Finite Group Databasebeta

← #11889700

Subgroups — #11889700

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5554C211yesmaximal, characteristic
2#10593960C211yesmaximal, characteristic, complemented
3#10592706C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5#10591461C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591414C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590518C211yesmaximal, characteristic, complemented
10#10590515C211yesmaximal, characteristic, complemented
11#10590440C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13#10590326C211yesmaximal, characteristic, complemented
14#10590276C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#79802—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64078C2211yescharacteristic, complemented
22C2×C3×#214C2211yescharacteristic
23C3×#930—21no—
24C2×C3×(C2×D3)⋊C4—21no—
25C3×#897C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#886—21no—
28C3×#882—21no—
29C3×#875C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic, complemented
32#63896—21no—
33#63896—21no—
34Dic3×D12—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic, complemented
37#63869—21no—
38#63856C2211yescharacteristic
39#63856C2211yescharacteristic, complemented
40C2×#3718C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63634C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#810C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#803C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5579—31no—
63#5554D311yescharacteristic
64#5543—31no—
65C3×#440—31no—
66#5239—31no—
67#5232—31no—
68#5218—31no—
69C2×#832—31no—
70#5173—31no—
71#5169—31no—
72#5055—31no—
73#5054—31no—
74#5051—31no—
75#5044—31no—
76#5042—31no—
77#5033—31no—
78#5028—31no—
79#5018D311yescharacteristic, complemented
80#5011—31no—
81#5007—31no—
82#5007—31no—
83#5007—61no—
84#4884—31no—
85#4882—31no—
86#4813—31no—
87#4812—31no—
88#4771—31no—
89D3×#102—31no—
90#4714—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—41no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12—21no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#214—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3718—41no—
141#3715—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#120—61no—
156C3×C4×Q8—31no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C2×C3×C22⋊C4—61no—
162#946—31no—
163#946—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#215—31no—
167D4×Dic3—61no—
168C2×#214—31no—
169C2×#214C2×D311yescharacteristic
170#930—21no—
171C2×(C2×D3)⋊C4—21no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174#924—31no—
175#924—31no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#897C2×D311yescharacteristic
181#896—61no—
182#896—61no—
183#895C2×D311yescharacteristic
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186#890—61no—
187#886—21no—
188#882—21no—
189#878—61no—
190#878—61no—
191#875C2×D311yescharacteristic
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#870—61no—
195#869—31no—
196#869—31no—
197#869—61no—
198C4×Dic6C2×D311yescharacteristic, complemented
199C3×#107—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×#97—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832—61no—
215#832C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#821—31no—
219#821—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816—31no—
224#810—31no—
225#810C2×D311yescharacteristic, complemented
226#809—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—61no—
232#807—61no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—81no—
255C3×#67—42no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—22no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—81no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275D3×Dic3—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—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—31no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—121no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—41no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323#237—22no—
324#237—41no—
325D3×D4—22no—
326D3×D4—41no—
327C2×D12—21no—
328C2×D12#6711yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—121no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×SD16—62no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—21no—
359C3×C42—61no—
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#217—61no—
363#217—61no—
364#216—121no—
365#216—121no—
366#215—121no—
367#214—22no—
368#214—121no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376(C2×D3)⋊C4#6711yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—121no—
389C4⋊Dic3#6711yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—21no—
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⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409ΓL(1,𝔽25)—121no—
410D3×C8—121no—
411C22×C32—22no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3#13712yes—
425C32×C4—21no—
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—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#125—181no—
446#124—31no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—31no—
454#121—61no—
455#120—61no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—181no—
459C4×D4D3211yescharacteristic
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—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—31no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3C2×#6711yescharacteristic
494C22×D3C2×#6711yescharacteristic
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—22no—
502C3×D4—41no—
503C3×D4—62no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—122no—
507C3×D4—122no—
508C3×D4—241no—
509C3×D4#23512yes—
510C3×D4#23712yes—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—81no—
527C2×C3×C4—81no—
528C2×C3×C4—82no—
529C2×C3×C4—122no—
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4C2×#6711yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—42no—
537#67—42no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—42no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—22no—
553D12—21no—
554D12—21no—
555D12—81no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—241no—
561C4×D3—241no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—241no—
567Dic6—241no—
568Dic6—242no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C3⋊C8—121no—
579C2×C32—42no—
580C2×C32#54611yescharacteristic
581C2×C32C2×#13711yescharacteristic
582C2×C32#57611yescharacteristic
583C3×D3—22no—
584C3×D3—41no—
585C3×D3—81no—
586C24—61no—
587#41—62no—
588#41—121no—
589C2×Q8—31no—
590C2×Q8—31no—
591C2×Q8—181no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4C2×D3211yescharacteristic
600C22×C4—21no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—181no—
605C22×C4—181no—
606Q16—361no—
607SD16—62no—
608SD16—361no—
609M16—361no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8—91no—
614C2×C8—361no—
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—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—61no—
637C42C2×D3211yescharacteristic
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—42no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—244no—
658C22×C3C2×D3×D411yescharacteristic
659C22×C3C22×#6711yescharacteristic
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—84no—
669C2×D3#95112yes—
670C3×C4—22no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23511yescharacteristic
687C3×C4C2×#23711yescharacteristic
688C3×C4#100411yescharacteristic
689C3×C4#100911yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—241no—
700Dic3—241no—
701C32#331411yescharacteristic, complemented, Sylow
702C23—21no—
703C23—31no—
704C23—31no—
705C23—61no—
706C23—122no—
707C23—122no—
708C23—241no—
709Q8—61no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—721no—
714D4—21no—
715D4—62no—
716D4—61no—
717D4—61no—
718D4—122no—
719D4—122no—
720D4—241no—
721D4#379512yes—
722C2×C4—21no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—81no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4D3×#6711yescharacteristic
739C2×C4D3×#6711yescharacteristic
740C2×C4C22×D3211yescharacteristic
741C8—61no—
742C8—61no—
743C8—181no—
744C8—181no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—42no—
750C2×C3—62no—
751C2×C3—82no—
752C2×C3—121no—
753C2×C3—241no—
754C2×C3#555011yescharacteristic
755C2×C3#577411yescharacteristic
756C2×C3D3×#13711yescharacteristic
757C2×C3#580611yescharacteristic
758C2×C3C2×#95111yescharacteristic
759C2×C3#583511yescharacteristic
760D3—22no—
761D3—41no—
762D3—81no—
763C22—22no—
764C22—32no—
765C22—41no—
766C22—41no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—244no—
776C22C2×D3×#6711yescharacteristic
777C4—21no—
778C4—21no—
779C4—41no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—361no—
786C4—361no—
787C4C2×#379511yescharacteristic
788C4#6430711yescharacteristic
789C3—21no—
790C3#7980211yescharacteristic, complemented
791C3#8349811yescharacteristic, complemented
792C2—42no—
793C2—62no—
794C2—121no—
795C2—241no—
796C2#1059488611yescharacteristic
797C2#1059509711yescharacteristic
798C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC4×D4D32
hypocenterC32#3314
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
2. #10593960C2semidirect
3. #10592706C2semidirect
4. C3×#5018C2semidirect
5. #10591461C2semidirect
6. #10591458C2semidirect
7. #10591414C2semidirect
8. D3×#832C2semidirect
9. #10590518C2semidirect
10. #10590515C2semidirect
11. #10590440C2semidirect
12. #10590438C2semidirect
13. #10590326C2semidirect
14. #10590276C2semidirect
15. #10590267C2semidirect
21. #64078C22semidirect
31. C3×C4×Dic6C22semidirect
36. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
40. C2×#3718C22semidirect
42. C2×#3711C22semidirect
46. #63634C22semidirect
47. #63634C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
50. C3×#810C22semidirect
51. C3×#807C22semidirect
52. C3×#803C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #5018D3semidirect
198. C4×Dic6C2×D3semidirect
225. #810C2×D3semidirect
233. #807C2×D3semidirect
237. #803C2×D3semidirect
701. C32#3314semidirect
790. C3#79802semidirect
791. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#55542
#105939602
#105927062
C3×#50182
#105914612
#105914582
#105914142
D3×#8322
#105905182
#105905152
#105904402
#105904382
#105903262
#105902762
#105902672
#834983
#798023