Finite Group Databasebeta

← #11868694

Subgroups — #11868694

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594605C211yesmaximal, characteristic
2#10594448C211yesmaximal, characteristic, complemented
3#10592560C211yesmaximal, characteristic, complemented
4C3×#4871C211yesmaximal, characteristic, complemented
5C3×#4870C211yesmaximal, characteristic, complemented
6#10590941C211yesmaximal, characteristic
7#10590767C211yesmaximal, characteristic, complemented
8#10590762C211yesmaximal, characteristic, complemented
9#10590666C211yesmaximal, characteristic, complemented
10#10590594C211yesmaximal, characteristic
11#10590583C211yesmaximal, characteristic, complemented
12#10590555C211yesmaximal, characteristic, complemented
13#10590545C211yesmaximal, characteristic, complemented
14#10590469C211yesmaximal, characteristic, complemented
15#10590465C211yesmaximal, characteristic, complemented
16#81166—31nomaximal
17#81060—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26C3×#888C2211yescharacteristic, complemented
27#63921—21no—
28#63918C2211yescharacteristic, complemented
29#63895—21no—
30Dic3×D12C2211yescharacteristic
31Dic3×D12C2211yescharacteristic
32#63888—21no—
33C4×#624C2211yescharacteristic
34#63879—21no—
35#63879—21no—
36#63869C2211yescharacteristic, complemented
37#63849C2211yescharacteristic
38#63843—21no—
39#63838—21no—
40C2×#3712C2211yescharacteristic
41C32×#106C2211yescharacteristic, complemented
42#63645C2211yescharacteristic, complemented
43#63635C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C3×#821C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic, complemented
48C3×Dic3⋊C8C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5728—31no—
62#5688—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#478—31no—
66C3×#476—31no—
67#5084—31no—
68#5066—31no—
69#5009—31no—
70#5007—31no—
71#4890—31no—
72#4881—31no—
73#4871—31no—
74#4871D311yescharacteristic, complemented
75#4870D311yescharacteristic, complemented
76#4861—31no—
77#4861—31no—
78#4861—31no—
79#4861—61no—
80#4847—31no—
81#4846—31no—
82#4837—31no—
83#4837—31no—
84#4770—31no—
85#4770—31no—
86#4770—31no—
87#4770—31no—
88#4766—31no—
89#4766—31no—
90#4761—31no—
91#4759—31no—
92C22×D32—21no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—21no—
100C2×#627—21no—
101C2×#625—21no—
102C2×#624D411yescharacteristic
103C2×#624D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802Q814yescomplemented
108C4×D32—44no—
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3743—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32D411yescharacteristic
138Dic32D411yescharacteristic
139#3712—22no—
140#3077—91noSylow
141C2×D3×D4—31no—
142C2×D3×D4—31no—
143C22×C4×D3—61no—
144C22×C4×D3—61no—
145C3×C4⋊Q8—31no—
146C3×#125—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149#946—61no—
150Q8×Dic3—61no—
151D4×Dic3—31no—
152D4×Dic3—31no—
153C4×#67—61no—
154C4×#67—61no—
155C2×ΓL(1,𝔽25)—31no—
156C2×ΓL(1,𝔽25)—31no—
157C2×ΓL(1,𝔽25)—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×ΓL(1,𝔽25)—61no—
160#897—61no—
161#896—61no—
162#896—61no—
163#893C2×D311yescharacteristic
164#893C2×D311yescharacteristic
165#892—31no—
166#892—31no—
167#892—31no—
168#892—31no—
169#892—61no—
170D3×C4⋊C4—31no—
171D3×C4⋊C4—31no—
172D3×C4⋊C4—61no—
173#890—31no—
174#890C2×D311yescharacteristic, complemented
175#888—31no—
176#888C2×D311yescharacteristic, complemented
177#887—61no—
178#887—61no—
179#887—61no—
180#67⋊C4—61no—
181#67⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184C4×D12—31no—
185C4×D12—31no—
186C42×D3—31no—
187C42×D3—31no—
188#870—31no—
189#869—31no—
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106C2×D311yescharacteristic, complemented
194C3×#106C2×D311yescharacteristic, complemented
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#821—31no—
206#821—31no—
207#821C2×D311yescharacteristic
208#821C2×D311yescharacteristic
209#818—31no—
210#818—31no—
211#818—31no—
212#818—61no—
213#817—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic, complemented
217Dic3⋊C8C2×D311yescharacteristic, complemented
218#809—31no—
219#809—31no—
220#809C2×D311yescharacteristic
221#809C2×D311yescharacteristic
222#808—31no—
223#808—31no—
224#808—31no—
225#808—61no—
226#808C2×D311yescharacteristic, complemented
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231#807C2×D311yescharacteristic, complemented
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C22×C3⋊D3C2×D411yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C2×D32—24no—
238C2×D32—42no—
239C2×D32—42no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4×C3⋊D3—42no—
247C4×C3⋊D3C2×Q812yes—
248C4×C3⋊D3#4112yes—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×D12C2×Q812yes—
258C3×D12C2×Q812yes—
259C3×C4×D3—42no—
260C3×C4×D3—42no—
261C3×Dic6—42no—
262#627—42no—
263#625—24no—
264#624—22no—
265#624—41no—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#533—91no—
273C2×C4×D4—91no—
274#478—31no—
275#478—91no—
276#478—91no—
277#478—91no—
278#476—31no—
279#476—91no—
280#474—91no—
281#474—91no—
282#428—91no—
283#428—91no—
284#423—91no—
285#418—91no—
286#418—91no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×Q8—61no—
290C2×C3×D4—31no—
291C2×C3×D4—31no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C2×#67—61no—
295C2×#67—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298D3×D4—34no—
299D3×D4—34no—
300D3×D4—62no—
301D3×D4—62no—
302C2×D12C22×D311yescharacteristic
303C2×D12C22×D311yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—121no—
318C2×C4×D3—124no—
319C2×C4×D3—124no—
320C2×Dic6—21no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8C22×D311yescharacteristic
327C2×C3×C8C22×D311yescharacteristic
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—31no—
342C3×C42—31no—
343#217—61no—
344#217—61no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—21no—
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—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365Dic3⋊C4—21no—
366Dic3⋊C4—21no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—121no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390ΓL(1,𝔽25)—62no—
391ΓL(1,𝔽25)—62no—
392ΓL(1,𝔽25)—62no—
393ΓL(1,𝔽25)—62no—
394ΓL(1,𝔽25)—64no—
395C22×C32C22×D411yescharacteristic
396C2×C3⋊D3—21no—
397C2×C3⋊D3—21no—
398C2×C3⋊D3C22⋊Q812yes—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405D32—48no—
406C32×C4—41no—
407C32×C4—41no—
408C32×C4C22×Q811yescharacteristic
409C32×C4C2×#4111yescharacteristic
410C3⋊Dic3—41no—
411C3⋊Dic3—41no—
412C3⋊Dic3C22⋊Q812yes—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3AGL(1,ℤ/8)12yes—
419C22×D4—91no—
420C23×C4—181no—
421C2×M16—91no—
422C2×M16—91no—
423C4⋊Q8—31no—
424C4⋊Q8—91no—
425#125—31no—
426#125—91no—
427C22⋊Q8—181no—
428C22⋊Q8—181no—
429C4×Q8—181no—
430C4×Q8—181no—
431C4×D4—31no—
432C4×D4—31no—
433C4×D4—91no—
434C4×D4—91no—
435C4×D4—181no—
436C4×D4—181no—
437#117—91no—
438#117—91no—
439C2×C4⋊C4—91no—
440C2×C22⋊C4—181no—
441C2×C42—91no—
442#107—31no—
443#107—91no—
444#107—91no—
445#107—91no—
446#106—31no—
447#106—91no—
448#106—91no—
449#106D3211yescharacteristic, complemented
450C4⋊C8—31no—
451C4⋊C8—31no—
452C4⋊C8—91no—
453C4⋊C8—91no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458#102—91no—
459#102—91no—
460#102—91no—
461#102—91no—
462C23×C3—61no—
463C23×C3—61no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—31no—
467C22×D3—31no—
468C22×D3—61no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3—122no—
474C22×D3—122no—
475C3×Q8—122no—
476C3×D4—32no—
477C3×D4—32no—
478C3×D4—61no—
479C3×D4—61no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—122no—
494C2×C3×C4—122no—
495C2×C3×C4C23×D311yescharacteristic
496C2×C3×C4C23×D311yescharacteristic
497#67—64no—
498#67—64no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3—122no—
511C2×Dic3—122no—
512C2×Dic3D3×D411yescharacteristic
513C2×Dic3D3×D411yescharacteristic
514C2×Dic3D3×D411yescharacteristic
515C2×Dic3D3×D411yescharacteristic
516D12—21no—
517D12—21no—
518D12D3×Q812yes—
519D12D3×Q812yes—
520C4×D3—32no—
521C4×D3—32no—
522C4×D3—32no—
523C4×D3—32no—
524C4×D3—42no—
525C4×D3—42no—
526C4×D3—62no—
527C4×D3—62no—
528C4×D3—62no—
529C4×D3—62no—
530C4×D3—121no—
531C4×D3—121no—
532C4×D3—122no—
533C4×D3—122no—
534C4×D3—122no—
535C4×D3—122no—
536C4×D3—242no—
537Dic6—42no—
538Dic6—122no—
539Dic6—122no—
540C3×C8—22no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—61no—
544C3×C8—61no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C3⋊C8—62no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C2×C32C2×C22⋊Q811yescharacteristic
551C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
552C2×C32#57511yescharacteristic
553C3⋊D3—22no—
554C3×D3—42no—
555C3×D3—42no—
556C24—181no—
557C2×Q8—61no—
558C2×Q8—181no—
559C2×D4—31no—
560C2×D4—31no—
561C2×D4—94no—
562C2×D4—182no—
563C2×D4—181no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—181no—
572C22×C4—364no—
573M16—182no—
574M16—182no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8—91no—
578C2×C8C2×D3211yescharacteristic
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4C2×D3211yescharacteristic
591C4⋊C4C2×D3211yescharacteristic
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C42—31no—
599C42—31no—
600C42—91no—
601C42—91no—
602C42—181no—
603C42—181no—
604C22×C3—21no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3C2×D3×D411yescharacteristic
612C22×C3C2×D3×D411yescharacteristic
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—32no—
616C2×D3—32no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—62no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—128no—
629C2×D3—128no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—32no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—81no—
641C3×C4—81no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4C2×D3×Q811yescharacteristic
645C3×C4C2×D3×Q811yescharacteristic
646C3×C4D3×#4111yescharacteristic
647C3×C4D3×#4111yescharacteristic
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—32no—
652Dic3—32no—
653Dic3—41no—
654Dic3—41no—
655Dic3—62no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—241no—
661Dic3—241no—
662Dic3#91412yes—
663C32#307711yescharacteristic, complemented, Sylow
664C23—61no—
665C23—61no—
666C23—91no—
667C23—184no—
668C23—362no—
669C23—362no—
670Q8—122no—
671Q8—362no—
672D4—32no—
673D4—32no—
674D4—61no—
675D4—61no—
676D4—184no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—91no—
686C2×C4—92no—
687C2×C4—92no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—182no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—362no—
694C2×C4—362no—
695C2×C4—361no—
696C2×C4—362no—
697C2×C4C22×D3211yescharacteristic
698C8—21no—
699C8—61no—
700C8—61no—
701C8—181no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—122no—
706C2×C3—122no—
707C2×C3D3×C22⋊Q811yescharacteristic
708C2×C3D3×C22⋊Q811yescharacteristic
709C2×C3C2×#91411yescharacteristic
710C2×C3#576811yescharacteristic
711C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
712C2×C3#577311yescharacteristic
713D3—42no—
714D3—42no—
715D3—62no—
716D3—62no—
717D3—122no—
718C22—62no—
719C22—62no—
720C22—92no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22—181no—
726C22—181no—
727C22—368no—
728C22D32×D411yescharacteristic
729C4—32no—
730C4—41no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—92no—
736C4—121no—
737C4—121no—
738C4—361no—
739C4—361no—
740C4#6430611yescharacteristic
741C4D32×Q811yescharacteristic
742C3—21no—
743C3#8106011yescharacteristic, complemented
744C3#8116611yescharacteristic, complemented
745C2—122no—
746C2—122no—
747C2—182no—
748C2#1059462411yescharacteristic
749C2D3×#91411yescharacteristic
750C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenter#106D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594448C2semidirect
3. #10592560C2semidirect
4. C3×#4871C2semidirect
5. C3×#4870C2semidirect
7. #10590767C2semidirect
8. #10590762C2semidirect
9. #10590666C2semidirect
11. #10590583C2semidirect
12. #10590555C2semidirect
13. #10590545C2semidirect
14. #10590469C2semidirect
15. #10590465C2semidirect
25. C3×#890C22semidirect
26. C3×#888C22semidirect
28. #63918C22semidirect
36. #63869C22semidirect
41. C32×#106C22semidirect
42. #63645C22semidirect
43. #63635C22semidirect
44. #63634C22semidirect
47. C3×Dic3⋊C8C22semidirect
48. C3×Dic3⋊C8C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. #63573C22semidirect
55. Dic3⋊(C3⋊C8)C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
74. #4871D3semidirect
75. #4870D3semidirect
107. #3802Q8semidirect
174. #890C2×D3semidirect
176. #888C2×D3semidirect
193. C3×#106C2×D3semidirect
194. C3×#106C2×D3semidirect
216. Dic3⋊C8C2×D3semidirect
217. Dic3⋊C8C2×D3semidirect
226. #808C2×D3semidirect
231. #807C2×D3semidirect
449. #106D32semidirect
663. C32#3077semidirect
743. C3#81060semidirect
744. C3#81166semidirect

Maximal subgroups

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

subgroupindex
#105946052
#105944482
#105925602
C3×#48712
C3×#48702
#105909412
#105907672
#105907622
#105906662
#105905942
#105905832
#105905552
#105905452
#105904692
#105904652
#811663
#810603