Finite Group Databasebeta

← #11868733

Subgroups — #11868733

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×Dic6C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592549C211yesmaximal, characteristic, complemented
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4837C211yesmaximal, characteristic
6#10590948C212yesmaximal
7#10590811C212yesmaximal, complemented
8#10590809C212yesmaximal, complemented
9#10590681C212yesmaximal
10#10590307C211yesmaximal, characteristic, complemented
11#10590283C211yesmaximal, characteristic, complemented
12#81011—31nomaximal
13#79068—31nomaximal
14C2×D3×Dic6C2211yescharacteristic
15#64078C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2212yes—
18C3×C42×D3C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C4×#627—21no—
22D3×C4⋊Dic3C2211yescharacteristic
23D3×Dic3⋊C4—21no—
24C4×D3×Dic3—21no—
25#63869C2212yes—
26#63857—21no—
27#63856—21no—
28#63844—21no—
29#63844C2211yescharacteristic
30Dic3×Dic6—21no—
31Dic3×Dic6C2211yescharacteristic
32#63841C2212yes—
33#63837—21no—
34C32×C4⋊C8C2211yescharacteristic
35#63645C2212yes—
36#63643C2212yes—
37C3×#817C2212yes—
38C3×#816C2212yes—
39C3×Dic3⋊C8C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63575C2212yes—
42#63573C2212yes—
43#63567C2212yes—
44#63566C2212yes—
45#5728—31no—
46C4×D3×Q8—31no—
47#5470—31no—
48C2×C4×Dic6—31no—
49C3×#475—31no—
50C3×#423—31no—
51#5121—32no—
52#5120—32no—
53#5094—31no—
54#5021—31no—
55#4861—32no—
56#4857—32no—
57#4851—31no—
58#4851D311yescharacteristic, complemented
59#4850—31no—
60#4850—31no—
61#4850—31no—
62#4850—61no—
63#4837D311yescharacteristic
64#4829—32no—
65#4829—32no—
66#4802—32no—
67#4796—32no—
68C2×#634—21no—
69C2×#634C2311yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—21no—
78D3×Dic6—22no—
79D3×Dic6Q814yescomplemented
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3D411yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C3×ΓL(1,𝔽25)—24no—
97#3724—22no—
98#3724—21no—
99Dic3⋊Dic3—21no—
100Dic3⋊Dic3—22no—
101Dic3⋊Dic3—21no—
102(C2×D3)⋊Dic3—22no—
103Dic32—21no—
104Dic32—21no—
105Dic32—22no—
106#3078—91noSylow
107C2×D3×Q8—31no—
108C22×Dic6—31no—
109C2×C3×M16—32no—
110C3×C4⋊Q8—31no—
111C3×C4×Q8—31no—
112C2×C3×C42—31no—
113#946—61no—
114Q8×Dic3—31no—
115Q8×Dic3—61no—
116#926—32no—
117C2×C4⋊Dic3—31no—
118#924—61no—
119#924—61no—
120C2×Dic3⋊C4—61no—
121C2×C4×Dic3—61no—
122C2×ΓL(1,𝔽25)C2×D312yes—
123#897—61no—
124#892—32no—
125D3×C4⋊C4—31no—
126D3×C4⋊C4—61no—
127#890—32no—
128#887—31no—
129#887—61no—
130#887—61no—
131C42×D3—61no—
132C42×D3C2×D311yescharacteristic
133#870—32no—
134#869—31no—
135#869—31no—
136#869—61no—
137#869C2×D311yescharacteristic
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—31no—
142C4×Dic6—61no—
143C4×Dic6—61no—
144C4×Dic6—61no—
145C4×Dic6—61no—
146C4×Dic6—61no—
147C4×Dic6—61no—
148C4×Dic6C2×D311yescharacteristic
149C3×#106—32no—
150C3×C4⋊C8—21no—
151C3×C4⋊C8—32no—
152C3×C4⋊C8—31no—
153C3×C4⋊C8C2×D311yescharacteristic
154C3×C4⋊C8C2×D311yescharacteristic
155C3×#103—32no—
156#835—32no—
157#818—32no—
158#818—32no—
159#818—32no—
160#818—62no—
161#817—32no—
162#817C2×D312yes—
163#816—32no—
164#816—32no—
165#816—32no—
166#816—32no—
167#816—62no—
168#816C2×D312yes—
169Dic3⋊C8C2×D312yes—
170#810—32no—
171#808—32no—
172#807—32no—
173C4⋊(C3⋊C8)C2×D311yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—21no—
181#634—21no—
182#634—42no—
183#634C2×Q812yes—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C3×C4×D3—22no—
191C3×C4×D3—41no—
192C3×C4×D3C2×Q812yes—
193C3×C4×D3#4112yes—
194C3×Dic6—21no—
195C3×Dic6—42no—
196C3×Dic6C2×Q812yes—
197#627—24no—
198D3×Dic3—24no—
199D3×Dic3—42no—
200C32×C8—22no—
201C3×C3⋊C8—22no—
202#533—91no—
203C2×C4×Q8—91no—
204#479—92no—
205#479—92no—
206#477—91no—
207#477—91no—
208#475—31no—
209#475—91no—
210#428—92no—
211#423—31no—
212#419—92no—
213C2×C3×Q8—31no—
214C2×C3×Q8—61no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220D3×Q8—34no—
221D3×Q8—62no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3D1211yescharacteristic
225C2×C4×D3D1211yescharacteristic
226C2×C4×D3C22×D311yescharacteristic
227C2×Dic6—21no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—34no—
231C2×Dic6—61no—
232C2×Dic6—62no—
233C2×Dic6—61no—
234C2×Dic6—61no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6C22×D311yescharacteristic
239C3×M16—64no—
240C2×C3×C8—22no—
241C2×C3×C8—32no—
242C2×C3×C8C22×D312yes—
243C2×C3×C8C22×D312yes—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—61no—
248C3×C42—21no—
249C3×C42—31no—
250C3×C42—31no—
251C3×C42—31no—
252C3×C42—61no—
253C3×C42C22×D311yescharacteristic
254C3×C42C22×D311yescharacteristic
255#217—62no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—21no—
258C4⋊Dic3—32no—
259C4⋊Dic3—31no—
260C4⋊Dic3—32no—
261C4⋊Dic3—31no—
262C4⋊Dic3—62no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3—121no—
270C4⋊Dic3C22×D312yes—
271C4⋊Dic3C22×D311yescharacteristic
272Dic3⋊C4—21no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280Dic3⋊C4—61no—
281Dic3⋊C4—62no—
282Dic3⋊C4—121no—
283C4×Dic3—21no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—62no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—62no—
292C4×Dic3—121no—
293C4×Dic3D1211yescharacteristic
294C4×Dic3D1211yescharacteristic
295C4×Dic3C22×D311yescharacteristic
296C2×C3⋊C8C22×D312yes—
297ΓL(1,𝔽25)—24no—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—21no—
300C2×C3×D3—21no—
301C2×C3×D3C22⋊Q812yes—
302C32×C4—21no—
303C32×C4#13712yes—
304C32×C4C22×Q811yescharacteristic
305C32×C4C2×#4111yescharacteristic
306C3⋊Dic3—22no—
307C3⋊Dic3—41no—
308C3⋊Dic3—42no—
309C3×Dic3—22no—
310C3×Dic3—21no—
311C3×Dic3—21no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3C22⋊Q812yes—
315C22×Q8—91no—
316C2×M16—32no—
317C4⋊Q8—31no—
318C4⋊Q8—91no—
319#125—92no—
320C22⋊Q8—181no—
321C22⋊Q8—181no—
322C4×Q8—31no—
323C4×Q8—91no—
324C4×Q8—91no—
325C4×Q8—91no—
326C4×Q8—181no—
327C4×Q8—181no—
328C4×Q8—181no—
329C4×Q8—181no—
330#117—92no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—181no—
333C2×C42—31no—
334C2×C42—181no—
335#107—92no—
336#107—92no—
337#106—32no—
338#106—92no—
339C4⋊C8—32no—
340C4⋊C8—31no—
341C4⋊C8D3211yescharacteristic
342#103—32no—
343#103—92no—
344#103—92no—
345#103—92no—
346C23×C3—31no—
347C22×D3C2×D1211yescharacteristic
348C3×Q8—32no—
349C3×Q8—61no—
350C3×Q8—122no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—31no—
355C2×C3×C4—32no—
356C2×C3×C4—32no—
357C2×C3×C4—31no—
358C2×C3×C4—31no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4—62no—
363C2×C3×C4—121no—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—64no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3C2×D1211yescharacteristic
385C2×Dic3C2×D1211yescharacteristic
386C2×Dic3C2×D1211yescharacteristic
387C4×D3—22no—
388C4×D3—41no—
389C4×D3—64no—
390C4×D3—122no—
391C4×D3#23712yes—
392C4×D3D3×Q812yes—
393Dic6—21no—
394Dic6—32no—
395Dic6—32no—
396Dic6—42no—
397Dic6—62no—
398Dic6—64no—
399Dic6—61no—
400Dic6—61no—
401Dic6—64no—
402Dic6—121no—
403Dic6—122no—
404Dic6—122no—
405Dic6—242no—
406Dic6D3×Q812yes—
407C3×C8—22no—
408C3×C8—22no—
409C3×C8—42no—
410C3×C8—62no—
411C3⋊C8—22no—
412C2×C32C2×C22⋊Q811yescharacteristic
413C2×C32C2×#13711yescharacteristic
414C2×C32#57511yescharacteristic
415C3×D3—22no—
416C2×Q8—31no—
417C2×Q8—61no—
418C2×Q8—94no—
419C2×Q8—91no—
420C2×Q8—181no—
421C2×Q8—182no—
422C2×Q8—181no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—181no—
427C22×C4—181no—
428M16—64no—
429C2×C8—32no—
430C2×C8C2×D3212yes—
431C4⋊C4—32no—
432C4⋊C4—31no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—92no—
436C4⋊C4—91no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—182no—
441C4⋊C4—182no—
442C4⋊C4—181no—
443C4⋊C4—181no—
444C22⋊C4—182no—
445C42—31no—
446C42—31no—
447C42—31no—
448C42—61no—
449C42—181no—
450C42—181no—
451C42—182no—
452C42—181no—
453C42C2×D3211yescharacteristic
454C22×C3—21no—
455C22×C3—32no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3C22×D1211yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C2×D3—21no—
461C2×D3—21no—
462C2×D3#89712yes—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—22no—
467C3×C4—21no—
468C3×C4—32no—
469C3×C4—41no—
470C3×C4—61no—
471C3×C4—62no—
472C3×C4—61no—
473C3×C4—122no—
474C3×C4—121no—
475C3×C4#90912yes—
476C3×C4#91512yes—
477C3×C4C2×#23711yescharacteristic
478C3×C4C2×D3×Q811yescharacteristic
479C3×C4C2×D3×Q811yescharacteristic
480C3×C4D3×#4111yescharacteristic
481Dic3—21no—
482Dic3—21no—
483Dic3—22no—
484Dic3—42no—
485Dic3—41no—
486Dic3—62no—
487Dic3—62no—
488Dic3—122no—
489Dic3—122no—
490Dic3—121no—
491Dic3—122no—
492Dic3—121no—
493Dic3—242no—
494Dic3—241no—
495Dic3#89712yes—
496C32#307811yescharacteristic, complemented, Sylow
497C23—31no—
498Q8—32no—
499Q8—61no—
500Q8—92no—
501Q8—122no—
502Q8—184no—
503Q8—181no—
504Q8—362no—
505C2×C4—31no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—31no—
509C2×C4—31no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—61no—
513C2×C4—62no—
514C2×C4—121no—
515C2×C4—184no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—182no—
519C2×C4—362no—
520C2×C4D3×D1211yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4C22×D3211yescharacteristic
523C8—22no—
524C8—62no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—62no—
529C2×C3C2×#89711yescharacteristic
530C2×C3D3×C22⋊Q811yescharacteristic
531C2×C3C2×#90911yescharacteristic
532C2×C3#574811yescharacteristic
533C2×C3C2×#91511yescharacteristic
534C2×C3#577711yescharacteristic
535D3—22no—
536C22—32no—
537C22—61no—
538C22—61no—
539C22C2×D3×D1211yescharacteristic
540C4—21no—
541C4—32no—
542C4—62no—
543C4—61no—
544C4—61no—
545C4—122no—
546C4—121no—
547C4—182no—
548C4—361no—
549C4—362no—
550C4#6380012yes—
551C4D3×#23711yescharacteristic
552C4D32×Q811yescharacteristic
553C3—21no—
554C3#7906811yescharacteristic, complemented
555C3#8101111yescharacteristic, complemented
556C2—62no—
557C2D3×#89711yescharacteristic
558C2C2×#6380011yescharacteristic
559C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #10592549C2semidirect
4. C3×#4851C2semidirect
7. #10590811C2semidirect
8. #10590809C2semidirect
10. #10590307C2semidirect
11. #10590283C2semidirect
58. #4851D3semidirect
79. D3×Dic6Q8semidirect
496. C32#3078semidirect
554. C3#79068semidirect
555. C3#81011semidirect

Maximal subgroups

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

subgroupindex
C4×D3×Dic62
#105938592
#105925492
C3×#48512
C3×#48372
#105909482
#105908112
#105908092
#105906812
#105903072
#105902832
#810113
#790683