Finite Group Databasebeta

← #11868967

Subgroups — #11868967

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595223C211yesmaximal, characteristic
2#10594325C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic
4C3×#4763C211yesmaximal, characteristic, complemented
5C3×#4761C211yesmaximal, characteristic, complemented
6#10591426C211yesmaximal, characteristic
7#10591410C211yesmaximal, characteristic, complemented
8#10591409C211yesmaximal, characteristic, complemented
9#10590769C211yesmaximal, characteristic, complemented
10#10590759C211yesmaximal, characteristic, complemented
11#10590712C211yesmaximal, characteristic, complemented
12#10590701C211yesmaximal, characteristic, complemented
13#10590583C211yesmaximal, characteristic, complemented
14#10590470C211yesmaximal, characteristic, complemented
15#10590464C211yesmaximal, characteristic, complemented
16#81168—31nomaximal
17#81062—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20C4⋊C4×C3⋊D3C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×#890C2211yescharacteristic, complemented
24C3×#888C2211yescharacteristic, complemented
25#63974—21no—
26C2×#3722—21no—
27#63952—21no—
28#63952—21no—
29#63918C2211yescharacteristic, complemented
30#63894C2211yescharacteristic
31#63894C2211yescharacteristic
32#63874C2211yescharacteristic
33#63871—21no—
34#63869C2211yescharacteristic, complemented
35#63865—21no—
36#63849C2211yescharacteristic
37#63849C2211yescharacteristic
38#63847—21no—
39#63839—21no—
40C2×#3712C2211yescharacteristic
41C32×#102C2211yescharacteristic
42#63659C2211yescharacteristic
43#63648C2211yescharacteristic
44#63636C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#817C2211yescharacteristic, complemented
48C3×#817C2211yescharacteristic, complemented
49C3×Dic3⋊C8C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5729—31no—
62#5689—31no—
63#5545—31no—
64#5545—31no—
65C3×#478—31no—
66C3×#476—31no—
67#5087—31no—
68#5066—31no—
69#5009—31no—
70#5007—31no—
71#4890—31no—
72#4881—31no—
73#4871—31no—
74#4871—31no—
75#4870—31no—
76#4861—31no—
77#4860—31no—
78#4860—31no—
79#4847—31no—
80#4842—31no—
81#4839—31no—
82#4839—31no—
83#4770—31no—
84#4770—31no—
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—61no—
88#4763—31no—
89#4763D311yescharacteristic, complemented
90#4761D311yescharacteristic, complemented
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⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C2×C3×Dic6—21no—
103C2×#627—21no—
104C2×#624—21no—
105C2×#624—21no—
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C8×C3⋊D3—22no—
112C3×#217—21no—
113C3×#217—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724D411yescharacteristic
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130#3722—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722D411yescharacteristic
135#3722D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138#3712—22no—
139#3081—91noSylow
140C2×D3×D4—31no—
141C2×D3×D4—31no—
142C2×D3×D4—61no—
143C3×C4⋊Q8—31no—
144C3×#125—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147#946—61no—
148#944—61no—
149D4×Dic3C2×D311yescharacteristic
150D4×Dic3C2×D311yescharacteristic
151C4×#67—61no—
152C4×#67—61no—
153C2×(C2×D3)⋊C4—61no—
154C2×(C2×D3)⋊C4—61no—
155C2×ΓL(1,𝔽25)—31no—
156C2×ΓL(1,𝔽25)—31no—
157C2×D3×C8—31no—
158C2×D3×C8—31no—
159C2×D3×C8—61no—
160#897—61no—
161#896—61no—
162#896—61no—
163#893—31no—
164#893—31no—
165#892—31no—
166#892—31no—
167#892—31no—
168#892—31no—
169D3×C4⋊C4—31no—
170D3×C4⋊C4—31no—
171D3×C4⋊C4—61no—
172#890—31no—
173#890C2×D311yescharacteristic, complemented
174#889—61no—
175#889—61no—
176#888—31no—
177#888—61no—
178#888C2×D311yescharacteristic, complemented
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#870—31no—
188#869—31no—
189C3×#107—31no—
190C3×#106—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#817—31no—
212#817C2×D311yescharacteristic, complemented
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#808C2×D311yescharacteristic, complemented
225#807—31no—
226#807—31no—
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⋊D3—81no—
249C4×C3⋊D3C2×Q812yes—
250C4×C3⋊D3#4112yes—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—81no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×Dic6—81no—
262#627—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—91no—
273#478—91no—
274#478—91no—
275#476—31no—
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×Q8—61no—
288C2×C3×D4—21no—
289C2×C3×D4C22×D311yescharacteristic
290C2×C3×D4C22×D311yescharacteristic
291C22×C3×C4—61no—
292C22×C3×C4—61no—
293C2×#67—61no—
294C2×#67—61no—
295C2×#67—121no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298D3×D4—34no—
299D3×D4—34no—
300D3×D4—64no—
301D3×D4—62no—
302D3×D4—62no—
303D3×D4—122no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—61no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
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×C4×D3—61no—
316C2×C4×D3—121no—
317C2×Dic6—21no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×C3×C8—21no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
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—
353C4⋊Dic3—21no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3C22×D311yescharacteristic
360C4⋊Dic3C22×D311yescharacteristic
361C4⋊Dic3C22×D311yescharacteristic
362C4⋊Dic3C22×D311yescharacteristic
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—121no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
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—
389D3×C8—62no—
390D3×C8—62no—
391D3×C8—122no—
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—31no—
420C4⋊Q8—91no—
421C4⋊Q8—181no—
422#125—31no—
423#125—91no—
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—91no—
441#107—91no—
442#107—91no—
443#106—31no—
444#106—31no—
445#106—31no—
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×Q8—241no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—22no—
481C3×D4—41no—
482C3×D4D3×Q812yes—
483C3×D4D3×Q812yes—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—241no—
497C2×C3×C4—241no—
498C2×C3×C4C23×D311yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500#67—64no—
501#67—64no—
502#67—124no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—81no—
513C2×Dic3—81no—
514C2×Dic3—121no—
515C2×Dic3D3×D411yescharacteristic
516C2×Dic3D3×D411yescharacteristic
517C2×Dic3D3×D411yescharacteristic
518C2×Dic3D3×D411yescharacteristic
519D12—32no—
520D12—32no—
521D12—62no—
522D12—61no—
523D12—61no—
524D12—121no—
525C4×D3—32no—
526C4×D3—32no—
527C4×D3—32no—
528C4×D3—32no—
529C4×D3—62no—
530C4×D3—62no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—241no—
537C4×D3—242no—
538Dic6—81no—
539Dic6—241no—
540Dic6—241no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—41no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—121no—
551C2×C32—42no—
552C2×C32C2×C22⋊Q811yescharacteristic
553C2×C32#57611yescharacteristic
554C2×C32#57711yescharacteristic
555C3⋊D3—22no—
556C3⋊D3—42no—
557C24—181no—
558C2×Q8—61no—
559C2×Q8—181no—
560C2×D4—94no—
561C2×D4—91no—
562C2×D4—182no—
563C2×D4—181no—
564C2×D4C2×D3211yescharacteristic
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—91no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571M16—182no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—91no—
575C2×C8—182no—
576C2×C8C2×D3211yescharacteristic
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
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⋊C4—181no—
591C4⋊C4C2×D3211yescharacteristic
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C22⋊C4—181no—
600C42—31no—
601C42—31no—
602C42—181no—
603C42—181no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3C2×D3×D411yescharacteristic
615C22×C3C2×D3×D411yescharacteristic
616C2×D3—32no—
617C2×D3—32no—
618C2×D3—62no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—122no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C2×D3—244no—
635C2×D3—244no—
636C2×D3—248no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×D3×Q811yescharacteristic
651C3×C4C2×D3×Q811yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—32no—
659Dic3—32no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—62no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668C32#308111yescharacteristic, complemented, Sylow
669C23—21no—
670C23—91no—
671C23—184no—
672C23—181no—
673C23—721no—
674C23—721no—
675Q8—241no—
676Q8—721no—
677D4—21no—
678D4—92no—
679D4—184no—
680D4—181no—
681D4#379712yes—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—91no—
692C2×C4—92no—
693C2×C4—92no—
694C2×C4—181no—
695C2×C4—241no—
696C2×C4—241no—
697C2×C4—721no—
698C2×C4—721no—
699C2×C4—721no—
700C2×C4C22×D3211yescharacteristic
701C8—21no—
702C8—61no—
703C8—61no—
704C8—181no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—42no—
709C2×C3—42no—
710C2×C3—82no—
711C2×C3D3×C22⋊Q811yescharacteristic
712C2×C3D3×C22⋊Q811yescharacteristic
713C2×C3#576211yescharacteristic
714C2×C3#577011yescharacteristic
715C2×C3#577411yescharacteristic
716C2×C3#577411yescharacteristic
717D3—64no—
718D3—62no—
719D3—62no—
720D3—122no—
721D3—122no—
722D3—242no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—92no—
727C22—181no—
728C22—181no—
729C22—182no—
730C22—361no—
731C22—361no—
732C22—724no—
733C22D32×D411yescharacteristic
734C4—41no—
735C4—61no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—92no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—361no—
745C4C2×#379711yescharacteristic
746C4#6431211yescharacteristic
747C3—21no—
748C3#8106211yescharacteristic, complemented
749C3#8116811yescharacteristic, complemented
750C2—42no—
751C2—182no—
752C2—362no—
753C2#1059406711yescharacteristic
754C2#1059473511yescharacteristic
755C2#1059475311yescharacteristic
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. #10594325C2semidirect
4. C3×#4763C2semidirect
5. C3×#4761C2semidirect
7. #10591410C2semidirect
8. #10591409C2semidirect
9. #10590769C2semidirect
10. #10590759C2semidirect
11. #10590712C2semidirect
12. #10590701C2semidirect
13. #10590583C2semidirect
14. #10590470C2semidirect
15. #10590464C2semidirect
23. C3×#890C22semidirect
24. C3×#888C22semidirect
29. #63918C22semidirect
34. #63869C22semidirect
47. C3×#817C22semidirect
48. C3×#817C22semidirect
49. C3×Dic3⋊C8C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. Dic3⋊(C3⋊C8)C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
89. #4763D3semidirect
90. #4761D3semidirect
96. D4×C3⋊D3Q8semidirect
173. #890C2×D3semidirect
178. #888C2×D3semidirect
212. #817C2×D3semidirect
213. #817C2×D3semidirect
216. Dic3⋊C8C2×D3semidirect
217. Dic3⋊C8C2×D3semidirect
224. #808C2×D3semidirect
230. #807C2×D3semidirect
668. C32#3081semidirect
748. C3#81062semidirect
749. C3#81168semidirect

Maximal subgroups

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

subgroupindex
#105952232
#105943252
C3⋊D3×#1022
C3×#47632
C3×#47612
#105914262
#105914102
#105914092
#105907692
#105907592
#105907122
#105907012
#105905832
#105904702
#105904642
#811683
#810623