Finite Group Databasebeta

← #11872278

Subgroups — #11872278

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5619C211yesmaximal, characteristic, complemented
2#10594990C211yesmaximal, characteristic, complemented
3#10592736C211yesmaximal, characteristic, complemented
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591439C211yesmaximal, characteristic, complemented
6#10591429C211yesmaximal, characteristic, complemented
7#10591405C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10591182C211yesmaximal, characteristic, complemented
10#10591089C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590589C211yesmaximal, characteristic, complemented
13#10590490C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590470C211yesmaximal, characteristic, complemented
16#83434—31nomaximal
17#81312—31nomaximal
18C2×#3828C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#939—21no—
24C3×#938—21no—
25C3×D4×Dic3C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#886—21no—
32C3×#883—21no—
33#63952—21no—
34#63952—21no—
35#63900—21no—
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic
38#63849—21no—
39#63844C2211yescharacteristic
40#63844C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63657C2211yescharacteristic
44#63637C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63576C2211yescharacteristic
52#63576C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#540—31no—
62#5619D311yescharacteristic, complemented
63#5523—31no—
64#5504—31no—
65C3×#481—31no—
66#5075—31no—
67#5072—31no—
68#5066—31no—
69#5063—31no—
70#5037—31no—
71#5037—31no—
72#5037—31no—
73#5037—61no—
74#5034D311yescharacteristic, complemented
75#5033—31no—
76#5018—31no—
77C4×#214—31no—
78#5014—31no—
79C4×#213—31no—
80#5000—31no—
81#4967—31no—
82#4871—31no—
83#4869—31no—
84#4857—31no—
85#4852—31no—
86#4786—31no—
87#4762—31no—
88#4757—31no—
89#4756—31no—
90#4734—31no—
91#4720—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96#3828—22no—
97#3828—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×#624—21no—
109C2×#624—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3754—22no—
113#3753—22no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135#3722—21no—
136#3722—21no—
137Dic32—21no—
138Dic32—21no—
139#3716—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#235—31no—
143C2×#235—31no—
144C2×#235—61no—
145C3×#127—31no—
146C3×#125—31no—
147C3×#123—61no—
148C3×#123—61no—
149C3×#121—21no—
150C3×#121—31no—
151C3×#121—61no—
152C3×#121—61no—
153C3×#121C2×D311yescharacteristic
154C3×#121C2×D311yescharacteristic
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158C2×C3×C4⋊C4—31no—
159#940C2×D311yescharacteristic
160#939—21no—
161#938—21no—
162D4×Dic3C2×D311yescharacteristic
163C2×#214—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—61no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—61no—
171#930C2×D311yescharacteristic
172C4×#67—61no—
173C4×#67—61no—
174#926C2×D311yescharacteristic
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×D24—31no—
177C2×#204—31no—
178#893—31no—
179#893—31no—
180#893C2×D311yescharacteristic
181#892—61no—
182#892—61no—
183D3×C4⋊C4—61no—
184D3×C4⋊C4—61no—
185#890C2×D311yescharacteristic
186#887—31no—
187#887—31no—
188#886—21no—
189#883—21no—
190#67⋊C4—61no—
191#67⋊C4—61no—
192C4×D12—31no—
193C4×D12—31no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#106—31no—
197C3×#106—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#832—31no—
202#832—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#830—31no—
206#830—31no—
207#830—61no—
208#830C2×D311yescharacteristic
209#821—31no—
210#816—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—61no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#808C2×D311yescharacteristic
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247#638—24no—
248C2×C3⋊Dic3—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—24no—
252#634—21no—
253#634#4112yes—
254C3×#67—81no—
255C3×#67—81no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—81no—
269#624—81no—
270#624—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—31no—
276#520—91no—
277#481—31no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4—41no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314#235—62no—
315#235—62no—
316#235—62no—
317#235—62no—
318#235—122no—
319#235—122no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357C3×C42—31no—
358#217—21no—
359#217#6711yescharacteristic
360#217#6711yescharacteristic
361#214—62no—
362#214—62no—
363#214—62no—
364#214—122no—
365#213—62no—
366#213—62no—
367#213—62no—
368#213—122no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3#6711yescharacteristic
378C4⋊Dic3#6711yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401D24—62no—
402#204—62no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—22no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C2×#41—91no—
429C2×SD16—91no—
430C2×SD16—91no—
431C2×D8—91no—
432C2×D8—91no—
433#127—31no—
434#125—31no—
435#123—61no—
436#123—61no—
437#121—31no—
438#121—61no—
439#121—61no—
440#121D3211yescharacteristic
441C4×Q8—91no—
442C4×Q8—91no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—181no—
448C4×D4—181no—
449#117—31no—
450#117—181no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—181no—
453#107—91no—
454#107—91no—
455#106—31no—
456#106—31no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459#103—91no—
460#103—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—91no—
469#97—91no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—61no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3—21no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—81no—
491C3×D4—81no—
492C3×D4—82no—
493C3×D4—241no—
494C3×D4—241no—
495C3×D4—241no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—64no—
522#67—64no—
523#67—81no—
524#67—81no—
525#67—81no—
526#67—124no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—81no—
533C2×Dic3—81no—
534C2×Dic3—121no—
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—62no—
544D12—61no—
545D12—61no—
546D12—121no—
547C4×D3—64no—
548C4×D3—64no—
549C4×D3—81no—
550C4×D3—124no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32—41no—
572C2×C32—81no—
573C2×C32#52511yescharacteristic
574C2×C32#57611yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—42no—
577C3×D3—81no—
578#41—182no—
579#41—182no—
580C2×Q8—91no—
581C2×D4—21no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—91no—
587C2×D4—181no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4C2×D3211yescharacteristic
596SD16—182no—
597SD16—182no—
598D8—182no—
599D8—182no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—91no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4C2×D3211yescharacteristic
615C22⋊C4—21no—
616C22⋊C4—31no—
617C22⋊C4—31no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C42—31no—
624C42—31no—
625C42—181no—
626C42—181no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C22×#6711yescharacteristic
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—241no—
662C2×D3—241no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4D3×#4111yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—62no—
690Dic3—62no—
691Dic3—122no—
692C32#311911yescharacteristic, complemented, Sylow
693C23—21no—
694C23—61no—
695C23—181no—
696C23D3×#6711yescharacteristic
697Q8—92no—
698Q8—181no—
699D4—21no—
700D4—21no—
701D4—61no—
702D4—61no—
703D4—81no—
704D4—92no—
705D4—184no—
706D4—181no—
707D4—241no—
708D4—241no—
709D4—241no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—184no—
721C2×C4—181no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4D3×#6711yescharacteristic
728C2×C4C22×D3211yescharacteristic
729C8—61no—
730C8—61no—
731C8—181no—
732C8—181no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—81no—
739C2×C3—81no—
740C2×C3—81no—
741C2×C3—161no—
742C2×C3—241no—
743C2×C3#565611yescharacteristic
744C2×C3#576211yescharacteristic
745C2×C3#577411yescharacteristic
746C2×C3#582811yescharacteristic
747C2×C3#583511yescharacteristic
748C2×C3#583611yescharacteristic
749D3—81no—
750D3—122no—
751D3—122no—
752D3—242no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—182no—
763C22—361no—
764C22—361no—
765C22C2×D3×#6711yescharacteristic
766C4—21no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—182no—
776C4#6431211yescharacteristic
777C4#6431211yescharacteristic
778C3—21no—
779C3#8131211yescharacteristic, complemented
780C3#8343411yescharacteristic, complemented
781C2—41no—
782C2—81no—
783C2—241no—
784C2—362no—
785C2#1059510511yescharacteristic
786C2#1059515911yescharacteristic
787C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5619C2semidirect
2. #10594990C2semidirect
3. #10592736C2semidirect
4. C3×#5034C2semidirect
5. #10591439C2semidirect
6. #10591429C2semidirect
7. #10591405C2semidirect
8. #10591400C2semidirect
9. #10591182C2semidirect
10. #10591089C2semidirect
11. #10591056C2semidirect
12. #10590589C2semidirect
13. #10590490C2semidirect
14. #10590479C2semidirect
15. #10590470C2semidirect
62. #5619D3semidirect
74. #5034D3semidirect
692. C32#3119semidirect
779. C3#81312semidirect
780. C3#83434semidirect

Maximal subgroups

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

subgroupindex
C3×#56192
#105949902
#105927362
C3×#50342
#105914392
#105914292
#105914052
#105914002
#105911822
#105910892
#105910562
#105905892
#105904902
#105904792
#105904702
#834343
#813123