Finite Group Databasebeta

← #11872148

Subgroups — #11872148

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2#10593877C211yesmaximal, characteristic, complemented
3#10592715C211yesmaximal, characteristic, complemented
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591459C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic
7#10591405C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590589C211yesmaximal, characteristic, complemented
10#10590479C211yesmaximal, characteristic, complemented
11#10590428C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82541—31nomaximal
17#81048—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22#64084C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×#869C2211yescharacteristic, complemented
33#63909C2211yescharacteristic
34#63907—21no—
35#63894C2211yescharacteristic, complemented
36#63888—21no—
37#63857C2211yescharacteristic
38#63854—21no—
39#63848—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63637C2211yescharacteristic, complemented
44#63636C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#808C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5733—31no—
63#5545D311yescharacteristic, complemented
64#5534—31no—
65C3×#476—31no—
66#5218—31no—
67#5217—31no—
68#5087—31no—
69#5018—31no—
70C4×#214—31no—
71#5016—31no—
72#5016—31no—
73#5016—31no—
74#5016—61no—
75#5014—31no—
76C4×#213—31no—
77#5008D311yescharacteristic, complemented
78#5007—31no—
79#5003—31no—
80#5000—31no—
81#4996—31no—
82#4869—31no—
83#4868—31no—
84#4866—31no—
85#4852—31no—
86#4844—31no—
87#4840—31no—
88#4776—31no—
89#4773—31no—
90#4757—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×#626—21no—
107C2×#624—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3754—22no—
112#3753—22no—
113#3752—21no—
114#3752—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3716—22no—
140#3714—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C3×C4⋊Q8—31no—
145C3×C4×D4—21no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×C4×D4C2×D311yescharacteristic
152C3×C4×D4C2×D311yescharacteristic
153C3×#117—31no—
154C3×#117—31no—
155C2×C3×C22⋊C4—61no—
156C2×C3×C22⋊C4—61no—
157#947—61no—
158#946—61no—
159D4×Dic3C2×D311yescharacteristic
160C2×#214—31no—
161C2×#214—31no—
162C2×#214—31no—
163C2×#214—61no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169C4×#67—21no—
170C2×(C2×D3)⋊C4—21no—
171#924—31no—
172C2×D24—31no—
173C2×#204—31no—
174#898—61no—
175#898—61no—
176#897—31no—
177#896—61no—
178#895—31no—
179#894—61no—
180#893—31no—
181#893C2×D311yescharacteristic
182#892C2×D311yescharacteristic
183#887—31no—
184#885—61no—
185#883—61no—
186#67⋊C4—21no—
187D3×C22⋊C4—21no—
188#875—31no—
189#875—31no—
190#875—61no—
191C4×D12—31no—
192C4×D12C2×D311yescharacteristic
193#872C2×D311yescharacteristic
194#869C2×D311yescharacteristic, complemented
195C4×Dic6—31no—
196C3×#106—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×#102—31no—
200C3×#102—31no—
201#832—31no—
202#832—31no—
203#832C2×D311yescharacteristic
204#832C2×D311yescharacteristic
205#830—31no—
206#830—31no—
207#821—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210#816—31no—
211#815—31no—
212C8×Dic3—31no—
213#810—31no—
214#810—31no—
215#810—31no—
216#810—61no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#808C2×D311yescharacteristic, complemented
224#808C2×D311yescharacteristic, complemented
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252#634—21no—
253#634—21no—
254C3×#67—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×Dic6—81no—
269#626—81no—
270#624—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—31no—
277#485—91no—
278#482—91no—
279#476—31no—
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—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—61no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—21no—
308C2×#67—61no—
309C22×Dic3—21no—
310D3×D4—22no—
311D3×D4—22no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3C22×D311yescharacteristic
322C2×Dic6—21no—
323C2×Dic6—31no—
324C2×Dic6—31no—
325C2×Dic6—61no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—21no—
352#217—61no—
353#214—62no—
354#214—62no—
355#214—62no—
356#214—122no—
357#213—62no—
358#213—62no—
359#213—62no—
360#213—122no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4#6711yescharacteristic
376(C2×D3)⋊C4#6711yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4#6711yescharacteristic
386Dic3⋊C4#6711yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399D24—62no—
400#204—62no—
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—84no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—31no—
428C2×SD16—91no—
429C2×SD16—91no—
430C2×D8—91no—
431C2×D8—91no—
432C4⋊Q8—31no—
433#126—181no—
434#124—91no—
435#124—181no—
436#123—181no—
437C22⋊Q8—91no—
438C22⋊Q8—181no—
439#121—91no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—61no—
445C4×D4—61no—
446C4×D4—91no—
447C4×D4D3211yescharacteristic
448#117—31no—
449#117—31no—
450C2×C22⋊C4—61no—
451C2×C22⋊C4—61no—
452#107—91no—
453#107—91no—
454#106—31no—
455#106—31no—
456C4⋊C8—31no—
457C4⋊C8—91no—
458#103—91no—
459#103—91no—
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468#97—91no—
469C4×C8—91no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—64no—
475C23×C3—61no—
476C23×C3—241no—
477C23×C3—241no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—81no—
483C22×D3—81no—
484C22×D3—121no—
485C22×D3C2×#6711yescharacteristic
486C3×Q8—241no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—32no—
491C3×D4—41no—
492C3×D4—64no—
493C3×D4—61no—
494C3×D4#23512yes—
495C3×D4#23912yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—81no—
511C2×C3×C4—81no—
512C2×C3×C4—82no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—24no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—81no—
530C2×Dic3—121no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534D12—21no—
535D12—61no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12—121no—
541D12—241no—
542D12#23512yes—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—241no—
548C4×D3—241no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—81no—
554Dic6—121no—
555Dic6—121no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C3⋊C8—121no—
566C2×C32—42no—
567C2×C32#52511yescharacteristic
568C2×C32#57611yescharacteristic
569C2×C32#57711yescharacteristic
570C3⋊D3—81no—
571C3×D3—41no—
572C3×D3—42no—
573C24—61no—
574C2×Q8—61no—
575C2×Q8—91no—
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—91no—
581C2×D4—181no—
582C2×D4C2×D3211yescharacteristic
583C22×C4—21no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—181no—
589SD16—182no—
590SD16—182no—
591D8—182no—
592D8—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8—91no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—61no—
620C42—181no—
621C42C2×D3211yescharacteristic
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—62no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—244no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—22no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—84no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—241no—
655C2×D3—241no—
656C2×D3—241no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4C2×#23511yescharacteristic
676C3×C4C2×#23911yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—121no—
685Dic3—121no—
686Dic3—241no—
687C32#311811yescharacteristic, complemented, Sylow
688C23—21no—
689C23—31no—
690C23—64no—
691C23—61no—
692C23—181no—
693C23—241no—
694C23—241no—
695Q8—181no—
696Q8—181no—
697Q8—241no—
698D4—21no—
699D4—32no—
700D4—64no—
701D4—61no—
702D4—181no—
703D4—181no—
704D4—721no—
705D4#379912yes—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—81no—
716C2×C4—181no—
717C2×C4—241no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—721no—
721C2×C4D3×#6711yescharacteristic
722C2×C4D3×#6711yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—61no—
725C8—61no—
726C8—181no—
727C8—181no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—82no—
734C2×C3—121no—
735C2×C3—122no—
736C2×C3#562711yescharacteristic
737C2×C3#576211yescharacteristic
738C2×C3#577411yescharacteristic
739C2×C3#579111yescharacteristic
740C2×C3#583511yescharacteristic
741C2×C3#583611yescharacteristic
742D3—41no—
743D3—42no—
744D3—241no—
745D3—241no—
746D3—481no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—62no—
754C22—121no—
755C22—121no—
756C22—244no—
757C22—361no—
758C22—361no—
759C22—361no—
760C22C2×D3×#6711yescharacteristic
761C4—21no—
762C4—21no—
763C4—41no—
764C4—61no—
765C4—61no—
766C4—61no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—361no—
771C4C2×#379911yescharacteristic
772C4D3×#23511yescharacteristic
773C3—21no—
774C3#8104811yescharacteristic, complemented
775C3#8254111yescharacteristic, complemented
776C2—42no—
777C2—121no—
778C2—122no—
779C2—721no—
780C2#1059500511yescharacteristic
781C2#1059510511yescharacteristic
782C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591448C2
hypercenterC4×D4D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5545C2semidirect
2. #10593877C2semidirect
3. #10592715C2semidirect
4. C3×#5008C2semidirect
5. #10591459C2semidirect
7. #10591405C2semidirect
8. #10591400C2semidirect
9. #10590589C2semidirect
10. #10590479C2semidirect
11. #10590428C2semidirect
12. #10590425C2semidirect
13. #10590366C2semidirect
14. #10590269C2semidirect
15. #10590253C2semidirect
22. #64084C22semidirect
32. C3×#869C22semidirect
35. #63894C22semidirect
40. #63844C22semidirect
43. #63637C22semidirect
44. #63636C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#808C22semidirect
49. C3×#808C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63567C22semidirect
54. #63564C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5545D3semidirect
77. #5008D3semidirect
194. #869C2×D3semidirect
223. #808C2×D3semidirect
224. #808C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
687. C32#3118semidirect
774. C3#81048semidirect
775. C3#82541semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105938772
#105927152
C3×#50082
#105914592
#105914482
#105914052
#105914002
#105905892
#105904792
#105904282
#105904252
#105903662
#105902692
#105902532
#825413
#810483