Finite Group Databasebeta

← #11887406

Subgroups — #11887406

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×#5514C211yesmaximal, characteristic, complemented
2#10595018C211yesmaximal, characteristic, complemented
3C2×#63636C211yesmaximal, characteristic, complemented
4C3×#4970C211yesmaximal, characteristic, complemented
5#10591179C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590615C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590576C211yesmaximal, characteristic, complemented
11#10590537C211yesmaximal, characteristic, complemented
12#10590534C211yesmaximal, characteristic, complemented
13#10590468C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#81485—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#930—21no—
23C3×#930C2211yescharacteristic
24C3×C4×#67—21no—
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#898—21no—
28C3×#895C2211yescharacteristic, complemented
29C3×#894—21no—
30C3×#893C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic, complemented
32C3×#890C2211yescharacteristic, complemented
33#63981—21no—
34#63974—21no—
35#63910—21no—
36#63909C2211yescharacteristic
37#63897—21no—
38#63894C2211yescharacteristic
39#63864C2211yescharacteristic
40C2×#3715C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#810C2211yescharacteristic, complemented
50C3×#810C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#553—31no—
62#5630—31no—
63#5550—31no—
64#5514D311yescharacteristic, complemented
65C3×#484—31no—
66#5068—31no—
67#5066—31no—
68#5048—31no—
69#5041—31no—
70#5038—31no—
71#5037—31no—
72#5036—31no—
73#5016—31no—
74C4×#213—31no—
75D4×C3⋊C8—31no—
76#5003—31no—
77#5002—31no—
78#4970D311yescharacteristic, complemented
79C2×#809—31no—
80C2×#809—31no—
81C2×#809—61no—
82#4891—31no—
83#4885—31no—
84#4883—31no—
85#4872—31no—
86#4819—31no—
87#4810—31no—
88#4804—31no—
89#4800—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×#624—21no—
111#3799—22no—
112#3799—41no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
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×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3715—41no—
141#3714—22no—
142#3714—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×#117—31no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4C2×D311yescharacteristic
163C2×C3×C4⋊C4C2×D311yescharacteristic
164#947—31no—
165C2×#215—31no—
166#937—61no—
167C2×#214—31no—
168C2×#213—31no—
169C2×#213—31no—
170#930—21no—
171#930—31no—
172#930C2×D311yescharacteristic
173C4×#67—21no—
174C4×#67C2×D311yescharacteristic
175#924C2×D311yescharacteristic
176C22×C3⋊C8—31no—
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×D24—31no—
181C2×D24—31no—
182C2×D3×C8—31no—
183#898—21no—
184#895—31no—
185#895—61no—
186#895C2×D311yescharacteristic, complemented
187#894—21no—
188#894—61no—
189#894—61no—
190#893—31no—
191#893C2×D311yescharacteristic, complemented
192#892C2×D311yescharacteristic, complemented
193#890C2×D311yescharacteristic, complemented
194#884—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198#875—31no—
199C4×D12—31no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205#835—31no—
206#832—31no—
207#830—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212Dic3⋊C8—31no—
213C8×Dic3—31no—
214#810—31no—
215#810C2×D311yescharacteristic, complemented
216#810C2×D311yescharacteristic, complemented
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809—61no—
230#809—61no—
231#809—61no—
232#808—31no—
233#808—31no—
234#807C2×D311yescharacteristic, complemented
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—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×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—42no—
257C4⋊(C3⋊D3)#4112yes—
258C3×#67—22no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—81no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274#626—42no—
275#626—81no—
276#624—42no—
277#624—81no—
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—31no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—121no—
300C2×C3×Q8—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67#6711yescharacteristic
317#239—62no—
318#239—121no—
319#235—62no—
320#235—121no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—62no—
330C2×D12—64no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—121no—
336C2×D12—121no—
337C2×D12—121no—
338C2×D12—122no—
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6C22×D311yescharacteristic
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372C3×C42—61no—
373#217—21no—
374#217#6711yescharacteristic
375#215—121no—
376#214—121no—
377#213—62no—
378#213—121no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4#6711yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—21no—
399C4×Dic3C22×D311yescharacteristic
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⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—122no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413D24—121no—
414D3×C8—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32#13512yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—84no—
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×C4—41no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—91no—
444C22×D4—91no—
445C2×SD16—91no—
446C2×D8—91no—
447C2×D8—91no—
448C22×C8—91no—
449C22×C8—91no—
450#126—61no—
451#125—31no—
452#124—91no—
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—181no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—61no—
465C4×D4—91no—
466#117—31no—
467C2×C4⋊C4D3211yescharacteristic
468C2×C22⋊C4—181no—
469#107—31no—
470#107—31no—
471#106—91no—
472C4⋊C8—91no—
473#103—31no—
474#103—31no—
475#103—91no—
476#102—91no—
477#102—91no—
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—31no—
488C23×C3—61no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3—21no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—121no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—124no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—242no—
504C22×D3—241no—
505C22×D3—241no—
506C22×D3—242no—
507C22×D3C2×#6711yescharacteristic
508C3×Q8—61no—
509C3×Q8—61no—
510C3×D4—62no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—241no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—81no—
538C2×C3×C4—81no—
539C2×C3×C4—82no—
540C2×C3×C4—241no—
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—22no—
546#67—42no—
547#67—122no—
548#67—241no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554C2×Dic3C2×#6711yescharacteristic
555D12—21no—
556D12—21no—
557D12—32no—
558D12—32no—
559D12—62no—
560D12—62no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—81no—
568D12—121no—
569D12—121no—
570D12—122no—
571D12—122no—
572D12—124no—
573D12—122no—
574D12—241no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—81no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—241no—
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#54611yescharacteristic
596C2×C32C2×#13511yescharacteristic
597C2×C32#57611yescharacteristic
598C3⋊D3—42no—
599C3⋊D3—81no—
600C3×D3—41no—
601C3×D3—81no—
602C24—181no—
603#41—182no—
604#41—361no—
605C2×Q8—31no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—182no—
613C2×D4—181no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—361no—
617C22×C4—21no—
618C22×C4—31no—
619C22×C4—61no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4C2×D3211yescharacteristic
623SD16—361no—
624D8—182no—
625D8—361no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—91no—
629C2×C8—91no—
630C2×C8—361no—
631C2×C8—361no—
632C4⋊C4—21no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4C2×D3211yescharacteristic
640C4⋊C4C2×D3211yescharacteristic
641C22⋊C4—31no—
642C22⋊C4—31no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—31no—
653C42—61no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—22no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3#91912yes—
669C22×C3#95012yes—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C22×#6711yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—122no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—122no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—241no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3—248no—
699C3×C4—22no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—61no—
709C3×C4—61no—
710C3×C4—61no—
711C3×C4—81no—
712C3×C4—81no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4D3×#4111yescharacteristic
717C3×C4D3×#4111yescharacteristic
718C3×C4#100911yescharacteristic
719C3×C4#100911yescharacteristic
720Dic3—21no—
721Dic3—21no—
722Dic3—21no—
723Dic3—41no—
724Dic3—41no—
725Dic3—41no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—31no—
728C23—61no—
729C23—181no—
730C23—181no—
731C23—362no—
732C23—362no—
733C23—721no—
734C23D3×#6711yescharacteristic
735Q8—61no—
736Q8—61no—
737D4—62no—
738D4—61no—
739D4—61no—
740D4—92no—
741D4—122no—
742D4—181no—
743D4—181no—
744D4—181no—
745D4—241no—
746D4—362no—
747D4—362no—
748D4—721no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—31no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—81no—
762C2×C4—241no—
763C2×C4—362no—
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—121no—
778C2×C3—241no—
779C2×C3#565411yescharacteristic
780C2×C3C2×#91911yescharacteristic
781C2×C3#577411yescharacteristic
782C2×C3C2×#95011yescharacteristic
783C2×C3#582911yescharacteristic
784C2×C3#583511yescharacteristic
785D3—41no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790D3—242no—
791D3—241no—
792D3—241no—
793C22—21no—
794C22—21no—
795C22—61no—
796C22—61no—
797C22—61no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—182no—
802C22—361no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—724no—
808C22#6394912yes—
809C22C2×D3×#6711yescharacteristic
810C4—21no—
811C4—41no—
812C4—41no—
813C4—61no—
814C4—61no—
815C4—61no—
816C4—121no—
817C4—121no—
818C4—121no—
819C4#6430611yescharacteristic
820C4#6430811yescharacteristic
821C3—21no—
822C3#8148511yescharacteristic, complemented
823C3#8361411yescharacteristic, complemented
824C2—22no—
825C2—121no—
826C2—241no—
827C2—362no—
828C2—721no—
829C2#1059506811yescharacteristic
830C2#1059509711yescharacteristic
831C2C2×#6394911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5514C2semidirect
2. #10595018C2semidirect
3. C2×#63636C2semidirect
4. C3×#4970C2semidirect
5. #10591179C2semidirect
6. #10591168C2semidirect
7. #67⋊(C3⋊C8)C2semidirect
8. #10590615C2semidirect
9. #10590610C2semidirect
10. #10590576C2semidirect
11. #10590537C2semidirect
12. #10590534C2semidirect
13. #10590468C2semidirect
14. #10590456C2semidirect
15. #10590424C2semidirect
28. C3×#895C22semidirect
30. C3×#893C22semidirect
31. C3×#892C22semidirect
32. C3×#890C22semidirect
40. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
49. C3×#810C22semidirect
50. C3×#810C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5514D3semidirect
78. #4970D3semidirect
186. #895C2×D3semidirect
191. #893C2×D3semidirect
192. #892C2×D3semidirect
193. #890C2×D3semidirect
215. #810C2×D3semidirect
216. #810C2×D3semidirect
234. #807C2×D3semidirect
235. #807C2×D3semidirect
726. C32#3297semidirect
822. C3#81485semidirect
823. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55142
#105950182
C2×#636362
C3×#49702
#105911792
#105911682
#67⋊(C3⋊C8)2
#105906152
#105906102
#105905762
#105905372
#105905342
#105904682
#105904562
#105904242
#836143
#814853