Finite Group Databasebeta

← #11887444

Subgroups — #11887444

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5558C211yesmaximal, characteristic, complemented
2#10594007C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×#5016C211yesmaximal, characteristic, complemented
5#10591521C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591499C211yesmaximal, characteristic, complemented
8#10591498C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic, complemented
11#10590517C211yesmaximal, characteristic, complemented
12#10590502C211yesmaximal, characteristic, complemented
13#10590329C211yesmaximal, characteristic, complemented
14#10590308C211yesmaximal, characteristic, complemented
15#10590278C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#80559—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic, complemented
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×#938C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#929—21no—
28C3×C4×#67—21no—
29C3×#892C2211yescharacteristic, complemented
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#884—21no—
32C3×#879—21no—
33C3×#875C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#870C2211yescharacteristic, complemented
36#63922—21no—
37#63921—21no—
38#63912—21no—
39#63908C2211yescharacteristic
40#63856C2211yescharacteristic
41#63854—21no—
42C2×D3×C3⋊C8C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63634C2211yescharacteristic, complemented
47C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#553—31no—
62#5676—31no—
63#5558D311yescharacteristic, complemented
64#5550—31no—
65C3×#463—31no—
66#5172—31no—
67#5171—31no—
68#5157—31no—
69#5156—31no—
70#5068—31no—
71#5066—31no—
72#5056—31no—
73#5041—31no—
74#5038—31no—
75#5037—31no—
76#5036—31no—
77#5016D311yescharacteristic, complemented
78C4×#213—31no—
79C4×#213—31no—
80C4×#213—61no—
81D4×C3⋊C8—31no—
82#5003—31no—
83#5002—31no—
84#4970—31no—
85C2×#809—31no—
86#4847—31no—
87#4834—31no—
88#4811—31no—
89#4804—31no—
90#4779—31no—
91D3×#102—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×D12D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#625—21no—
108C2×#624—21no—
109D3×D12—22no—
110D3×D12—41no—
111#3799—22no—
112#3799—41no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3753—22no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#214—41no—
124C3×#213—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142D3×C3⋊C8—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#124—31no—
154C3×#123—61no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×C4×D4—21no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C3×C4×D4C2×D311yescharacteristic, complemented
162C3×C4×D4C2×D311yescharacteristic, complemented
163C3×#117—31no—
164C2×C3×C4⋊C4—31no—
165#946—31no—
166#938—31no—
167#938C2×D311yescharacteristic
168#938C2×D311yescharacteristic, complemented
169#937—61no—
170C2×#214C2×D311yescharacteristic, complemented
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—61no—
174C2×#213C2×D311yescharacteristic
175#930—31no—
176#929—21no—
177C4×#67—21no—
178#924—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8—31no—
183#894—61no—
184#892C2×D311yescharacteristic, complemented
185D3×C4⋊C4C2×D311yescharacteristic
186#884—21no—
187#884—61no—
188#884—61no—
189#883—61no—
190#882—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193#879—21no—
194#875C2×D311yescharacteristic
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199#870C2×D311yescharacteristic, complemented
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#102—31no—
203#835—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#830—31no—
211#830—31no—
212#821—31no—
213#821—31no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8—31no—
216#818—31no—
217#817—31no—
218#810—31no—
219#810—31no—
220#810C2×D311yescharacteristic, complemented
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#808—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C4×C3⋊C8—31no—
236C4×C3⋊C8—31no—
237C4×C3⋊C8—61no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—81no—
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—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#626—42no—
275#626—42no—
276#625—81no—
277#624—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—31no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—41no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319#239—62no—
320#239—121no—
321D3×D4—62no—
322D3×D4—121no—
323#235—62no—
324#235—121no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—121no—
332C2×D12#6711yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—121no—
340C2×C4×D3C22×D311yescharacteristic
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—121no—
344C3×D8—121no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—21no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#217—21no—
371#217—21no—
372#217—61no—
373#217—61no—
374#214—41no—
375#213—41no—
376#213—62no—
377#213—62no—
378#213—64no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—121no—
387(C2×D3)⋊C4#6711yescharacteristic
388(C2×D3)⋊C4#6711yescharacteristic
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3#6711yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—21no—
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⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D3×C8—121no—
412D3×C8—121no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3#13512yes—
429D32—84no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—91no—
442C22×D4—91no—
443C2×SD16—31no—
444C2×D8—31no—
445C2×D8—91no—
446C22×C8—91no—
447C22×C8—91no—
448#126—61no—
449#125—31no—
450#124—31no—
451#123—61no—
452#123—181no—
453C22⋊Q8—91no—
454#121—31no—
455#121—31no—
456#121—61no—
457#121—91no—
458#121—181no—
459#120—181no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4—91no—
463C4×D4D3211yescharacteristic, complemented
464#117—31no—
465C2×C4⋊C4—31no—
466C2×C22⋊C4—181no—
467#107—91no—
468#107—91no—
469#106—91no—
470C4⋊C8—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483C4×C8—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—121no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—122no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3C2×#6711yescharacteristic
501C22×D3C2×#6711yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—22no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—41no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—241no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
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—81no—
531C2×C3×C4—81no—
532C2×C3×C4—82no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—42no—
541#67—81no—
542#67—122no—
543#67—122no—
544#67—241no—
545#67—241no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—22no—
555D12—21no—
556D12—21no—
557D12—32no—
558D12—32no—
559D12—62no—
560D12—61no—
561D12—61no—
562D12—121no—
563D12—122no—
564D12—122no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—81no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—242no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—62no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—121no—
587C2×C32—81no—
588C2×C32#54611yescharacteristic
589C2×C32C2×#13511yescharacteristic
590C2×C32#57611yescharacteristic
591C3⋊D3—42no—
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—81no—
595C24—181no—
596#41—182no—
597#41—361no—
598C2×Q8—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—181no—
605C2×D4—182no—
606C2×D4—181no—
607C2×D4—181no—
608C2×D4—361no—
609C2×D4C2×D3211yescharacteristic
610C22×C4—21no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—181no—
615C22×C4—181no—
616SD16—121no—
617D8—121no—
618D8—182no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—91no—
622C2×C8—91no—
623C2×C8—361no—
624C2×C8—361no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4C2×D3211yescharacteristic
634C22⋊C4—21no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—61no—
646C42C2×D3211yescharacteristic
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—42no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C22×#6711yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—62no—
677C2×D3—62no—
678C2×D3—122no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—244no—
686C2×D3—244no—
687C2×D3#95012yes—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—81no—
701C3×C4—121no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4#100411yescharacteristic
705C3×C4D3×#4111yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4#100911yescharacteristic
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—41no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#329711yescharacteristic, complemented, Sylow
717C23—21no—
718C23—31no—
719C23—31no—
720C23—61no—
721C23—181no—
722C23—362no—
723C23—362no—
724C23—721no—
725Q8—61no—
726Q8—61no—
727D4—21no—
728D4—21no—
729D4—62no—
730D4—61no—
731D4—61no—
732D4—92no—
733D4—122no—
734D4—181no—
735D4—241no—
736D4—362no—
737D4—362no—
738D4—721no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—81no—
750C2×C4—181no—
751C2×C4—241no—
752C2×C4—362no—
753C2×C4—721no—
754C2×C4D3×#6711yescharacteristic
755C2×C4D3×#6711yescharacteristic
756C2×C4C22×D3211yescharacteristic
757C8—61no—
758C8—61no—
759C8—181no—
760C8—181no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—62no—
765C2×C3—82no—
766C2×C3—81no—
767C2×C3—81no—
768C2×C3—121no—
769C2×C3—241no—
770C2×C3#561211yescharacteristic
771C2×C3D3×#13511yescharacteristic
772C2×C3#577411yescharacteristic
773C2×C3C2×#95011yescharacteristic
774C2×C3#582911yescharacteristic
775C2×C3#583511yescharacteristic
776D3—22no—
777D3—41no—
778D3—81no—
779D3—122no—
780D3—122no—
781D3—242no—
782C22—32no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—182no—
795C22—361no—
796C22—361no—
797C22—724no—
798C22C2×D3×#6711yescharacteristic
799C4—21no—
800C4—21no—
801C4—41no—
802C4—61no—
803C4—61no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—361no—
808C4#6430611yescharacteristic
809C4#6430711yescharacteristic
810C3—21no—
811C3#8055911yescharacteristic, complemented
812C3#8361411yescharacteristic, complemented
813C2—62no—
814C2—81no—
815C2—121no—
816C2—241no—
817C2—362no—
818C2#1059507011yescharacteristic
819C2#1059509711yescharacteristic
820C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3297
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×#5558C2semidirect
2. #10594007C2semidirect
3. C4×#3753C2semidirect
4. C3×#5016C2semidirect
5. #10591521C2semidirect
6. #10591515C2semidirect
7. #10591499C2semidirect
8. #10591498C2semidirect
9. #10590610C2semidirect
10. D3×#809C2semidirect
11. #10590517C2semidirect
12. #10590502C2semidirect
13. #10590329C2semidirect
14. #10590308C2semidirect
15. #10590278C2semidirect
20. C32×C4×D4C22semidirect
24. C3×#938C22semidirect
25. C2×C3×#214C22semidirect
29. C3×#892C22semidirect
35. C3×#870C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
46. #63634C22semidirect
47. C4×C3⋊(C3⋊C8)C22semidirect
48. C3×#810C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
63. #5558D3semidirect
77. #5016D3semidirect
161. C3×C4×D4C2×D3semidirect
162. C3×C4×D4C2×D3semidirect
168. #938C2×D3semidirect
170. C2×#214C2×D3semidirect
184. #892C2×D3semidirect
199. #870C2×D3semidirect
220. #810C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
463. C4×D4D32semidirect
716. C32#3297semidirect
811. C3#80559semidirect
812. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55582
#105940072
C4×#37532
C3×#50162
#105915212
#105915152
#105914992
#105914982
#105906102
D3×#8092
#105905172
#105905022
#105903292
#105903082
#105902782
#836143
#805593