Finite Group Databasebeta

← #11889765

Subgroups — #11889765

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5676C211yesmaximal, characteristic
2#10593956C211yesmaximal, characteristic, complemented
3#10592753C211yesmaximal, characteristic, complemented
4C3×#5055C211yesmaximal, characteristic, complemented
5#10591599C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591551C211yesmaximal, characteristic, complemented
8#10591550C211yesmaximal, characteristic, complemented
9#10591462C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591413C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590269C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#81700—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#884—21no—
27C3×#883—21no—
28C3×#882—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#869C2211yescharacteristic, complemented
33#63898—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63887—21no—
37#63887—21no—
38#63872—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63659C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#803C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#546—31no—
62#5730—31no—
63#5676D311yescharacteristic
64#5543—31no—
65C3×#489—31no—
66#5239—31no—
67#5232—31no—
68#5218—31no—
69C2×#832—31no—
70#5087—31no—
71#5055D311yescharacteristic, complemented
72#5054—31no—
73#5054—31no—
74#5054—61no—
75#5051—31no—
76#5044—31no—
77#5042—31no—
78#5033—31no—
79#5018—31no—
80#5011—31no—
81#5007—31no—
82#4813—31no—
83#4811—31no—
84#4808—31no—
85#4803—31no—
86#4780—31no—
87#4776—31no—
88#4774—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#239—22no—
99C3×#239—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3756—41no—
116#3754—41no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—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×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3716—22no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C2×D311yescharacteristic
148C2×D3×D4C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×#124—21no—
151C3×#124C2×D311yescharacteristic
152C3×#124C2×D311yescharacteristic
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#120—61no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C2×C3×C22⋊C4—61no—
161#946—61no—
162#946—61no—
163#946C2×D311yescharacteristic
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—61no—
167#938C2×D311yescharacteristic
168D4×Dic3—61no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—61no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175#924—31no—
176#924—31no—
177C2×#208—31no—
178C22×C3⋊C8—31no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#897—31no—
183#897—31no—
184#893—61no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187#890—61no—
188#890—61no—
189#884—21no—
190#883—21no—
191#882—21no—
192D3×C22⋊C4—21no—
193#878—61no—
194#878—61no—
195C4×D12C2×D311yescharacteristic
196C4×D12C2×D311yescharacteristic
197#869C2×D311yescharacteristic, complemented
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#97—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#835C2×D311yescharacteristic, complemented
210#835C2×D311yescharacteristic, complemented
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#821—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#818—31no—
225#816—31no—
226#810—31no—
227#809—31no—
228#809—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
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×Q8—21no—
246C32×Q8—21no—
247C32×D4—21no—
248C32×D4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—22no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×C4×D3—81no—
274C3×Dic6—81no—
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—31no—
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—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—61no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322#239—22no—
323#239—41no—
324D3×D4—22no—
325D3×D4—41no—
326C2×D12—21no—
327C2×D12#6711yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—21no—
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—61no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—21no—
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361#217—21no—
362#217—61no—
363#217—61no—
364#216—121no—
365#216—121no—
366#216—122no—
367#214—62no—
368#214—121no—
369#214—121no—
370#214—122no—
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—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3#6711yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—62no—
411ΓL(1,𝔽25)—121no—
412D3×C8—121no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13712yes—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—31no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447#125—181no—
448#124D3211yescharacteristic
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—31no—
456#121—61no—
457#120—61no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—61no—
465#107—91no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—31no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C22×D3—21no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—81no—
495C22×D3C2×#6711yescharacteristic
496C22×D3C2×#6711yescharacteristic
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×Q8—241no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—62no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—122no—
515C3×D4—241no—
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—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—122no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—42no—
540#67—81no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—22no—
555D12—21no—
556D12—42no—
557D12#23712yes—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—42no—
563C4×D3—81no—
564C4×D3—241no—
565C4×D3—241no—
566Dic6—62no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—81no—
572Dic6—121no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C2×C32—81no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—22no—
588C3×D3—41no—
589C3×D3—42no—
590C24—61no—
591#41—62no—
592#41—121no—
593C2×Q8—61no—
594C2×Q8—91no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—62no—
601C2×D4—61no—
602C2×D4—121no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—182no—
612SD16—361no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—91no—
618C2×C8—361no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—181no—
641C42C2×D3211yescharacteristic
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—62no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—244no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C22×#6711yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—22no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C2×D3#95112yes—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4C2×#23711yescharacteristic
691C3×C4#100411yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4#100911yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—122no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—21no—
707C23—31no—
708C23—31no—
709C23—61no—
710C23—122no—
711C23—122no—
712C23—241no—
713Q8—21no—
714Q8—21no—
715Q8—181no—
716Q8—181no—
717Q8—241no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—62no—
722D4—61no—
723D4—122no—
724D4—122no—
725D4—241no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—122no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4D3×#6711yescharacteristic
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—62no—
753C2×C3—81no—
754C2×C3—81no—
755C2×C3—121no—
756C2×C3—122no—
757C2×C3—161no—
758C2×C3#567611yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3D3×#13711yescharacteristic
761C2×C3#580611yescharacteristic
762C2×C3C2×#95111yescharacteristic
763C2×C3#583511yescharacteristic
764D3—22no—
765D3—41no—
766D3—42no—
767C22—32no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—244no—
780C22C2×D3×#6711yescharacteristic
781C4—21no—
782C4—21no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—361no—
790C4—361no—
791C4D3×#23711yescharacteristic
792C4#6431411yescharacteristic
793C3—21no—
794C3#8170011yescharacteristic, complemented
795C3#8349811yescharacteristic, complemented
796C2—62no—
797C2—81no—
798C2—121no—
799C2—122no—
800C2#1059522911yescharacteristic
801C2#1059545411yescharacteristic
802C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radicalC3×#5676C2
hypercenter#124D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593956C2semidirect
3. #10592753C2semidirect
4. C3×#5055C2semidirect
5. #10591599C2semidirect
6. #10591596C2semidirect
7. #10591551C2semidirect
8. #10591550C2semidirect
9. #10591462C2semidirect
10. #10591459C2semidirect
11. #10591413C2semidirect
12. D3×#832C2semidirect
13. #10590360C2semidirect
14. #10590326C2semidirect
15. #10590269C2semidirect
21. C2×#3756C22semidirect
23. C4×#634C22semidirect
32. C3×#869C22semidirect
35. D3×C4⋊Dic3C22semidirect
40. #63857C22semidirect
42. C2×#3711C22semidirect
44. #63662C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#803C22semidirect
52. #63576C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
71. #5055D3semidirect
197. #869C2×D3semidirect
209. #835C2×D3semidirect
210. #835C2×D3semidirect
237. #803C2×D3semidirect
705. C32#3314semidirect
794. C3#81700semidirect
795. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#56762
#105939562
#105927532
C3×#50552
#105915992
#105915962
#105915512
#105915502
#105914622
#105914592
#105914132
D3×#8322
#105903602
#105903262
#105902692
#834983
#817003