—
35#4991—61no—
36#4732—31no—
37#4731—31no—
38C3×#324—31no—
39#4538—31no—
40#4537—31no—
41#4528D311yescharacteristic, complemented
42#4470—31no—
43#4467—31no—
44C23×C3⋊D3—21no—
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—42no—
52C2×C3×#67—21no—
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3752—42no—
59#3752—42no—
60C3×#217—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C3×Dic3⋊C4—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3717—42no—
75#3714—42no—
76#1597—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C3×#126—61no—
81C3×#125—61no—
82C3×#123—61no—
83C3×#123—61no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—61no—
86C3×#121—31no—
87C3×C4×D4—61no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×#215—61no—
92C2×#213—61no—
93#930C2×D311yescharacteristic
94#929—21no—
95C4×#67—21no—
96C2×(C2×D3)⋊C4—62no—
97C2×(C2×D3)⋊C4—62no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102#924C2×D311yescharacteristic
103C2×D24—61no—
104C2×#204—61no—
105#898—21no—
106#896—21no—
107#894—21no—
108#889—21no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8—31no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—61no—
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—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
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×C4×D3—81no—
151C3×Dic6—41no—
152C3×C3⋊C8—41no—
153C3×C3⋊C8—41no—
154#539—31no—
155#450—91no—
156#447—91no—
157#394—91no—
158#328—91no—
159#327—91no—
160#324—31no—
161C23×D3—62no—
162C23×D3—61no—
163C23×D3—61no—
164C2×C3×Q8—31no—
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4D1211yescharacteristic
172C22×C3×C4D1211yescharacteristic
173C22×C3×C4#6711yescharacteristic
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—21no—
178C22×Dic3—62no—
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×D12#6711yescharacteristic
191C2×C4×D3—21no—
192C2×Dic6#6711yescharacteristic
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—31no—
200C3×C4⋊C4—31no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊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—21no—
214#215—122no—
215#213—122no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220(C2×D3)⋊C4—124no—
221(C2×D3)⋊C4—122no—
222(C2×D3)⋊C4—122no—
223(C2×D3)⋊C4—122no—
224(C2×D3)⋊C4—122no—
225(C2×D3)⋊C4—124no—
226C4⋊Dic3#6711yescharacteristic
227C4⋊Dic3#6711yescharacteristic
228Dic3⋊C4—21no—
229Dic3⋊C4—21no—
230Dic3⋊C4—21no—
231Dic3⋊C4—21no—
232C4×Dic3—21no—
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—41no—
255C32×C4—41no—
256C3⋊Dic3—81no—
257C3×Dic3—41no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C22×D4—91no—
261C2×SD16—181no—
262C2×D8—181no—
263#126—61no—
264#125—61no—
265#123—61no—
266#123—61no—
267C22⋊Q8—31no—
268C22⋊Q8—61no—
269#121—31no—
270C4×D4—61no—
271C2×C4⋊C4D3211yescharacteristic
272C2×C22⋊C4—181no—
273C2×C22⋊C4—181no—
274#102—181no—
275#102—181no—
276C22⋊C8—31no—
277C22⋊C8—31no—
278#95—91no—
279C23×C3—21no—
280C23×C3—61no—
281C23×C3C2×D1211yescharacteristic
282C23×C3C2×#6711yescharacteristic
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—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—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—42no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—42no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—241no—
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—41no—
338#67—41no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—122no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
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—81no—
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—61no—
385C22×C4—181no—
386C22×C4#62611yescharacteristic
387C22×C4#62611yescharacteristic
388C22×C4C2×D3211yescharacteristic
389SD16—362no—
390D8—362no—
391C2×C8—61no—
392C2×C8—61no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—31no—
396C4⋊C4—31no—
397C4⋊C4—61no—
398C4⋊C4—61no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C22⋊C4—61no—
402C22⋊C4—61no—
403C22⋊C4—61no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—362no—
407C22⋊C4—362no—
408C42—61no—
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#90411yescharacteristic
423C22×C3#90811yescharacteristic
424C22×C3#94911yescharacteristic
425C22×C3#95011yescharacteristic
426C22×C3#95311yescharacteristic
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—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—81no—
463C3×C4—121no—
464C3×C4—121no—
465C3×C4—121no—
466Dic3—41no—
467Dic3—41no—
468Dic3—41no—
469Dic3—242no—
470Dic3—241no—
471Dic3—241no—
472C32#159711yescharacteristic, complemented, Sylow
473C23—61no—
474C23—182no—
475C23—361no—
476C23—361no—
477C23—361no—
478C23—361no—
479C23—361no—
480C23—361no—
481C23C2×#62611yescharacteristic
482Q8—121no—
483D4—121no—
484D4—121no—
485D4—121no—
486D4—182no—
487D4—182no—
488D4—361no—
489D4—361no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—241no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—361no—
503C2×C4D3×#6711yescharacteristic
504C2×C4D3×#6711yescharacteristic
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#473411yescharacteristic
518C2×C3#474111yescharacteristic
519C2×C3#475311yescharacteristic
520C2×C3#523811yescharacteristic
521C2×C3#524411yescharacteristic
522C2×C3#524511yescharacteristic
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#6382511yescharacteristic
540C22#6382911yescharacteristic
541C22#6397711yescharacteristic
542C4—21no—
543C4—21no—
544C4—41no—
545C4—41no—
546C4—121no—
547C4—121no—
548C4—121no—
549C4—721no—
550C3—21no—
551C3#6813011yescharacteristic, complemented
552C3#7188811yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—241no—
556C2—722no—
557C2#1059116311yescharacteristic
558C2#1059153111yescharacteristic
559C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#10591168C2
hypercenterC2×C4⋊C4D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5515C2semidirect
2. #10592690C2semidirect
3. #10591183C2semidirect
5. C3×#4528C2semidirect
6. #10589152C2semidirect
7. #10589150C2semidirect
30. #5515D3semidirect
41. #4528D3semidirect
472. C32#1597semidirect
551. C3#68130semidirect
552. C3#71888semidirect

Maximal subgroups

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

subgroupindex
C3×#55152
#105926902
#105911832
#105911682
C3×#45282
#105891522
#105891502
#718883
#681303