Finite Group Databasebeta

← #11868956

Subgroups — #11868956

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic
2#10593959C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4839C211yesmaximal, characteristic, complemented
6#10590939C211yesmaximal, characteristic
7D3×#821C211yesmaximal, characteristic
8#10590772C211yesmaximal, characteristic, complemented
9#10590769C211yesmaximal, characteristic, complemented
10#10590764C211yesmaximal, characteristic, complemented
11#10590757C211yesmaximal, characteristic, complemented
12#10590706C211yesmaximal, characteristic, complemented
13#10590683C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590272C211yesmaximal, characteristic, complemented
16#81168—31nomaximal
17#79090—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×#870C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63918C2211yescharacteristic, complemented
29#63904—21no—
30#63896—21no—
31#63894C2211yescharacteristic
32#63893—21no—
33Dic3×D12C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63881—21no—
36#63869C2211yescharacteristic, complemented
37#63845—21no—
38#63841C2211yescharacteristic
39#63841C2211yescharacteristic
40#63840—21no—
41C32×C4⋊C8C2211yescharacteristic, complemented
42#63648C2211yescharacteristic
43#63648C2211yescharacteristic
44#63644C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#818C2211yescharacteristic, complemented
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5689—31no—
62#5545—31no—
63#5521—31no—
64#5519—31no—
65C3×#478—31no—
66C3×#424—31no—
67#5131—31no—
68#5121—31no—
69C2×#821—31no—
70#5106—31no—
71#5066—31no—
72#5007—31no—
73#4890—31no—
74#4881—31no—
75#4871—31no—
76#4860—31no—
77#4847—31no—
78#4847—31no—
79#4847—31no—
80#4847D311yescharacteristic, complemented
81#4846—31no—
82#4846—31no—
83#4842—31no—
84#4842—31no—
85#4842—31no—
86#4842—61no—
87#4839D311yescharacteristic, complemented
88#4770—31no—
89D3×#102—31no—
90#4763—31no—
91#4761—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×#627—21no—
100C2×#626—21no—
101C2×#624—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104D3×D12—22no—
105D3×D12Q814yescomplemented
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C42C2311yescharacteristic
109#3752—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4D411yescharacteristic
116C3×(C2×D3)⋊C4D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C3×ΓL(1,𝔽25)—22no—
128C3×D3×C8—22no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3081—91noSylow
140C2×D3×D4—31no—
141C22×D12—31no—
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C3×#125—31no—
145C3×C4×D4—31no—
146C3×#117—31no—
147D4×Dic3—31no—
148C4×#67—61no—
149C2×(C2×D3)⋊C4—61no—
150#926—31no—
151#926—31no—
152C2×C4⋊Dic3—31no—
153C2×ΓL(1,𝔽25)C2×D311yescharacteristic
154C2×D3×C8C2×D311yescharacteristic
155#897—61no—
156#896—61no—
157#893—31no—
158#893—61no—
159#893—61no—
160#892—31no—
161#892—31no—
162D3×C4⋊C4—31no—
163#890—31no—
164#890—61no—
165#889—61no—
166#888—31no—
167#888—61no—
168#888—61no—
169#67⋊C4—61no—
170D3×C22⋊C4—61no—
171D3×C22⋊C4—61no—
172D3×C22⋊C4—61no—
173#878—61no—
174#878—61no—
175C4×D12—31no—
176C4×D12—31no—
177C4×D12—31no—
178C4×D12—31no—
179C4×D12—61no—
180C4×D12C2×D311yescharacteristic
181#872C2×D311yescharacteristic
182#870—31no—
183#870C2×D311yescharacteristic, complemented
184#869—31no—
185#869—31no—
186#869—31no—
187#869—61no—
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—21no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8C2×D311yescharacteristic, complemented
195C3×C4⋊C8C2×D311yescharacteristic, complemented
196C3×#102—31no—
197C3×#102—31no—
198#832—31no—
199#832—31no—
200#821—31no—
201#821—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—61no—
209#821—61no—
210#821C2×D311yescharacteristic
211#821C2×D311yescharacteristic
212#818—31no—
213#818—31no—
214#818—31no—
215#818C2×D311yescharacteristic, complemented
216#817—31no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#817—61no—
223#817C2×D311yescharacteristic, complemented
224Dic3⋊C8C2×D311yescharacteristic, complemented
225Dic3⋊C8C2×D311yescharacteristic, complemented
226#809—31no—
227#809—31no—
228#808—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233C22×C3⋊D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3C2×D411yescharacteristic
236C2×D32—24no—
237C2×D32—81no—
238C2×D32—81no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)C2×Q812yes—
247C4×C3⋊D3—81no—
248#634—81no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12C2×Q812yes—
257C3×C4×D3—81no—
258C3×C4×D3C2×Q812yes—
259C3×C4×D3#4112yes—
260#627—81no—
261#626—24no—
262#624—81no—
263D3×Dic3—81no—
264D3×Dic3—81no—
265C32×C8—21no—
266C32×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—91no—
276#476—91no—
277#474—91no—
278#474—91no—
279#428—91no—
280#427—91no—
281#424—31no—
282#418—91no—
283C2×#102—91no—
284C23×D3—61no—
285C23×D3—61no—
286C2×C3×D4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—61no—
289C2×#67—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292D3×D4—34no—
293D3×D4—62no—
294C2×D12—31no—
295C2×D12—31no—
296C2×D12—34no—
297C2×D12—61no—
298C2×D12—62no—
299C2×D12—61no—
300C2×D12C22×D311yescharacteristic
301C2×C4×D3—21no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3—121no—
309C2×C4×D3C22×D311yescharacteristic
310C2×Dic6—61no—
311C2×Dic6—61no—
312C2×Dic6—61no—
313C2×Dic6—61no—
314C2×Dic6—121no—
315C3×M16—62no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—31no—
319C2×C3×C8—31no—
320C2×C3×C8—62no—
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C3×C4⋊C4—31no—
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×C22⋊C4—31no—
333C3×C22⋊C4—31no—
334C3×C22⋊C4—61no—
335C3×C42—21no—
336C3×C42—31no—
337C3×C42C22×D311yescharacteristic
338C3×C42C22×D311yescharacteristic
339#217—61no—
340#217—61no—
341#217—61no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
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—121no—
351(C2×D3)⋊C4D1211yescharacteristic
352(C2×D3)⋊C4D1211yescharacteristic
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—121no—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4D1211yescharacteristic
379Dic3⋊C4D1211yescharacteristic
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387ΓL(1,𝔽25)—22no—
388D3×C8—22no—
389C22×C32C22×D411yescharacteristic
390C2×C3⋊D3—22no—
391C2×C3⋊D3—41no—
392C2×C3⋊D3—41no—
393C2×C3×D3—21no—
394C2×C3×D3—21no—
395C2×C3×D3—22no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C2×C3×D3C22⋊Q812yes—
399D32—84no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4C22×Q811yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3⋊Dic3—41no—
405C3⋊Dic3—41no—
406C3⋊Dic3—41no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3C22⋊Q812yes—
413C22×D4—91no—
414C2×M16—31no—
415C22×C8—31no—
416C4⋊Q8—91no—
417C4⋊Q8—91no—
418C4⋊Q8—181no—
419#125—31no—
420#125—91no—
421#125—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C4×D4—31no—
425C4×D4—91no—
426C4×D4—91no—
427C4×D4—91no—
428C4×D4—181no—
429C4×D4—181no—
430#117—31no—
431#117—91no—
432#117—91no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—181no—
435C2×C22⋊C4—181no—
436#107—31no—
437#107—91no—
438#107—91no—
439#107—91no—
440#106—31no—
441#106—91no—
442#106—91no—
443#106—91no—
444C4⋊C8—31no—
445C4⋊C8—31no—
446C4⋊C8—31no—
447C4⋊C8D3211yescharacteristic, complemented
448#102—31no—
449#102—31no—
450#102—91no—
451#102—91no—
452#102—91no—
453#102—91no—
454#102—91no—
455#102—91no—
456C23×C3—31no—
457C23×C3—61no—
458C22×D3—21no—
459C22×D3—64no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—64no—
463C22×D3—121no—
464C22×D3—241no—
465C22×D3—241no—
466C22×D3—241no—
467C22×D3—241no—
468C22×D3C2×D1211yescharacteristic
469C3×D4—32no—
470C3×D4—61no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—32no—
476C2×C3×C4—32no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—241no—
483C2×C3×C4C2×D1211yescharacteristic
484C2×C3×C4C2×D1211yescharacteristic
485C2×C3×C4D3×D411yescharacteristic
486C2×C3×C4D3×D411yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489#67—64no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3—241no—
503C2×Dic3—241no—
504C2×Dic3C2×D1211yescharacteristic
505C2×Dic3C2×D1211yescharacteristic
506C2×Dic3C2×D1211yescharacteristic
507D12—21no—
508D12—32no—
509D12—32no—
510D12—62no—
511D12—64no—
512D12—61no—
513D12—61no—
514D12—121no—
515D12D3×Q812yes—
516C4×D3—81no—
517C4×D3—241no—
518C4×D3—241no—
519C4×D3—241no—
520C4×D3—241no—
521C4×D3—241no—
522C4×D3—241no—
523C4×D3—242no—
524C4×D3#23712yes—
525C4×D3D3×Q812yes—
526Dic6—241no—
527Dic6—241no—
528Dic6—241no—
529Dic6—241no—
530Dic6—242no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—41no—
536C3×C8—41no—
537C3×C8—61no—
538C3×C8—61no—
539C3⋊C8—21no—
540C3⋊C8—21no—
541C2×C32C2×C22⋊Q811yescharacteristic
542C2×C32#57611yescharacteristic
543C2×C32#57711yescharacteristic
544C3⋊D3—42no—
545C3×D3—22no—
546C3×D3—42no—
547C24—181no—
548C2×Q8—181no—
549C2×Q8—181no—
550C2×D4—31no—
551C2×D4—94no—
552C2×D4—91no—
553C2×D4—182no—
554C2×D4—181no—
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—181no—
558C22×C4—181no—
559C22×C4—181no—
560C22×C4—181no—
561M16—62no—
562C2×C8—31no—
563C2×C8—31no—
564C2×C8—62no—
565C2×C8C2×D3211yescharacteristic
566C2×C8C2×D3211yescharacteristic
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—61no—
585C22⋊C4—181no—
586C22⋊C4—181no—
587C22⋊C4—181no—
588C22⋊C4—181no—
589C22⋊C4—181no—
590C42—31no—
591C42—181no—
592C42—181no—
593C42C2×D3211yescharacteristic
594C22×C3—21no—
595C22×C3—32no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—62no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3C22×D1211yescharacteristic
602C22×C3C2×D3×D411yescharacteristic
603C2×D3—21no—
604C2×D3—21no—
605C2×D3—22no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—122no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C2×D3—241no—
616C2×D3—241no—
617C2×D3—244no—
618C2×D3—244no—
619C2×D3#89712yes—
620C3×C4—22no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—32no—
628C3×C4—41no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4C2×#23711yescharacteristic
635C3×C4C2×D3×Q811yescharacteristic
636C3×C4C2×D3×Q811yescharacteristic
637C3×C4D3×#4111yescharacteristic
638Dic3—21no—
639Dic3—21no—
640Dic3—41no—
641Dic3—41no—
642Dic3—41no—
643Dic3—121no—
644Dic3—121no—
645Dic3—121no—
646Dic3—121no—
647Dic3—121no—
648Dic3—121no—
649Dic3—241no—
650Dic3—241no—
651Dic3—241no—
652Dic3#89712yes—
653C32#308111yescharacteristic, complemented, Sylow
654C23—31no—
655C23—61no—
656C23—184no—
657C23—181no—
658C23—721no—
659C23—721no—
660Q8—721no—
661Q8—721no—
662D4—32no—
663D4—61no—
664D4—92no—
665D4—184no—
666D4—181no—
667C2×C4—31no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—241no—
679C2×C4—721no—
680C2×C4—721no—
681C2×C4—721no—
682C2×C4—721no—
683C2×C4D3×D1211yescharacteristic
684C2×C4D3×D1211yescharacteristic
685C2×C4C22×D3211yescharacteristic
686C8—21no—
687C8—21no—
688C8—61no—
689C8—61no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—62no—
694C2×C3—122no—
695C2×C3C2×#89711yescharacteristic
696C2×C3D3×C22⋊Q811yescharacteristic
697C2×C3#575111yescharacteristic
698C2×C3#575211yescharacteristic
699C2×C3#577011yescharacteristic
700C2×C3#577411yescharacteristic
701D3—22no—
702D3—42no—
703D3—122no—
704D3—122no—
705D3—242no—
706C22—32no—
707C22—61no—
708C22—61no—
709C22—62no—
710C22—121no—
711C22—121no—
712C22—182no—
713C22—361no—
714C22—361no—
715C22—724no—
716C22C2×D3×D1211yescharacteristic
717C4—21no—
718C4—21no—
719C4—32no—
720C4—61no—
721C4—61no—
722C4—121no—
723C4—121no—
724C4—121no—
725C4—361no—
726C4—361no—
727C4—361no—
728C4D3×#23711yescharacteristic
729C4D32×Q811yescharacteristic
730C3—21no—
731C3#7909011yescharacteristic, complemented
732C3#8116811yescharacteristic, complemented
733C2—62no—
734C2—122no—
735C2—362no—
736C2D3×#89711yescharacteristic
737C2#1059467911yescharacteristic
738C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊C8D32
hypocenterC32#3081
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
2. #10593959C2semidirect
3. #10592541C2semidirect
4. C3×#4847C2semidirect
5. C3×#4839C2semidirect
8. #10590772C2semidirect
9. #10590769C2semidirect
10. #10590764C2semidirect
11. #10590757C2semidirect
12. #10590706C2semidirect
13. #10590683C2semidirect
14. #10590308C2semidirect
15. #10590272C2semidirect
20. #64078C22semidirect
25. C3×#870C22semidirect
28. #63918C22semidirect
36. #63869C22semidirect
41. C32×C4⋊C8C22semidirect
44. #63644C22semidirect
45. #63644C22semidirect
48. C3×#818C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
80. #4847D3semidirect
87. #4839D3semidirect
105. D3×D12Q8semidirect
183. #870C2×D3semidirect
194. C3×C4⋊C8C2×D3semidirect
195. C3×C4⋊C8C2×D3semidirect
215. #818C2×D3semidirect
223. #817C2×D3semidirect
224. Dic3⋊C8C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
447. C4⋊C8D32semidirect
653. C32#3081semidirect
731. C3#79090semidirect
732. C3#81168semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105939592
#105925412
C3×#48472
C3×#48392
#105909392
D3×#8212
#105907722
#105907692
#105907642
#105907572
#105907062
#105906832
#105903082
#105902722
#811683
#790903