Finite Group Databasebeta

← #11886545

Subgroups — #11886545

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic, complemented
2C2×#63808C211yesmaximal, characteristic, complemented
3#10594524C212yesmaximal, complemented
4#10592582C211yesmaximal, characteristic, complemented
5C3×#4883C211yesmaximal, characteristic, complemented
6C3×#4873C211yesmaximal, characteristic, complemented
7#10590880C211yesmaximal, characteristic, complemented
8C8×#626C211yesmaximal, characteristic, complemented
9#10590617C212yesmaximal, complemented
10#10590615C212yesmaximal, complemented
11#10590549C212yesmaximal, complemented
12#80735—31nomaximal
13#79734—31nomaximal
14C2×#3799C2212yes—
15C2×#3796C2212yes—
16C2×#3745C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18#64104C2212yes—
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C3×#895C2212yes—
23C3×#887C2212yes—
24#63911—22no—
25#63911C2212yes—
26#63910—22no—
27C4×#626C2211yescharacteristic
28#63886—22no—
29#63880—22no—
30C2×#3717C2212yes—
31C2×#3715C2212yes—
32C2×#3714C2212yes—
33#63810—24no—
34#63808—24no—
35C32×#107C2211yescharacteristic
36#63636C2212yes—
37C3×C8×Dic3C2211yescharacteristic
38C3×#810C2212yes—
39C3×#809C2212yes—
40Dic3⋊(C3⋊C8)C2211yescharacteristic
41#63557C2211yescharacteristic
42(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
43C2×#919—31no—
44C2×#919—31no—
45C2×#912—31no—
46C2×#904—31no—
47#5599—32no—
48#5577—32no—
49C3×#466—31no—
50C3×C4×Q16—31no—
51#5151—31no—
52C8×#67—31no—
53#5037—32no—
54#5027—32no—
55#4883—31no—
56#4883—31no—
57#4883—61no—
58#4883D311yescharacteristic, complemented
59#4873D311yescharacteristic, complemented
60#4810—32no—
61#4810—32no—
62#4781—32no—
63#4762—32no—
64#4695—31no—
65C8×D12—31no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C3×D12—22no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×#626—22no—
74C2×#626—22no—
75C2×#626—22no—
76C2×#626—22no—
77C2×#626D411yescharacteristic
78C2×#624—22no—
79C2×D3×Dic3—22no—
80#3799—24no—
81#3799—42no—
82#3796—24no—
83#3796—42no—
84C2×C32×C8C2311yescharacteristic
85C32×C4⋊C4C2312yes—
86#3752—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3745—22no—
89C8×C3⋊D3—22no—
90C3×(C2×D3)⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C3×Dic12D414yescomplemented
97C3×D24—22no—
98C3×D3×C8—22no—
99Dic3⋊Dic3D411yescharacteristic
100#3722D411yescharacteristic
101(C2×D3)⋊Dic3D411yescharacteristic
102#3717—24no—
103#3715—24no—
104#3714—42no—
105#3287—91noSylow
106C2×#239—32no—
107C2×#239—32no—
108C2×#237—32no—
109C2×#235—32no—
110C2×C3×Q16—31no—
111C2×C3×D8—31no—
112C22×C3×C8—31no—
113C3×#121—32no—
114C3×C4×Q8—32no—
115C2×#215—32no—
116C2×#215—32no—
117#940—32no—
118#940—62no—
119#939—62no—
120C2×#214—32no—
121C2×#213—32no—
122C4×#67—31no—
123#919—64no—
124#919—64no—
125#912—64no—
126C2×Dic12C2×D311yescharacteristic
127#904—64no—
128C2×D24—31no—
129C2×D24—31no—
130C2×D24—32no—
131C2×D24—61no—
132C2×D24C2×D311yescharacteristic
133C2×#204—32no—
134C2×D3×C8—31no—
135C2×D3×C8—31no—
136C2×D3×C8—61no—
137C2×D3×C8C2×D311yescharacteristic
138#895—32no—
139#895—32no—
140#895—62no—
141#895—62no—
142#895—62no—
143#895C2×D312yes—
144#887C2×D312yes—
145#884—62no—
146#67⋊C4—62no—
147#874—32no—
148#874—62no—
149C4×D12—31no—
150C4×D12—62no—
151C3×#107—21no—
152C3×#107C2×D311yescharacteristic
153C3×#107C2×D311yescharacteristic
154C3×#103—32no—
155C3×#102—32no—
156C3×C4×C8—31no—
157#830—31no—
158(C2×D3)⋊C8—31no—
159(C2×D3)⋊C8—31no—
160(C2×D3)⋊C8—31no—
161Dic3⋊C8—31no—
162C8×Dic3C2×D311yescharacteristic
163#810C2×D312yes—
164#809—32no—
165#809—32no—
166#809—62no—
167#809C2×D312yes—
168C4⋊(C3⋊C8)—31no—
169C22×C3⋊D3—22no—
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3C2×D411yescharacteristic
173C2×C32×C4—22no—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3C2×D411yescharacteristic
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—82no—
179C4×C3⋊D3—21no—
180C4×C3⋊D3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3C2×D411yescharacteristic
183C2×C3×Dic3C2×D411yescharacteristic
184C2×C3×Dic3C2×D411yescharacteristic
185C3×D12—22no—
186C3×D12—22no—
187C3×D12—82no—
188C3×C4×D3—21no—
189C3×C4×D3—21no—
190C3×Dic6—22no—
191C3×Dic6C2×D414yes—
192#626—22no—
193#626—44no—
194#626—44no—
195#626—44no—
196#626—82no—
197#624—44no—
198D3×Dic3—44no—
199C32×C8C2×D412yes—
200C3⋊(C3⋊C8)—21no—
201C3×C3⋊C8—21no—
202C3×C3⋊C8—21no—
203C2×#135—91no—
204C2×#135—91no—
205#550—92no—
206#493—91no—
207#466—31no—
208#466—91no—
209#460—92no—
210#449—92no—
211#449—92no—
212C4×Q16—31no—
213C8×D4—91no—
214C2×C3×Q8—32no—
215C2×C3×D4—32no—
216C2×C3×D4—62no—
217C22×C3×C4—31no—
218C2×#67—31no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—62no—
223C22×Dic3—62no—
224#239—64no—
225#239—64no—
226#239—122no—
227#239—122no—
228#237—64no—
229#237—122no—
230#235—64no—
231#235—122no—
232C2×D12—22no—
233C2×D12—31no—
234C2×D12—32no—
235C2×D12—32no—
236C2×D12—62no—
237C2×D12—62no—
238C2×D12—62no—
239C2×D12—62no—
240C2×D12—62no—
241C2×D12—62no—
242C2×D12—62no—
243C2×D12—122no—
244C2×D12C22×D312yes—
245C2×C4×D3—31no—
246C2×C4×D3—31no—
247C2×C4×D3—61no—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3C22×D311yescharacteristic
252C2×Dic6C22×D312yes—
253C3×Q16—34no—
254C3×D8—62no—
255C2×C3×C8—21no—
256C2×C3×C8—31no—
257C2×C3×C8—31no—
258C2×C3×C8—62no—
259C2×C3×C8C22×D311yescharacteristic
260C2×C3×C8C22×D311yescharacteristic
261C3×C4⋊C4—22no—
262C3×C4⋊C4—62no—
263C3×C4⋊C4C22×D312yes—
264C3×C4⋊C4C22×D312yes—
265C3×C22⋊C4—62no—
266C3×C42—31no—
267C3×C42—62no—
268#217—31no—
269#215—64no—
270#215—64no—
271#214—64no—
272#213—122no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—31no—
275(C2×D3)⋊C4—31no—
276(C2×D3)⋊C4—31no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—122no—
280C4⋊Dic3—31no—
281Dic3⋊C4—22no—
282Dic3⋊C4—31no—
283C4×Dic3—22no—
284C4×Dic3C22×D311yescharacteristic
285C2×C3⋊C8—31no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8C22×D311yescharacteristic
289C2×C3⋊C8C22×D311yescharacteristic
290Dic12D1214yescomplemented
291D24—22no—
292D24—62no—
293D24—62no—
294D24—122no—
295D24—122no—
296#204—64no—
297D3×C8—22no—
298D3×C8—62no—
299D3×C8—62no—
300D3×C8—122no—
301C22×C32C22×D411yescharacteristic
302C2×C3⋊D3—21no—
303C2×C3⋊D3—21no—
304C2×C3⋊D3—21no—
305C2×C3⋊D3—42no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C32×C4—42no—
315C32×C4C22×D411yescharacteristic
316C32×C4H(5,𝔽2)11yescharacteristic
317C3⋊Dic3—21no—
318C3×Dic3—24no—
319C3×Dic3—21no—
320C3×Dic3—21no—
321C3×Dic3#13512yescomplemented
322C2×#41—92no—
323C2×#41—92no—
324#135—184no—
325#135—184no—
326C2×Q16—31no—
327C2×SD16—92no—
328C2×SD16—92no—
329C2×D8—31no—
330C2×D8—92no—
331C2×D8—91no—
332C22×C8—31no—
333C22×C8—91no—
334#127—92no—
335#127—182no—
336#121—32no—
337#121—92no—
338#121—182no—
339#121—182no—
340C4×Q8—32no—
341C4×D4—91no—
342C4×D4—182no—
343#107D3211yescharacteristic
344C4⋊C8—91no—
345#103—32no—
346#102—32no—
347#102—92no—
348C22⋊C8—91no—
349C22⋊C8—91no—
350C4×C8—31no—
351C23×C3—31no—
352C23×C3—62no—
353C22×D3—22no—
354C22×D3—31no—
355C22×D3—31no—
356C22×D3—61no—
357C22×D3—62no—
358C22×D3—62no—
359C22×D3—122no—
360C22×D3D3×D411yescharacteristic
361C3×Q8—34no—
362C3×Q8—62no—
363C3×D4—62no—
364C3×D4—62no—
365C3×D4—242no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—31no—
370C2×C3×C4—31no—
371C2×C3×C4—31no—
372C2×C3×C4—42no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—62no—
379#67—124no—
380#67—124no—
381#67—124no—
382#67—242no—
383C2×Dic3—22no—
384C2×Dic3—31no—
385C2×Dic3—31no—
386C2×Dic3—61no—
387C2×Dic3—124no—
388C2×Dic3D3×D411yescharacteristic
389C2×Dic3D3×D411yescharacteristic
390C2×Dic3D3×D411yescharacteristic
391D12—22no—
392D12—22no—
393D12—62no—
394D12—62no—
395D12—62no—
396D12—62no—
397D12—62no—
398D12—82no—
399D12—122no—
400D12—122no—
401D12—124no—
402D12—124no—
403D12—124no—
404D12—242no—
405D12—242no—
406D12—242no—
407D12—244no—
408C4×D3—21no—
409C4×D3—21no—
410C4×D3—61no—
411C4×D3—61no—
412C4×D3—61no—
413C4×D3—61no—
414C4×D3—121no—
415C4×D3—121no—
416C4×D3—124no—
417C4×D3—124no—
418C4×D3—124no—
419Dic6—22no—
420Dic6C2×D1214yes—
421C3×C8—22no—
422C3×C8—61no—
423C3×C8—61no—
424C3×C8C2×D1212yes—
425C3×C8D3×D412yes—
426C3⋊C8—21no—
427C3⋊C8—21no—
428C3⋊C8—61no—
429C3⋊C8—61no—
430C3⋊C8—121no—
431C2×C32D4211yescharacteristic
432C2×C32C2×#13511yescharacteristic
433C2×C32#57611yescharacteristic
434C3⋊D3—41no—
435C3⋊D3—82no—
436C3×D3—41no—
437C3×D3—82no—
438#41—184no—
439#41—184no—
440#41—362no—
441#41—362no—
442C2×Q8—32no—
443C2×D4—32no—
444C2×D4—62no—
445C2×D4—91no—
446C2×D4—92no—
447C2×D4—182no—
448C2×D4—182no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4—182no—
452C22×C4—31no—
453C22×C4—91no—
454C22×C4—182no—
455C22×C4—182no—
456Q16—34no—
457SD16—184no—
458SD16—184no—
459D8—62no—
460D8—182no—
461D8—362no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—62no—
465C2×C8—91no—
466C2×C8—182no—
467C2×C8C2×D3211yescharacteristic
468C4⋊C4—62no—
469C4⋊C4—91no—
470C4⋊C4C2×D3212yes—
471C22⋊C4—62no—
472C22⋊C4—91no—
473C22⋊C4—91no—
474C22⋊C4—182no—
475C42—31no—
476C42—62no—
477C22×C3—21no—
478C22×C3—61no—
479C22×C3—61no—
480C22×C3—61no—
481C22×C3—122no—
482C22×C3—122no—
483C22×C3—122no—
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C2×D3—21no—
487C2×D3—21no—
488C2×D3—21no—
489C2×D3—42no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—62no—
493C2×D3—61no—
494C2×D3—61no—
495C2×D3—61no—
496C2×D3—61no—
497C2×D3—61no—
498C2×D3—61no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—242no—
508C2×D3—242no—
509C2×D3—242no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—32no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—64no—
518C3×C4—82no—
519C3×C4C22×D1211yescharacteristic
520C3×C4C2×D3×D411yescharacteristic
521C3×C4#100911yescharacteristic
522C3×C4#100911yescharacteristic
523Dic3—21no—
524Dic3—24no—
525Dic3—21no—
526Dic3—61no—
527Dic3—61no—
528Dic3—121no—
529Dic3#91912yescomplemented
530C32#328711yescharacteristic, complemented, Sylow
531C23—31no—
532C23—62no—
533C23—91no—
534C23—182no—
535Q8—34no—
536Q8—62no—
537D4—62no—
538D4—62no—
539D4—182no—
540D4—182no—
541D4—182no—
542D4—242no—
543D4—364no—
544D4—364no—
545D4—364no—
546D4—722no—
547D4—722no—
548C2×C4—22no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—91no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—364no—
559C2×C4—364no—
560C2×C4C22×D3211yescharacteristic
561C8—61no—
562C8—61no—
563C8—181no—
564C8D3×D1212yes—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—121no—
569C2×C3—242no—
570C2×C3D4×D1211yescharacteristic
571C2×C3#560911yescharacteristic
572C2×C3#575711yescharacteristic
573C2×C3C2×#91911yescharacteristic
574C2×C3D3×#13511yescharacteristic
575C2×C3#576911yescharacteristic
576D3—41no—
577D3—82no—
578D3—122no—
579D3—121no—
580D3—121no—
581D3—242no—
582D3—242no—
583D3—482no—
584C22—61no—
585C22—61no—
586C22—61no—
587C22—122no—
588C22—122no—
589C22—122no—
590C22—181no—
591C22—181no—
592C22—181no—
593C22—362no—
594C22—362no—
595C22—362no—
596C22D32×D411yescharacteristic
597C4—32no—
598C4—42no—
599C4—61no—
600C4—64no—
601C4—61no—
602C4—181no—
603C4C2×D3×D1211yescharacteristic
604C4#6432011yescharacteristic
605C3—21no—
606C3#7973411yescharacteristic, complemented
607C3#8073511yescharacteristic, complemented
608C2—121no—
609C2—242no—
610C2—361no—
611C2—722no—
612C2#1059462111yescharacteristic
613C2#1059473411yescharacteristic
614C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3287
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#63810C2semidirect
2. C2×#63808C2semidirect
3. #10594524C2semidirect
4. #10592582C2semidirect
5. C3×#4883C2semidirect
6. C3×#4873C2semidirect
7. #10590880C2semidirect
8. C8×#626C2semidirect
9. #10590617C2semidirect
10. #10590615C2semidirect
11. #10590549C2semidirect
58. #4883D3semidirect
59. #4873D3semidirect
96. C3×Dic12D4semidirect
290. Dic12D12semidirect
321. C3×Dic3#135semidirect
529. Dic3#919semidirect
530. C32#3287semidirect
606. C3#79734semidirect
607. C3#80735semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
C2×#638082
#105945242
#105925822
C3×#48832
C3×#48732
#105908802
C8×#6262
#105906172
#105906152
#105905492
#807353
#797343