Finite Group Databasebeta

← #11870593

Subgroups — #11870593

Order 1152.

840 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×#5624C211yesmaximal, characteristic, complemented
2Dic3×#235C211yesmaximal, characteristic, complemented
3#10592744C211yesmaximal, characteristic, complemented
4C3×#5047C211yesmaximal, characteristic, complemented
5#10591578C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7#10591567C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10591161C211yesmaximal, characteristic
10#10591093C211yesmaximal, characteristic, complemented
11#10591053C211yesmaximal, characteristic, complemented
12#10590493C211yesmaximal, characteristic, complemented
13#10590475C211yesmaximal, characteristic, complemented
14#10590469C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83140—31nomaximal
17#80212—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#898—21no—
28C3×#893C2211yescharacteristic
29C3×#892—21no—
30C3×#890C2211yescharacteristic
31C3×#886—21no—
32C3×#67⋊C4—21no—
33Dic3×#67—21no—
34Dic3×#67—21no—
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37C4×D3×Dic3—21no—
38#63855—21no—
39Dic3×Dic6C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63657C2211yescharacteristic
46#63635C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#809C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63565C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#529—31no—
62Dic3×#41—31no—
63#5624D311yescharacteristic, complemented
64C4×#235—31no—
65C3×#452—31no—
66#5238—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5165—31no—
70Dic3×SD16—31no—
71#5066—31no—
72#5063—31no—
73#5057—31no—
74#5054—31no—
75#5047D311yescharacteristic, complemented
76#5045—31no—
77#5045—31no—
78#5045—61no—
79#5037—31no—
80#5035—31no—
81C4×#216—31no—
82C4×#215—31no—
83C4×#214—31no—
84C4×#213—31no—
85#4925—31no—
86#4799—31no—
87#4788—31no—
88#4766—31no—
89#4756—31no—
90#4737—31no—
91#4718—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3D411yescharacteristic
97C22×C3×Dic3D411yescharacteristic
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110#3757—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#216—22no—
117C3×#215—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3D411yescharacteristic
128C3×C4×Dic3D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3715—22no—
140#3713—22no—
141#3102—91noSylow
142C2×C3×#41—31no—
143C2×#235C2×D311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C3×#126—61no—
147C3×#125—31no—
148C3×#124—31no—
149C3×#123—61no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8C2×D311yescharacteristic
152C3×C22⋊Q8C2×D311yescharacteristic
153C3×#121—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C3×C4×D4—61no—
157C3×#117—61no—
158C2×C3×C42—31no—
159#947C2×D311yescharacteristic
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3C2×D311yescharacteristic
163C2×#216C2×D311yescharacteristic
164C2×#215—31no—
165C2×#215C2×D311yescharacteristic
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170C2×#214—31no—
171C2×#213—31no—
172C2×#213—31no—
173#930C2×D311yescharacteristic
174C4×#67—61no—
175C4×#67—61no—
176#926—31no—
177#926—31no—
178#926—61no—
179#926—61no—
180C2×C4×Dic3—61no—
181C2×C4×Dic3C2×D311yescharacteristic
182#898—21no—
183#893C2×D311yescharacteristic
184#892—21no—
185#890C2×D311yescharacteristic
186#886—21no—
187#67⋊C4—21no—
188C4×D12—31no—
189C4×D12—31no—
190#872—61no—
191C42×D3—61no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×C22⋊C8—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835—61no—
204#832—31no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210#830C2×D311yescharacteristic
211#821—31no—
212#821—31no—
213#818—31no—
214#817—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219#810—31no—
220#810C2×D311yescharacteristic
221#809—31no—
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C32×Q8—21no—
239C32×Q8—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C3×#67—24no—
249C3×#67—42no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—41no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—24no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6#4112yes—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—91no—
274#485—91no—
275#482—91no—
276#479—91no—
277#478—91no—
278#464—91no—
279#463—91no—
280#452—31no—
281#449—91no—
282C4×Q16—91no—
283C4×SD16—91no—
284C4×SD16—91no—
285C4×D8—91no—
286#431—91no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—21no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3#6711yescharacteristic
309C22×Dic3#6711yescharacteristic
310#235—22no—
311#235—22no—
312C2×D12C22×D311yescharacteristic
313C2×D12C22×D311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×Dic6C22×D311yescharacteristic
319C3×Q16—62no—
320C3×SD16—62no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—41no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4C22×D311yescharacteristic
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C22⋊C4—21no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—41no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C42—31no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42—31no—
344C3×C42—61no—
345#217—61no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—121no—
350#216—22no—
351#215—22no—
352#215—62no—
353#214—62no—
354#213—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—61no—
361(C2×D3)⋊C4—61no—
362C4⋊Dic3—21no—
363C4⋊Dic3—21no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376C4×Dic3—21no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—121no—
384C4×Dic3#6711yescharacteristic
385C4×Dic3#6711yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—22no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4C2×#4111yescharacteristic
410C32×C4C2×#4111yescharacteristic
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3×Dic3—22no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3#13512yes—
419C2×#41—31no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—91no—
423C2×D8—91no—
424#126—61no—
425#125—31no—
426#124—31no—
427#123—61no—
428C22⋊Q8D3211yescharacteristic
429#121—31no—
430C4×Q8—31no—
431C4×Q8—91no—
432C4×Q8—91no—
433C4×D4—31no—
434C4×D4—61no—
435C4×D4—91no—
436C4×D4—91no—
437C4×D4—181no—
438C4×D4—181no—
439#117—61no—
440#117—91no—
441#117—181no—
442C2×C42—31no—
443C2×C42—181no—
444#107—91no—
445#107—91no—
446#106—91no—
447#106—91no—
448C4⋊C8—91no—
449C4⋊C8—91no—
450#103—31no—
451#103—91no—
452#103—91no—
453#103—91no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458C22⋊C8—31no—
459C22⋊C8—91no—
460C4×C8—91no—
461C4×C8—91no—
462C23×C3—21no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3D3×D411yescharacteristic
466C23×C3C2×#6711yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—32no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—61no—
477C3×D4—32no—
478C3×D4—64no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4—122no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—64no—
502C2×C3×C4—62no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—122no—
506C2×C3×C4—121no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C2×#6711yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—24no—
512#67—42no—
513C2×Dic3—21no—
514C2×Dic3—22no—
515C2×Dic3—21no—
516C2×Dic3—41no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529D12—21no—
530D12—21no—
531D12—21no—
532D12#23712yes—
533C4×D3—24no—
534C4×D3—42no—
535C4×D3—122no—
536C4×D3—122no—
537Dic6—21no—
538Dic6#23712yes—
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—41no—
550C2×C32#52511yescharacteristic
551C2×C32C2×#13511yescharacteristic
552C2×C32#57511yescharacteristic
553C3×D3—42no—
554C3×D3—81no—
555#41—62no—
556#41—62no—
557C2×Q8—31no—
558C2×Q8C2×D3211yescharacteristic
559C2×D4—31no—
560C2×D4—31no—
561C2×D4—61no—
562C2×D4—61no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—181no—
568C22×C4—181no—
569C22×C4C2×D3211yescharacteristic
570Q16—62no—
571SD16—62no—
572SD16—182no—
573D8—182no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—91no—
577C2×C8—91no—
578C4⋊C4—21no—
579C4⋊C4—31no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—181no—
586C4⋊C4—181no—
587C4⋊C4C2×D3211yescharacteristic
588C22⋊C4—21no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—181no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C42—31no—
597C42—31no—
598C42—31no—
599C42—31no—
600C42—61no—
601C42—181no—
602C42—181no—
603C42—181no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—62no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—32no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—62no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4—121no—
645C3×C4C2×#23711yescharacteristic
646C3×C4C2×#23711yescharacteristic
647C3×C4D3×#4111yescharacteristic
648C3×C4D3×#4111yescharacteristic
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—22no—
653Dic3—41no—
654Dic3—121no—
655Dic3—121no—
656Dic3—121no—
657Dic3—121no—
658Dic3—241no—
659Dic3—241no—
660Dic3#95012yes—
661C32#310211yescharacteristic, complemented, Sylow
662C23—61no—
663C23—61no—
664C23D3×#6711yescharacteristic
665Q8—21no—
666Q8—21no—
667Q8—32no—
668Q8—61no—
669D4—32no—
670D4—64no—
671D4—61no—
672D4—61no—
673D4—61no—
674D4—122no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—122no—
688C2×C4—121no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—362no—
692C2×C4—362no—
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—41no—
703C2×C3—41no—
704C2×C3—81no—
705C2×C3—122no—
706C2×C3—241no—
707C2×C3#558611yescharacteristic
708C2×C3D3×#13511yescharacteristic
709C2×C3#577711yescharacteristic
710C2×C3C2×#95011yescharacteristic
711C2×C3#582211yescharacteristic
712C2×C3#582811yescharacteristic
713D3—42no—
714D3—81no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22C2×D3×#6711yescharacteristic
725C4—21no—
726C4—32no—
727C4—41no—
728C4—41no—
729C4—62no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—121no—
734C4—361no—
735C4—361no—
736C4D3×#23711yescharacteristic
737C4D3×#23711yescharacteristic
738C3—21no—
739C3#8021211yescharacteristic, complemented
740C3#8314011yescharacteristic, complemented
741C2—41no—
742C2—122no—
743C2—241no—
744C2#1059515411yescharacteristic
745C2#1059531711yescharacteristic
746C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10591161C2
hypercenterC22⋊Q8D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5624C2semidirect
2. Dic3×#235C2semidirect
3. #10592744C2semidirect
4. C3×#5047C2semidirect
5. #10591578C2semidirect
6. Dic3×#216C2semidirect
7. #10591567C2semidirect
8. Dic3×#215C2semidirect
10. #10591093C2semidirect
11. #10591053C2semidirect
12. #10590493C2semidirect
13. #10590475C2semidirect
14. #10590469C2semidirect
15. #10590452C2semidirect
63. #5624D3semidirect
75. #5047D3semidirect
661. C32#3102semidirect
739. C3#80212semidirect
740. C3#83140semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
Dic3×#2352
#105927442
C3×#50472
#105915782
Dic3×#2162
#105915672
Dic3×#2152
#105911612
#105910932
#105910532
#105904932
#105904752
#105904692
#105904522
#831403
#802123