Finite Group Databasebeta

← #11868740

Subgroups — #11868740

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3C3×#5021C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591615C212yesmaximal, complemented
6#10591562C212yesmaximal
7#10590583C212yesmaximal
8#10590434C212yesmaximal, complemented
9#10590340C211yesmaximal, characteristic
10#10590307C211yesmaximal, characteristic, complemented
11#10590284C211yesmaximal, characteristic, complemented
12#81108—31nomaximal
13#81011—31nomaximal
14C2×Q8×C3⋊D3C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16Q8×C3⋊Dic3C2211yescharacteristic
17C4⋊C4×C3⋊D3—21no—
18C4⋊C4×C3⋊D3C2211yescharacteristic
19#64096—21no—
20#64096C2211yescharacteristic
21C42×C3⋊D3—21no—
22C42×C3⋊D3C2211yescharacteristic
23C4×#634—21no—
24C4×#634C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27#63872C2212yes—
28#63871—21no—
29#63871—21no—
30#63849C2212yes—
31#63843—21no—
32#63843—21no—
33C2×#3712C2212yes—
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#808C2212yes—
37C3×#807C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63573C2212yes—
42#63572C2212yes—
43#63567C2212yes—
44#63567C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×Q8—31no—
48C4×D3×Q8—31no—
49C4×D3×Q8—61no—
50C3×#477—31no—
51C3×#475—31no—
52#5094—31no—
53#5091—31no—
54#5021D311yescharacteristic, complemented
55#5020D311yescharacteristic, complemented
56#4881—32no—
57#4877—32no—
58#4861—32no—
59#4857—32no—
60#4851—31no—
61#4850—31no—
62#4837—31no—
63#4837—31no—
64#4802—32no—
65#4802—32no—
66#4799—32no—
67#4796—32no—
68C2×C32×Q8C2311yescharacteristic
69Q8×C3⋊D3—22no—
70Q8×C3⋊D3Q814yescomplemented
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3D411yescharacteristic
75C2×C4×C3⋊D3C2311yescharacteristic
76C2×#634—21no—
77C2×#634C2311yescharacteristic
78C2×C3×Dic6—21no—
79C2×C3×Dic6—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87#3750—21no—
88#3750—21no—
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4⋊Dic3C2312yes—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—22no—
103#3722—22no—
104Dic32—22no—
105#3712—24no—
106#3078—91noSylow
107C2×D3×Q8—31no—
108C2×D3×Q8—31no—
109C2×D3×Q8—61no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—31no—
112C3×C4×Q8—21no—
113C3×C4×Q8C2×D311yescharacteristic
114C3×C4×Q8C2×D311yescharacteristic
115#946—61no—
116#946—61no—
117Q8×Dic3—31no—
118Q8×Dic3—31no—
119Q8×Dic3—61no—
120Q8×Dic3—61no—
121Q8×Dic3—61no—
122C2×ΓL(1,𝔽25)—32no—
123C2×ΓL(1,𝔽25)—32no—
124#897—61no—
125#897—61no—
126#892—32no—
127#892—32no—
128D3×C4⋊C4—31no—
129D3×C4⋊C4—31no—
130D3×C4⋊C4—61no—
131D3×C4⋊C4—61no—
132D3×C4⋊C4—61no—
133D3×C4⋊C4—62no—
134#890—32no—
135#890—32no—
136#887—31no—
137#887—31no—
138#887—61no—
139#887—61no—
140#887—61no—
141#887—61no—
142#887—61no—
143#887—62no—
144C42×D3—31no—
145C42×D3—31no—
146C42×D3—61no—
147C42×D3—61no—
148C42×D3—61no—
149C42×D3—62no—
150#869C2×D311yescharacteristic
151#869C2×D311yescharacteristic
152C4×Dic6—31no—
153C4×Dic6—31no—
154C4×Dic6—61no—
155C4×Dic6—61no—
156C4×Dic6—61no—
157C4×Dic6—62no—
158C3×#107—32no—
159C3×#106—32no—
160C3×C4⋊C8—31no—
161C3×C4⋊C8—31no—
162C3×#103—32no—
163C3×#103—32no—
164#835C2×D312yes—
165#835C2×D312yes—
166#818—32no—
167#817—32no—
168#816—32no—
169#816—32no—
170Dic3⋊C8—32no—
171Dic3⋊C8—32no—
172#810—32no—
173#810—32no—
174#808—32no—
175#808C2×D312yes—
176#807—32no—
177#807C2×D312yes—
178C4⋊(C3⋊C8)C2×D311yescharacteristic
179C4⋊(C3⋊C8)C2×D311yescharacteristic
180C22×C3⋊D3C2×D411yescharacteristic
181C32×Q8—21no—
182C32×Q8C2×Q812yes—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4×C3⋊D3—24no—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—41no—
196C4×C3⋊D3—42no—
197C4×C3⋊D3C2×Q812yes—
198C4×C3⋊D3#4112yes—
199#634—21no—
200#634—24no—
201#634C2×Q812yes—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C3×Dic6—42no—
205C3×Dic6—42no—
206C3×C3⋊C8—22no—
207C3×C3⋊C8—22no—
208#533—91no—
209C2×C4×Q8—91no—
210#479—92no—
211#479—92no—
212#477—31no—
213#477—91no—
214#475—31no—
215#475—91no—
216#428—92no—
217#423—91no—
218#419—92no—
219C2×C3×Q8—21no—
220C2×C3×Q8—61no—
221C2×C3×Q8—61no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224D3×Q8—34no—
225D3×Q8—34no—
226D3×Q8—64no—
227D3×Q8—62no—
228D3×Q8—62no—
229D3×Q8—64no—
230C2×C4×D3—31no—
231C2×C4×D3—31no—
232C2×C4×D3—31no—
233C2×C4×D3—31no—
234C2×C4×D3—31no—
235C2×C4×D3—31no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—62no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—62no—
245C2×Dic6—21no—
246C2×Dic6—21no—
247C2×Dic6—31no—
248C2×Dic6—31no—
249C2×Dic6—61no—
250C2×Dic6—61no—
251C2×Dic6—61no—
252C2×Dic6—62no—
253C2×C3×C8—32no—
254C2×C3×C8—32no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C42—22no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42C22×D311yescharacteristic
270C3×C42C22×D311yescharacteristic
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—61no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—62no—
283C4⋊Dic3C22×D312yes—
284C4⋊Dic3C22×D312yes—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294Dic3⋊C4—61no—
295Dic3⋊C4—61no—
296C4×Dic3—31no—
297C4×Dic3—31no—
298C4×Dic3—31no—
299C4×Dic3—31no—
300C4×Dic3—31no—
301C4×Dic3—31no—
302C4×Dic3—61no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3—61no—
308C4×Dic3—61no—
309C4×Dic3—61no—
310C4×Dic3—61no—
311C4×Dic3—62no—
312C4×Dic3—62no—
313C4×Dic3—62no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316C2×C3⋊C8C22×D312yes—
317C2×C3⋊C8C22×D312yes—
318ΓL(1,𝔽25)—64no—
319ΓL(1,𝔽25)—64no—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—21no—
322C2×C3⋊D3—21no—
323C2×C3⋊D3C22⋊Q812yes—
324C32×C4—22no—
325C32×C4—21no—
326C32×C4—41no—
327C32×C4#13712yes—
328C32×C4C22×Q811yescharacteristic
329C32×C4C2×#4111yescharacteristic
330C3⋊Dic3—22no—
331C3⋊Dic3—21no—
332C3⋊Dic3—21no—
333C3⋊Dic3—41no—
334C3⋊Dic3C22⋊Q812yes—
335C3×Dic3—42no—
336C3×Dic3—42no—
337C22×Q8—91no—
338C2×M16—92no—
339C4⋊Q8—31no—
340C4⋊Q8—31no—
341#125—92no—
342C22⋊Q8—181no—
343C22⋊Q8—181no—
344C4×Q8—91no—
345C4×Q8—91no—
346C4×Q8—91no—
347C4×Q8—181no—
348C4×Q8—181no—
349C4×Q8—181no—
350C4×Q8—181no—
351C4×Q8D3211yescharacteristic
352#117—92no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—181no—
355C2×C42—91no—
356C2×C42—181no—
357#107—32no—
358#107—92no—
359#106—32no—
360#106—92no—
361C4⋊C8—31no—
362C4⋊C8—31no—
363C4⋊C8—92no—
364#103—32no—
365#103—32no—
366#103—92no—
367#103—92no—
368C22×D3—31no—
369C22×D3—31no—
370C22×D3—61no—
371C3×Q8—22no—
372C3×Q8—21no—
373C3×Q8—21no—
374C3×Q8—22no—
375C3×Q8—122no—
376C3×Q8—122no—
377C3×Q8D3×Q812yes—
378C3×Q8D3×Q812yes—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—31no—
403C2×Dic3—31no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—62no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C4×D3—32no—
414C4×D3—32no—
415C4×D3—32no—
416C4×D3—32no—
417C4×D3—62no—
418C4×D3—62no—
419C4×D3—64no—
420C4×D3—64no—
421C4×D3—64no—
422C4×D3—68no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—121no—
426C4×D3—121no—
427C4×D3—122no—
428C4×D3—124no—
429C4×D3—122no—
430C4×D3—122no—
431Dic6—32no—
432Dic6—32no—
433Dic6—42no—
434Dic6—42no—
435Dic6—62no—
436Dic6—64no—
437Dic6—64no—
438Dic6—68no—
439Dic6—62no—
440Dic6—61no—
441Dic6—61no—
442C3×C8—62no—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—22no—
446C2×C32C2×C22⋊Q811yescharacteristic
447C2×C32C2×#13711yescharacteristic
448C2×C32#57511yescharacteristic
449C3⋊D3—22no—
450C2×Q8—61no—
451C2×Q8—61no—
452C2×Q8—94no—
453C2×Q8—91no—
454C2×Q8—181no—
455C2×Q8—182no—
456C2×Q8C2×D3211yescharacteristic
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—181no—
461C22×C4—181no—
462M16—184no—
463C2×C8—32no—
464C2×C8—32no—
465C4⋊C4—21no—
466C4⋊C4—32no—
467C4⋊C4—32no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C4⋊C4—91no—
471C4⋊C4—181no—
472C4⋊C4—181no—
473C4⋊C4—181no—
474C4⋊C4—182no—
475C4⋊C4—182no—
476C4⋊C4—181no—
477C4⋊C4C2×D3211yescharacteristic
478C22⋊C4—182no—
479C42—21no—
480C42—91no—
481C42—91no—
482C42—91no—
483C42—181no—
484C42—181no—
485C42—182no—
486C42—181no—
487C42C2×D3211yescharacteristic
488C22×C3—21no—
489C22×C3C2×D3×D411yescharacteristic
490C22×C3C2×D3×D411yescharacteristic
491C2×D3—32no—
492C2×D3—32no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—61no—
497C2×D3—61no—
498C2×D3—61no—
499C2×D3—61no—
500C3×C4—24no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—41no—
509C3×C4—42no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—122no—
513C3×C4—122no—
514C3×C4#91512yes—
515C3×C4#91812yes—
516C3×C4C2×D3×Q811yescharacteristic
517C3×C4C2×D3×Q811yescharacteristic
518C3×C4D3×#4111yescharacteristic
519C3×C4D3×#4111yescharacteristic
520Dic3—32no—
521Dic3—32no—
522Dic3—42no—
523Dic3—42no—
524Dic3—62no—
525Dic3—64no—
526Dic3—62no—
527Dic3—61no—
528Dic3—61no—
529Dic3—61no—
530Dic3—61no—
531Dic3—62no—
532Dic3—62no—
533Dic3—121no—
534Dic3—122no—
535Dic3—121no—
536Dic3—121no—
537C32#307811yescharacteristic, complemented, Sylow
538C23—91no—
539Q8—21no—
540Q8—92no—
541Q8—122no—
542Q8—122no—
543Q8—184no—
544Q8—181no—
545Q8#379712yes—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—91no—
551C2×C4—92no—
552C2×C4—92no—
553C2×C4—91no—
554C2×C4—91no—
555C2×C4—184no—
556C2×C4—181no—
557C2×C4—182no—
558C2×C4—181no—
559C2×C4—361no—
560C2×C4—362no—
561C2×C4#381111yescharacteristic
562C2×C4#381111yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—62no—
565C8—62no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3D3×C22⋊Q811yescharacteristic
570C2×C3D3×C22⋊Q811yescharacteristic
571C2×C3C2×#91511yescharacteristic
572C2×C3C2×#91811yescharacteristic
573C2×C3#577311yescharacteristic
574C2×C3#577711yescharacteristic
575D3—64no—
576D3—62no—
577D3—62no—
578C22—92no—
579C22—181no—
580C22—181no—
581C22C2×#381111yescharacteristic
582C4—22no—
583C4—21no—
584C4—41no—
585C4—92no—
586C4—122no—
587C4—122no—
588C4—181no—
589C4—182no—
590C4—181no—
591C4—361no—
592C4#6395112yes—
593C4C2×#379711yescharacteristic
594C4#6430611yescharacteristic
595C3—21no—
596C3#8101111yescharacteristic, complemented
597C3#8110811yescharacteristic, complemented
598C2—182no—
599C2#1059492511yescharacteristic
600C2C2×#6395111yescharacteristic
601C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3078
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
3. C3×#5021C2semidirect
4. C3×#5020C2semidirect
5. #10591615C2semidirect
8. #10590434C2semidirect
10. #10590307C2semidirect
11. #10590284C2semidirect
54. #5021D3semidirect
55. #5020D3semidirect
70. Q8×C3⋊D3Q8semidirect
537. C32#3078semidirect
596. C3#81011semidirect
597. C3#81108semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105938662
C3×#50212
C3×#50202
#105916152
#105915622
#105905832
#105904342
#105903402
#105903072
#105902842
#811083
#810113