Finite Group Databasebeta

← #11778082

Subgroups — #11778082

Order 1152.

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

normal subgroups only

This group has 638 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#10594973C211yesmaximal, characteristic, complemented
2#10592430C211yesmaximal, characteristic, complemented
3#10591321C211yesmaximal, characteristic, complemented
4#10591168C211yesmaximal, characteristic
5C3×#4470C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68292—31nomaximal
9#68130—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C2×#3744—21no—
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4C2211yescharacteristic
15Dic3×#67—21no—
16C2×#3722—21no—
17C2×#3722—21no—
18#63961—21no—
19#63896—21no—
20#63884—21no—
21#63861—21no—
22#63847—21no—
23C2×#3714—21no—
24C32×C22⋊C8C2211yescharacteristic
25#63648—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28#63564—21no—
29#5602—31no—
30#5515—31no—
31#5036—31no—
32#4991—31no—
33#4732—31no—
34#4731—31no—
35#4731—31no—
36#4731—61no—
37#4672—31no—
38C3×#327—31no—
39C3×#324—31no—
40#4470D311yescharacteristic, complemented
41#4469D311yescharacteristic, complemented
42#4467—31no—
43#4452—31no—
44C23×C3⋊D3—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—42no—
49C2×#634D411yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D411yescharacteristic
53C22×C3×Dic3D411yescharacteristic
54C2×C3×D12D411yescharacteristic
55C2×D3×Dic3—21no—
56C2×C32×C8—21no—
57#3757—21no—
58C4⋊(C3⋊Dic3)D411yescharacteristic
59#3750—21no—
60#3744—42no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66#3724—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69#3722—42no—
70#3722—42no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74Dic32—21no—
75#3714—42no—
76#1597—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C3×#121—31no—
81C2×C3×C4⋊C4—31no—
82#935—61no—
83#935—61no—
84D4×Dic3—61no—
85C2×#213—61no—
86#930C2×D311yescharacteristic
87#929—61no—
88C4×#67—61no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93#924—31no—
94#924—31no—
95#924—61no—
96C2×Dic3⋊C4C2×D311yescharacteristic
97C2×D24—61no—
98C2×#204—61no—
99C2×#204—61no—
100C2×#204—62no—
101#898—61no—
102#896—61no—
103#894—61no—
104#889—61no—
105#889—61no—
106#879—61no—
107#878—61no—
108C3×C22⋊C8—21no—
109C3×C22⋊C8—31no—
110C3×C22⋊C8C2×D311yescharacteristic
111C3×C22⋊C8C2×D311yescharacteristic
112C3×#95—31no—
113C3⋊#95C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115#821—61no—
116#821—61no—
117#821—62no—
118#821—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×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—41no—
137C4⋊(C3⋊D3)—41no—
138#634—41no—
139C3×#67—41no—
140C3×#67—41no—
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—
150C3×D12—41no—
151D3×Dic3—81no—
152C32×C8—41no—
153C3×C3⋊C8—41no—
154#539—91no—
155#450—91no—
156#447—91no—
157#394—91no—
158#328—91no—
159#327—31no—
160#324—31no—
161C23×D3—61no—
162C23×D3—61no—
163C23×D3—121no—
164C2×C3×D4—31no—
165C2×C3×D4—61no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—21no—
173C22×Dic3—21no—
174C22×Dic3—61no—
175C22×Dic3D1211yescharacteristic
176C22×Dic3D1211yescharacteristic
177C2×D12—62no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—121no—
183C2×D12—122no—
184C2×D12—122no—
185C2×D12—124no—
186C2×D12D1211yescharacteristic
187C2×C4×D3—61no—
188C2×Dic6—31no—
189C2×Dic6—31no—
190C2×Dic6—61no—
191C2×C3×C8—22no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—61no—
195C3×C4⋊C4—31no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—61no—
199#217—61no—
200#217—61no—
201#217—61no—
202#217—61no—
203#217—61no—
204#217—121no—
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—122no—
211(C2×D3)⋊C4—122no—
212(C2×D3)⋊C4—122no—
213(C2×D3)⋊C4—122no—
214C4⋊Dic3—31no—
215C4⋊Dic3—31no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3D1211yescharacteristic
219Dic3⋊C4—21no—
220Dic3⋊C4—21no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—61no—
227Dic3⋊C4—61no—
228Dic3⋊C4—121no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C2×C3⋊C8—21no—
232D24—122no—
233#204—122no—
234#204—122no—
235#204—124no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32#12011yescharacteristic
239C22×C32#13511yescharacteristic
240C22×C32AGL(1,ℤ/8)11yescharacteristic
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—81no—
245C2×C3⋊D3—81no—
246C2×C3⋊D3—81no—
247C2×C3⋊D3—81no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C32×C4—21no—
252C32×C4—21no—
253C3⋊Dic3—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—181no—
263#125—181no—
264#123—181no—
265#123—181no—
266C22⋊Q8—91no—
267C22⋊Q8—181no—
268#121—31no—
269C4×D4—181no—
270C2×C4⋊C4—31no—
271C2×C22⋊C4—181no—
272C2×C22⋊C4—181no—
273#102—181no—
274#102—181no—
275C22⋊C8—31no—
276C22⋊C8D3211yescharacteristic
277#95—31no—
278C23×C3—21no—
279C23×C3—61no—
280C23×C3C2×D1211yescharacteristic
281C23×C3D3×D411yescharacteristic
282C22×D3—21no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—121no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—122no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—121no—
299C22×D3—121no—
300C22×D3—241no—
301C22×D3—241no—
302C22×D3—241no—
303C22×D3—241no—
304C3×D4—121no—
305C3×D4—121no—
306C3×D4—121no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—42no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325#67—41no—
326#67—41no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—241no—
343D12—41no—
344D12—64no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—122no—
350D12—122no—
351D12—121no—
352D12—121no—
353D12—121no—
354D12—121no—
355D12—122no—
356C4×D3—241no—
357Dic6—121no—
358Dic6—121no—
359Dic6—122no—
360C3×C8—42no—
361C3×C8—41no—
362C3×C8—41no—
363C3×C8—121no—
364C3⋊C8—41no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32#44911yescharacteristic
368C2×C32#45411yescharacteristic
369C2×C32B(4,𝔽2)11yescharacteristic
370C3⋊D3—82no—
371C3×D3—81no—
372C24—181no—
373C2×Q8—91no—
374C2×D4—31no—
375C2×D4—61no—
376C2×D4—181no—
377C2×D4—181no—
378C2×D4—362no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—61no—
382C22×C4—181no—
383C22×C4C2×D3211yescharacteristic
384SD16—362no—
385D8—362no—
386C2×C8—21no—
387C2×C8—61no—
388C4⋊C4—31no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—91no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C22⋊C4—61no—
397C22⋊C4—181no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—362no—
402C22⋊C4—362no—
403C42—181no—
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—121no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3#88211yescharacteristic
417C22×C3#88211yescharacteristic
418C22×C3#90411yescharacteristic
419C22×C3#90811yescharacteristic
420C22×C3#91111yescharacteristic
421C22×C3#91611yescharacteristic
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—124no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—122no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—242no—
433C2×D3—242no—
434C2×D3—241no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—241no—
438C2×D3—242no—
439C2×D3—242no—
440C2×D3—242no—
441C2×D3—242no—
442C2×D3—241no—
443C2×D3—241no—
444C2×D3—241no—
445C2×D3—241no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—41no—
452C3×C4—121no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4—241no—
456Dic3—41no—
457Dic3—41no—
458Dic3—41no—
459Dic3—81no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—121no—
464Dic3—241no—
465Dic3—241no—
466C32#159711yescharacteristic, complemented, Sylow
467C23—61no—
468C23—182no—
469C23—361no—
470C23—361no—
471C23—361no—
472C23—361no—
473C23—361no—
474C23—361no—
475C23D3×D1211yescharacteristic
476Q8—361no—
477D4—121no—
478D4—121no—
479D4—121no—
480D4—182no—
481D4—182no—
482D4—361no—
483D4—361no—
484C2×C4—41no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—721no—
497C2×C4D3×D1211yescharacteristic
498C2×C4#381111yescharacteristic
499C8—41no—
500C8—121no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—241no—
511C2×C3#473411yescharacteristic
512C2×C3#474111yescharacteristic
513C2×C3#474111yescharacteristic
514C2×C3#475311yescharacteristic
515C2×C3#478111yescharacteristic
516C2×C3#482711yescharacteristic
517D3—81no—
518D3—244no—
519D3—242no—
520D3—242no—
521C22—21no—
522C22—21no—
523C22—121no—
524C22—121no—
525C22—121no—
526C22—362no—
527C22—362no—
528C22—362no—
529C22—721no—
530C22—721no—
531C22—721no—
532C22—721no—
533C22#6379511yescharacteristic
534C22#6380611yescharacteristic
535C22#6392311yescharacteristic
536C4—21no—
537C4—21no—
538C4—121no—
539C4—121no—
540C4—121no—
541C4—241no—
542C4—361no—
543C4—361no—
544C3—21no—
545C3#6813011yescharacteristic, complemented
546C3#6829211yescharacteristic, complemented
547C2—21no—
548C2—21no—
549C2—241no—
550C2—722no—
551C2#1059041011yescharacteristic
552C2#1059096811yescharacteristic
553C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#10591168C2
hypercenterC22⋊C8D32
hypocenterC32#1597
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594973C2semidirect
2. #10592430C2semidirect
3. #10591321C2semidirect
5. C3×#4470C2semidirect
6. C3×#4469C2semidirect
7. #10589154C2semidirect
40. #4470D3semidirect
41. #4469D3semidirect
466. C32#1597semidirect
545. C3#68130semidirect
546. C3#68292semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105924302
#105913212
#105911682
C3×#44702
C3×#44692
#105891542
#682923
#681303