Finite Group Databasebeta

← #11887407

Subgroups — #11887407

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5514C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic, complemented
3#10592669C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591175C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic, complemented
8#10590613C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590533C211yesmaximal, characteristic, complemented
11#10590530C211yesmaximal, characteristic, complemented
12#10590502C211yesmaximal, characteristic, complemented
13#10590499C211yesmaximal, characteristic, complemented
14#10590467C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83614—31nomaximal
17#78760—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930—21no—
23C3×#930C2211yescharacteristic
24C3×C4×#67—21no—
25C3×C4×#67C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#898—21no—
28C3×#895C2211yescharacteristic, complemented
29C3×#894—21no—
30C3×#893C2211yescharacteristic, complemented
31C3×#892C2211yescharacteristic, complemented
32C3×#890C2211yescharacteristic, complemented
33#63976—21no—
34D3×#217—21no—
35#63908C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63885—21no—
38#63884—21no—
39#63860C2211yescharacteristic
40C2×#3716C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#553—31no—
62#5806—31no—
63#5550—31no—
64#5514D311yescharacteristic, complemented
65C2×C3×#102—31no—
66#5217—31no—
67#5114—31no—
68C8×#67—31no—
69#5068—31no—
70#5066—31no—
71#5041—31no—
72#5038—31no—
73#5037—31no—
74#5036—31no—
75#5016—31no—
76C4×#213—31no—
77D4×C3⋊C8—31no—
78#5003—31no—
79#5002—31no—
80#4970—31no—
81#4970—31no—
82#4970—61no—
83C2×#809D311yescharacteristic, complemented
84#4787—31no—
85#4781—31no—
86#4779—31no—
87#4775—31no—
88#4772—31no—
89#4768—31no—
90#4763—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—41no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3716—41no—
141#3713—22no—
142#3713—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#121—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C3×#117—31no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163#953—61no—
164C2×#217—61no—
165#939—61no—
166#938—31no—
167#937—61no—
168#936—31no—
169#935—61no—
170D4×Dic3—31no—
171C2×#214—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176#930—21no—
177#930—31no—
178#930C2×D311yescharacteristic
179C4×#67—21no—
180C4×#67C2×D311yescharacteristic
181#924—31no—
182#924—31no—
183#924—61no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×#204—31no—
187C2×D3×C8—31no—
188#898—21no—
189#895C2×D311yescharacteristic, complemented
190#894—21no—
191#894—61no—
192#893C2×D311yescharacteristic, complemented
193#892C2×D311yescharacteristic, complemented
194#890C2×D311yescharacteristic, complemented
195#884—61no—
196D3×C22⋊C4—61no—
197#875—31no—
198C4×D12—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213#816—31no—
214Dic3⋊C8—31no—
215C8×Dic3—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810—61no—
223#809—31no—
224#809—31no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
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
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12—81no—
270C3×D12#4112yes—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—81no—
274#625—42no—
275#625—81no—
276D3×Dic3—42no—
277D3×Dic3—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—91no—
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—31no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—41no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—21no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67#6711yescharacteristic
322C22×Dic3—61no—
323C22×Dic3—61no—
324#237—62no—
325#237—121no—
326#235—62no—
327#235—121no—
328C2×D12—22no—
329C2×D12—21no—
330C2×D12—21no—
331C2×D12—41no—
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—121no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—31no—
365C3×C42—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—121no—
373#217#6711yescharacteristic
374#214—121no—
375#213—62no—
376#213—62no—
377#213—121no—
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#6711yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
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—41no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—121no—
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32#13512yes—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—22no—
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—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C32×C4—21no—
430C32×C4—41no—
431C32×C4—41no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—91no—
447#126—61no—
448#125—31no—
449#124—91no—
450#123—61no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—31no—
455#121—61no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4—91no—
463#117—31no—
464C2×C4⋊C4D3211yescharacteristic
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—81no—
499C22×D3C2×#6711yescharacteristic
500C3×D4—32no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C3×D4—122no—
509C3×D4—241no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
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—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
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×C4C2×#6711yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—22no—
539#67—42no—
540#67—122no—
541#67—122no—
542#67—241no—
543#67—241no—
544C2×Dic3—21no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3—241no—
553C2×Dic3C2×#6711yescharacteristic
554C2×Dic3C2×#6711yescharacteristic
555C2×Dic3C2×#6711yescharacteristic
556D12—21no—
557D12—21no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—42no—
562D12—81no—
563D12#23512yes—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—81no—
567C4×D3—122no—
568C4×D3—241no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—121no—
574Dic6—121no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8—121no—
585C2×C32—22no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57611yescharacteristic
589C3×D3—41no—
590C3×D3—42no—
591C3×D3—81no—
592C3×D3—81no—
593C24—61no—
594#41—182no—
595#41—361no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—121no—
606C2×D4—181no—
607C2×D4—181no—
608C22×C4—21no—
609C22×C4—31no—
610C22×C4—61no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—361no—
615D8—182no—
616D8—361no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—91no—
621C2×C8—121no—
622C2×C8—361no—
623C4⋊C4—21no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—31no—
644C42—61no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—62no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3#91612yes—
667C22×C3#95012yes—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C22×#6711yescharacteristic
670C2×D3—22no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—84no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—121no—
698C3×C4C2×#23511yescharacteristic
699C3×C4#100411yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4#100911yescharacteristic
702Dic3—21no—
703Dic3—21no—
704Dic3—21no—
705Dic3—41no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711Dic3—241no—
712C32#329711yescharacteristic, complemented, Sylow
713C23—31no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—122no—
718C23—122no—
719C23—241no—
720C23D3×#6711yescharacteristic
721Q8—181no—
722Q8—181no—
723D4—32no—
724D4—62no—
725D4—61no—
726D4—61no—
727D4—61no—
728D4—61no—
729D4—61no—
730D4—122no—
731D4—122no—
732D4—241no—
733D4—362no—
734D4—721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—81no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—241no—
749C2×C4—362no—
750C2×C4—721no—
751C2×C4D3×#6711yescharacteristic
752C2×C4C22×D3211yescharacteristic
753C8—61no—
754C8—61no—
755C8—181no—
756C8—181no—
757C2×C3—22no—
758C2×C3—22no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—122no—
764C2×C3—121no—
765C2×C3—241no—
766C2×C3—241no—
767C2×C3#549011yescharacteristic
768C2×C3#575711yescharacteristic
769C2×C3C2×#91611yescharacteristic
770C2×C3C2×#95011yescharacteristic
771C2×C3#582911yescharacteristic
772C2×C3#583511yescharacteristic
773D3—41no—
774D3—42no—
775D3—81no—
776D3—81no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—62no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—244no—
792C22#6394712yes—
793C22C2×D3×#6711yescharacteristic
794C4—21no—
795C4—41no—
796C4—41no—
797C4—61no—
798C4—61no—
799C4—61no—
800C4—121no—
801C4—361no—
802C4—361no—
803C4D3×#23511yescharacteristic
804C4#6430711yescharacteristic
805C3—21no—
806C3#7876011yescharacteristic, complemented
807C3#8361411yescharacteristic, complemented
808C2—22no—
809C2—121no—
810C2—122no—
811C2—241no—
812C2—241no—
813C2#1059506511yescharacteristic
814C2#1059509611yescharacteristic
815C2C2×#6394711yescharacteristic
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. #10594886C2semidirect
3. #10592669C2semidirect
4. C2×C3×#809C2semidirect
5. #10591175C2semidirect
6. #10591160C2semidirect
7. C3⋊C8×#67C2semidirect
8. #10590613C2semidirect
9. #10590608C2semidirect
10. #10590533C2semidirect
11. #10590530C2semidirect
12. #10590502C2semidirect
13. #10590499C2semidirect
14. #10590467C2semidirect
15. #10590452C2semidirect
28. C3×#895C22semidirect
30. C3×#893C22semidirect
31. C3×#892C22semidirect
32. C3×#890C22semidirect
40. C2×#3716C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63637C22semidirect
46. #63637C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63563C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5514D3semidirect
83. C2×#809D3semidirect
189. #895C2×D3semidirect
192. #893C2×D3semidirect
193. #892C2×D3semidirect
194. #890C2×D3semidirect
712. C32#3297semidirect
806. C3#78760semidirect
807. C3#83614semidirect

Maximal subgroups

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

subgroupindex
C3×#55142
#105948862
#105926692
C2×C3×#8092
#105911752
#105911602
C3⋊C8×#672
#105906132
#105906082
#105905332
#105905302
#105905022
#105904992
#105904672
#105904522
#836143
#787603