Finite Group Databasebeta

← #11909843

Subgroups — #11909843

Order 1152.

2976 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic, complemented
2Q8×#638C211yesmaximal, characteristic, complemented
3Q8×#638C211yesmaximal, characteristic, complemented
4#10596283C211yesmaximal, characteristic, complemented
5C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10596202C213yesmaximal, complemented
7#10596192C213yesmaximal, complemented
8#10596113C213yesmaximal, complemented
9#10596112C213yesmaximal, complemented
10#10596096C213yesmaximal, complemented
11#10596093C213yesmaximal, complemented
12#10596043C211yesmaximal, characteristic, complemented
13#10596040C211yesmaximal, characteristic, complemented
14#10596012C213yesmaximal, complemented
15#10596009C213yesmaximal
16#86752—34nomaximal
17C22×C32×Q8C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C32×C4⋊Q8C2213yes—
21C32×C22⋊Q8C2213yes—
22C32×C22⋊Q8C2213yes—
23C32×C4×Q8C2211yescharacteristic
24C32×C4×D4C2213yes—
25#64155C2213yes—
26#64155C2213yes—
27Q8×C3⋊Dic3C2213yes—
28Q8×C3⋊Dic3C2213yes—
29Q8×C3⋊Dic3C2213yes—
30Q8×C3⋊Dic3C2213yes—
31Q8×C3⋊Dic3C2211yescharacteristic
32Q8×C3⋊Dic3C2211yescharacteristic
33Q8×C3⋊Dic3C2211yescharacteristic
34#64153C2213yes—
35#64153C2213yes—
36#64148C2211yescharacteristic
37#64144C2213yes—
38C4×#638C2213yes—
39C4×#638C2213yes—
40#64135C2213yes—
41#64135C2213yes—
42C2×C4⋊(C3⋊Dic3)C2213yes—
43#64133C2213yes—
44#64133C2213yes—
45C2×C4×C3⋊Dic3C2213yes—
46#64107C2216yes—
47#64107C2213yes—
48#64101C2213yes—
49#64099C2216yes—
50#64099C2213yes—
51#64098C2216yes—
52#64098C2213yes—
53#64098C2216yes—
54#64097C2213yes—
55#64096C2213yes—
56#64096C2216yes—
57#64095C2213yes—
58#64094C2213yes—
59#64088C2213yes—
60#64088C2216yes—
61#64087C2213yes—
62#64086C2216yes—
63#64081C2213yes—
64#64079C2213yes—
65C4×#634C2213yes—
66C4×#634C2213yes—
67C3×D4×Q8D314yescomplemented
68Q8×#67—34no—
69Q8×#67—34no—
70#5812—34no—
71C2×Q8×Dic3—34no—
72#5731—312no—
73#5721—312no—
74#5642—312no—
75#5641—312no—
76#5625—312no—
77#5622—312no—
78#5572—34no—
79#5569—34no—
80#5541—312no—
81#5538—312no—
82C2×C32×Q8—24no—
83C2×C32×Q8—24no—
84C2×C32×Q8C2313yes—
85C2×C32×Q8C2313yes—
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4C2311yescharacteristic
88C22×C32×C4C2313yes—
89C22×C32×C4C2313yes—
90C2×#638C2311yescharacteristic
91C2×#638C2311yescharacteristic
92C22×C3⋊Dic3C2313yes—
93C22×C3⋊Dic3C2311yescharacteristic
94Q8×C3⋊D3—24no—
95C2×C4×C3⋊D3C2313yes—
96C2×#634C2313yes—
97C2×#634C2313yes—
98C32×C4⋊C4C2313yes—
99C32×C4⋊C4C2316yes—
100C32×C4⋊C4C2313yes—
101C32×C22⋊C4C2313yes—
102C32×C22⋊C4C2313yes—
103C32×C42C2313yes—
104#3757C2313yes—
105#3757C2313yes—
106#3757C2311yescharacteristic
107#3757C2313yes—
108#3752C2311yescharacteristic
109#3752C2313yes—
110#3752C2313yes—
111#3752C2313yes—
112C4⋊(C3⋊Dic3)C2313yes—
113C4⋊(C3⋊Dic3)C2313yes—
114C4⋊(C3⋊Dic3)C2313yes—
115C4⋊(C3⋊Dic3)C2313yes—
116C4⋊(C3⋊Dic3)C2313yes—
117C4⋊(C3⋊Dic3)C2316yes—
118C4⋊(C3⋊Dic3)C2313yes—
119#3750C2311yescharacteristic
120#3750C2313yes—
121#3750C2313yes—
122#3750C2316yes—
123#3750C2313yes—
124#3750C2316yes—
125#3750C2313yes—
126#3750C2316yes—
127#3750C2313yes—
128C4×C3⋊Dic3C2316yes—
129C4×C3⋊Dic3C2313yes—
130C4×C3⋊Dic3C2313yes—
131C4×C3⋊Dic3C2313yes—
132C4×C3⋊Dic3C2316yes—
133C4×C3⋊Dic3C2313yes—
134C4×C3⋊Dic3C2313yes—
135#3523—91noSylow
136C22×C3×Q8C2×D314yes—
137C22×C3×Q8C2×D314yes—
138C2×D3×Q8—34no—
139C3×C4⋊Q8C2×D3112yes—
140C3×C22⋊Q8C2×D3112yes—
141C3×C22⋊Q8C2×D3112yes—
142C3×C4×Q8C2×D314yes—
143C3×C4×D4C2×D3112yes—
144#946—312no—
145#946—312no—
146Q8×Dic3—312no—
147Q8×Dic3—312no—
148Q8×Dic3—312no—
149Q8×Dic3—312no—
150Q8×Dic3—34no—
151Q8×Dic3—34no—
152Q8×Dic3—34no—
153#944—312no—
154#944—312no—
155#939—34no—
156#935—312no—
157C4×#67—312no—
158C4×#67—312no—
159#926—312no—
160#926—312no—
161C2×C4⋊Dic3—312no—
162#924—312no—
163#924—312no—
164C2×C4×Dic3—312no—
165#898—324no—
166#898—312no—
167#892—312no—
168#890—324no—
169#890—312no—
170#889—312no—
171#889—324no—
172#889—324no—
173#888—312no—
174#887—324no—
175#887—312no—
176#886—312no—
177#885—312no—
178#879—324no—
179#879—312no—
180#878—312no—
181#877—324no—
182#872—312no—
183#870—312no—
184C4×Dic6—312no—
185C4×Dic6—312no—
186C23×C32C2411yescharacteristic
187C23×C32C2411yescharacteristic
188C22×C3⋊D3C2411yescharacteristic
189C32×Q8—26no—
190C32×Q8—26no—
191C32×Q8#4114yes—
192C32×D4—22no—
193C2×C32×C4—26no—
194C2×C32×C4—26no—
195C2×C32×C4C2413yes—
196C2×C32×C4C2413yes—
197C2×C32×C4C2413yes—
198C2×C32×C4C2411yescharacteristic
199C2×C32×C4C2413yes—
200#638—22no—
201#638—22no—
202C2×C3⋊Dic3—26no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3C2411yescharacteristic
205C2×C3⋊Dic3C2413yes—
206C2×C3⋊Dic3C2413yes—
207C2×C3⋊Dic3C2411yescharacteristic
208C2×C3⋊Dic3C2413yes—
209C2×C3⋊Dic3C2413yes—
210C2×C3⋊Dic3C2411yescharacteristic
211C4×C3⋊D3—26no—
212#634—26no—
213#634—26no—
214#557—93no—
215#557—91no—
216#556—93no—
217#552—93no—
218#552—93no—
219D4×Q8—91no—
220D4×Q8—91no—
221D4×Q8C3⋊D311yescharacteristic, complemented
222#541—93no—
223#541—93no—
224#533—93no—
225#529—93no—
226#519—91no—
227#519—91no—
228C2×C4×Q8—91no—
229C2×C3×Q8—216no—
230C2×C3×Q8—216no—
231C2×C3×Q8C22×D3112yes—
232C2×C3×Q8C22×D3112yes—
233C2×C3×Q8C22×D314yes—
234C2×C3×D4C22×D314yes—
235C22×C3×C4C22×D3112yes—
236C22×C3×C4C22×D3112yes—
237C2×#67—34no—
238C2×#67—34no—
239C22×Dic3—312no—
240C22×Dic3—34no—
241D3×Q8—616no—
242C2×C4×D3—312no—
243C2×Dic6—312no—
244C2×Dic6—312no—
245C3×C4⋊C4C22×D3112yes—
246C3×C4⋊C4C22×D3124yes—
247C3×C4⋊C4C22×D3112yes—
248C3×C22⋊C4C22×D3112yes—
249C3×C22⋊C4C22×D3112yes—
250C3×C42C22×D3112yes—
251#217—312no—
252#217—312no—
253#217—34no—
254#217—312no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—312no—
257(C2×D3)⋊C4—312no—
258(C2×D3)⋊C4—312no—
259C4⋊Dic3—312no—
260C4⋊Dic3—312no—
261C4⋊Dic3—312no—
262C4⋊Dic3—312no—
263C4⋊Dic3—312no—
264C4⋊Dic3—324no—
265C4⋊Dic3—312no—
266Dic3⋊C4—34no—
267Dic3⋊C4—312no—
268Dic3⋊C4—312no—
269Dic3⋊C4—324no—
270Dic3⋊C4—312no—
271Dic3⋊C4—324no—
272Dic3⋊C4—312no—
273Dic3⋊C4—324no—
274Dic3⋊C4—312no—
275C4×Dic3—324no—
276C4×Dic3—312no—
277C4×Dic3—312no—
278C4×Dic3—312no—
279C4×Dic3—324no—
280C4×Dic3—312no—
281C4×Dic3—312no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C322−1+412yes—
288C22×C32C2511yescharacteristic
289C2×C3⋊D3—21no—
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C32×C4—23no—
293C32×C4—23no—
294C32×C4—23no—
295C32×C4—21no—
296C32×C4C2×#4116yes—
297C3⋊Dic3—23no—
298C3⋊Dic3—23no—
299C3⋊Dic3—23no—
300C3⋊Dic3—23no—
301C3⋊Dic3—21no—
302C3⋊Dic3—21no—
303C3⋊Dic32−1+412yes—
304C22×Q8—91no—
305C22×Q8C2×C3⋊D311yescharacteristic
306C22×Q8C2×C3⋊D311yescharacteristic
307C4⋊Q8—93no—
308C4⋊Q8—93no—
309C4⋊Q8—93no—
310C4⋊Q8C2×C3⋊D313yes—
311#126—93no—
312#126—96no—
313#126—93no—
314#126—96no—
315#125—93no—
316#125—96no—
317#125—96no—
318#125—96no—
319#125—93no—
320#125—93no—
321#124—93no—
322#123—93no—
323#123—93no—
324C22⋊Q8—93no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328C22⋊Q8—93no—
329C22⋊Q8C2×C3⋊D313yes—
330C22⋊Q8C2×C3⋊D313yes—
331#121—91no—
332C4×Q8—91no—
333C4×Q8—93no—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—93no—
337C4×Q8—91no—
338C4×Q8—93no—
339C4×Q8—93no—
340C4×Q8—96no—
341C4×Q8—93no—
342C4×Q8—93no—
343C4×Q8C2×C3⋊D311yescharacteristic
344C4×D4—93no—
345C4×D4—93no—
346C4×D4C2×C3⋊D313yes—
347#117—93no—
348#117—93no—
349#117—93no—
350#117—96no—
351#117—93no—
352C2×C4⋊C4—93no—
353C2×C42—93no—
354C23×C3C23×D314yes—
355C23×C3C23×D314yes—
356C22×D3—34no—
357C3×Q8—224no—
358C3×Q8—224no—
359C3×Q8#237116yes—
360C3×D4—28no—
361C2×C3×C4—224no—
362C2×C3×C4—224no—
363C2×C3×C4C23×D3112yes—
364C2×C3×C4C23×D3112yes—
365C2×C3×C4C23×D3112yes—
366C2×C3×C4C23×D314yes—
367C2×C3×C4C23×D3112yes—
368#67—68no—
369#67—68no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—312no—
373C2×Dic3—312no—
374C2×Dic3—34no—
375C2×Dic3—312no—
376C2×Dic3—312no—
377C2×Dic3—68no—
378C2×Dic3—624no—
379C4×D3—624no—
380Dic6—624no—
381Dic6—624no—
382C2×C32—22no—
383C2×C32—41no—
384C2×C32C22×#4111yescharacteristic
385C2×C32C2×2−1+411yescharacteristic
386C2×C32C2×2−1+411yescharacteristic
387C3⋊D3—41no—
388C2×Q8—24no—
389C2×Q8—24no—
390C2×Q8—93no—
391C2×Q8—93no—
392C2×Q8—184no—
393C2×Q8C22×C3⋊D313yes—
394C2×Q8C22×C3⋊D313yes—
395C2×Q8C22×C3⋊D311yescharacteristic
396C2×D4—91no—
397C2×D4—91no—
398C2×D4C22×C3⋊D311yescharacteristic
399C22×C4—91no—
400C22×C4—93no—
401C22×C4—93no—
402C22×C4C22×C3⋊D313yes—
403C22×C4C22×C3⋊D313yes—
404C4⋊C4—93no—
405C4⋊C4—93no—
406C4⋊C4—96no—
407C4⋊C4—93no—
408C4⋊C4—93no—
409C4⋊C4—93no—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—96no—
413C4⋊C4—96no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—91no—
417C4⋊C4—96no—
418C4⋊C4—93no—
419C4⋊C4—93no—
420C4⋊C4C22×C3⋊D313yes—
421C4⋊C4C22×C3⋊D313yes—
422C4⋊C4C22×C3⋊D316yes—
423C22⋊C4—91no—
424C22⋊C4—93no—
425C22⋊C4—93no—
426C22⋊C4—93no—
427C22⋊C4—91no—
428C22⋊C4—93no—
429C22⋊C4—93no—
430C22⋊C4—93no—
431C22⋊C4C22×C3⋊D313yes—
432C22⋊C4C22×C3⋊D313yes—
433C42—93no—
434C42—93no—
435C42—93no—
436C42—93no—
437C42—96no—
438C42—96no—
439C42—93no—
440C42C22×C3⋊D313yes—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3#100718yes—
447C22×C3C24×D314yes—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—64no—
451C3×C4—212no—
452C3×C4—212no—
453C3×C4—24no—
454C3×C4—212no—
455C3×C4C2×#237124yes—
456Dic3—38no—
457Dic3—612no—
458Dic3—612no—
459Dic3—612no—
460Dic3—64no—
461Dic3—612no—
462Dic3—64no—
463C32#352311yescharacteristic, complemented, Sylow
464C23—91no—
465C23C23×C3⋊D311yescharacteristic
466C23C23×C3⋊D311yescharacteristic
467Q8—26no—
468Q8—26no—
469Q8—186no—
470Q8—186no—
471Q8#383014yes—
472D4—22no—
473D4—182no—
474D4—182no—
475C2×C4—26no—
476C2×C4—26no—
477C2×C4—91no—
478C2×C4—93no—
479C2×C4—91no—
480C2×C4—93no—
481C2×C4—91no—
482C2×C4—93no—
483C2×C4—93no—
484C2×C4—182no—
485C2×C4—186no—
486C2×C4—186no—
487C2×C4C23×C3⋊D313yes—
488C2×C4C23×C3⋊D313yes—
489C2×C4C23×C3⋊D313yes—
490C2×C4C23×C3⋊D311yescharacteristic
491C2×C4C23×C3⋊D313yes—
492C2×C3—28no—
493C2×C3—44no—
494C2×C3C22×#23714yes—
495C2×C3C2×#100714yes—
496C2×C3D3×2−1+414yes—
497D3—124no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—181no—
504C22—181no—
505C22—181no—
506C22#6436412yes—
507C22C24×C3⋊D311yescharacteristic
508C4—23no—
509C4—23no—
510C4—21no—
511C4—23no—
512C4—92no—
513C4—183no—
514C4—183no—
515C4—183no—
516C4—181no—
517C4—181no—
518C4—183no—
519C4C2×#383016yes—
520C3#8675214yescomplemented
521C2—22no—
522C2—41no—
523C2—361no—
524C2C22×#383011yescharacteristic
525C2C2×#6436411yescharacteristic
526C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×D4×Q8C2
prime radical#64148C22
hypercenterD4×Q8C3⋊D3
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C32×D4×Q8C2semidirect
2. Q8×#638C2semidirect
3. Q8×#638C2semidirect
4. #10596283C2semidirect
5. C2×Q8×C3⋊Dic3C2semidirect
6. #10596202C2semidirect
7. #10596192C2semidirect
8. #10596113C2semidirect
9. #10596112C2semidirect
10. #10596096C2semidirect
11. #10596093C2semidirect
12. #10596043C2semidirect
13. #10596040C2semidirect
14. #10596012C2semidirect
67. C3×D4×Q8D3semidirect
221. D4×Q8C3⋊D3semidirect
463. C32#3523semidirect
520. C3#86752semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
Q8×#6382
#105962832
C2×Q8×C3⋊Dic32
#105962022
#105961922
#105961132
#105961122
#105960962
#105960932
#105960432
#105960402
#105960122
#105960092
#867523