Finite Group Databasebeta

← #11778065

Subgroups — #11778065

Order 1152.

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

normal subgroups only

This group has 643 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×#5602C211yesmaximal, characteristic, complemented
2#10592735C211yesmaximal, characteristic
3#10591321C211yesmaximal, characteristic, complemented
4#10591183C211yesmaximal, characteristic, complemented
5C3×#4537C211yesmaximal, characteristic, complemented
6#10589153C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#71888—31nomaximal
9#68292—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C32×#121C2211yescharacteristic
12C2×#3753—21no—
13C3×#935—21no—
14C3×#935—21no—
15C3×D4×Dic3—21no—
16C3×#924C2211yescharacteristic
17C2×C3×Dic3⋊C4C2211yescharacteristic
18C3×#889—21no—
19C3×#879—21no—
20C3×#878—21no—
21C2×#3722—21no—
22C2×#3722—21no—
23C2×#3717—21no—
24#63657C2211yescharacteristic
25#63636—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63564—21no—
29C3×#539—31no—
30#5602D311yescharacteristic, complemented
31#5046—31no—
32#5036—31no—
33#5036—31no—
34#5036—61no—
35#4991—31no—
36#4731—31no—
37#4672—31no—
38C3×#327—31no—
39#4538—31no—
40#4537D311yescharacteristic, complemented
41#4528—31no—
42#4469—31no—
43#4452—31no—
44C23×C3⋊D3—21no—
45C2×C32×D4—21no—
46C2×C32×D4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—42no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58#3753—42no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
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—
73#3722—42no—
74#3722—42no—
75#3717—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—21no—
87C3×#121C2×D311yescharacteristic
88C3×#121C2×D311yescharacteristic
89C3×C4×D4—61no—
90C2×C3×C4⋊C4—31no—
91C2×#215—61no—
92#935—21no—
93#935—21no—
94D4×Dic3—21no—
95C2×#213—62no—
96C2×#213—61no—
97C2×#213—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102#924C2×D311yescharacteristic
103C2×Dic3⋊C4C2×D311yescharacteristic
104C2×#204—61no—
105#889—21no—
106#879—21no—
107#878—21no—
108C3×C22⋊C8—31no—
109C3×#95—31no—
110C3⋊#95C2×D311yescharacteristic
111#830—31no—
112#830—31no—
113#830—61no—
114#830C2×D311yescharacteristic
115#821—61no—
116#809—61no—
117#809—62no—
118#809—61no—
119#809—61no—
120C23×C32—21no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C32×D4—41no—
130C32×D4—41no—
131C32×D4—41no—
132C2×C32×C4—21no—
133C2×C32×C4—41no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C4⋊(C3⋊D3)—22no—
137C4⋊(C3⋊D3)—22no—
138C4⋊(C3⋊D3)—41no—
139C4⋊(C3⋊D3)—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—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—31no—
160#324—91no—
161C23×D3—61no—
162C23×D3—61no—
163C23×D3—121no—
164C2×C3×Q8—31no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—41no—
169C2×C3×D4D1211yescharacteristic
170C2×C3×D4#6711yescharacteristic
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3#6711yescharacteristic
181C22×Dic3#6711yescharacteristic
182C2×D12—62no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—121no—
188C2×D12—122no—
189C2×D12—122no—
190C2×D12—124no—
191C2×Dic6#6711yescharacteristic
192C2×C3×C8—61no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—31no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4D1211yescharacteristic
202C3×C4⋊C4#6711yescharacteristic
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—41no—
206C3×C22⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C42—61no—
211#217—21no—
212#217—21no—
213#217—21no—
214#217—21no—
215#215—122no—
216#213—122no—
217#213—122no—
218#213—124no—
219(C2×D3)⋊C4—122no—
220(C2×D3)⋊C4—122no—
221(C2×D3)⋊C4—122no—
222(C2×D3)⋊C4—122no—
223C4⋊Dic3—21no—
224C4⋊Dic3#6711yescharacteristic
225Dic3⋊C4—21no—
226Dic3⋊C4—21no—
227Dic3⋊C4—21no—
228Dic3⋊C4—21no—
229Dic3⋊C4—21no—
230C4×Dic3—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235#204—122no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32—41no—
239C22×C32—41no—
240C22×C32—41no—
241C22×C32#12011yescharacteristic
242C22×C32#13511yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C2×C3⋊D3—42no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—81no—
248C2×C3⋊D3—81no—
249C2×C3⋊D3—81no—
250C2×C3⋊D3—81no—
251C32×C4—21no—
252C32×C4—21no—
253C32×C4—41no—
254C3×Dic3—41no—
255C3×Dic3—41no—
256C3×Dic3—41no—
257C3×Dic3—41no—
258C3×Dic3—81no—
259C22×D4—91no—
260C2×SD16—181no—
261C2×D8—181no—
262#126—61no—
263#125—61no—
264#123—61no—
265#123—61no—
266C22⋊Q8—31no—
267C22⋊Q8—61no—
268#121D3211yescharacteristic
269C4×D4—61no—
270C2×C4⋊C4—31no—
271C2×C22⋊C4—181no—
272C2×C22⋊C4—181no—
273#102—181no—
274#102—181no—
275C22⋊C8—31no—
276C22⋊C8—91no—
277#95—31no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—41no—
282C23×C3D3×D411yescharacteristic
283C23×C3C2×#6711yescharacteristic
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—122no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—121no—
301C22×D3—241no—
302C22×D3—241no—
303C22×D3—241no—
304C22×D3—241no—
305C3×Q8—121no—
306C3×D4—41no—
307C3×D4—41no—
308C3×D4—42no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—81no—
314C3×D4—81no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—42no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—241no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—81no—
349D12—62no—
350D12—64no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—121no—
357D12—121no—
358D12—121no—
359D12—121no—
360D12—122no—
361Dic6—41no—
362C3×C8—121no—
363C3⋊C8—41no—
364C3⋊C8—122no—
365C3⋊C8—121no—
366C3⋊C8—121no—
367C2×C32—21no—
368C2×C32—21no—
369C2×C32—81no—
370C2×C32#44911yescharacteristic
371C2×C32#45411yescharacteristic
372C2×C32B(4,𝔽2)11yescharacteristic
373C3⋊D3—82no—
374C24—181no—
375C2×Q8—31no—
376C2×D4—21no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—362no—
380C2×D4#62611yescharacteristic
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4C2×D3211yescharacteristic
386SD16—362no—
387D8—362no—
388C2×C8—61no—
389C2×C8—181no—
390C4⋊C4—31no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—61no—
397C4⋊C4#62611yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—61no—
400C22⋊C4—61no—
401C22⋊C4—61no—
402C22⋊C4—61no—
403C22⋊C4—362no—
404C22⋊C4—362no—
405C42—61no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—81no—
422C22×C3—81no—
423C22×C3—81no—
424C22×C3#88211yescharacteristic
425C22×C3#91111yescharacteristic
426C22×C3#91611yescharacteristic
427C22×C3#94911yescharacteristic
428C22×C3#95011yescharacteristic
429C22×C3#95311yescharacteristic
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—242no—
438C2×D3—242no—
439C2×D3—241no—
440C2×D3—241no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—242no—
444C2×D3—242no—
445C2×D3—242no—
446C2×D3—242no—
447C2×D3—241no—
448C2×D3—241no—
449C2×D3—241no—
450C2×D3—241no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—81no—
460C3×C4—121no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4—241no—
465Dic3—41no—
466Dic3—41no—
467Dic3—41no—
468Dic3—41no—
469Dic3—81no—
470C32#159711yescharacteristic, complemented, Sylow
471C23—21no—
472C23—182no—
473C23—361no—
474C23—361no—
475C23—361no—
476C23—361no—
477C23—361no—
478C23—361no—
479C23D3×#6711yescharacteristic
480Q8—121no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—182no—
485D4—182no—
486D4—361no—
487D4—361no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—121no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—121no—
500C2×C4—241no—
501C2×C4C2×#62611yescharacteristic
502C2×C4D3×#6711yescharacteristic
503C8—121no—
504C8—361no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3—81no—
515C2×C3—81no—
516C2×C3—161no—
517C2×C3#474111yescharacteristic
518C2×C3#478111yescharacteristic
519C2×C3#482711yescharacteristic
520C2×C3#523811yescharacteristic
521C2×C3#524411yescharacteristic
522C2×C3#524511yescharacteristic
523D3—244no—
524D3—242no—
525D3—242no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—362no—
532C22—362no—
533C22—362no—
534C22—721no—
535C22—721no—
536C22—721no—
537C22—721no—
538C22#6392511yescharacteristic
539C22#6393511yescharacteristic
540C22#6397711yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—121no—
548C4—241no—
549C3—21no—
550C3#6829211yescharacteristic, complemented
551C3#7188811yescharacteristic, complemented
552C2—21no—
553C2—21no—
554C2—81no—
555C2—722no—
556C2#1059145211yescharacteristic
557C2#1059153111yescharacteristic
558C2#1059168511yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32#120
prime radical#10592735C2
hypercenter#121D32
hypocenterC32#1597
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
1. C3×#5602C2semidirect
3. #10591321C2semidirect
4. #10591183C2semidirect
5. C3×#4537C2semidirect
6. #10589153C2semidirect
7. #10589147C2semidirect
30. #5602D3semidirect
40. #4537D3semidirect
470. C32#1597semidirect
550. C3#68292semidirect
551. C3#71888semidirect

Maximal subgroups

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

subgroupindex
C3×#56022
#105927352
#105913212
#105911832
C3×#45372
#105891532
#105891472
#718883
#682923