Finite Group Databasebeta

← #11887257

Subgroups — #11887257

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2#10594853C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10591499C211yesmaximal, characteristic, complemented
6#10591478C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591442C211yesmaximal, characteristic, complemented
9Dic3×#214C211yesmaximal, characteristic, complemented
10#10591422C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591409C211yesmaximal, characteristic, complemented
13#10591188C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591126C211yesmaximal, characteristic, complemented
16#83494—31nomaximal
17#80159—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×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34#63962—21no—
35#63957—21no—
36#63869C2211yescharacteristic, complemented
37#63861—21no—
38#63856C2211yescharacteristic, complemented
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3718C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5806D311yescharacteristic
63#5642—31no—
64#5541—31no—
65C3×#450—31no—
66#5239—31no—
67#5233—31no—
68#5218D311yescharacteristic, complemented
69C2×#832—31no—
70C2×#832—31no—
71C2×#832—61no—
72#5173—31no—
73#5171—31no—
74#5166—31no—
75Dic3×SD16—31no—
76#5056—31no—
77#5054—31no—
78#5051—31no—
79#5051—31no—
80#5043—31no—
81#5041—31no—
82#5035—31no—
83C4×#214—31no—
84D4×C3⋊C8—31no—
85#5009—31no—
86#4779—31no—
87#4772—31no—
88#4768—31no—
89#4763—31no—
90#67⋊C8—31no—
91#4721—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×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)—41no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#214—22no—
124C3×#214—41no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—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—
164#946—31no—
165Q8×Dic3—31no—
166C2×#216—31no—
167C2×#216—31no—
168#939—21no—
169#938C2×D311yescharacteristic
170#936C2×D311yescharacteristic
171#935—21no—
172#935—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214C2×D311yescharacteristic
175C2×#214C2×D311yescharacteristic
176C4×#67C2×D311yescharacteristic
177#926—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—61no—
181#924—31no—
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—61no—
188C2×D3×C8—31no—
189#898—61no—
190#892—31no—
191#890—31no—
192#890—61no—
193#889—61no—
194#886—61no—
195#879—61no—
196#877—61no—
197#877—61no—
198#870—31no—
199C4×Dic6—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—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#817—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230#810—31no—
231#810—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×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—42no—
257C3×#67—22no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—31no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C24×C3—21no—
295C24×C3—21no—
296C24×C3—41no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×D4—24no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—41no—
310C2×C3×D4—41no—
311C2×C3×D4—41no—
312C2×C3×D4—42no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67#6711yescharacteristic
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—121no—
333#237—22no—
334#237—41no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C3×SD16—62no—
339C3×SD16—121no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356#217—21no—
357#217—21no—
358#217—21no—
359#217—21no—
360#217—21no—
361#217—21no—
362#217—61no—
363#217—61no—
364#217#6711yescharacteristic
365#216—121no—
366#216—121no—
367#214—22no—
368#214—41no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4#6711yescharacteristic
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4#6711yescharacteristic
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—122no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D3×C8—121no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—84no—
421C22×C32#13512yes—
422C22×C32C22×D411yescharacteristic
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—31no—
439C22×D4D3211yescharacteristic
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—31no—
443C22×C8—91no—
444C22×C8—91no—
445#126—181no—
446#125—91no—
447#125—181no—
448#124—31no—
449#123—61no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454#121—31no—
455#121—61no—
456#120—61no—
457C4×Q8—91no—
458C4×D4—31no—
459C4×D4—31no—
460#117—91no—
461#117—181no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—61no—
464#107—91no—
465#106—91no—
466#106—91no—
467C4⋊C8—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—42no—
490C23×C3—42no—
491C23×C3—44no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—82no—
495C23×C3—81no—
496C23×C3—81no—
497C23×C3—82no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3C2×#6711yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—22no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—42no—
516C3×D4—42no—
517C3×D4—44no—
518C3×D4—62no—
519C3×D4—122no—
520C3×D4—241no—
521C3×D4#23712yes—
522C3×D4#23712yes—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—122no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—22no—
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—42no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—81no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—242no—
564C2×Dic3C2×#6711yescharacteristic
565C2×Dic3C2×#6711yescharacteristic
566C2×Dic3C2×#6711yescharacteristic
567C4×D3—21no—
568C4×D3—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—21no—
572Dic6—21no—
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—22no—
584C2×C32—42no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57711yescharacteristic
589C3×D3—41no—
590C24—21no—
591#41—62no—
592#41—121no—
593C2×Q8—31no—
594C2×Q8—31no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—31no—
598C2×D4—41no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4C2×D3211yescharacteristic
602C2×D4C2×D3211yescharacteristic
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4C2×D3211yescharacteristic
608Q16—361no—
609SD16—62no—
610SD16—121no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8—361no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—181no—
641C42—181no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—84no—
672C22×C3—84no—
673C22×C3—88no—
674C22×C3#91612yes—
675C22×C3#95012yes—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C22×#6711yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C3×C4—22no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4C2×#23711yescharacteristic
694C3×C4C2×#23711yescharacteristic
695C3×C4#100411yescharacteristic
696C3×C4#100411yescharacteristic
697Dic3—21no—
698Dic3—21no—
699Dic3—21no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3—241no—
710C32#329611yescharacteristic, complemented, Sylow
711C23—21no—
712C23—21no—
713C23—31no—
714C23—42no—
715C23—42no—
716C23—81no—
717C23D3×#6711yescharacteristic
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—61no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—42no—
726D4—62no—
727D4—122no—
728D4—241no—
729D4#380512yes—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—122no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—241no—
745C2×C4—362no—
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—61no—
749C8—61no—
750C8—181no—
751C8—181no—
752C2×C3—24no—
753C2×C3—22no—
754C2×C3—22no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—42no—
759C2×C3—42no—
760C2×C3—82no—
761C2×C3—82no—
762C2×C3—81no—
763C2×C3—81no—
764C2×C3—121no—
765C2×C3#559111yescharacteristic
766C2×C3C2×#91611yescharacteristic
767C2×C3#577511yescharacteristic
768C2×C3#580611yescharacteristic
769C2×C3C2×#95011yescharacteristic
770C2×C3#583611yescharacteristic
771D3—41no—
772C22—21no—
773C22—21no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—84no—
784C22#6393512yes—
785C22C2×D3×#6711yescharacteristic
786C4—21no—
787C4—61no—
788C4—61no—
789C4—61no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—121no—
794C4—361no—
795C4—361no—
796C4C2×#380511yescharacteristic
797C4#6433011yescharacteristic
798C3—21no—
799C3#8015911yescharacteristic, complemented
800C3#8349411yescharacteristic, complemented
801C2—22no—
802C2—42no—
803C2—81no—
804C2—121no—
805C2#1059510611yescharacteristic
806C2C2×#6393511yescharacteristic
807C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3296
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
2. #10594853C2semidirect
3. C2×#63659C2semidirect
4. C3×#5218C2semidirect
5. #10591499C2semidirect
6. #10591478C2semidirect
7. #10591461C2semidirect
8. #10591442C2semidirect
9. Dic3×#214C2semidirect
10. #10591422C2semidirect
11. #10591420C2semidirect
12. #10591409C2semidirect
13. #10591188C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591126C2semidirect
36. #63869C22semidirect
38. #63856C22semidirect
40. Dic3×Dic6C22semidirect
41. #63841C22semidirect
42. C2×#3718C22semidirect
43. C2×D3×C3⋊C8C22semidirect
51. #63576C22semidirect
52. #63573C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
68. #5218D3semidirect
710. C32#3296semidirect
799. C3#80159semidirect
800. C3#83494semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
#105948532
C2×#636592
C3×#52182
#105914992
#105914782
#105914612
#105914422
Dic3×#2142
#105914222
#105914202
#105914092
#105911882
#67⋊(C3⋊C8)2
#105911262
#834943
#801593