Finite Group Databasebeta

← #11884120

Subgroups — #11884120

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic, complemented
2C3×#5829C211yesmaximal, characteristic
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594915C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591627C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10591577C211yesmaximal, characteristic, complemented
10#10591489C211yesmaximal, characteristic, complemented
11#10591459C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591181C211yesmaximal, characteristic, complemented
14#10591180C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83506—31nomaximal
17#80241—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C22×#634C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22#64160—24no—
23C2×#3756C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C2×#3748C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic, complemented
31C3×#939—21no—
32C3×#937—21no—
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#214C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×#929—21no—
37C3×C4×#67C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4—21no—
39C3×#924C2211yescharacteristic, complemented
40#63982—21no—
41#67⋊Dic3—21no—
42D3×#214—24no—
43#63896—21no—
44#63866C2211yescharacteristic, complemented
45#63857C2211yescharacteristic
46#63844C2211yescharacteristic, complemented
47#63840—21no—
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64#5829D311yescharacteristic
65C2×#951—31no—
66C2×#951—31no—
67C2×#951—61no—
68C22×#214—31no—
69C2×D3×SD16—31no—
70#5632—31no—
71D4×Dic6—31no—
72C3×#452—31no—
73#5239D311yescharacteristic, complemented
74#5218—31no—
75#5190—31no—
76#5186—31no—
77#5162—31no—
78#5060—31no—
79#5054—31no—
80#5051—31no—
81#5050—31no—
82#5049—31no—
83#5042—31no—
84#5040—31no—
85#5019—31no—
86#5018—31no—
87#5011—31no—
88#4813—31no—
89#4798—31no—
90#4776—31no—
91#4757—31no—
92#4738—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3—21no—
103C2×#634—22no—
104C2×#634—21no—
105C2×#634—41no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C3×D3×D4—22no—
113C3×D3×D4—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×D3×Dic3—21no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121#3756—22no—
122#3756—22no—
123#3754—22no—
124#3754D414yescomplemented
125#3748—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—41no—
132C3×#214—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
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#3716—22no—
153#3716—41no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×D4—31no—
161C2×D3×Q8—31no—
162C2×D3×D4C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—31no—
166C22×Dic6—61no—
167C2×C3×Q16—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#951—64no—
180#951—64no—
181#951—68no—
182#947C2×D311yescharacteristic
183#946C2×D311yescharacteristic
184#944—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—61no—
190C2×#216—61no—
191C2×#216C2×D311yescharacteristic, complemented
192C2×#215—31no—
193#939—21no—
194#937—21no—
195D4×Dic3—61no—
196D4×Dic3C2×D311yescharacteristic
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—61no—
205C2×#214—61no—
206C2×#214—64no—
207C2×#214C2×D311yescharacteristic
208#930C2×D311yescharacteristic
209#929—21no—
210C4×#67C2×D311yescharacteristic
211C2×(C2×D3)⋊C4—21no—
212#924—31no—
213#924C2×D311yescharacteristic, complemented
214C2×#208—31no—
215C2×#208—31no—
216C2×#208—61no—
217C22×C3⋊C8—31no—
218D3×SD16—64no—
219C2×#204—31no—
220C2×#204—31no—
221C2×D3×C8—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×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835C2×D311yescharacteristic, complemented
238#832—31no—
239#832C2×D311yescharacteristic
240#830—31no—
241#830C2×D311yescharacteristic, complemented
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#809—31no—
251#807—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×D4—21no—
265C32×D4—42no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—42no—
276#634—21no—
277#634—21no—
278#634—21no—
279#634—42no—
280#634C2×D412yes—
281C3×#67—22no—
282C3×#67—42no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—81no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—21no—
292C3×D12—21no—
293C3×C4×D3—21no—
294C3×C4×D3—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—31no—
313#451—91no—
314#450—91no—
315#448—91no—
316#440—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—24no—
321C3×#41—22no—
322C3×#41—22no—
323C3×#41—41no—
324C3×#41—41no—
325C3×#41—42no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—41no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—61no—
339C2×C3×D4—121no—
340C2×C3×D4C22×D311yescharacteristic
341C2×C3×D4C22×D311yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—41no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67#6711yescharacteristic
353C22×Dic3—21no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—121no—
358D3×Q8—62no—
359D3×Q8—121no—
360D3×D4—22no—
361D3×D4—41no—
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—31no—
368C2×Dic6—31no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—64no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—61no—
379C2×Dic6—121no—
380C2×Dic6—121no—
381C2×Dic6—121no—
382C2×Dic6—121no—
383C2×Dic6—122no—
384C2×Dic6C22×D311yescharacteristic
385C3×Q16—121no—
386C3×SD16—62no—
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—61no—
406#217#6711yescharacteristic
407#216—41no—
408#216—62no—
409#216—62no—
410#216—62no—
411#216—62no—
412#216—64no—
413#216—64no—
414#215—62no—
415#214—22no—
416#214—34no—
417#214—34no—
418#214—64no—
419#214—62no—
420#214—62no—
421#214—64no—
422#214—62no—
423#214—62no—
424#214—121no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
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—
448#208—62no—
449#208—64no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459#204—62no—
460#204—121no—
461D3×C8—62no—
462C22×C32—21no—
463C22×C32—22no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32C22×D411yescharacteristic
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—84no—
475C2×C3×D3#13712yescomplemented
476C32×C4—21no—
477C32×C4—41no—
478C32×C4C22×D411yescharacteristic
479C32×C4H(5,𝔽2)11yescharacteristic
480C3⋊Dic3—22no—
481C3⋊Dic3—41no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41D3211yescharacteristic
489C22×Q8—91no—
490C22×Q8—91no—
491C22×D4—31no—
492#137—184no—
493C2×Q16—31no—
494C2×Q16—91no—
495C2×Q16—91no—
496C2×SD16—31no—
497C2×SD16—91no—
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—31no—
525#103—91no—
526#103—91no—
527#103—91no—
528#102—31no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—241no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×#6711yescharacteristic
544C22×D3—21no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—81no—
548C22×D3C2×#6711yescharacteristic
549C3×Q8—22no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—41no—
561C3×D4—42no—
562C3×D4—42no—
563C3×D4—44no—
564C3×D4—62no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—122no—
568C3×D4—241no—
569C3×D4D3×D412yes—
570C3×D4D3×D412yes—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—42no—
586C2×C3×C4—42no—
587C2×C3×C4—44no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
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—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—81no—
609C2×Dic3—121no—
610C2×Dic3—121no—
611C2×Dic3—122no—
612C2×Dic3—122no—
613C2×Dic3—122no—
614C2×Dic3—124no—
615C2×Dic3C2×#6711yescharacteristic
616C2×Dic3C2×#6711yescharacteristic
617C2×Dic3C2×#6711yescharacteristic
618D12—21no—
619D12—21no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—122no—
623Dic6—21no—
624Dic6—21no—
625Dic6—32no—
626Dic6—32no—
627Dic6—62no—
628Dic6—61no—
629Dic6—61no—
630Dic6—62no—
631Dic6—61no—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—121no—
636Dic6—121no—
637Dic6—122no—
638Dic6—122no—
639Dic6—122no—
640Dic6—122no—
641Dic6—124no—
642C3×C8—61no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—21no—
646C3⋊C8—32no—
647C3⋊C8—32no—
648C3⋊C8—62no—
649C3⋊C8—62no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C2×C32—41no—
653C2×C32—42no—
654C2×C32D4211yescharacteristic
655C2×C32C2×#13711yescharacteristic
656C2×C32#57711yescharacteristic
657C3×D3—22no—
658C3×D3—81no—
659C24—61no—
660#41—22no—
661#41—41no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×Q8—91no—
665C2×Q8—182no—
666C2×Q8—181no—
667C2×Q8—182no—
668C2×Q8—181no—
669C2×Q8—361no—
670C2×Q8—361no—
671C2×Q8C2×D3211yescharacteristic
672C2×D4—21no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—61no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—121no—
679C2×D4C2×D3211yescharacteristic
680C22×C4—21no—
681C22×C4—31no—
682C22×C4—61no—
683C22×C4—181no—
684C22×C4—181no—
685C22×C4C2×D3211yescharacteristic
686Q16—121no—
687Q16—182no—
688Q16—182no—
689SD16—62no—
690SD16—94no—
691SD16—182no—
692SD16—182no—
693SD16—182no—
694SD16—361no—
695M16—182no—
696C2×C8—31no—
697C2×C8—31no—
698C2×C8—91no—
699C2×C8—91no—
700C2×C8—182no—
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—31no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4—181no—
707C4⋊C4—181no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C22⋊C4—31no—
711C22⋊C4—31no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—181no—
719C42—31no—
720C42—181no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—32no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—42no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—244no—
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C22×#6711yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—84no—
755C2×D3#95112yescomplemented
756C3×C4—22no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—42no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4C2×D3×D411yescharacteristic
771C3×C4C2×D3×D411yescharacteristic
772C3×C4#100411yescharacteristic
773C3×C4#100411yescharacteristic
774Dic3—21no—
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779Dic3—41no—
780Dic3—62no—
781Dic3—62no—
782Dic3—122no—
783Dic3—122no—
784Dic3—121no—
785Dic3—121no—
786C32#326611yescharacteristic, complemented, Sylow
787C23—21no—
788C23—31no—
789C23—61no—
790C23—122no—
791C23—122no—
792C23—241no—
793C23D3×#6711yescharacteristic
794Q8—21no—
795Q8—21no—
796Q8—61no—
797Q8—61no—
798Q8—92no—
799Q8—181no—
800Q8—181no—
801Q8—181no—
802Q8—362no—
803Q8—362no—
804D4—21no—
805D4—42no—
806D4—62no—
807D4—61no—
808D4—61no—
809D4—122no—
810D4—241no—
811D4#381112yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—31no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—42no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—241no—
827C2×C4—362no—
828C2×C4—362no—
829C2×C4D3×#6711yescharacteristic
830C2×C4C22×D3211yescharacteristic
831C8—61no—
832C8—61no—
833C8—92no—
834C8—181no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—42no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—42no—
843C2×C3—62no—
844C2×C3—82no—
845C2×C3—241no—
846C2×C3#559011yescharacteristic
847C2×C3#577011yescharacteristic
848C2×C3D3×#13711yescharacteristic
849C2×C3D4×#6711yescharacteristic
850C2×C3C2×#95111yescharacteristic
851C2×C3#583611yescharacteristic
852D3—22no—
853D3—81no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—22no—
858C22—32no—
859C22—41no—
860C22—41no—
861C22—61no—
862C22—61no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—244no—
867C22C2×D3×#6711yescharacteristic
868C4—21no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—121no—
876C4—182no—
877C4—361no—
878C4C2×#381111yescharacteristic
879C4#6433011yescharacteristic
880C3—21no—
881C3#8024111yescharacteristic, complemented
882C3#8350611yescharacteristic, complemented
883C2—41no—
884C2—42no—
885C2—62no—
886C2—241no—
887C2D3×#95111yescharacteristic
888C2#1059546611yescharacteristic
889C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC2×#41D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64160C2semidirect
3. C2×D3×#214C2semidirect
4. #10594915C2semidirect
5. C3×#5239C2semidirect
6. #10591653C2semidirect
7. #10591627C2semidirect
8. #10591596C2semidirect
9. #10591577C2semidirect
10. #10591489C2semidirect
11. #10591459C2semidirect
12. #10591405C2semidirect
13. #10591181C2semidirect
14. #10591180C2semidirect
15. #10591151C2semidirect
19. C22×#634C22semidirect
23. C2×#3756C22semidirect
24. C2×#3756C22semidirect
27. C2×#3748C22semidirect
30. C2×C3×#216C22semidirect
39. C3×#924C22semidirect
44. #63866C22semidirect
46. #63844C22semidirect
52. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63565C22semidirect
62. #63554C22semidirect
73. #5239D3semidirect
124. #3754D4semidirect
191. C2×#216C2×D3semidirect
213. #924C2×D3semidirect
237. #835C2×D3semidirect
241. #830C2×D3semidirect
475. C2×C3×D3#137semidirect
755. C2×D3#951semidirect
786. C32#3266semidirect
881. C3#80241semidirect
882. C3#83506semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C3×#58292
C2×D3×#2142
#105949152
C3×#52392
#105916532
#105916272
#105915962
#105915772
#105914892
#105914592
#105914052
#105911812
#105911802
#105911512
#835063
#802413