Finite Group Databasebeta

← #11872981

Subgroups — #11872981

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5733C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3#10592786C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5#10590616C211yesmaximal, characteristic, complemented
6#10590615C211yesmaximal, characteristic
7#10590478C211yesmaximal, characteristic, complemented
8#10590476C211yesmaximal, characteristic, complemented
9#10590457C211yesmaximal, characteristic, complemented
10#10590456C211yesmaximal, characteristic, complemented
11#10590440C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590267C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83461—31nomaximal
17#81097—31nomaximal
18C2×#3799C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C3×#947—21no—
22C3×#946—21no—
23C3×#898—21no—
24C3×#897C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#894—21no—
27C3×#893C2211yescharacteristic
28C3×#887C2211yescharacteristic
29C3×#875C2211yescharacteristic
30C3×#872C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63894C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63883—21no—
35#63881—21no—
36#63880—21no—
37Dic3×Dic6C2211yescharacteristic
38#63836—21no—
39C2×#3718C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63636C2211yescharacteristic
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic
46#63634C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63565C2211yescharacteristic
55#63563C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#542—31no—
62#5733D311yescharacteristic, complemented
63#5574—31no—
64#5523—31no—
65C3×#477—31no—
66#5091D311yescharacteristic, complemented
67#5087—31no—
68#5087—31no—
69#5087—61no—
70#5057—31no—
71#5054—31no—
72#5047—31no—
73#5044—31no—
74#5037—31no—
75#5033—31no—
76C4×#216—31no—
77#5028—31no—
78#5026—31no—
79#5018—31no—
80C4×#213—31no—
81#5000—31no—
82#4889—31no—
83#4884—31no—
84#4882—31no—
85#4872—31no—
86#4844—31no—
87#4840—31no—
88#4817—31no—
89#4810—31no—
90#4808—31no—
91#4790—31no—
92C2×C32×Q8—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105#3799—22no—
106#3799—22no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C42C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136Dic32—21no—
137#3718—22no—
138#3717—22no—
139#3715—22no—
140#3714—22no—
141#3124—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C3×C4⋊Q8—21no—
145C3×C4⋊Q8C2×D311yescharacteristic
146C3×C4⋊Q8C2×D311yescharacteristic
147C3×#126—61no—
148C3×#124—31no—
149C3×#124—61no—
150C3×#123—61no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—61no—
153C3×#121—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158#947—21no—
159#946—21no—
160Q8×Dic3—31no—
161C2×#216—31no—
162C2×#216—31no—
163C2×#215—31no—
164C2×#215—31no—
165C2×#214—31no—
166C2×#213—31no—
167C2×C4⋊Dic3—31no—
168C2×D24—31no—
169C2×#204—31no—
170#898—21no—
171#897C2×D311yescharacteristic
172#895C2×D311yescharacteristic
173#894—21no—
174#893—31no—
175#893—61no—
176#893C2×D311yescharacteristic
177#892—61no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—61no—
180D3×C4⋊C4—61no—
181#887C2×D311yescharacteristic
182#67⋊C4—61no—
183#67⋊C4—61no—
184#875C2×D311yescharacteristic
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190#872—61no—
191#872C2×D311yescharacteristic
192C4×Dic6—31no—
193C4×Dic6C2×D311yescharacteristic
194C3×#107—31no—
195C3×#107—31no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#103—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#832—31no—
203#830—31no—
204#830—31no—
205#821—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208#816—31no—
209#815—31no—
210C8×Dic3—31no—
211#810—31no—
212#810C2×D311yescharacteristic
213#810C2×D311yescharacteristic
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#809—61no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—61no—
226#807—61no—
227#807C2×D311yescharacteristic
228#807C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—81no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)#4112yes—
247C4×C3⋊D3—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—81no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—81no—
260C3×Dic6—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6#4112yes—
264#626—24no—
265#624—24no—
266#624—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#542—31no—
273#520—91no—
274#484—91no—
275#480—91no—
276#477—31no—
277#474—91no—
278#464—91no—
279#463—91no—
280#452—91no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×Q8—41no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C22×C3×C4—31no—
295C22×C3×C4—61no—
296C2×#67—61no—
297C22×Dic3—61no—
298#239—62no—
299#239—62no—
300#235—62no—
301#235—62no—
302C2×D12—21no—
303C2×D12—31no—
304C2×D12—31no—
305C2×D12—61no—
306C2×D12—61no—
307C2×D12C22×D311yescharacteristic
308C2×C4×D3—21no—
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×C4×D3C22×D311yescharacteristic
318C2×Dic6C22×D311yescharacteristic
319C2×Dic6C22×D311yescharacteristic
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—41no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42—61no—
348C3×C42C22×D311yescharacteristic
349C3×C42C22×D311yescharacteristic
350#216—62no—
351#216—62no—
352#215—62no—
353#215—62no—
354#214—62no—
355#213—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—121no—
366(C2×D3)⋊C4#6711yescharacteristic
367(C2×D3)⋊C4#6711yescharacteristic
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4#6711yescharacteristic
380Dic3⋊C4#6711yescharacteristic
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—61no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394D24—62no—
395#204—62no—
396C22×C32C22×D411yescharacteristic
397C2×C3⋊D3—22no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—41no—
413C3×Dic3—21no—
414C3×Dic3—22no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C2×#41—91no—
420C2×Q16—91no—
421C2×SD16—91no—
422C2×SD16—91no—
423C2×D8—91no—
424C4⋊Q8D3211yescharacteristic
425#126—61no—
426#124—31no—
427#124—61no—
428#123—61no—
429C22⋊Q8—31no—
430C22⋊Q8—61no—
431#121—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—91no—
435C4×D4—31no—
436C4×D4—91no—
437C4×D4—91no—
438C4×D4—181no—
439C4×D4—181no—
440#117—31no—
441#117—181no—
442C2×C4⋊C4—91no—
443C2×C4⋊C4—181no—
444#107—31no—
445#107—31no—
446#107—91no—
447#107—91no—
448C4⋊C8—31no—
449C4⋊C8—91no—
450#103—31no—
451#103—31no—
452#103—91no—
453#103—91no—
454#102—91no—
455#102—91no—
456#102—91no—
457#102—91no—
458C22⋊C8—91no—
459C22⋊C8—91no—
460#97—91no—
461C4×C8—91no—
462C23×C3—31no—
463C23×C3—61no—
464C22×D3—21no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—121no—
468C22×D3C2×#6711yescharacteristic
469C3×Q8—32no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×Q8—81no—
474C3×Q8—81no—
475C3×Q8—82no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—241no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
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—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—241no—
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4C2×#6711yescharacteristic
500C2×C3×C4C2×#6711yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503#67—64no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—121no—
510C2×Dic3—241no—
511C2×Dic3C2×#6711yescharacteristic
512C2×Dic3C2×#6711yescharacteristic
513C2×Dic3C2×#6711yescharacteristic
514D12—21no—
515D12—21no—
516D12—32no—
517D12—32no—
518D12—62no—
519D12—64no—
520D12—61no—
521D12—61no—
522D12—81no—
523D12—121no—
524C4×D3—21no—
525C4×D3—21no—
526C4×D3—64no—
527C4×D3—64no—
528C4×D3—81no—
529C4×D3—241no—
530C4×D3—241no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—242no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6#23912yes—
539C3×C8—61no—
540C3×C8—61no—
541C3⋊C8—21no—
542C3⋊C8—21no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—121no—
548C3⋊C8—121no—
549C2×C32#52511yescharacteristic
550C2×C32#57611yescharacteristic
551C2×C32#57811yescharacteristic
552C3⋊D3—42no—
553C3×D3—41no—
554C3×D3—81no—
555#41—182no—
556#41—182no—
557C2×Q8—21no—
558C2×Q8—31no—
559C2×Q8—31no—
560C2×D4—31no—
561C2×D4—61no—
562C2×D4—91no—
563C2×D4—181no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—181no—
567C22×C4—181no—
568C22×C4—181no—
569C22×C4—181no—
570Q16—182no—
571SD16—182no—
572SD16—182no—
573D8—182no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—91no—
577C2×C8—91no—
578C4⋊C4—21no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—91no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4C2×D3211yescharacteristic
589C4⋊C4C2×D3211yescharacteristic
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C42—31no—
600C42—61no—
601C42—61no—
602C42—181no—
603C42C2×D3211yescharacteristic
604C22×C3—21no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3C2×D3×D411yescharacteristic
612C22×C3C22×#6711yescharacteristic
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—62no—
620C2×D3—62no—
621C2×D3—122no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—241no—
627C2×D3—241no—
628C3×C4—22no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—62no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C2×#23911yescharacteristic
649C3×C4D3×#4111yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4D3×#4111yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—22no—
656Dic3—41no—
657Dic3—41no—
658Dic3—121no—
659Dic3—121no—
660Dic3—241no—
661C32#312411yescharacteristic, complemented, Sylow
662C23—31no—
663C23—61no—
664C23—181no—
665Q8—32no—
666Q8—61no—
667Q8—61no—
668Q8—61no—
669Q8—81no—
670D4—61no—
671D4—61no—
672D4—92no—
673D4—184no—
674D4—181no—
675D4—241no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—184no—
687C2×C4—181no—
688C2×C4—241no—
689C2×C4—721no—
690C2×C4—721no—
691C2×C4—721no—
692C2×C4D3×#6711yescharacteristic
693C2×C4D3×#6711yescharacteristic
694C2×C4C22×D3211yescharacteristic
695C8—61no—
696C8—61no—
697C8—181no—
698C8—181no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—121no—
703C2×C3—241no—
704C2×C3#562711yescharacteristic
705C2×C3#576611yescharacteristic
706C2×C3#577411yescharacteristic
707C2×C3#582811yescharacteristic
708C2×C3#583511yescharacteristic
709C2×C3#583811yescharacteristic
710D3—41no—
711D3—81no—
712D3—122no—
713D3—122no—
714D3—242no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—182no—
722C22—361no—
723C22—361no—
724C22C2×D3×#6711yescharacteristic
725C4—21no—
726C4—21no—
727C4—41no—
728C4—41no—
729C4—61no—
730C4—61no—
731C4—62no—
732C4—61no—
733C4—121no—
734C4—121no—
735C4—361no—
736C4D3×#23911yescharacteristic
737C4#6431911yescharacteristic
738C3—21no—
739C3#8109711yescharacteristic, complemented
740C3#8346111yescharacteristic, complemented
741C2—121no—
742C2—241no—
743C2—362no—
744C2#1059509711yescharacteristic
745C2#1059532711yescharacteristic
746C2#1059542411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10590615C2
hypercenterC4⋊Q8D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5733C2semidirect
2. #10593890C2semidirect
3. #10592786C2semidirect
4. C3×#5091C2semidirect
5. #10590616C2semidirect
7. #10590478C2semidirect
8. #10590476C2semidirect
9. #10590457C2semidirect
10. #10590456C2semidirect
11. #10590440C2semidirect
12. #10590438C2semidirect
13. #10590356C2semidirect
14. #10590267C2semidirect
15. #10590253C2semidirect
62. #5733D3semidirect
66. #5091D3semidirect
661. C32#3124semidirect
739. C3#81097semidirect
740. C3#83461semidirect

Maximal subgroups

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

subgroupindex
C3×#57332
#105938902
#105927862
C3×#50912
#105906162
#105906152
#105904782
#105904762
#105904572
#105904562
#105904402
#105904382
#105903562
#105902672
#105902532
#834613
#810973