Finite Group Databasebeta

← #11889250

Subgroups — #11889250

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5#10591638C211yesmaximal, characteristic, complemented
6#10591624C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic, complemented
8#10591558C211yesmaximal, characteristic, complemented
9#10591458C211yesmaximal, characteristic, complemented
10#10591440C211yesmaximal, characteristic, complemented
11#10591421C211yesmaximal, characteristic, complemented
12#10591408C211yesmaximal, characteristic, complemented
13#10591179C211yesmaximal, characteristic, complemented
14#10591158C211yesmaximal, characteristic, complemented
15#10591093C211yesmaximal, characteristic, complemented
16#83497—31nomaximal
17#80250—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20#64135C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic, complemented
25C3×#939—21no—
26C3×#937—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#929—21no—
31C3×C4×#67C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4—21no—
33C3×#924C2211yescharacteristic, complemented
34#63959—21no—
35#63956—21no—
36#63918C2211yescharacteristic, complemented
37#63862—21no—
38#63856C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic
41#63838—21no—
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5829D311yescharacteristic
63#5641—31no—
64#5542—31no—
65C3×#452—31no—
66#5239D311yescharacteristic, complemented
67#5233—31no—
68#5233—31no—
69#5233—61no—
70#5218—31no—
71#5215—31no—
72#5189—31no—
73#5185—31no—
74#5169—31no—
75#5164—31no—
76#5055—31no—
77#5054—31no—
78#5052—31no—
79#5048—31no—
80#5045—31no—
81#5041—31no—
82#5035—31no—
83#5018—31no—
84#5011—31no—
85#5008—31no—
86#4814—31no—
87#4794—31no—
88#4770—31no—
89#4761—31no—
90#4737—31no—
91#4730—31no—
92C23×C3×D3—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110#3757—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4×C3⋊Dic3—21no—
114C2×C3⋊(C3⋊C8)—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×#214—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3715—41no—
143#3711—41no—
144#3311—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C2×D311yescharacteristic
148C22×C3×D4—31no—
149C2×D3×D4C2×D311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C22⋊C4—61no—
162#947C2×D311yescharacteristic
163#946—31no—
164#946C2×D311yescharacteristic
165Q8×Dic3—31no—
166C2×#216C2×D311yescharacteristic, complemented
167C2×#215—31no—
168#939—21no—
169#937—21no—
170#936—61no—
171D4×Dic3C2×D311yescharacteristic
172C2×#214—31no—
173C2×#214C2×D311yescharacteristic
174#930C2×D311yescharacteristic
175#929—21no—
176C4×#67C2×D311yescharacteristic
177C2×(C2×D3)⋊C4—21no—
178#926—31no—
179#926—31no—
180#926—31no—
181#926—61no—
182#924—31no—
183#924C2×D311yescharacteristic, complemented
184C2×#208—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—61no—
188C2×ΓL(1,𝔽25)—31no—
189#898—61no—
190#892—31no—
191#888—31no—
192#887—61no—
193#887—61no—
194#885—61no—
195#879—61no—
196#879—61no—
197#879—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835—61no—
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—61no—
219#832—61no—
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226#818—31no—
227#817—31no—
228#815—31no—
229Dic3⋊C8—31no—
230#810—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C3×#67—41no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#627—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—31no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—31no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—91no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—24no—
297C3×#41—22no—
298C3×#41—22no—
299C3×#41—41no—
300C3×#41—41no—
301C3×#41—42no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—41no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—121no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C2×#67—21no—
327C2×#67—21no—
328C2×#67#6711yescharacteristic
329C22×Dic3—21no—
330D3×D4—22no—
331D3×D4—41no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—121no—
338C3×SD16—62no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—21no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#217#6711yescharacteristic
363#216—41no—
364#215—121no—
365#214—22no—
366#214—121no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4#6711yescharacteristic
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—121no—
398C4×Dic3C22×D311yescharacteristic
399#208—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411ΓL(1,𝔽25)—121no—
412C22×C32—21no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41D3211yescharacteristic
439C22×D4—31no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—91no—
444C22×C8—91no—
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—31no—
449#124—181no—
450#123—61no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454#121—31no—
455#121—61no—
456#120—61no—
457C4×Q8—91no—
458C4×Q8—181no—
459C4×D4—31no—
460C4×D4—31no—
461#117—91no—
462#117—91no—
463C2×C22⋊C4—61no—
464#107—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480#97—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—122no—
488C23×C3—122no—
489C23×C3—241no—
490C23×C3D3×D411yescharacteristic
491C23×C3C2×#6711yescharacteristic
492C22×D3—21no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—81no—
496C22×D3C2×#6711yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—42no—
510C3×D4—42no—
511C3×D4—44no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—121no—
515C3×D4—122no—
516C3×D4—241no—
517C3×D4#23712yes—
518C3×D4#23712yes—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—41no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—44no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—41no—
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—81no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—21no—
563D12—21no—
564C4×D3—21no—
565C4×D3—21no—
566Dic6—21no—
567Dic6—21no—
568Dic6—122no—
569Dic6—122no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C3⋊C8—121no—
580C2×C32—41no—
581C2×C32—42no—
582C2×C32#54611yescharacteristic
583C2×C32#57511yescharacteristic
584C2×C32#57711yescharacteristic
585C3×D3—41no—
586C3×D3—81no—
587C24—61no—
588#41—22no—
589#41—41no—
590C2×Q8—31no—
591C2×Q8—181no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—21no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4—62no—
598C2×D4—61no—
599C2×D4—121no—
600C2×D4C2×D3211yescharacteristic
601C22×C4—21no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4C2×D3211yescharacteristic
605Q16—121no—
606SD16—62no—
607SD16—361no—
608M16—361no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—91no—
612C2×C8—91no—
613C2×C8—361no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C42—31no—
636C42—181no—
637C42—181no—
638C42—181no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—244no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C22×#6711yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—84no—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4C2×#23711yescharacteristic
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4#100411yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—241no—
703Dic3—241no—
704C32#331111yescharacteristic, complemented, Sylow
705C23—21no—
706C23—31no—
707C23—61no—
708C23—122no—
709C23—122no—
710C23—241no—
711C23D3×#6711yescharacteristic
712Q8—21no—
713Q8—21no—
714Q8—61no—
715Q8—61no—
716Q8—362no—
717D4—21no—
718D4—42no—
719D4—61no—
720D4—61no—
721D4—121no—
722D4—122no—
723D4—241no—
724D4#380512yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—42no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4D3×#6711yescharacteristic
741C2×C4C22×D3211yescharacteristic
742C8—61no—
743C8—61no—
744C8—181no—
745C8—181no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—42no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—42no—
754C2×C3—82no—
755C2×C3—121no—
756C2×C3—241no—
757C2×C3#559111yescharacteristic
758C2×C3#576811yescharacteristic
759C2×C3#577811yescharacteristic
760C2×C3#580611yescharacteristic
761C2×C3#582211yescharacteristic
762C2×C3#583611yescharacteristic
763D3—41no—
764D3—81no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—244no—
778C22C2×D3×#6711yescharacteristic
779C4—21no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—121no—
787C4—361no—
788C4—361no—
789C4C2×#380511yescharacteristic
790C4#6433011yescharacteristic
791C3—21no—
792C3#8025011yescharacteristic, complemented
793C3#8349711yescharacteristic, complemented
794C2—41no—
795C2—42no—
796C2—121no—
797C2—241no—
798C2#1059545311yescharacteristic
799C2#1059546411yescharacteristic
800C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC2×#41D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594841C2semidirect
3. #10592932C2semidirect
4. C3×#5239C2semidirect
5. #10591638C2semidirect
6. #10591624C2semidirect
7. #10591578C2semidirect
8. #10591558C2semidirect
9. #10591458C2semidirect
10. #10591440C2semidirect
11. #10591421C2semidirect
12. #10591408C2semidirect
13. #10591179C2semidirect
14. #10591158C2semidirect
15. #10591093C2semidirect
20. #64135C22semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
24. C2×C3×#216C22semidirect
33. C3×#924C22semidirect
36. #63918C22semidirect
39. Dic3×Dic6C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
48. C3×#835C22semidirect
50. C3×#830C22semidirect
51. #63575C22semidirect
52. #63574C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
60. #63554C22semidirect
66. #5239D3semidirect
166. C2×#216C2×D3semidirect
183. #924C2×D3semidirect
210. #835C2×D3semidirect
222. #830C2×D3semidirect
704. C32#3311semidirect
792. C3#80250semidirect
793. C3#83497semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
#105948412
#105929322
C3×#52392
#105916382
#105916242
#105915782
#105915582
#105914582
#105914402
#105914212
#105914082
#105911792
#105911582
#105910932
#834973
#802503