Finite Group Databasebeta

← #11778330

Subgroups — #11778330

Order 1152.

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

normal subgroups only

This group has 643 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#10594911C211yesmaximal, characteristic
2#10592926C211yesmaximal, characteristic, complemented
3C3×#5230C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic, complemented
5#10589151C211yesmaximal, characteristic, complemented
6#10589149C211yesmaximal, characteristic, complemented
7#10589147C211yesmaximal, characteristic, complemented
8#70975—31nomaximal
9#69706—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C2×#3804—21no—
12C2×#3755—21no—
13#64139C2211yescharacteristic
14C2×C3×#215—21no—
15C3×#930C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×Dic3⋊C4C2211yescharacteristic
18#63978—21no—
19#63910—21no—
20#63895—21no—
21#63893—21no—
22#63886—21no—
23#63662—21no—
24#63657C2211yescharacteristic
25C3×#835—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95C2211yescharacteristic
28C3×#830C2211yescharacteristic
29#5597—31no—
30#5510—31no—
31C3×#448—31no—
32C3×#395—31no—
33#5230D311yescharacteristic, complemented
34#5227—31no—
35#5227—31no—
36#5227—61no—
37#5227D311yescharacteristic, complemented
38#4537—31no—
39#4528—31no—
40#4470—31no—
41#4469—31no—
42#4451—31no—
43#4451—31no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—42no—
47C22×C32×C4—21no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12D411yescharacteristic
56C2×#627—21no—
57C2×#626—21no—
58C2×#626—21no—
59C2×#624—21no—
60#3804—42no—
61#3804—42no—
62C2×D3×Dic3—21no—
63#3755—42no—
64#3752—21no—
65C4⋊(C3⋊Dic3)D411yescharacteristic
66C2×C3⋊(C3⋊C8)—21no—
67C3×#215—42no—
68C3×(C2×D3)⋊C4—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—42no—
73C2×C3×C3⋊C8—21no—
74Dic3⋊Dic3—21no—
75#3722—21no—
76(C2×D3)⋊Dic3—21no—
77#1604—91noSylow
78C22×C3×Q8—21no—
79C22×C3×Q8C2×D311yescharacteristic
80C22×C3×Q8C2×D311yescharacteristic
81C2×#237—61no—
82C2×#235—61no—
83C2×C3×SD16—61no—
84C3×#121—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—61no—
87C2×#215—21no—
88C2×#215—61no—
89C2×#215—61no—
90C2×#215—62no—
91#939—61no—
92#939—61no—
93#930—31no—
94#930—31no—
95#930—61no—
96#930—61no—
97#930C2×D311yescharacteristic
98C2×Dic3⋊C4—21no—
99C2×Dic3⋊C4C2×D311yescharacteristic
100#897—61no—
101#897—61no—
102#896—61no—
103#895—61no—
104#895—61no—
105#884—61no—
106#878—61no—
107C3×#103—61no—
108C3×C22⋊C8—31no—
109C3×#95—31no—
110C3×#95—61no—
111#835—21no—
112#835—61no—
113#835—61no—
114#835—62no—
115C3⋊#95—21no—
116C3⋊#95C2×D311yescharacteristic
117#830—31no—
118#830—31no—
119#830—61no—
120#830C2×D311yescharacteristic
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3×D3—21no—
124C32×Q8—22no—
125C32×Q8—22no—
126C32×Q8—41no—
127C32×Q8—41no—
128C2×C32×C4—22no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134#638—41no—
135#638—41no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—41no—
138C3×#67—41no—
139C3×#67—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3SD1612yescomplemented
149C3×D12—41no—
150#627—42no—
151#626—42no—
152#626—81no—
153#624—42no—
154D3×Dic3—42no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—41no—
157#537—91no—
158#448—31no—
159#448—91no—
160#395—31no—
161#327—91no—
162#327—91no—
163#324—91no—
164C2×C3×Q8—22no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—41no—
170C2×C3×Q8—42no—
171C2×C3×Q8—42no—
172C2×C3×Q8—44no—
173C2×C3×D4—31no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C2×#67—61no—
186C2×#67—61no—
187C2×#67—61no—
188C2×#67—61no—
189C2×#67—121no—
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3#6711yescharacteristic
193C22×Dic3#6711yescharacteristic
194#237—122no—
195#237—122no—
196#235—122no—
197#235—122no—
198C2×D12—31no—
199C2×D12—31no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12#6711yescharacteristic
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C3×SD16—122no—
210C2×C3×C8—61no—
211C3×C4⋊C4—31no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—122no—
215C3×C22⋊C4—61no—
216#217—61no—
217#215—42no—
218#215—122no—
219#215—122no—
220#215—124no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—61no—
223(C2×D3)⋊C4—61no—
224(C2×D3)⋊C4—61no—
225(C2×D3)⋊C4—61no—
226(C2×D3)⋊C4—61no—
227(C2×D3)⋊C4—121no—
228C4⋊Dic3—31no—
229C4⋊Dic3—31no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3#6711yescharacteristic
233Dic3⋊C4—21no—
234Dic3⋊C4—21no—
235Dic3⋊C4—42no—
236Dic3⋊C4—61no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32#12011yescharacteristic
244C22×C32C2×SD1611yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C2×C3⋊D3—41no—
247C2×C3⋊D3—41no—
248C2×C3⋊D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3—41no—
251C2×C3×D3—41no—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—42no—
255C3⋊Dic3—41no—
256C3×Dic3—22no—
257C3×Dic3—42no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C2×#41—181no—
261C22×Q8D3211yescharacteristic
262C2×SD16—61no—
263C2×SD16—181no—
264C22⋊Q8—181no—
265C22⋊Q8—181no—
266#121—31no—
267#121—91no—
268#121—181no—
269#121—181no—
270#121—181no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—61no—
273#103—61no—
274#103—181no—
275C22⋊C8—31no—
276C22⋊C8—91no—
277#95—31no—
278#95—61no—
279C23×C3—21no—
280C23×C3—61no—
281C23×C3D3×D411yescharacteristic
282C23×C3C2×#6711yescharacteristic
283C22×D3—21no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—121no—
287C3×Q8—22no—
288C3×Q8—24no—
289C3×Q8—22no—
290C3×Q8—22no—
291C3×Q8—22no—
292C3×Q8—42no—
293C3×Q8—42no—
294C3×Q8—41no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8—42no—
299C3×D4—121no—
300C3×D4—121no—
301C3×D4—121no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—32no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—42no—
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—61no—
318C2×C3×C4—61no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329#67—41no—
330#67—41no—
331#67—122no—
332#67—121no—
333#67—121no—
334#67—121no—
335#67—121no—
336#67—241no—
337#67—241no—
338#67—241no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—22no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—121no—
350C2×Dic3—122no—
351C2×Dic3#21512yescomplemented
352D12—41no—
353D12—121no—
354D12—121no—
355D12—122no—
356D12—122no—
357D12—241no—
358C4×D3—122no—
359C4×D3—122no—
360C4×D3—122no—
361Dic6—122no—
362Dic6—122no—
363C3×C8—121no—
364C3⋊C8—41no—
365C3⋊C8—122no—
366C3⋊C8—121no—
367C3⋊C8—121no—
368C2×C32—21no—
369C2×C32—21no—
370C2×C32#45011yescharacteristic
371C2×C32#45611yescharacteristic
372C2×C32B(4,𝔽2)11yescharacteristic
373C3⋊D3—81no—
374C3×D3—81no—
375#41—362no—
376#41—362no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—42no—
380C2×Q8—181no—
381C2×D4—31no—
382C2×D4—61no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4—181no—
386C2×D4—181no—
387C22×C4—21no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—61no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4C2×D3211yescharacteristic
394SD16—122no—
395SD16—362no—
396C2×C8—61no—
397C2×C8—181no—
398C4⋊C4—31no—
399C4⋊C4—61no—
400C4⋊C4—61no—
401C4⋊C4—91no—
402C4⋊C4—122no—
403C4⋊C4—181no—
404C22⋊C4—61no—
405C22⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3D3×SD1611yescharacteristic
421C22×C3#91411yescharacteristic
422C22×C3#93711yescharacteristic
423C22×C3#93711yescharacteristic
424C22×C3C2×#21511yescharacteristic
425C22×C3#94911yescharacteristic
426C2×D3—41no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—241no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—41no—
444C3×C4—44no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—62no—
448C3×C4—122no—
449C3×C4—121no—
450C3×C4—121no—
451Dic3—22no—
452Dic3—42no—
453Dic3—41no—
454Dic3—41no—
455Dic3—121no—
456Dic3—121no—
457Dic3—241no—
458C32#160411yescharacteristic, complemented, Sylow
459C23—61no—
460C23—181no—
461C23D3×#6711yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—41no—
465Q8—41no—
466Q8—362no—
467D4—121no—
468D4—121no—
469D4—121no—
470D4—361no—
471D4—362no—
472D4—361no—
473D4—361no—
474D4—721no—
475C2×C4—22no—
476C2×C4—32no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—181no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4D3×#6711yescharacteristic
492C2×C4#381111yescharacteristic
493C8—121no—
494C8—361no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—241no—
505C2×C3#503211yescharacteristic
506C2×C3#503211yescharacteristic
507C2×C3#504611yescharacteristic
508C2×C3#509511yescharacteristic
509C2×C3#516911yescharacteristic
510C2×C3#520511yescharacteristic
511D3—81no—
512D3—241no—
513D3—241no—
514D3—481no—
515C22—21no—
516C22—21no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22D3×#21511yescharacteristic
524C22#6393911yescharacteristic
525C22#6398311yescharacteristic
526C4—21no—
527C4—21no—
528C4—42no—
529C4—62no—
530C4—122no—
531C4—121no—
532C4—121no—
533C4—361no—
534C3—21no—
535C3#6970611yescharacteristic, complemented
536C3#7097511yescharacteristic, complemented
537C2—21no—
538C2—21no—
539C2—241no—
540C2—721no—
541C2#1059165111yescharacteristic
542C2#1059166111yescharacteristic
543C2#1059172511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radical#10594911C2
hypercenterC22×Q8D32
hypocenterC32#1604
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. #10592926C2semidirect
3. C3×#5230C2semidirect
4. C3×#5227C2semidirect
5. #10589151C2semidirect
6. #10589149C2semidirect
7. #10589147C2semidirect
33. #5230D3semidirect
37. #5227D3semidirect
148. C2×C3×Dic3SD16semidirect
351. C2×Dic3#215semidirect
458. C32#1604semidirect
535. C3#69706semidirect
536. C3#70975semidirect

Maximal subgroups

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

subgroupindex
#105949112
#105929262
C3×#52302
C3×#52272
#105891512
#105891492
#105891472
#709753
#697063