Finite Group Databasebeta

← #11878588

Subgroups — #11878588

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5608C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic, complemented
3#10592736C211yesmaximal, characteristic, complemented
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591463C211yesmaximal, characteristic, complemented
6#10591460C211yesmaximal, characteristic, complemented
7#10591453C211yesmaximal, characteristic, complemented
8#10591452C211yesmaximal, characteristic, complemented
9#10591184C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591101C211yesmaximal, characteristic, complemented
12#10590587C211yesmaximal, characteristic, complemented
13#10590577C211yesmaximal, characteristic, complemented
14#10590426C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#83429—31nomaximal
17#81341—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24C3×#939—21no—
25C3×#938—21no—
26C3×#938C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#884—21no—
32C3×#878—21no—
33#63978—21no—
34#63978—21no—
35#63916—21no—
36#63909C2211yescharacteristic
37#63909C2211yescharacteristic
38#63871—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63574C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5608D311yescharacteristic, complemented
64#5510—31no—
65C3×#481—31no—
66#5239—31no—
67#5238—31no—
68#5234—31no—
69#5052—31no—
70#5048—31no—
71#5047—31no—
72#5043—31no—
73#5041—31no—
74#5039—31no—
75#5037—31no—
76#5037—31no—
77#5037—61no—
78#5034D311yescharacteristic, complemented
79#4971—31no—
80#4971—31no—
81#4968—31no—
82#4867—31no—
83#4864—31no—
84#4863—31no—
85#4862—31no—
86#4783—31no—
87#4782—31no—
88#4781—31no—
89#4778—31no—
90#4733—31no—
91#4727—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96#3828—41no—
97#3828—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C3×#237—41no—
108C3×#237—41no—
109C3×#235—41no—
110C3×#235—41no—
111C2×C3×D12D411yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6D411yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4—21no—
121#3754—41no—
122#3753—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#217—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3719—41no—
144#3717—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3204—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#237C2×D311yescharacteristic
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C2×#235C2×D311yescharacteristic
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×#121—21no—
159C3×#121—31no—
160C3×#121—61no—
161C3×#121—61no—
162C3×#121—61no—
163C3×#121C2×D311yescharacteristic
164C3×#121C2×D311yescharacteristic
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167#946—61no—
168C2×#216—31no—
169C2×#215—31no—
170#939—21no—
171#939—61no—
172#939—61no—
173#938—21no—
174#938—61no—
175#938C2×D311yescharacteristic
176C2×#214—31no—
177C2×#214—31no—
178C2×#214—61no—
179C2×#213—31no—
180C2×#213—31no—
181C2×#213—61no—
182#930—31no—
183#930—31no—
184#930—61no—
185#930—61no—
186C2×C4⋊Dic3C2×D311yescharacteristic
187#924—31no—
188#924—31no—
189#924C2×D311yescharacteristic
190C2×#208—31no—
191C22×C3⋊C8—31no—
192C2×Dic12—31no—
193C2×#204—31no—
194C2×ΓL(1,𝔽25)—31no—
195C2×D3×C8—31no—
196#897—31no—
197#897—31no—
198#897—61no—
199#897C2×D311yescharacteristic
200#895—31no—
201#895—31no—
202#895—61no—
203D3×C4⋊C4C2×D311yescharacteristic
204#884—21no—
205#878—21no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#835—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—61no—
220#830C2×D311yescharacteristic
221#821—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224#816—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#808C2×D311yescharacteristic
240#808C2×D311yescharacteristic
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4×C3⋊D3—42no—
259#634—21no—
260#634—21no—
261C3×#67—41no—
262C3×#67—41no—
263C3×#67—42no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—42no—
270C2×C3×Dic3—81no—
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C3×D12—41no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—81no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—41no—
282#626—81no—
283#626—81no—
284C3⋊(C3⋊C8)—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—91no—
290#483—91no—
291#483—91no—
292#481—31no—
293#481—91no—
294#470—91no—
295#469—91no—
296#465—91no—
297#465—91no—
298#452—91no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—91no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C2×C3×Q8—31no—
308C2×C3×Q8—31no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—41no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—121no—
335C2×#67#6711yescharacteristic
336C2×#67#6711yescharacteristic
337C22×Dic3—21no—
338C22×Dic3—21no—
339#237—41no—
340#237—41no—
341#235—41no—
342#235—41no—
343#235—121no—
344#235—121no—
345#235—121no—
346#235—121no—
347#235—122no—
348#235—122no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12#6711yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—121no—
359C2×C4×D3C22×D311yescharacteristic
360C2×C4×D3C22×D311yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6#6711yescharacteristic
365C2×Dic6C22×D311yescharacteristic
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384#217—21no—
385#217—21no—
386#217—61no—
387#217—61no—
388#216—121no—
389#215—121no—
390#214—121no—
391#214—121no—
392#214—122no—
393#213—121no—
394#213—121no—
395#213—122no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403C4⋊Dic3—21no—
404C4⋊Dic3—21no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414#208—121no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—121no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424Dic12—121no—
425#204—121no—
426ΓL(1,𝔽25)—121no—
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—21no—
443C2×C3×D3—21no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4H(5,𝔽2)11yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—41no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—31no—
457C2×#41—91no—
458C2×Q16—91no—
459C2×SD16—91no—
460C2×SD16—91no—
461C2×D8—91no—
462C2×M16—91no—
463C22×C8—91no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—61no—
467C22⋊Q8—91no—
468C22⋊Q8—91no—
469C22⋊Q8—181no—
470#121—31no—
471#121—61no—
472#121—61no—
473#121—61no—
474#121—91no—
475#121—91no—
476#121—181no—
477#121—181no—
478#121—181no—
479#121D3211yescharacteristic
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482#106—31no—
483#106—31no—
484#106—91no—
485#106—91no—
486#103—91no—
487#103—91no—
488#103—91no—
489#103—91no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494C22⋊C8—31no—
495C22⋊C8—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3D3×D411yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—121no—
509C22×D3C2×#6711yescharacteristic
510C22×D3C2×#6711yescharacteristic
511C3×Q8—61no—
512C3×Q8—61no—
513C3×Q8—121no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—81no—
521C3×D4—81no—
522C3×D4—82no—
523C3×D4—121no—
524C3×D4—121no—
525C3×D4—121no—
526C3×D4—122no—
527C3×D4—241no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—122no—
550C2×C3×C4—241no—
551C2×C3×C4—241no—
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—41no—
557#67—41no—
558#67—42no—
559#67—81no—
560#67—122no—
561#67—122no—
562#67—124no—
563#67—241no—
564#67—241no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—42no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—81no—
573C2×Dic3—121no—
574C2×Dic3C2×#6711yescharacteristic
575C2×Dic3C2×#6711yescharacteristic
576D12—41no—
577D12—62no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—61no—
582D12—121no—
583D12—241no—
584D12—241no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—21no—
589C4×D3—81no—
590C4×D3—122no—
591C4×D3—122no—
592C4×D3—124no—
593Dic6—21no—
594Dic6—21no—
595Dic6—41no—
596Dic6—62no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—61no—
601Dic6—121no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—61no—
610C3⋊C8—121no—
611C3⋊C8—121no—
612C2×C32—41no—
613C2×C32—81no—
614C2×C32#53411yescharacteristic
615C2×C32#57711yescharacteristic
616C2×C32#57711yescharacteristic
617C3⋊D3—81no—
618C3×D3—41no—
619C3×D3—41no—
620#41—121no—
621#41—121no—
622#41—121no—
623#41—121no—
624#41—361no—
625#41—361no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8—91no—
629C2×D4—21no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—91no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4C2×D3211yescharacteristic
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—61no—
645C22×C4—181no—
646C22×C4C2×D3211yescharacteristic
647Q16—361no—
648SD16—361no—
649SD16—361no—
650D8—361no—
651M16—361no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—91no—
655C2×C8—91no—
656C2×C8—361no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C4⋊C4C2×D3211yescharacteristic
667C22⋊C4—21no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C22×#6711yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—122no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—241no—
716C2×D3—241no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—81no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4#100411yescharacteristic
732C3×C4#100411yescharacteristic
733C3×C4#100911yescharacteristic
734C3×C4#100911yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—41no—
741Dic3—122no—
742Dic3—121no—
743Dic3—121no—
744C32#320411yescharacteristic, complemented, Sylow
745C23—21no—
746C23—31no—
747C23—31no—
748C23—181no—
749C23D3×#6711yescharacteristic
750Q8—61no—
751Q8—61no—
752Q8—121no—
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—21no—
757D4—81no—
758D4—121no—
759D4—121no—
760D4—121no—
761D4—122no—
762D4—181no—
763D4—181no—
764D4—241no—
765D4—362no—
766D4—721no—
767D4—721no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—122no—
782C2×C4—181no—
783C2×C4—241no—
784C2×C4—241no—
785C2×C4—362no—
786C2×C4D3×#6711yescharacteristic
787C2×C4C22×D3211yescharacteristic
788C8—61no—
789C8—61no—
790C8—181no—
791C8—181no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—81no—
798C2×C3—81no—
799C2×C3—81no—
800C2×C3—121no—
801C2×C3—121no—
802C2×C3—161no—
803C2×C3#565311yescharacteristic
804C2×C3#576211yescharacteristic
805C2×C3#577511yescharacteristic
806C2×C3#580411yescharacteristic
807C2×C3#583611yescharacteristic
808C2×C3#583711yescharacteristic
809D3—41no—
810D3—41no—
811D3—242no—
812D3—241no—
813D3—241no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—361no—
827C22—361no—
828C22—361no—
829C22C2×D3×#6711yescharacteristic
830C4—21no—
831C4—41no—
832C4—61no—
833C4—61no—
834C4—121no—
835C4—121no—
836C4—121no—
837C4—121no—
838C4—361no—
839C4#6431411yescharacteristic
840C4#6431411yescharacteristic
841C3—21no—
842C3#8134111yescharacteristic, complemented
843C3#8342911yescharacteristic, complemented
844C2—41no—
845C2—81no—
846C2—121no—
847C2—121no—
848C2—721no—
849C2#1059510511yescharacteristic
850C2#1059523411yescharacteristic
851C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3204
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5608C2semidirect
2. #10595043C2semidirect
3. #10592736C2semidirect
4. C3×#5034C2semidirect
5. #10591463C2semidirect
6. #10591460C2semidirect
7. #10591453C2semidirect
8. #10591452C2semidirect
9. #10591184C2semidirect
10. #10591145C2semidirect
11. #10591101C2semidirect
12. #10590587C2semidirect
13. #10590577C2semidirect
14. #10590426C2semidirect
15. #10590423C2semidirect
63. #5608D3semidirect
78. #5034D3semidirect
744. C32#3204semidirect
842. C3#81341semidirect
843. C3#83429semidirect

Maximal subgroups

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

subgroupindex
C3×#56082
#105950432
#105927362
C3×#50342
#105914632
#105914602
#105914532
#105914522
#105911842
#105911452
#105911012
#105905872
#105905772
#105904262
#105904232
#834293
#813413