Finite Group Databasebeta

← #11872124

Subgroups — #11872124

Order 1152.

911 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5603C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic, complemented
3#10592735C211yesmaximal, characteristic
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591432C211yesmaximal, characteristic, complemented
6#10591432C211yesmaximal, characteristic, complemented
7#10591404C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10591183C211yesmaximal, characteristic, complemented
10#10591102C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590466C211yesmaximal, characteristic, complemented
13#10590464C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#83460—31nomaximal
17#81352—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C3×#936—21no—
23C3×#936C2211yescharacteristic, complemented
24C3×#935—21no—
25C3×D4×Dic3C2211yescharacteristic, complemented
26C3×#926C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#888C2211yescharacteristic, complemented
30C3×#887C2211yescharacteristic, complemented
31C3×#879—21no—
32C3×#878—21no—
33#63974—21no—
34#63974—21no—
35#63894—21no—
36#63894—21no—
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63657C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#542—31no—
62#5603D311yescharacteristic, complemented
63#5521—31no—
64#5521—31no—
65C3×#482—31no—
66#5087—31no—
67#5084—31no—
68#5057—31no—
69#5057—31no—
70#5046—31no—
71#5045—31no—
72#5036—31no—
73#5036—31no—
74#5036—61no—
75#5035D311yescharacteristic, complemented
76#5026—31no—
77C4×#215—31no—
78#5014—31no—
79C4×#213—31no—
80#5000—31no—
81#4996—31no—
82#4890—31no—
83#4889—31no—
84#4870—31no—
85#4852—31no—
86#4787—31no—
87#4787—31no—
88#4785—31no—
89#4756—31no—
90#4731—31no—
91#4720—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C22×C3×Dic3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#624—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110#3753—22no—
111#3753—22no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#217D411yescharacteristic
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3717—22no—
140#3717—22no—
141#3118—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#124—31no—
148C3×#124—61no—
149C3×#123—61no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—61no—
152C3×#121—21no—
153C3×#121C2×D311yescharacteristic
154C3×#121C2×D311yescharacteristic
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158C3×#117—31no—
159C2×#215—31no—
160C2×#215—31no—
161#936—21no—
162#936C2×D311yescharacteristic, complemented
163#935—21no—
164D4×Dic3C2×D311yescharacteristic, complemented
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170C2×#213—61no—
171#926C2×D311yescharacteristic
172#926C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C2×#204—31no—
175C2×#204—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—61no—
181#893—61no—
182#888C2×D311yescharacteristic, complemented
183#887C2×D311yescharacteristic, complemented
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—21no—
189#878—21no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12—61no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#832C2×D311yescharacteristic, complemented
204#832C2×D311yescharacteristic, complemented
205#830—31no—
206#830—31no—
207#830—61no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809—61no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic, complemented
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—
239C22×C3⋊D3—24no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3—81no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C4⋊(C3⋊D3)—24no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4⋊(C3⋊D3)#4112yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—81no—
267#624—81no—
268#624—81no—
269#624—81no—
270#624—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—31no—
276#518—91no—
277#485—91no—
278#482—31no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C23×D3—121no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—41no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×Dic3—21no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—62no—
313C2×D12—62no—
314C2×D12—62no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—122no—
319C2×D12—122no—
320C2×D12—121no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—21no—
330C2×Dic6C22×D311yescharacteristic
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—31no—
356C3×C42—61no—
357C3×C42—61no—
358#217—21no—
359#217—21no—
360#217—21no—
361#217—21no—
362#217—21no—
363#217#6711yescharacteristic
364#217#6711yescharacteristic
365#215—62no—
366#215—62no—
367#213—62no—
368#213—62no—
369#213—62no—
370#213—62no—
371#213—122no—
372#213—122no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381C4⋊Dic3#6711yescharacteristic
382C4⋊Dic3#6711yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
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
401#204—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—22no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—84no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×D4—91no—
430C2×SD16—91no—
431C2×SD16—91no—
432C2×D8—91no—
433C2×D8—91no—
434C4⋊Q8—31no—
435#126—61no—
436#124—31no—
437#124—61no—
438#123—61no—
439C22⋊Q8—31no—
440C22⋊Q8—61no—
441#121D3211yescharacteristic
442C4×Q8—31no—
443C4×D4—31no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—181no—
449C4×D4—181no—
450#117—31no—
451#117—31no—
452C2×C22⋊C4—181no—
453C2×C22⋊C4—181no—
454#107—31no—
455#107—91no—
456#106—31no—
457#106—91no—
458C4⋊C8—91no—
459C4⋊C8—91no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—31no—
469C22⋊C8—91no—
470#97—91no—
471C4×C8—91no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—64no—
483C22×D3—64no—
484C22×D3—121no—
485C22×D3—121no—
486C22×D3—124no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—242no—
492C22×D3—242no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—241no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—81no—
503C3×D4—81no—
504C3×D4—82no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—81no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538D12—32no—
539D12—32no—
540D12—32no—
541D12—32no—
542D12—62no—
543D12—62no—
544D12—64no—
545D12—64no—
546D12—61no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12—121no—
552D12—124no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561Dic6—21no—
562Dic6—21no—
563Dic6—81no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8—121no—
574C2×C32—41no—
575C2×C32—81no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57711yescharacteristic
579C3⋊D3—42no—
580C3⋊D3—42no—
581C24—181no—
582C2×Q8—31no—
583C2×Q8—61no—
584C2×D4—21no—
585C2×D4—91no—
586C2×D4—91no—
587C2×D4—182no—
588C2×D4—182no—
589C2×D4—181no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—61no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4C2×D3211yescharacteristic
597SD16—182no—
598SD16—182no—
599D8—182no—
600D8—182no—
601C2×C8—31no—
602C2×C8—31no—
603C2×C8—91no—
604C2×C8—91no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—31no—
628C42—61no—
629C42—61no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C22×#6711yescharacteristic
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—241no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3—248no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4D3×#4111yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691C3×C4D3×#4111yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700C32#311811yescharacteristic, complemented, Sylow
701C23—21no—
702C23—184no—
703C23—181no—
704C23—181no—
705C23—721no—
706C23—721no—
707C23D3×#6711yescharacteristic
708Q8—61no—
709Q8—61no—
710Q8—241no—
711D4—21no—
712D4—21no—
713D4—81no—
714D4—92no—
715D4—92no—
716D4—184no—
717D4—181no—
718D4—181no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—241no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4—721no—
735C2×C4D3×#6711yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—61no—
738C8—61no—
739C8—181no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—42no—
745C2×C3—41no—
746C2×C3—41no—
747C2×C3—81no—
748C2×C3—81no—
749C2×C3—161no—
750C2×C3#565611yescharacteristic
751C2×C3#577011yescharacteristic
752C2×C3#577411yescharacteristic
753C2×C3#582811yescharacteristic
754C2×C3#583511yescharacteristic
755C2×C3#583711yescharacteristic
756D3—122no—
757D3—122no—
758D3—122no—
759D3—122no—
760D3—242no—
761D3—242no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—182no—
769C22—182no—
770C22—361no—
771C22—361no—
772C22—361no—
773C22—361no—
774C22—724no—
775C22C2×D3×#6711yescharacteristic
776C4—21no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4#6431211yescharacteristic
787C4#6431211yescharacteristic
788C3—21no—
789C3#8135211yescharacteristic, complemented
790C3#8346011yescharacteristic, complemented
791C2—41no—
792C2—81no—
793C2—362no—
794C2—362no—
795C2#1059509711yescharacteristic
796C2#1059515911yescharacteristic
797C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radical#10592735C2
hypercenter#121D32
hypocenterC32#3118
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×#5603C2semidirect
2. #10594996C2semidirect
4. C3×#5035C2semidirect
5. #10591432C2semidirect
6. #10591432C2semidirect
7. #10591404C2semidirect
8. #10591400C2semidirect
9. #10591183C2semidirect
10. #10591102C2semidirect
11. #10591056C2semidirect
12. #10590466C2semidirect
13. #10590464C2semidirect
14. #10590458C2semidirect
15. #10590457C2semidirect
23. C3×#936C22semidirect
25. C3×D4×Dic3C22semidirect
29. C3×#888C22semidirect
30. C3×#887C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5603D3semidirect
75. #5035D3semidirect
162. #936C2×D3semidirect
164. D4×Dic3C2×D3semidirect
182. #888C2×D3semidirect
183. #887C2×D3semidirect
203. #832C2×D3semidirect
204. #832C2×D3semidirect
227. #808C2×D3semidirect
230. #807C2×D3semidirect
700. C32#3118semidirect
789. C3#81352semidirect
790. C3#83460semidirect

Maximal subgroups

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

subgroupindex
C3×#56032
#105949962
#105927352
C3×#50352
#105914322
#105914042
#105914002
#105911832
#105911022
#105910562
#105904662
#105904642
#105904582
#105904572
#834603
#813523