Finite Group Databasebeta

← #11889721

Subgroups — #11889721

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3#10592743C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5#10591624C211yesmaximal, characteristic, complemented
6#10591597C211yesmaximal, characteristic, complemented
7#10591578C211yesmaximal, characteristic, complemented
8#10591550C211yesmaximal, characteristic, complemented
9#10591169C211yesmaximal, characteristic, complemented
10#10591155C211yesmaximal, characteristic, complemented
11C2×#63563C211yesmaximal, characteristic, complemented
12#10590555C211yesmaximal, characteristic, complemented
13#10590515C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#80777—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#895—21no—
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893C2211yescharacteristic
31C3×#882—21no—
32C3×D3×C22⋊C4—21no—
33#63982—21no—
34#67⋊Dic3—21no—
35#63918C2211yescharacteristic, complemented
36#63893—21no—
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63856C2211yescharacteristic, complemented
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63657C2211yescharacteristic
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#835C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5635—31no—
63#5630D311yescharacteristic
64#5543—31no—
65C3×#467—31no—
66#5239—31no—
67#5232—31no—
68#5218—31no—
69C2×#832—31no—
70#5187—31no—
71#5185—31no—
72C2×#821—31no—
73#5111—31no—
74#5055—31no—
75#5054—31no—
76#5051D311yescharacteristic, complemented
77#5046—31no—
78#5044—31no—
79#5044—31no—
80#5044—61no—
81#5042—31no—
82#5033—31no—
83#5018—31no—
84#5011—31no—
85#5007—31no—
86#4890—31no—
87#4882—31no—
88#4817—31no—
89#4812—31no—
90#4803—31no—
91#4794—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67D411yescharacteristic
97C3×#239—22no—
98C3×#239—41no—
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#216—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3715—22no—
142#3715—41no—
143#3711—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C22⋊Q8C2×D311yescharacteristic
157C3×#121—31no—
158C3×#121—61no—
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#947C2×D311yescharacteristic
164#946—31no—
165Q8×Dic3—31no—
166C2×#216C2×D311yescharacteristic, complemented
167C2×#215—31no—
168C2×#215—31no—
169D4×Dic3—61no—
170C2×#214—31no—
171C2×#214—31no—
172C4×#67C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177#924—31no—
178#924C2×D311yescharacteristic
179C2×#208—31no—
180C22×C3⋊C8C2×D311yescharacteristic
181C2×ΓL(1,𝔽25)—31no—
182#897—61no—
183#895—21no—
184#895C2×D311yescharacteristic
185#894—21no—
186#893C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#888—31no—
191#882—21no—
192#67⋊C4—61no—
193D3×C22⋊C4—21no—
194#878—61no—
195#878—61no—
196#878—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#107—31no—
200C3×#103—31no—
201C3×#103—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#835—61no—
208#835C2×D311yescharacteristic, complemented
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224#815—31no—
225Dic3⋊C8—31no—
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
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—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12—42no—
267C3×D12—81no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#627—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—31no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—31no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67#6711yescharacteristic
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—121no—
323#239—22no—
324#239—41no—
325C2×D12—22no—
326C2×D12—21no—
327C2×D12—21no—
328C2×D12—21no—
329C2×D12—41no—
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—61no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—121no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—121no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—41no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—21no—
364#217—61no—
365#217#6711yescharacteristic
366#216—41no—
367#215—62no—
368#215—121no—
369#214—62no—
370#214—121no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4#6711yescharacteristic
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—121no—
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—41no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410ΓL(1,𝔽25)—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13712yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—41no—
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—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—31no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—31no—
444C4⋊Q8—91no—
445#125—181no—
446#124—31no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—181no—
451C22⋊Q8—181no—
452C22⋊Q8D3211yescharacteristic
453#121—31no—
454#121—61no—
455#120—61no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—61no—
463#107—31no—
464#107—91no—
465#107—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—81no—
494C22×D3C2×#6711yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—32no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—122no—
509C3×D4—122no—
510C3×D4—241no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—122no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—22no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—242no—
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—21no—
555D12—21no—
556D12—21no—
557D12—42no—
558D12—42no—
559D12—81no—
560D12#23712yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—42no—
564C4×D3—81no—
565C4×D3—241no—
566Dic6—21no—
567Dic6—21no—
568Dic6—241no—
569Dic6—241no—
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—22no—
581C2×C32#54611yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C2×C32#57611yescharacteristic
584C3×D3—41no—
585C3×D3—42no—
586C3×D3—81no—
587C24—61no—
588#41—62no—
589#41—121no—
590C2×Q8—31no—
591C2×Q8—181no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—121no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607Q16—121no—
608SD16—182no—
609SD16—361no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—121no—
616C4⋊C4—21no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—244no—
657C22×C3#91812yes—
658C22×C3#95112yes—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—21no—
662C2×D3—22no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4C2×#23711yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4#100411yescharacteristic
690C3×C4D3×#4111yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#331411yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—61no—
706C23—122no—
707C23—122no—
708C23—241no—
709C23D3×#6711yescharacteristic
710Q8—21no—
711Q8—21no—
712Q8—61no—
713Q8—61no—
714Q8—721no—
715D4—32no—
716D4—62no—
717D4—61no—
718D4—61no—
719D4—61no—
720D4—122no—
721D4—122no—
722D4—241no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—122no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—721no—
739C2×C4—721no—
740C2×C4D3×#6711yescharacteristic
741C2×C4C22×D3211yescharacteristic
742C8—61no—
743C8—61no—
744C8—181no—
745C8—181no—
746C2×C3—22no—
747C2×C3—22no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—42no—
752C2×C3—121no—
753C2×C3—122no—
754C2×C3—241no—
755C2×C3#561011yescharacteristic
756C2×C3C2×#91811yescharacteristic
757C2×C3#576911yescharacteristic
758C2×C3#580611yescharacteristic
759C2×C3C2×#95111yescharacteristic
760C2×C3#583511yescharacteristic
761D3—41no—
762D3—42no—
763D3—81no—
764C22—21no—
765C22—21no—
766C22—61no—
767C22—62no—
768C22—61no—
769C22—61no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—244no—
776C22#6394312yes—
777C22C2×D3×#6711yescharacteristic
778C4—21no—
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4—121no—
786C4—361no—
787C4—361no—
788C4D3×#23711yescharacteristic
789C4#6431311yescharacteristic
790C3—21no—
791C3#8077711yescharacteristic, complemented
792C3#8349811yescharacteristic, complemented
793C2—22no—
794C2—121no—
795C2—122no—
796C2—241no—
797C2#1059515011yescharacteristic
798C2C2×#6394311yescharacteristic
799C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#5630C2
hypercenterC22⋊Q8D32
hypocenterC32#3314
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
2. #10594993C2semidirect
3. #10592743C2semidirect
4. C3×#5051C2semidirect
5. #10591624C2semidirect
6. #10591597C2semidirect
7. #10591578C2semidirect
8. #10591550C2semidirect
9. #10591169C2semidirect
10. #10591155C2semidirect
11. C2×#63563C2semidirect
12. #10590555C2semidirect
13. #10590515C2semidirect
14. #10590478C2semidirect
15. #10590438C2semidirect
23. C2×C3×#216C22semidirect
35. #63918C22semidirect
37. D3×C4⋊Dic3C22semidirect
38. #63856C22semidirect
40. Dic3×Dic6C22semidirect
43. C2×#3711C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
49. C3×#835C22semidirect
50. C3×#810C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
76. #5051D3semidirect
166. C2×#216C2×D3semidirect
208. #835C2×D3semidirect
226. #810C2×D3semidirect
235. #807C2×D3semidirect
702. C32#3314semidirect
791. C3#80777semidirect
792. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
#105949932
#105927432
C3×#50512
#105916242
#105915972
#105915782
#105915502
#105911692
#105911552
C2×#635632
#105905552
#105905152
#105904782
#105904382
#834983
#807773