Finite Group Databasebeta

← #11878371

Subgroups — #11878371

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic
3#10592750C211yesmaximal, characteristic, complemented
4C3×#5049C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591595C211yesmaximal, characteristic, complemented
7#10591583C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591179C211yesmaximal, characteristic, complemented
10#10591121C211yesmaximal, characteristic, complemented
11#10591071C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590502C211yesmaximal, characteristic, complemented
14#10590440C211yesmaximal, characteristic, complemented
15#10590429C211yesmaximal, characteristic, complemented
16#83408—31nomaximal
17#80817—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64133C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#894—21no—
32C3×#892C2211yescharacteristic
33C3×#888—21no—
34C3×#885—21no—
35C3×#883—21no—
36#63970—21no—
37#63970—21no—
38#63908C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63887—21no—
41#63885—21no—
42#63857C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45#63662C2211yescharacteristic
46#63637C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5833—31no—
63#5628D311yescharacteristic, complemented
64#5608—31no—
65C3×#468—31no—
66#5234—31no—
67#5228—31no—
68#5227—31no—
69#5173—31no—
70#5170—31no—
71#5137—31no—
72#5129—31no—
73#5052—31no—
74#5051—31no—
75#5051—31no—
76#5051—61no—
77#5049D311yescharacteristic, complemented
78#5048—31no—
79#5047—31no—
80#5047—31no—
81#5044—31no—
82#5043—31no—
83#5041—31no—
84#5003—31no—
85#4996—31no—
86#4888—31no—
87#4884—31no—
88#4809—31no—
89#4805—31no—
90#4783—31no—
91#4779—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C2×C3×#67D411yescharacteristic
98C3×D3×Q8—41no—
99C3×D3×Q8—41no—
100C3×#235—41no—
101C3×#235—41no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6D411yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#625—21no—
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3795—41no—
115#3795—41no—
116C32×C4⋊C4—21no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119#3757—21no—
120#3756—41no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C2×C3⋊(C3⋊C8)—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#215—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C3×#208—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3719—41no—
146#3715—41no—
147#3201—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C2×D3×Q8C2×D311yescharacteristic
151C2×#237—31no—
152C2×#235—31no—
153C2×#235C2×D311yescharacteristic
154C2×C3×SD16—31no—
155C2×C3×M16—31no—
156C3×C4⋊Q8—61no—
157C3×#124—61no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×C22⋊Q8C2×D311yescharacteristic
166C3×#121—31no—
167C3×#117—31no—
168#946—61no—
169#946C2×D311yescharacteristic
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—61no—
174C2×#215—31no—
175C2×#215C2×D311yescharacteristic
176#939—61no—
177#939—61no—
178#939—61no—
179#938—31no—
180#938—61no—
181#938—61no—
182C2×#214—31no—
183#930—31no—
184#930C2×D311yescharacteristic
185C2×C4⋊Dic3—31no—
186#924—31no—
187#924—31no—
188#924—31no—
189#924—61no—
190#924C2×D311yescharacteristic
191C2×#208C2×D311yescharacteristic
192C22×C3⋊C8—31no—
193C22×C3⋊C8—31no—
194C22×C3⋊C8—61no—
195C2×Dic12—31no—
196#897—31no—
197#897C2×D311yescharacteristic
198#894—21no—
199#892C2×D311yescharacteristic
200D3×C4⋊C4—31no—
201#888—21no—
202#885—21no—
203#884—61no—
204#883—21no—
205#878—61no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#817—31no—
225#816—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240#807C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255#634—21no—
256#634—21no—
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—41no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—41no—
276C3×Dic6—42no—
277#625—42no—
278#625—81no—
279D3×Dic3—42no—
280D3×Dic3—81no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#537—91no—
286#536—31no—
287#485—91no—
288#484—91no—
289#483—91no—
290#482—91no—
291#470—91no—
292#468—31no—
293#467—91no—
294#465—91no—
295#452—91no—
296#452—91no—
297#451—91no—
298#448—91no—
299#408—91no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8—31no—
305C2×C3×Q8—61no—
306C2×C3×Q8—121no—
307C2×C3×Q8—121no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67#6711yescharacteristic
327C2×#67#6711yescharacteristic
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×Q8—41no—
331D3×Q8—41no—
332#237—121no—
333#237—121no—
334#235—41no—
335#235—41no—
336#235—121no—
337#235—121no—
338C2×D12#6711yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3C22×D311yescharacteristic
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6—21no—
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×Dic6#6711yescharacteristic
350C2×Dic6C22×D311yescharacteristic
351C3×SD16—121no—
352C3×M16—121no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—41no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—61no—
375#217—21no—
376#217—61no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—121no—
381#216—121no—
382#216—121no—
383#216—121no—
384#216—122no—
385#215—41no—
386#215—121no—
387#214—121no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394C4⋊Dic3—21no—
395C4⋊Dic3—31no—
396C4⋊Dic3—31no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—121no—
409C4×Dic3—21no—
410#208—41no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8—122no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—121no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32C22×D411yescharacteristic
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C32×C4—21no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4H(5,𝔽2)11yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C2×#41—31no—
449C2×#41—91no—
450C22×Q8—31no—
451C2×Q16—91no—
452C2×Q16—91no—
453C2×SD16—31no—
454C2×SD16—91no—
455C2×M16—31no—
456C22×C8—91no—
457C4⋊Q8—61no—
458#124—61no—
459#123—61no—
460#123—61no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8D3211yescharacteristic
468#121—31no—
469#121—91no—
470#121—181no—
471#121—181no—
472#121—181no—
473#117—31no—
474C2×C4⋊C4—91no—
475#107—31no—
476#107—91no—
477#106—91no—
478#106—91no—
479#103—31no—
480#103—91no—
481#103—91no—
482#103—91no—
483#103—91no—
484#103—91no—
485#102—31no—
486#102—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490C22⋊C8—91no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—31no—
494C23×C3—61no—
495C23×C3D3×D411yescharacteristic
496C23×C3C2×#6711yescharacteristic
497C22×D3—21no—
498C22×D3C2×#6711yescharacteristic
499C22×D3C2×#6711yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—121no—
509C3×Q8—122no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—121no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—241no—
516C2×C3×C4—21no—
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—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
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—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544#67—41no—
545#67—41no—
546#67—81no—
547#67—122no—
548#67—122no—
549#67—241no—
550#67—241no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—122no—
561C2×Dic3—241no—
562C2×Dic3C2×#6711yescharacteristic
563C2×Dic3C2×#6711yescharacteristic
564D12—21no—
565D12—21no—
566D12—41no—
567C4×D3—21no—
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—42no—
572C4×D3—122no—
573C4×D3—241no—
574Dic6—21no—
575Dic6—21no—
576Dic6—41no—
577Dic6—42no—
578Dic6—61no—
579Dic6—61no—
580Dic6—61no—
581Dic6—61no—
582Dic6—121no—
583Dic6—121no—
584C3×C8—61no—
585C3×C8—61no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—62no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—121no—
594C2×C32—41no—
595C2×C32#53411yescharacteristic
596C2×C32#57711yescharacteristic
597C2×C32#57811yescharacteristic
598C3×D3—41no—
599C3×D3—41no—
600C3×D3—81no—
601#41—121no—
602#41—121no—
603#41—361no—
604#41—361no—
605C2×Q8—31no—
606C2×Q8—31no—
607C2×Q8—61no—
608C2×Q8—91no—
609C2×Q8—121no—
610C2×Q8—121no—
611C2×Q8C2×D3211yescharacteristic
612C2×D4—31no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—61no—
617C2×D4—181no—
618C2×D4—181no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4C2×D3211yescharacteristic
625Q16—361no—
626Q16—361no—
627SD16—121no—
628SD16—361no—
629M16—121no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C2×C8—361no—
635C4⋊C4—21no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—91no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—21no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—61no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C22×#6711yescharacteristic
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—81no—
698C3×C4—81no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4#100411yescharacteristic
703C3×C4#100411yescharacteristic
704C3×C4#100411yescharacteristic
705C3×C4#100911yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716Dic3—241no—
717C32#320111yescharacteristic, complemented, Sylow
718C23—31no—
719C23—31no—
720C23—61no—
721C23D3×#6711yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—61no—
725Q8—61no—
726Q8—121no—
727Q8—122no—
728Q8—181no—
729Q8—181no—
730D4—61no—
731D4—61no—
732D4—121no—
733D4—121no—
734D4—121no—
735D4—241no—
736D4—362no—
737D4—721no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—122no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—362no—
755C2×C4—721no—
756C2×C4D3×#6711yescharacteristic
757C2×C4C22×D3211yescharacteristic
758C8—61no—
759C8—61no—
760C8—181no—
761C8—181no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—42no—
766C2×C3—41no—
767C2×C3—41no—
768C2×C3—121no—
769C2×C3—121no—
770C2×C3—241no—
771C2×C3#560511yescharacteristic
772C2×C3#577511yescharacteristic
773C2×C3#577911yescharacteristic
774C2×C3#580411yescharacteristic
775C2×C3#583711yescharacteristic
776C2×C3#583811yescharacteristic
777D3—41no—
778D3—41no—
779D3—81no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22C2×D3×#6711yescharacteristic
793C4—21no—
794C4—41no—
795C4—41no—
796C4—61no—
797C4—61no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—361no—
802C4—361no—
803C4#6431311yescharacteristic
804C4#6431411yescharacteristic
805C3—21no—
806C3#8081711yescharacteristic, complemented
807C3#8340811yescharacteristic, complemented
808C2—41no—
809C2—121no—
810C2—121no—
811C2—241no—
812C2#1059530211yescharacteristic
813C2#1059532811yescharacteristic
814C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595004C2
hypercenterC22⋊Q8D32
hypocenterC32#3201
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5628C2semidirect
3. #10592750C2semidirect
4. C3×#5049C2semidirect
5. #10591655C2semidirect
6. #10591595C2semidirect
7. #10591583C2semidirect
8. #10591549C2semidirect
9. #10591179C2semidirect
10. #10591121C2semidirect
11. #10591071C2semidirect
12. #10590614C2semidirect
13. #10590502C2semidirect
14. #10590440C2semidirect
15. #10590429C2semidirect
63. #5628D3semidirect
77. #5049D3semidirect
717. C32#3201semidirect
806. C3#80817semidirect
807. C3#83408semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105950042
#105927502
C3×#50492
#105916552
#105915952
#105915832
#105915492
#105911792
#105911212
#105910712
#105906142
#105905022
#105904402
#105904292
#834083
#808173