Finite Group Databasebeta

← #11895159

Subgroups — #11895159

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5721C211yesmaximal, characteristic, complemented
2#10593903C211yesmaximal, characteristic
3#10592782C211yesmaximal, characteristic
4C3×#5079C211yesmaximal, characteristic, complemented
5#10591623C212yesmaximal, complemented
6#10591565C212yesmaximal
7#10591544C212yesmaximal, complemented
8#10591536C212yesmaximal
9C4×#3717C211yesmaximal, characteristic
10#10590285C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83688—31nomaximal
13#81620—31nomaximal
14C2×#3797—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C2×#3755C2212yes—
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×Q8×Dic3C2212yes—
19C3×#944C2212yes—
20C3×#890—21no—
21C3×#889—22no—
22C3×#887—21no—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2212yes—
27#63895—22no—
28#63894C2212yes—
29#63871—21no—
30C2×#3717C2211yescharacteristic
31#63662C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×C4×C3⋊C8C2211yescharacteristic
36#63574C2212yes—
37#63573C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63566C2211yescharacteristic
40#63565C2212yes—
41#63564C2211yescharacteristic
42Dic3×C3⋊C8C2212yes—
43C3×#557—31no—
44#5727—31no—
45#5721D311yescharacteristic, complemented
46Q8×D12—31no—
47C3×#487—31no—
48#5094—31no—
49#5083—31no—
50#5083—31no—
51#5083—32no—
52#5083—61no—
53#5079—32no—
54#5079D311yescharacteristic, complemented
55C4×#215—32no—
56C4×#215—31no—
57Q8×C3⋊C8—31no—
58#5020—31no—
59#5020—32no—
60#4818—32no—
61#4792—32no—
62#4791—32no—
63#4788—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8C2312yes—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×#624—22no—
74#3797—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4—21no—
77C32×C42C2311yescharacteristic
78#3755—24no—
79#3752—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×C4⋊Dic3C2312yes—
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96Dic3⋊Dic3—22no—
97#3722—22no—
98#3717—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—32no—
104C3×C4⋊Q8—31no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C2×D311yescharacteristic
107C3×#125—62no—
108C3×#125—61no—
109C3×C4×Q8—31no—
110C3×C4×Q8—32no—
111C3×C4×Q8—31no—
112C3×C4×Q8—61no—
113#946—61no—
114Q8×Dic3C2×D312yes—
115#944C2×D312yes—
116C2×#215—32no—
117C2×#215—32no—
118C2×#215—31no—
119C2×#215—62no—
120C2×#204—31no—
121#897—62no—
122#897—61no—
123#896—62no—
124#893—32no—
125#890—21no—
126#889—22no—
127#888—32no—
128#887—21no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133#869—32no—
134#869C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#103—32no—
138C3×#103—32no—
139C3×C4×C8—31no—
140#835—32no—
141#835—32no—
142#835—32no—
143#835—31no—
144#835—62no—
145#835C2×D312yes—
146#835C2×D312yes—
147#821—31no—
148#817—31no—
149#816—31no—
150Dic3⋊C8—32no—
151C8×Dic3—32no—
152#810—32no—
153#809—31no—
154#808—32no—
155#808—32no—
156#808—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C32×Q8—22no—
165C32×Q8—22no—
166C2×C32×C4—22no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)#4112yes—
173C4×C3⋊D3—42no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—42no—
182C3×Dic6SD1614yescomplemented
183#627—44no—
184#624—44no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—31no—
189D4×Q8—91no—
190#487—31no—
191#487—92no—
192#475—92no—
193#475—91no—
194#461—92no—
195#461—91no—
196C8×Q8—91no—
197C4×SD16—91no—
198C4×SD16—92no—
199C2×C3×Q8—22no—
200C2×C3×Q8—31no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8C22×D312yes—
204C2×C3×Q8C22×D312yes—
205D3×Q8—124no—
206D3×Q8—124no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—61no—
210C2×C4×D3—62no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—62no—
214C2×C4×D3—121no—
215C2×Dic6—21no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6#6711yescharacteristic
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—41no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42—62no—
240C3×C42—61no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#215—62no—
244#215—64no—
245#215—64no—
246#215—124no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—121no—
252C4⋊Dic3—21no—
253C4⋊Dic3—22no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—61no—
257C4⋊Dic3—62no—
258C4⋊Dic3#6711yescharacteristic
259C4⋊Dic3C22×D311yescharacteristic
260C4⋊Dic3C22×D312yes—
261Dic3⋊C4—21no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—21no—
267C4×Dic3—22no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—62no—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274#204—62no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4—42no—
281C32×C4C2×SD1612yes—
282C32×C4C2×#4111yescharacteristic
283C32×C42−1+411yescharacteristic
284C3⋊Dic3—41no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3C2×SD1614yes—
290C22×Q8—181no—
291C2×SD16—91no—
292C2×SD16—92no—
293C4⋊Q8—32no—
294C4⋊Q8—31no—
295C4⋊Q8—92no—
296C4⋊Q8D3211yescharacteristic
297#125—62no—
298#125—61no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C4×Q8—31no—
302C4×Q8—32no—
303C4×Q8—31no—
304C4×Q8—61no—
305C4×D4—92no—
306C4×D4—91no—
307#106—92no—
308#106—91no—
309C4⋊C8—92no—
310C4⋊C8—91no—
311#103—32no—
312#103—32no—
313#103—92no—
314#103—91no—
315#103—92no—
316#102—91no—
317C4×C8—31no—
318C4×C8—92no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—34no—
327C3×Q8—42no—
328C3×Q8—42no—
329C3×Q8—61no—
330C3×Q8—61no—
331C3×Q8—122no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—21no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—121no—
355C2×Dic3C2×#6712yes—
356C2×Dic3C2×#6712yes—
357D12—32no—
358D12—32no—
359D12—62no—
360D12—61no—
361D12—61no—
362D12—121no—
363C4×D3—124no—
364C4×D3—122no—
365C4×D3—122no—
366C4×D3—124no—
367C4×D3—242no—
368Dic6—21no—
369Dic6—21no—
370Dic6—42no—
371Dic6—124no—
372Dic6—124no—
373Dic6#21514yescomplemented
374C3×C8—61no—
375C3×C8—61no—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—122no—
381C2×C32#54811yescharacteristic
382C2×C32C22×SD1611yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—42no—
385C2×Q8—31no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8—182no—
389C2×Q8—364no—
390C2×Q8C2×D3212yes—
391C2×D4—91no—
392C22×C4—182no—
393C22×C4—181no—
394SD16—182no—
395SD16—184no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—92no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—32no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—62no—
407C4⋊C4—62no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—91no—
411C4⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—32no—
415C42—62no—
416C42—61no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C22×#6711yescharacteristic
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—122no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—241no—
429C2×D3—241no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—34no—
436C3×C4—41no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—62no—
440C3×C4—82no—
441C3×C4—121no—
442C3×C4—121no—
443C3×C4—122no—
444C3×C4D3×SD1612yes—
445C3×C4C2×#21512yes—
446C3×C4D3×#4111yescharacteristic
447C3×C4D3×#4111yescharacteristic
448C3×C4#101011yescharacteristic
449C3×C4#101011yescharacteristic
450Dic3—22no—
451Dic3—42no—
452Dic3—41no—
453Dic3—41no—
454Dic3—121no—
455Dic3—121no—
456Dic3—241no—
457Dic3C2×#21514yes—
458C32#335911yescharacteristic, complemented, Sylow
459C23—181no—
460Q8—22no—
461Q8—22no—
462Q8—34no—
463Q8—61no—
464Q8—61no—
465Q8—122no—
466Q8—364no—
467D4—92no—
468D4—181no—
469C2×C4—22no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—181no—
476C2×C4—364no—
477C2×C4—362no—
478C2×C4D3×#6711yescharacteristic
479C2×C4D3×#6711yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—61no—
482C8—61no—
483C8—182no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3#567711yescharacteristic
488C2×C3C2×D3×SD1611yescharacteristic
489C2×C3#576611yescharacteristic
490C2×C3C22×#21511yescharacteristic
491C2×C3#583111yescharacteristic
492C2×C3#583811yescharacteristic
493D3—122no—
494D3—122no—
495D3—242no—
496C22—182no—
497C22—361no—
498C22—361no—
499C22C2×D3×#6711yescharacteristic
500C4—21no—
501C4—34no—
502C4—42no—
503C4—62no—
504C4—121no—
505C4—122no—
506C4—121no—
507C4—361no—
508C4D3×#21512yes—
509C4#6430911yescharacteristic
510C4#6431211yescharacteristic
511C3—21no—
512C3#8162011yescharacteristic, complemented
513C3#8368811yescharacteristic, complemented
514C2—362no—
515C2#1059523711yescharacteristic
516C2C2×D3×#21511yescharacteristic
517C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4⋊Q8D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5721C2semidirect
4. C3×#5079C2semidirect
5. #10591623C2semidirect
7. #10591544C2semidirect
10. #10590285C2semidirect
11. C3⋊C8×Dic6C2semidirect
45. #5721D3semidirect
54. #5079D3semidirect
182. C3×Dic6SD16semidirect
373. Dic6#215semidirect
458. C32#3359semidirect
512. C3#81620semidirect
513. C3#83688semidirect

Maximal subgroups

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

subgroupindex
C3×#57212
#105939032
#105927822
C3×#50792
#105916232
#105915652
#105915442
#105915362
C4×#37172
#105902852
C3⋊C8×Dic62
#836883
#816203