Finite Group Databasebeta

← #11887411

Subgroups — #11887411

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic, complemented
2#10594995C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic, complemented
5#10591498C211yesmaximal, characteristic, complemented
6#10591478C211yesmaximal, characteristic, complemented
7#10591450C211yesmaximal, characteristic, complemented
8#10591431C211yesmaximal, characteristic, complemented
9Dic3×#213C211yesmaximal, characteristic, complemented
10#10591423C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591411C211yesmaximal, characteristic, complemented
13#10591179C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591103C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#80015—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#953—21no—
23C2×C3×#217—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#936C2211yescharacteristic
27C3×#935—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×#930C2211yescharacteristic
32C3×C4×#67C2211yescharacteristic
33C3×#924C2211yescharacteristic
34#63980—21no—
35#67⋊Dic3—21no—
36#63908C2211yescharacteristic, complemented
37Dic3×D12C2211yescharacteristic, complemented
38#63891—21no—
39#63869C2211yescharacteristic, complemented
40#63861—21no—
41#63841C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5806D311yescharacteristic, complemented
63#5618—31no—
64#5565—31no—
65C3×#447—31no—
66#5238—31no—
67#5233—31no—
68#5217D311yescharacteristic, complemented
69C2×#832—31no—
70C2×#832—31no—
71C2×#832—61no—
72#5158—31no—
73#5157—31no—
74#5153—31no—
75Dic3×D8—31no—
76#5057—31no—
77#5056—31no—
78#5048—31no—
79#5044—31no—
80#5041—31no—
81#5038—31no—
82#5035—31no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5009—31no—
86#4784—31no—
87#4772—31no—
88#4768—31no—
89#4766—31no—
90#67⋊C8—31no—
91#4722—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×#213—22no—
126C3×#213—41no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3715—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C22⋊C4—61no—
162#953—21no—
163C2×#217—21no—
164C2×#215—31no—
165#939—21no—
166#939—61no—
167#939—61no—
168#938—31no—
169#938C2×D311yescharacteristic
170#936C2×D311yescharacteristic
171#935—21no—
172D4×Dic3—31no—
173D4×Dic3—61no—
174D4×Dic3C2×D311yescharacteristic
175C2×#214—31no—
176C2×#213C2×D311yescharacteristic
177C2×#213C2×D311yescharacteristic
178#930—31no—
179#930C2×D311yescharacteristic
180C4×#67C2×D311yescharacteristic
181#926—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185#924C2×D311yescharacteristic
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—61no—
190C2×D3×C8—31no—
191#898—61no—
192#892—31no—
193#890—31no—
194#886—61no—
195#883—61no—
196#67⋊C4—61no—
197#879—61no—
198C4×D12—31no—
199#870—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—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—31no—
214#832—31no—
215#832—61no—
216#832—61no—
217#832—61no—
218#832—61no—
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#818—31no—
225#818—31no—
226#816—31no—
227#816—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230#810—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—81no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4—42no—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—81no—
258C3×#67—22no—
259C3×#67—42no—
260C3×#67—42no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—81no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#625—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—31no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—21no—
298C24×C3—21no—
299C24×C3—41no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×D4—24no—
304C2×C3×D4—22no—
305C2×C3×D4—22no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—41no—
313C2×C3×D4—41no—
314C2×C3×D4—41no—
315C2×C3×D4—42no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C2×C3×D4C22×D311yescharacteristic
323C22×C3×C4—21no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C2×#67—21no—
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67#6711yescharacteristic
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341#237—22no—
342#237—41no—
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C3×D8—62no—
348C3×D8—121no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364#217—21no—
365#217—21no—
366#217—21no—
367#217—21no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217#6711yescharacteristic
373#215—121no—
374#214—121no—
375#213—22no—
376#213—41no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—121no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8—122no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414D3×C8—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—84no—
424C22×C32#13512yes—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C32×C4—21no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—31no—
444C22×D4D3211yescharacteristic
445C2×SD16—91no—
446C2×D8—31no—
447C2×D8—31no—
448C22×C8—91no—
449C22×C8—91no—
450#126—181no—
451#125—91no—
452#124—31no—
453#123—61no—
454#123—181no—
455C22⋊Q8—31no—
456#121—31no—
457#121—31no—
458#121—61no—
459#121—91no—
460#121—181no—
461#120—61no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—181no—
466#117—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—61no—
469#107—91no—
470#107—91no—
471#106—91no—
472C4⋊C8—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—31no—
484C22⋊C8—91no—
485C4×C8—91no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—44no—
497C23×C3—42no—
498C23×C3—42no—
499C23×C3—61no—
500C23×C3—82no—
501C23×C3—81no—
502C23×C3—81no—
503C23×C3—82no—
504C23×C3D3×D411yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C22×D3—21no—
507C22×D3C2×#6711yescharacteristic
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—22no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—22no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—42no—
521C3×D4—42no—
522C3×D4—44no—
523C3×D4—62no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—122no—
527C3×D4—122no—
528C3×D4—241no—
529C3×D4#23712yes—
530C3×D4#23712yes—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—22no—
554#67—42no—
555#67—42no—
556#67—81no—
557#67—241no—
558#67—241no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—42no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—81no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—241no—
571C2×Dic3—241no—
572C2×Dic3—241no—
573C2×Dic3—242no—
574C2×Dic3C2×#6711yescharacteristic
575C2×Dic3C2×#6711yescharacteristic
576C2×Dic3C2×#6711yescharacteristic
577D12—21no—
578D12—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—241no—
582Dic6—21no—
583Dic6—21no—
584C3×C8—61no—
585C3×C8—61no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C3⋊C8—121no—
594C2×C32—22no—
595C2×C32—42no—
596C2×C32—81no—
597C2×C32#54611yescharacteristic
598C2×C32C2×#13511yescharacteristic
599C2×C32#57611yescharacteristic
600C3×D3—41no—
601C3×D3—81no—
602C24—21no—
603#41—62no—
604#41—121no—
605C2×Q8—31no—
606C2×D4—22no—
607C2×D4—21no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—41no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—181no—
615C2×D4C2×D3211yescharacteristic
616C2×D4C2×D3211yescharacteristic
617C22×C4—31no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4C2×D3211yescharacteristic
623SD16—361no—
624D8—62no—
625D8—121no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—91no—
629C2×C8—91no—
630C2×C8—361no—
631C2×C8—361no—
632C4⋊C4—31no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C22⋊C4—31no—
642C22⋊C4—31no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—31no—
653C42—181no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—21no—
663C22×C3—22no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—84no—
684C22×C3—84no—
685C22×C3—88no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3#91212yes—
690C22×C3#95012yes—
691C22×C3C2×D3×D411yescharacteristic
692C22×C3C22×#6711yescharacteristic
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C3×C4—22no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23711yescharacteristic
711C3×C4C2×#23711yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4#100411yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—241no—
725Dic3—241no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—31no—
730C23—42no—
731C23—42no—
732C23—61no—
733C23—81no—
734C23D3×#6711yescharacteristic
735Q8—61no—
736Q8—61no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—62no—
742D4—61no—
743D4—61no—
744D4—122no—
745D4—122no—
746D4—241no—
747D4—721no—
748D4#380512yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—122no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—721no—
764C2×C4—721no—
765C2×C4D3×#6711yescharacteristic
766C2×C4C22×D3211yescharacteristic
767C8—61no—
768C8—61no—
769C8—181no—
770C8—181no—
771C2×C3—24no—
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—42no—
778C2×C3—42no—
779C2×C3—82no—
780C2×C3—82no—
781C2×C3—81no—
782C2×C3—81no—
783C2×C3—121no—
784C2×C3—241no—
785C2×C3#559111yescharacteristic
786C2×C3C2×#91211yescharacteristic
787C2×C3#577411yescharacteristic
788C2×C3#580611yescharacteristic
789C2×C3C2×#95011yescharacteristic
790C2×C3#583511yescharacteristic
791D3—41no—
792D3—81no—
793C22—21no—
794C22—21no—
795C22—22no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—84no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22#6393312yes—
809C22C2×D3×#6711yescharacteristic
810C4—21no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—121no—
815C4—121no—
816C4—121no—
817C4—361no—
818C4—361no—
819C4C2×#380511yescharacteristic
820C4#6433011yescharacteristic
821C3—21no—
822C3#8001511yescharacteristic, complemented
823C3#8349511yescharacteristic, complemented
824C2—22no—
825C2—42no—
826C2—81no—
827C2—121no—
828C2—241no—
829C2#1059509711yescharacteristic
830C2C2×#6393311yescharacteristic
831C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5806C2semidirect
2. #10594995C2semidirect
3. C2×#63659C2semidirect
4. C3×#5217C2semidirect
5. #10591498C2semidirect
6. #10591478C2semidirect
7. #10591450C2semidirect
8. #10591431C2semidirect
9. Dic3×#213C2semidirect
10. #10591423C2semidirect
11. #10591420C2semidirect
12. #10591411C2semidirect
13. #10591179C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591103C2semidirect
36. #63908C22semidirect
37. Dic3×D12C22semidirect
39. #63869C22semidirect
41. #63841C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63575C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5806D3semidirect
68. #5217D3semidirect
726. C32#3297semidirect
822. C3#80015semidirect
823. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
#105949952
C2×#636592
C3×#52172
#105914982
#105914782
#105914502
#105914312
Dic3×#2132
#105914232
#105914202
#105914112
#105911792
#67⋊(C3⋊C8)2
#105911032
#834953
#800153