Finite Group Databasebeta

← #11868973

Subgroups — #11868973

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic
2#10594508C211yesmaximal, characteristic, complemented
3#10592469C211yesmaximal, characteristic
4C3×#4766C211yesmaximal, characteristic, complemented
5C3×#4763C211yesmaximal, characteristic, complemented
6#10591416C211yesmaximal, characteristic
7#10591410C211yesmaximal, characteristic, complemented
8#10591408C211yesmaximal, characteristic, complemented
9#10590764C211yesmaximal, characteristic, complemented
10#10590759C211yesmaximal, characteristic, complemented
11#10590702C211yesmaximal, characteristic, complemented
12#10590688C211yesmaximal, characteristic, complemented
13#10590574C211yesmaximal, characteristic, complemented
14#10590470C211yesmaximal, characteristic, complemented
15#10590468C211yesmaximal, characteristic, complemented
16#81169—31nomaximal
17#81168—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20#64101C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×#890C2211yescharacteristic, complemented
24C3×#890C2211yescharacteristic, complemented
25#63974—21no—
26C2×#3722—21no—
27#63952—21no—
28#63952—21no—
29#63919—21no—
30#63918C2211yescharacteristic, complemented
31#63918C2211yescharacteristic, complemented
32#63900C2211yescharacteristic
33#63895—21no—
34#63895—21no—
35#63894C2211yescharacteristic
36#63894C2211yescharacteristic
37#63874C2211yescharacteristic
38#63870—21no—
39#63849C2211yescharacteristic
40C2×#3710C2211yescharacteristic
41C32×#102C2211yescharacteristic
42#63659C2211yescharacteristic
43#63648C2211yescharacteristic
44#63636C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×#817C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5689—31no—
62#5689—31no—
63#5545—31no—
64#5545—31no—
65C3×#478—31no—
66C3×#478—31no—
67#5066—31no—
68#5066—31no—
69#5008—31no—
70#5007—31no—
71#4891—31no—
72#4890—31no—
73#4881—31no—
74#4880—31no—
75#4871—31no—
76#4870—31no—
77#4861—31no—
78#4860—31no—
79#4846—31no—
80#4842—31no—
81#4839—31no—
82#4839—31no—
83#4770—31no—
84#4770—31no—
85#4770—61no—
86D3×#102—31no—
87D3×#102—31no—
88#4766D311yescharacteristic, complemented
89#4763D311yescharacteristic, complemented
90#4761—31no—
91#4759—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3Q814yescomplemented
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C2×#627—21no—
102C2×#627—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4×C3⋊Dic3—21no—
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112#3743—22no—
113C3×#217—21no—
114C3×#217—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724D411yescharacteristic
129#3724D411yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133#3722—21no—
134#3722—21no—
135#3722D411yescharacteristic
136#3722D411yescharacteristic
137Dic32—21no—
138#3710—22no—
139#3081—91noSylow
140C2×D3×D4—31no—
141C2×D3×D4—31no—
142C2×D3×D4—61no—
143C3×#125—31no—
144C3×#125—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147D4×Dic3C2×D311yescharacteristic
148D4×Dic3C2×D311yescharacteristic
149C4×#67—61no—
150C4×#67—61no—
151C2×(C2×D3)⋊C4—61no—
152C2×(C2×D3)⋊C4—61no—
153C2×ΓL(1,𝔽25)—31no—
154C2×ΓL(1,𝔽25)—31no—
155C2×ΓL(1,𝔽25)—61no—
156C2×D3×C8—31no—
157C2×D3×C8—31no—
158#897—61no—
159#897—61no—
160#896—61no—
161#896—61no—
162#893—31no—
163#893—31no—
164#892—31no—
165#892—31no—
166#892—31no—
167#892—31no—
168#892—61no—
169D3×C4⋊C4—31no—
170D3×C4⋊C4—31no—
171#890C2×D311yescharacteristic, complemented
172#890C2×D311yescharacteristic, complemented
173#889—61no—
174#889—61no—
175#888—31no—
176#888—31no—
177#888—61no—
178#888—61no—
179#67⋊C4—61no—
180#67⋊C4—61no—
181D3×C22⋊C4—61no—
182D3×C22⋊C4—61no—
183C4×D12—31no—
184C4×D12—31no—
185#872—31no—
186#872—31no—
187#869—31no—
188#869—31no—
189C3×#107—31no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#102—21no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102C2×D311yescharacteristic
199C3×#102C2×D311yescharacteristic
200#832—31no—
201#832—31no—
202#832—61no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#818—31no—
211#818C2×D311yescharacteristic, complemented
212#817—31no—
213#817C2×D311yescharacteristic, complemented
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic, complemented
217Dic3⋊C8C2×D311yescharacteristic, complemented
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808C2×D311yescharacteristic, complemented
227#807—31no—
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C23×C32—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—24no—
236C22×C3⋊D3—81no—
237C22×C3⋊D3—81no—
238C22×C3⋊D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4C2×Q812yes—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243#638—24no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)C2×Q812yes—
248C4×C3⋊D3C2×Q812yes—
249C4×C3⋊D3#4112yes—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260#627—81no—
261#627—81no—
262#624—81no—
263#624—81no—
264#624—81no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#544—91no—
270#518—91no—
271#478—31no—
272#478—31no—
273#478—91no—
274#478—91no—
275#476—91no—
276#476—91no—
277#474—91no—
278#474—91no—
279#428—91no—
280#427—91no—
281#424—91no—
282#418—91no—
283C2×#102—91no—
284C23×D3—61no—
285C23×D3—61no—
286C23×D3—121no—
287C2×C3×D4—21no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C22×D311yescharacteristic
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C2×#67—61no—
293C2×#67—61no—
294C2×#67—121no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297D3×D4—34no—
298D3×D4—34no—
299D3×D4—64no—
300D3×D4—62no—
301D3×D4—62no—
302D3×D4—122no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×Dic6—61no—
316C2×Dic6—61no—
317C2×Dic6—61no—
318C2×Dic6—61no—
319C2×C3×C8—21no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C22×D311yescharacteristic
324C3×C4⋊C4—21no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C22⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C42—31no—
338C3×C42—31no—
339#217—21no—
340#217—21no—
341(C2×D3)⋊C4—31no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—31no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—121no—
354C4⋊Dic3—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3C22×D311yescharacteristic
362C4⋊Dic3C22×D311yescharacteristic
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—31no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—121no—
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387ΓL(1,𝔽25)—62no—
388ΓL(1,𝔽25)—62no—
389ΓL(1,𝔽25)—122no—
390D3×C8—62no—
391D3×C8—62no—
392C22×C32—22no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32C22×D411yescharacteristic
396C2×C3⋊D3—21no—
397C2×C3⋊D3—21no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—84no—
402C2×C3⋊D3C22⋊Q812yes—
403C32×C4—41no—
404C32×C4C22×Q811yescharacteristic
405C32×C4C2×#4111yescharacteristic
406C3⋊Dic3—41no—
407C3⋊Dic3C22⋊Q812yes—
408C3×Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C22×D4—91no—
417C2×M16—91no—
418C22×C8—91no—
419C4⋊Q8—91no—
420C4⋊Q8—91no—
421C4⋊Q8—181no—
422#125—31no—
423#125—31no—
424#125—181no—
425C22⋊Q8—181no—
426C22⋊Q8—181no—
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—181no—
432C4×D4—181no—
433#117—91no—
434#117—91no—
435#117—91no—
436C2×C4⋊C4—91no—
437C2×C22⋊C4—181no—
438C2×C22⋊C4—181no—
439#107—31no—
440#107—31no—
441#107—91no—
442#107—91no—
443#106—31no—
444#106—31no—
445#106—91no—
446#106—91no—
447C4⋊C8—31no—
448C4⋊C8—31no—
449C4⋊C8—91no—
450C4⋊C8—91no—
451#102—31no—
452#102—31no—
453#102—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102D3211yescharacteristic
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—41no—
462C22×D3—31no—
463C22×D3—31no—
464C22×D3—61no—
465C22×D3—64no—
466C22×D3—64no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—124no—
470C22×D3—121no—
471C22×D3—241no—
472C22×D3—241no—
473C22×D3—241no—
474C22×D3—241no—
475C22×D3—242no—
476C22×D3—242no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—22no—
480C3×D4—41no—
481C3×D4D3×Q812yes—
482C3×D4D3×Q812yes—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—241no—
496C2×C3×C4—241no—
497C2×C3×C4C23×D311yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499#67—64no—
500#67—64no—
501#67—124no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—81no—
512C2×Dic3—81no—
513C2×Dic3—121no—
514C2×Dic3D3×D411yescharacteristic
515C2×Dic3D3×D411yescharacteristic
516C2×Dic3D3×D411yescharacteristic
517C2×Dic3D3×D411yescharacteristic
518D12—32no—
519D12—32no—
520D12—62no—
521D12—61no—
522D12—61no—
523D12—121no—
524C4×D3—32no—
525C4×D3—32no—
526C4×D3—32no—
527C4×D3—32no—
528C4×D3—62no—
529C4×D3—62no—
530C4×D3—241no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—241no—
535C4×D3—241no—
536Dic6—241no—
537Dic6—241no—
538Dic6—241no—
539Dic6—241no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—41no—
543C3×C8—61no—
544C3×C8—61no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—121no—
550C2×C32—42no—
551C2×C32C2×C22⋊Q811yescharacteristic
552C2×C32#57611yescharacteristic
553C2×C32#57711yescharacteristic
554C3⋊D3—22no—
555C3⋊D3—42no—
556C24—181no—
557C2×Q8—181no—
558C2×Q8—181no—
559C2×D4—94no—
560C2×D4—91no—
561C2×D4—182no—
562C2×D4—181no—
563C2×D4C2×D3211yescharacteristic
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—91no—
567C22×C4—181no—
568C22×C4—181no—
569C22×C4—181no—
570M16—182no—
571C2×C8—31no—
572C2×C8—31no—
573C2×C8—91no—
574C2×C8—182no—
575C2×C8C2×D3211yescharacteristic
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4C2×D3211yescharacteristic
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C42—31no—
600C42—31no—
601C42—181no—
602C42—181no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—21no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3C2×D3×D411yescharacteristic
614C22×C3C2×D3×D411yescharacteristic
615C2×D3—32no—
616C2×D3—32no—
617C2×D3—62no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—122no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—241no—
632C2×D3—241no—
633C2×D3—244no—
634C2×D3—244no—
635C2×D3—248no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4C2×D3×Q811yescharacteristic
650C3×C4C2×D3×Q811yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4D3×#4111yescharacteristic
653Dic3—21no—
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—32no—
658Dic3—32no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—62no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667C32#308111yescharacteristic, complemented, Sylow
668C23—21no—
669C23—91no—
670C23—184no—
671C23—181no—
672C23—721no—
673C23—721no—
674Q8—721no—
675Q8—721no—
676D4—21no—
677D4—92no—
678D4—184no—
679D4—181no—
680D4#379712yes—
681C2×C4—21no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—91no—
691C2×C4—92no—
692C2×C4—92no—
693C2×C4—181no—
694C2×C4—241no—
695C2×C4—241no—
696C2×C4—721no—
697C2×C4—721no—
698C2×C4—721no—
699C2×C4C22×D3211yescharacteristic
700C8—21no—
701C8—61no—
702C8—61no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3D3×C22⋊Q811yescharacteristic
711C2×C3D3×C22⋊Q811yescharacteristic
712C2×C3#576911yescharacteristic
713C2×C3#577011yescharacteristic
714C2×C3#577411yescharacteristic
715C2×C3#577511yescharacteristic
716D3—62no—
717D3—62no—
718D3—122no—
719D3—122no—
720D3—122no—
721D3—242no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—92no—
726C22—181no—
727C22—181no—
728C22—182no—
729C22—361no—
730C22—361no—
731C22—724no—
732C22D32×D411yescharacteristic
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—61no—
738C4—92no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—361no—
744C4C2×#379711yescharacteristic
745C4#6431211yescharacteristic
746C3—21no—
747C3#8116811yescharacteristic, complemented
748C3#8116911yescharacteristic, complemented
749C2—42no—
750C2—182no—
751C2—362no—
752C2#1059406711yescharacteristic
753C2#1059473611yescharacteristic
754C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#102D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594508C2semidirect
4. C3×#4766C2semidirect
5. C3×#4763C2semidirect
7. #10591410C2semidirect
8. #10591408C2semidirect
9. #10590764C2semidirect
10. #10590759C2semidirect
11. #10590702C2semidirect
12. #10590688C2semidirect
13. #10590574C2semidirect
14. #10590470C2semidirect
15. #10590468C2semidirect
23. C3×#890C22semidirect
24. C3×#890C22semidirect
30. #63918C22semidirect
31. #63918C22semidirect
47. C3×#818C22semidirect
48. C3×#817C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. #63573C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
88. #4766D3semidirect
89. #4763D3semidirect
96. D4×C3⋊D3Q8semidirect
171. #890C2×D3semidirect
172. #890C2×D3semidirect
211. #818C2×D3semidirect
213. #817C2×D3semidirect
216. Dic3⋊C8C2×D3semidirect
217. Dic3⋊C8C2×D3semidirect
226. #808C2×D3semidirect
230. #807C2×D3semidirect
667. C32#3081semidirect
747. C3#81168semidirect
748. C3#81169semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105945082
#105924692
C3×#47662
C3×#47632
#105914162
#105914102
#105914082
#105907642
#105907592
#105907022
#105906882
#105905742
#105904702
#105904682
#811693
#811683