Finite Group Databasebeta

← #11868732

Subgroups — #11868732

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3797C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3#10592536C211yesmaximal, characteristic
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4850C211yesmaximal, characteristic, complemented
6#10590821C212yesmaximal, complemented
7#10590820C212yesmaximal, complemented
8#10590691C212yesmaximal
9#10590688C212yesmaximal
10#10590310C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#81108—31nomaximal
13#81011—31nomaximal
14C2×#3797C2211yescharacteristic
15C2×#3743C2212yes—
16C42×C3⋊D3C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C4×#627—21no—
22#63900C2211yescharacteristic
23#63883—21no—
24C4×#624—21no—
25#63872C2212yes—
26#63871—21no—
27#63871—21no—
28#63849C2212yes—
29#63843—21no—
30#63843—21no—
31#63843C2211yescharacteristic
32#63843C2211yescharacteristic
33#63838—21no—
34C32×C4⋊C8C2211yescharacteristic
35#63641C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#818C2212yes—
38C3×#817C2212yes—
39C3×#816C2212yes—
40C3×#816C2212yes—
41#63576C2212yes—
42#63574C2212yes—
43#63565C2212yes—
44#63565C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×Q8—31no—
48C4×D3×Q8—31no—
49C3×#477—31no—
50C3×#475—31no—
51#5094—31no—
52#5091—31no—
53#5021—31no—
54#5020—31no—
55#4881—32no—
56#4877—32no—
57#4861—32no—
58#4857—32no—
59#4851D311yescharacteristic, complemented
60#4850D311yescharacteristic, complemented
61#4837—31no—
62#4837—31no—
63#4837—61no—
64#4802—32no—
65#4802—32no—
66#4799—32no—
67#4796—32no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×#624—21no—
77C2×#624—21no—
78#3797—22no—
79#3797Q814yescomplemented
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82C4×C3⋊Dic3D411yescharacteristic
83C4×C3⋊Dic3D411yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86#3743—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—21no—
97#3724—21no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102#3722—22no—
103Dic32—21no—
104Dic32—21no—
105Dic32—22no—
106#3078—91noSylow
107C2×D3×Q8—31no—
108C2×D3×Q8—31no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8—31no—
111C3×C4×Q8—31no—
112C3×C4×Q8—31no—
113#946—61no—
114#946—61no—
115Q8×Dic3—31no—
116Q8×Dic3—31no—
117Q8×Dic3—61no—
118Q8×Dic3—61no—
119C2×ΓL(1,𝔽25)—32no—
120C2×ΓL(1,𝔽25)—32no—
121C2×ΓL(1,𝔽25)—62no—
122#897—61no—
123#897—61no—
124#892—32no—
125#892—32no—
126D3×C4⋊C4—31no—
127D3×C4⋊C4—31no—
128D3×C4⋊C4—61no—
129D3×C4⋊C4—61no—
130#890—32no—
131#890—32no—
132#887—31no—
133#887—31no—
134#887—61no—
135#887—61no—
136#887—61no—
137#887—61no—
138C42×D3—31no—
139C42×D3—31no—
140C42×D3—61no—
141C42×D3—61no—
142C42×D3—61no—
143#869C2×D311yescharacteristic
144#869C2×D311yescharacteristic
145C4×Dic6—61no—
146C4×Dic6—61no—
147C4×Dic6C2×D311yescharacteristic
148C4×Dic6C2×D311yescharacteristic
149C3×#107—32no—
150C3×#106—32no—
151C3×C4⋊C8—21no—
152C3×C4⋊C8C2×D311yescharacteristic
153C3×C4⋊C8C2×D311yescharacteristic
154C3×#103—32no—
155C3×#103—32no—
156#835—32no—
157#835—32no—
158#818C2×D312yes—
159#817C2×D312yes—
160#816C2×D312yes—
161#816C2×D312yes—
162Dic3⋊C8—32no—
163Dic3⋊C8—32no—
164Dic3⋊C8—62no—
165#810—32no—
166#810—32no—
167#808—32no—
168#808—32no—
169#807—32no—
170#807—32no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—61no—
174C22×C3⋊D3C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3C2×D411yescharacteristic
179C2×C3⋊Dic3C2×D411yescharacteristic
180C2×C3⋊Dic3C2×D411yescharacteristic
181C4×C3⋊D3—22no—
182C4×C3⋊D3—41no—
183C4×C3⋊D3C2×Q812yes—
184C4×C3⋊D3#4112yes—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C3×Dic6—21no—
192C3×Dic6—21no—
193C3×Dic6—42no—
194C3×Dic6—42no—
195C3×Dic6C2×Q812yes—
196C3×Dic6C2×Q812yes—
197#627—24no—
198#624—24no—
199#624—42no—
200C32×C8—22no—
201C3⋊(C3⋊C8)—22no—
202#533—91no—
203C2×C4×Q8—91no—
204#479—92no—
205#479—92no—
206#477—31no—
207#477—91no—
208#475—31no—
209#475—91no—
210#428—92no—
211#423—91no—
212#419—92no—
213C2×C3×Q8—31no—
214C2×C3×Q8—31no—
215C2×C3×Q8—61no—
216C2×C3×Q8—61no—
217D3×Q8—34no—
218D3×Q8—34no—
219D3×Q8—62no—
220D3×Q8—62no—
221C2×C4×D3—31no—
222C2×C4×D3—31no—
223C2×C4×D3—31no—
224C2×C4×D3—31no—
225C2×C4×D3—31no—
226C2×C4×D3—31no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6C22×D311yescharacteristic
239C2×Dic6C22×D311yescharacteristic
240C2×C3×C8—22no—
241C2×C3×C8C22×D312yes—
242C2×C3×C8C22×D312yes—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C42—21no—
252C3×C42—61no—
253C3×C42—61no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3C22×D311yescharacteristic
265C4⋊Dic3C22×D312yes—
266C4⋊Dic3C22×D311yescharacteristic
267C4⋊Dic3C22×D312yes—
268Dic3⋊C4—21no—
269Dic3⋊C4—21no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—21no—
277C4×Dic3—21no—
278C4×Dic3—31no—
279C4×Dic3—31no—
280C4×Dic3—31no—
281C4×Dic3—31no—
282C4×Dic3—31no—
283C4×Dic3—31no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C2×C3⋊C8—32no—
294C2×C3⋊C8—32no—
295C2×C3⋊C8—62no—
296ΓL(1,𝔽25)—64no—
297ΓL(1,𝔽25)—64no—
298ΓL(1,𝔽25)—124no—
299C22×C32C22×D411yescharacteristic
300C2×C3⋊D3—21no—
301C2×C3⋊D3—21no—
302C2×C3⋊D3C22⋊Q812yes—
303C32×C4—21no—
304C32×C4#13712yes—
305C32×C4C22×Q811yescharacteristic
306C32×C4C2×#4111yescharacteristic
307C3⋊Dic3—21no—
308C3⋊Dic3—21no—
309C3⋊Dic3C22⋊Q812yes—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3—41no—
315C3×Dic3—42no—
316C22×Q8—91no—
317C2×M16—92no—
318C4⋊Q8—31no—
319C4⋊Q8—31no—
320#125—92no—
321C22⋊Q8—181no—
322C22⋊Q8—181no—
323C4×Q8—31no—
324C4×Q8—31no—
325C4×Q8—91no—
326C4×Q8—91no—
327C4×Q8—181no—
328C4×Q8—181no—
329C4×Q8—181no—
330C4×Q8—181no—
331#117—92no—
332C2×C4⋊C4—91no—
333C2×C4⋊C4—181no—
334C2×C42—91no—
335C2×C42—181no—
336#107—32no—
337#107—92no—
338#106—32no—
339#106—92no—
340C4⋊C8—92no—
341C4⋊C8—91no—
342C4⋊C8D3211yescharacteristic
343#103—32no—
344#103—32no—
345#103—92no—
346#103—92no—
347C22×D3—31no—
348C22×D3—31no—
349C22×D3—61no—
350C3×Q8—32no—
351C3×Q8—32no—
352C3×Q8—61no—
353C3×Q8—61no—
354C3×Q8—122no—
355C3×Q8—122no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—31no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C4×D3—32no—
387C4×D3—32no—
388C4×D3—32no—
389C4×D3—32no—
390C4×D3—62no—
391C4×D3—62no—
392C4×D3—64no—
393C4×D3—64no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—122no—
397C4×D3—122no—
398C4×D3—122no—
399C4×D3—121no—
400C4×D3—121no—
401C4×D3—122no—
402Dic6—21no—
403Dic6—21no—
404Dic6—42no—
405Dic6—42no—
406Dic6—64no—
407Dic6—64no—
408Dic6D3×Q812yes—
409Dic6D3×Q812yes—
410C3×C8—22no—
411C3×C8—22no—
412C3×C8—42no—
413C3⋊C8—62no—
414C3⋊C8—62no—
415C3⋊C8—122no—
416C2×C32C2×C22⋊Q811yescharacteristic
417C2×C32C2×#13711yescharacteristic
418C2×C32#57511yescharacteristic
419C3⋊D3—22no—
420C2×Q8—31no—
421C2×Q8—31no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—94no—
425C2×Q8—181no—
426C2×Q8—182no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—181no—
431C22×C4—181no—
432M16—184no—
433C2×C8—92no—
434C2×C8C2×D3212yes—
435C4⋊C4—32no—
436C4⋊C4—32no—
437C4⋊C4—31no—
438C4⋊C4—31no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—181no—
444C4⋊C4—181no—
445C4⋊C4—181no—
446C4⋊C4—182no—
447C4⋊C4—182no—
448C22⋊C4—182no—
449C42—61no—
450C42—61no—
451C42—91no—
452C42—91no—
453C42—91no—
454C42—181no—
455C42—181no—
456C42—182no—
457C42C2×D3211yescharacteristic
458C22×C3—21no—
459C22×C3C2×D3×D411yescharacteristic
460C22×C3C2×D3×D411yescharacteristic
461C2×D3—32no—
462C2×D3—32no—
463C2×D3—62no—
464C2×D3—61no—
465C2×D3—61no—
466C2×D3—61no—
467C2×D3—61no—
468C2×D3—121no—
469C2×D3—121no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—41no—
476C3×C4—62no—
477C3×C4—62no—
478C3×C4—122no—
479C3×C4—121no—
480C3×C4—121no—
481C3×C4—122no—
482C3×C4#91512yes—
483C3×C4#91812yes—
484C3×C4C2×D3×Q811yescharacteristic
485C3×C4C2×D3×Q811yescharacteristic
486C3×C4D3×#4111yescharacteristic
487C3×C4D3×#4111yescharacteristic
488Dic3—22no—
489Dic3—22no—
490Dic3—32no—
491Dic3—32no—
492Dic3—42no—
493Dic3—42no—
494Dic3—41no—
495Dic3—41no—
496Dic3—62no—
497Dic3—62no—
498Dic3—61no—
499Dic3—61no—
500Dic3—61no—
501Dic3—61no—
502Dic3—121no—
503C32#307811yescharacteristic, complemented, Sylow
504C23—91no—
505Q8—32no—
506Q8—32no—
507Q8—61no—
508Q8—61no—
509Q8—122no—
510Q8—122no—
511Q8—184no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—91no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—91no—
522C2×C4—91no—
523C2×C4—184no—
524C2×C4—182no—
525C2×C4—361no—
526C2×C4—362no—
527C2×C4#380211yescharacteristic
528C2×C4#380211yescharacteristic
529C2×C4C22×D3211yescharacteristic
530C8—22no—
531C8—182no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3D3×C22⋊Q811yescharacteristic
536C2×C3D3×C22⋊Q811yescharacteristic
537C2×C3C2×#91511yescharacteristic
538C2×C3C2×#91811yescharacteristic
539C2×C3#577311yescharacteristic
540C2×C3#577711yescharacteristic
541D3—62no—
542D3—62no—
543D3—122no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22C2×#380211yescharacteristic
548C4—21no—
549C4—62no—
550C4—62no—
551C4—92no—
552C4—122no—
553C4—121no—
554C4—121no—
555C4—122no—
556C4—181no—
557C4—181no—
558C4#6381112yes—
559C4#6431211yescharacteristic
560C4D32×Q811yescharacteristic
561C3—21no—
562C3#8101111yescharacteristic, complemented
563C3#8110811yescharacteristic, complemented
564C2—182no—
565C2#1059463111yescharacteristic
566C2C2×#6381111yescharacteristic
567C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
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
4. C3×#4851C2semidirect
5. C3×#4850C2semidirect
6. #10590821C2semidirect
7. #10590820C2semidirect
10. #10590310C2semidirect
11. #10590285C2semidirect
59. #4851D3semidirect
60. #4850D3semidirect
79. #3797Q8semidirect
503. C32#3078semidirect
562. C3#81011semidirect
563. C3#81108semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105938662
#105925362
C3×#48512
C3×#48502
#105908212
#105908202
#105906912
#105906882
#105903102
#105902852
#811083
#810113