Finite Group Databasebeta

← #11868698

Subgroups — #11868698

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×D12C211yesmaximal, characteristic
2#10593874C211yesmaximal, characteristic, complemented
3#10592546C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4837C211yesmaximal, characteristic, complemented
6#10590939C211yesmaximal, characteristic
7#10590939C211yesmaximal, characteristic
8#10590764C211yesmaximal, characteristic, complemented
9#10590762C211yesmaximal, characteristic, complemented
10#10590759C211yesmaximal, characteristic, complemented
11#10590757C211yesmaximal, characteristic, complemented
12#10590683C211yesmaximal, characteristic, complemented
13#10590681C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#81166—31nomaximal
17#79059—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21#64079C2211yescharacteristic, complemented
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×C42×D3C2211yescharacteristic
26C3×#870C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28#63918C2211yescharacteristic, complemented
29#63918C2211yescharacteristic, complemented
30C4×#626—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63880—21no—
35#63851—21no—
36#63851—21no—
37#63841C2211yescharacteristic
38#63841C2211yescharacteristic
39#63837—21no—
40#63837—21no—
41C32×C4⋊C8C2211yescharacteristic, complemented
42#63648C2211yescharacteristic
43#63648C2211yescharacteristic
44#63645C2211yescharacteristic, 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#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5688—31no—
62C4×D3×D4—31no—
63C2×C4×D12—31no—
64#5470—31no—
65C3×#478—31no—
66C3×#423—31no—
67#5131—31no—
68#5131—31no—
69#5121—31no—
70#5121—31no—
71#5066—31no—
72#5009—31no—
73#4890—31no—
74#4881—31no—
75#4870—31no—
76#4861—31no—
77#4847—31no—
78#4847—31no—
79#4847—31no—
80#4847—31no—
81#4847—61no—
82#4847D311yescharacteristic, complemented
83#4846—31no—
84#4846—31no—
85#4842—31no—
86#4842—31no—
87#4837D311yescharacteristic, complemented
88#4770—31no—
89#4770—31no—
90#4761—31no—
91#4759—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3D411yescharacteristic
98C2×C3×C4×D3D411yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×#627—21no—
101C2×#627—21no—
102C2×#626—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12Q814yescomplemented
108C4×D32—44no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C42C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×C4×Dic3D411yescharacteristic
125C3×C4×Dic3D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×ΓL(1,𝔽25)—22no—
130C3×ΓL(1,𝔽25)—22no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140#3077—91noSylow
141C2×D3×D4—31no—
142C22×D12—31no—
143C22×C4×D3—61no—
144C22×C4×D3—61no—
145C2×C3×M16—31no—
146C2×C3×M16—31no—
147C3×#125—31no—
148C3×C4×D4—31no—
149C2×C3×C42—31no—
150D4×Dic3—31no—
151C4×#67—61no—
152C2×(C2×D3)⋊C4—61no—
153#926—31no—
154#926—31no—
155C2×C4⋊Dic3—31no—
156#924—61no—
157#924—61no—
158C2×ΓL(1,𝔽25)C2×D311yescharacteristic
159C2×ΓL(1,𝔽25)C2×D311yescharacteristic
160#896—61no—
161#896—61no—
162#893—31no—
163#892—31no—
164#892—31no—
165D3×C4⋊C4—31no—
166#888—31no—
167#888—31no—
168#887—61no—
169#887—61no—
170#67⋊C4—61no—
171D3×C22⋊C4—61no—
172C4×D12—31no—
173C4×D12—31no—
174C4×D12—31no—
175C4×D12—31no—
176C4×D12—61no—
177C4×D12—61no—
178C4×D12—61no—
179C4×D12C2×D311yescharacteristic
180C42×D3C2×D311yescharacteristic
181#870—31no—
182#870—31no—
183#870—61no—
184#870C2×D311yescharacteristic, complemented
185#869—31no—
186#869—31no—
187C4×Dic6—61no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—31no—
191C3×C4⋊C8—21no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8C2×D311yescharacteristic, complemented
196C3×C4⋊C8C2×D311yescharacteristic, complemented
197C3×#102—31no—
198C3×#102—31no—
199#832—31no—
200#832—31no—
201#821—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210#821—61no—
211#821C2×D311yescharacteristic
212#821C2×D311yescharacteristic
213#818—31no—
214#818—31no—
215#818—31no—
216#818—31no—
217#818—61no—
218#818C2×D311yescharacteristic, complemented
219#817—31no—
220#817—31no—
221#817—31no—
222#817—31no—
223#817—61no—
224#817C2×D311yescharacteristic, complemented
225Dic3⋊C8C2×D311yescharacteristic, complemented
226Dic3⋊C8C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#808—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
234C22×C3⋊D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C2×D32—24no—
238C2×D32—42no—
239C2×D32—42no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)C2×Q812yes—
248C4×C3⋊D3—42no—
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—22no—
258C3×C4×D3—41no—
259C3×C4×D3—42no—
260C3×C4×D3C2×Q812yes—
261C3×C4×D3#4112yes—
262#627—42no—
263#627—42no—
264#626—24no—
265#624—42no—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C32×C8—21no—
269C32×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—91no—
279#476—91no—
280#474—91no—
281#474—91no—
282#428—91no—
283#428—91no—
284#423—31no—
285#418—91no—
286#418—91no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×D4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294C2×#67—61no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297D3×D4—34no—
298D3×D4—62no—
299C2×D12—31no—
300C2×D12—31no—
301C2×D12—34no—
302C2×D12—61no—
303C2×D12—62no—
304C2×D12—61no—
305C2×D12C22×D311yescharacteristic
306C2×C4×D3—21no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—121no—
314C2×C4×D3—124no—
315C2×C4×D3—124no—
316C2×C4×D3D1211yescharacteristic
317C2×C4×D3D1211yescharacteristic
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C3×M16—62no—
324C3×M16—62no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C42—21no—
340C3×C42—31no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42C22×D311yescharacteristic
344C3×C42C22×D311yescharacteristic
345#217—61no—
346#217—61no—
347#217—61no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—121no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3D1211yescharacteristic
388C4×Dic3D1211yescharacteristic
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392ΓL(1,𝔽25)—22no—
393ΓL(1,𝔽25)—22no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3C22⋊Q812yes—
404D32—48no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4C22×Q811yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—41no—
410C3⋊Dic3—41no—
411C3⋊Dic3—41no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3C22⋊Q812yes—
417C3×Dic3AGL(1,ℤ/8)12yes—
418C22×D4—91no—
419C23×C4—181no—
420C2×M16—31no—
421C2×M16—31no—
422C4⋊Q8—91no—
423C4⋊Q8—91no—
424#125—31no—
425#125—91no—
426C22⋊Q8—181no—
427C22⋊Q8—181no—
428C4×Q8—181no—
429C4×Q8—181no—
430C4×D4—31no—
431C4×D4—91no—
432C4×D4—91no—
433C4×D4—91no—
434C4×D4—181no—
435C4×D4—181no—
436#117—91no—
437#117—91no—
438C2×C4⋊C4—91no—
439C2×C22⋊C4—181no—
440C2×C42—31no—
441#107—31no—
442#107—91no—
443#107—91no—
444#107—91no—
445#106—31no—
446#106—91no—
447#106—91no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—31no—
451C4⋊C8—31no—
452C4⋊C8D3211yescharacteristic, complemented
453#102—31no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461C23×C3—31no—
462C23×C3—61no—
463C22×D3—21no—
464C22×D3—64no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—64no—
468C22×D3—121no—
469C22×D3—122no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3C2×D1211yescharacteristic
474C3×D4—32no—
475C3×D4—61no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—31no—
484C2×C3×C4—62no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—121no—
489C2×C3×C4—122no—
490C2×C3×C4C2×D1211yescharacteristic
491C2×C3×C4C2×D1211yescharacteristic
492C2×C3×C4D3×D411yescharacteristic
493C2×C3×C4D3×D411yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495C2×C3×C4C23×D311yescharacteristic
496#67—64no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—121no—
507C2×Dic3—121no—
508C2×Dic3—121no—
509C2×Dic3—122no—
510C2×Dic3—122no—
511C2×Dic3C2×D1211yescharacteristic
512C2×Dic3C2×D1211yescharacteristic
513C2×Dic3C2×D1211yescharacteristic
514D12—21no—
515D12—32no—
516D12—32no—
517D12—62no—
518D12—64no—
519D12—61no—
520D12—61no—
521D12—121no—
522D12D3×Q812yes—
523C4×D3—22no—
524C4×D3—41no—
525C4×D3—42no—
526C4×D3—122no—
527C4×D3—122no—
528C4×D3—122no—
529C4×D3—122no—
530C4×D3—122no—
531C4×D3—122no—
532C4×D3—242no—
533C4×D3#23712yes—
534C4×D3D3×Q812yes—
535Dic6—122no—
536Dic6—122no—
537Dic6—122no—
538Dic6—122no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—41no—
544C3×C8—41no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C2×C32C2×C22⋊Q811yescharacteristic
550C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
551C2×C32#57511yescharacteristic
552C3⋊D3—42no—
553C3×D3—22no—
554C3×D3—42no—
555C24—181no—
556C2×Q8—181no—
557C2×Q8—181no—
558C2×D4—31no—
559C2×D4—94no—
560C2×D4—91no—
561C2×D4—182no—
562C2×D4—181no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—61no—
567C22×C4—181no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—364no—
572M16—62no—
573M16—62no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8C2×D3211yescharacteristic
577C2×C8C2×D3211yescharacteristic
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C22⋊C4—61no—
592C22⋊C4—181no—
593C22⋊C4—181no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C42—31no—
598C42—31no—
599C42—31no—
600C42—181no—
601C42—181no—
602C42C2×D3211yescharacteristic
603C22×C3—21no—
604C22×C3—32no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—62no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3C22×D1211yescharacteristic
611C22×C3C2×D3×D411yescharacteristic
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—22no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—122no—
620C2×D3—128no—
621C2×D3—128no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—241no—
627C2×D3—241no—
628C2×D3#89712yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—32no—
636C3×C4—32no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—61no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4C2×#23711yescharacteristic
644C3×C4C2×D3×Q811yescharacteristic
645C3×C4C2×D3×Q811yescharacteristic
646C3×C4D3×#4111yescharacteristic
647Dic3—21no—
648Dic3—41no—
649Dic3—41no—
650Dic3—41no—
651Dic3—121no—
652Dic3—121no—
653Dic3—121no—
654Dic3—121no—
655Dic3—121no—
656Dic3—121no—
657Dic3—241no—
658Dic3—241no—
659Dic3—241no—
660Dic3#89712yes—
661Dic3#90812yes—
662C32#307711yescharacteristic, complemented, Sylow
663C23—31no—
664C23—61no—
665C23—184no—
666C23—181no—
667C23—362no—
668C23—362no—
669Q8—362no—
670Q8—362no—
671D4—32no—
672D4—61no—
673D4—92no—
674D4—184no—
675D4—181no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—31no—
681C2×C4—62no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—121no—
686C2×C4—122no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—362no—
691C2×C4—362no—
692C2×C4—362no—
693C2×C4—362no—
694C2×C4D3×D1211yescharacteristic
695C2×C4D3×D1211yescharacteristic
696C2×C4C22×D3211yescharacteristic
697C8—21no—
698C8—21no—
699C8—61no—
700C8—61no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—62no—
705C2×C3—122no—
706C2×C3C2×#89711yescharacteristic
707C2×C3D3×C22⋊Q811yescharacteristic
708C2×C3C2×#90811yescharacteristic
709C2×C3#574811yescharacteristic
710C2×C3#576811yescharacteristic
711C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
712D3—22no—
713D3—42no—
714D3—122no—
715D3—122no—
716D3—242no—
717C22—32no—
718C22—61no—
719C22—61no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—182no—
724C22—368no—
725C22—361no—
726C22—361no—
727C22C2×D3×D1211yescharacteristic
728C4—21no—
729C4—21no—
730C4—32no—
731C4—32no—
732C4—61no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4D3×#23711yescharacteristic
740C4D32×Q811yescharacteristic
741C3—21no—
742C3#7905911yescharacteristic, complemented
743C3#8116611yescharacteristic, complemented
744C2—62no—
745C2—122no—
746C2—362no—
747C2D3×#89711yescharacteristic
748C2#1059467611yescharacteristic
749C2D3×#90811yescharacteristic
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#3077
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. #10593874C2semidirect
3. #10592546C2semidirect
4. C3×#4847C2semidirect
5. C3×#4837C2semidirect
8. #10590764C2semidirect
9. #10590762C2semidirect
10. #10590759C2semidirect
11. #10590757C2semidirect
12. #10590683C2semidirect
13. #10590681C2semidirect
14. #10590308C2semidirect
15. #10590271C2semidirect
21. #64079C22semidirect
26. C3×#870C22semidirect
28. #63918C22semidirect
29. #63918C22semidirect
41. C32×C4⋊C8C22semidirect
44. #63645C22semidirect
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. #63573C22semidirect
56. #63573C22semidirect
82. #4847D3semidirect
87. #4837D3semidirect
107. D3×D12Q8semidirect
184. #870C2×D3semidirect
195. C3×C4⋊C8C2×D3semidirect
196. C3×C4⋊C8C2×D3semidirect
218. #818C2×D3semidirect
224. #817C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
233. C4⋊(C3⋊C8)C2×D3semidirect
452. C4⋊C8D32semidirect
662. C32#3077semidirect
742. C3#79059semidirect
743. C3#81166semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105938742
#105925462
C3×#48472
C3×#48372
#105909392
#105907642
#105907622
#105907592
#105907572
#105906832
#105906812
#105903082
#105902712
#811663
#790593