Finite Group Databasebeta

← #11884127

Subgroups — #11884127

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic, complemented
2C3×#5806C211yesmaximal, characteristic
3C2×#63929C211yesmaximal, characteristic, complemented
4#10594915C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6#10591517C211yesmaximal, characteristic, complemented
7#10591491C211yesmaximal, characteristic, complemented
8#10591489C211yesmaximal, characteristic, complemented
9#10591463C211yesmaximal, characteristic, complemented
10#10591462C211yesmaximal, characteristic, complemented
11#10591441C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591190C211yesmaximal, characteristic, complemented
14#10591188C211yesmaximal, characteristic, complemented
15#10591158C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#80169—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C2×#3754—24no—
23C2×#3754C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28C3×#953—21no—
29C2×C3×#217—21no—
30C3×#939—21no—
31C3×#938C2211yescharacteristic
32C3×#936C2211yescharacteristic
33C3×#935—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C3×C4×#67C2211yescharacteristic
38C3×#924C2211yescharacteristic
39C3×#924C2211yescharacteristic
40#63982—21no—
41#67⋊Dic3—21no—
42#63929—24no—
43#63896—21no—
44#63866C2211yescharacteristic, complemented
45#63857C2211yescharacteristic, complemented
46#63844C2211yescharacteristic, complemented
47#63840—21no—
48C2×#3719C2211yescharacteristic, complemented
49C2×#3719C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#951—31no—
65#5806D311yescharacteristic
66C22×#214—31no—
67C22×#214—31no—
68C22×#214—61no—
69C2×#915—31no—
70#5632—31no—
71D4×Dic6—31no—
72C3×#450—31no—
73#5239—31no—
74#5218D311yescharacteristic, complemented
75#5170—31no—
76#5167—31no—
77#5162—31no—
78#5060—31no—
79#5054—31no—
80#5051—31no—
81#5051—31no—
82#5050—31no—
83#5042—31no—
84#5040—31no—
85#5019—31no—
86#5018—31no—
87#5011—31no—
88#4783—31no—
89#4780—31no—
90#4767—31no—
91#4757—31no—
92#4739—31no—
93#4730—31no—
94C24×C32—21no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3—21no—
102C2×#634—22no—
103C2×#634—21no—
104C2×#634—41no—
105C2×#634C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C3×#237—22no—
113C3×#237—41no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121#3754—22no—
122#3754—22no—
123#3754—22no—
124#3754D414yescomplemented
125C2×C3⋊(C3⋊C8)—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217D411yescharacteristic
135C3×#214—22no—
136C3×#214—41no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146#3724—21no—
147Dic3⋊Dic3—21no—
148Dic3⋊Dic3—21no—
149Dic3⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151Dic32—21no—
152#3719—22no—
153#3719—41no—
154#3718—22no—
155#3711—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—21no—
159C22×C3×D4C2×D311yescharacteristic
160C22×C3×D4C2×D311yescharacteristic
161C2×D3×Q8—31no—
162C2×#237C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—31no—
166C22×Dic6—61no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×#124—31no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#120—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C22⋊C4—61no—
179#953—21no—
180C2×#217—21no—
181#951—64no—
182#944—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187#939—21no—
188#938C2×D311yescharacteristic
189#936C2×D311yescharacteristic
190#935—21no—
191D4×Dic3—61no—
192D4×Dic3C2×D311yescharacteristic
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—61no—
202C2×#214—61no—
203C2×#214—61no—
204C2×#214—61no—
205C2×#214—64no—
206C2×#214—64no—
207C2×#214—68no—
208C2×#214C2×D311yescharacteristic
209C2×#214C2×D311yescharacteristic
210C4×#67C2×D311yescharacteristic
211#924—31no—
212#924C2×D311yescharacteristic
213#924C2×D311yescharacteristic
214C2×#208—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218#915—64no—
219C2×Dic12—31no—
220C2×Dic12—31no—
221C2×ΓL(1,𝔽25)—31no—
222#897—31no—
223#896—61no—
224#888—61no—
225#888—61no—
226#887—31no—
227#67⋊C4—61no—
228#878—61no—
229#878—61no—
230#878—61no—
231#869—31no—
232C4×Dic6—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835—31no—
238#832C2×D311yescharacteristic
239#832C2×D311yescharacteristic
240#830—31no—
241#830C2×D311yescharacteristic
242(C2×D3)⋊C8—31no—
243#816—31no—
244#816—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#810—31no—
249#810—31no—
250#810—31no—
251#807—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—42no—
274#634—21no—
275#634—21no—
276#634—21no—
277#634—42no—
278#634C2×D412yes—
279C3×#67—22no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#627—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—91no—
304C22×SD16—91no—
305D4×Q8—91no—
306#546—31no—
307#497—91no—
308#468—91no—
309#467—91no—
310#464—91no—
311#461—91no—
312#452—91no—
313#451—91no—
314#450—31no—
315#448—91no—
316#440—91no—
317#435—91no—
318C24×C3—21no—
319C24×C3—21no—
320C24×C3—41no—
321C3×#41—62no—
322C3×#41—121no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×D4—24no—
326C2×C3×D4—22no—
327C2×C3×D4—22no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—41no—
334C2×C3×D4—41no—
335C2×C3×D4—41no—
336C2×C3×D4—42no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—21no—
350C2×#67—21no—
351C2×#67#6711yescharacteristic
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—121no—
358D3×Q8—62no—
359D3×Q8—121no—
360#237—22no—
361#237—41no—
362C2×C4×D3—61no—
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—62no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—64no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—121no—
379C2×Dic6—121no—
380C2×Dic6—121no—
381C2×Dic6—121no—
382C2×Dic6—122no—
383C2×Dic6C22×D311yescharacteristic
384C2×Dic6C22×D311yescharacteristic
385C3×SD16—62no—
386C3×SD16—121no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—31no—
403#217—21no—
404#217—21no—
405#217—21no—
406#217—21no—
407#217—21no—
408#217—21no—
409#217—61no—
410#217#6711yescharacteristic
411#216—62no—
412#216—62no—
413#216—62no—
414#216—121no—
415#214—22no—
416#214—34no—
417#214—34no—
418#214—41no—
419#214—64no—
420#214—62no—
421#214—62no—
422#214—62no—
423#214—62no—
424#214—64no—
425#214—64no—
426#214—64no—
427#214—62no—
428#214—62no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4#6711yescharacteristic
431C4⋊Dic3—61no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435C4⋊Dic3C22×D311yescharacteristic
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4#6711yescharacteristic
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3C22×D311yescharacteristic
447#208—62no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—62no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8—64no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459Dic12—62no—
460Dic12—121no—
461ΓL(1,𝔽25)—62no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—84no—
471C22×C32#13712yescomplemented
472C22×C32C22×D411yescharacteristic
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C32×C4—21no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3⋊Dic3—22no—
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C22×Q8—91no—
490C22×Q8—91no—
491C22×D4D3211yescharacteristic
492#137—184no—
493C2×Q16—91no—
494C2×Q16—91no—
495C2×Q16—91no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—184no—
503C2×M16—91no—
504C22×C8—91no—
505C4⋊Q8—91no—
506C4⋊Q8—181no—
507#124—31no—
508#123—61no—
509C22⋊Q8—31no—
510C22⋊Q8—31no—
511C22⋊Q8—91no—
512C22⋊Q8—181no—
513C22⋊Q8—181no—
514#121—31no—
515#121—61no—
516#120—61no—
517C4×Q8—91no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—181no—
521C2×C22⋊C4—61no—
522#107—91no—
523C4⋊C8—91no—
524#103—91no—
525#103—91no—
526#103—91no—
527#103—91no—
528#102—31no—
529#102—31no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—41no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—44no—
544C23×C3—42no—
545C23×C3—42no—
546C23×C3—82no—
547C23×C3—81no—
548C23×C3—81no—
549C23×C3—82no—
550C23×C3D3×D411yescharacteristic
551C23×C3C2×#6711yescharacteristic
552C22×D3C2×#6711yescharacteristic
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—22no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—22no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—42no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—62no—
571C3×D4—122no—
572C3×D4—241no—
573C3×D4D3×D412yes—
574C3×D4D3×D412yes—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4—241no—
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4C2×#6711yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D311yescharacteristic
598#67—22no—
599#67—42no—
600#67—81no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—42no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—81no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×Dic3—122no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—124no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—122no—
623Dic6—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—32no—
628Dic6—32no—
629Dic6—62no—
630Dic6—61no—
631Dic6—61no—
632Dic6—62no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—61no—
637Dic6—121no—
638Dic6—121no—
639Dic6—122no—
640Dic6—122no—
641Dic6—122no—
642Dic6—122no—
643Dic6—124no—
644C3×C8—61no—
645C3×C8—61no—
646C3⋊C8—21no—
647C3⋊C8—21no—
648C3⋊C8—32no—
649C3⋊C8—32no—
650C3⋊C8—62no—
651C3⋊C8—62no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C2×C32—22no—
655C2×C32—42no—
656C2×C32—81no—
657C2×C32D4211yescharacteristic
658C2×C32C2×#13711yescharacteristic
659C2×C32#57711yescharacteristic
660C3×D3—41no—
661C24—21no—
662#41—62no—
663#41—121no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8—91no—
667C2×Q8—91no—
668C2×Q8—182no—
669C2×Q8—181no—
670C2×Q8—182no—
671C2×Q8—181no—
672C2×Q8—361no—
673C2×Q8—361no—
674C2×D4—22no—
675C2×D4—21no—
676C2×D4—31no—
677C2×D4—41no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4C2×D3211yescharacteristic
681C2×D4C2×D3211yescharacteristic
682C22×C4—31no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—181no—
686C22×C4—181no—
687C22×C4C2×D3211yescharacteristic
688Q16—182no—
689Q16—182no—
690Q16—361no—
691SD16—62no—
692SD16—94no—
693SD16—121no—
694SD16—182no—
695SD16—182no—
696SD16—182no—
697M16—182no—
698C2×C8—31no—
699C2×C8—31no—
700C2×C8—91no—
701C2×C8—91no—
702C2×C8—182no—
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C4⋊C4—181no—
711C4⋊C4—181no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—181no—
721C42—31no—
722C42—181no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—84no—
753C22×C3—84no—
754C22×C3—88no—
755C22×C3#91512yescomplemented
756C22×C3#95112yescomplemented
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C22×#6711yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—21no—
762C3×C4—22no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4C2×D3×D411yescharacteristic
775C3×C4C2×D3×D411yescharacteristic
776C3×C4#100411yescharacteristic
777C3×C4#100411yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—21no—
781Dic3—41no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—62no—
786Dic3—62no—
787Dic3—122no—
788Dic3—122no—
789Dic3—121no—
790Dic3—121no—
791C32#326611yescharacteristic, complemented, Sylow
792C23—21no—
793C23—21no—
794C23—31no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23D3×#6711yescharacteristic
799Q8—61no—
800Q8—61no—
801Q8—61no—
802Q8—61no—
803Q8—92no—
804Q8—181no—
805Q8—181no—
806Q8—181no—
807Q8—362no—
808Q8—362no—
809D4—21no—
810D4—21no—
811D4—21no—
812D4—42no—
813D4—62no—
814D4—122no—
815D4—241no—
816D4#381112yes—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—31no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—122no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—241no—
832C2×C4—362no—
833C2×C4—362no—
834C2×C4D3×#6711yescharacteristic
835C2×C4C22×D3211yescharacteristic
836C8—61no—
837C8—61no—
838C8—92no—
839C8—181no—
840C2×C3—24no—
841C2×C3—22no—
842C2×C3—22no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—42no—
847C2×C3—42no—
848C2×C3—82no—
849C2×C3—82no—
850C2×C3—81no—
851C2×C3—81no—
852C2×C3—121no—
853C2×C3#559011yescharacteristic
854C2×C3C2×#91511yescharacteristic
855C2×C3#577511yescharacteristic
856C2×C3D4×#6711yescharacteristic
857C2×C3C2×#95111yescharacteristic
858C2×C3#583611yescharacteristic
859D3—41no—
860C22—21no—
861C22—21no—
862C22—22no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—84no—
872C22#6392912yescomplemented
873C22C2×D3×#6711yescharacteristic
874C4—21no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—121no—
879C4—121no—
880C4—121no—
881C4—121no—
882C4—182no—
883C4—361no—
884C4C2×#381111yescharacteristic
885C4#6433011yescharacteristic
886C3—21no—
887C3#8016911yescharacteristic, complemented
888C3#8350611yescharacteristic, complemented
889C2—22no—
890C2—42no—
891C2—81no—
892C2—121no—
893C2C2×#6392911yescharacteristic
894C2#1059510611yescharacteristic
895C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3266
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. C22×#3754C2semidirect
3. C2×#63929C2semidirect
4. #10594915C2semidirect
5. C3×#5218C2semidirect
6. #10591517C2semidirect
7. #10591491C2semidirect
8. #10591489C2semidirect
9. #10591463C2semidirect
10. #10591462C2semidirect
11. #10591441C2semidirect
12. #10591405C2semidirect
13. #10591190C2semidirect
14. #10591188C2semidirect
15. #10591158C2semidirect
21. C2×D3×Dic6C22semidirect
44. #63866C22semidirect
45. #63857C22semidirect
46. #63844C22semidirect
48. C2×#3719C22semidirect
49. C2×#3719C22semidirect
50. C2×#3718C22semidirect
51. C2×#3711C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
74. #5218D3semidirect
124. #3754D4semidirect
471. C22×C32#137semidirect
755. C22×C3#915semidirect
756. C22×C3#951semidirect
791. C32#3266semidirect
872. C22#63929semidirect
887. C3#80169semidirect
888. C3#83506semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C3×#58062
C2×#639292
#105949152
C3×#52182
#105915172
#105914912
#105914892
#105914632
#105914622
#105914412
#105914052
#105911902
#105911882
#105911582
#835063
#801693