Finite Group Databasebeta

← #11900889

Subgroups — #11900889

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4#10595377C212yesmaximal, complemented
5#10595368C212yesmaximal, complemented
6#10595202C214yesmaximal, complemented
7#10595173C212yesmaximal, complemented
8#10595133C212yesmaximal, complemented
9#10595130C214yesmaximal, complemented
10#10595049C211yesmaximal, characteristic, complemented
11#10595022C211yesmaximal, characteristic, complemented
12#10594958C211yesmaximal, characteristic, complemented
13#10594934C214yesmaximal, complemented
14C4×#3805C214yesmaximal, complemented
15C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
16#86219—31nomaximal
17#86018—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×#3805C2214yes—
22C22×D3×Dic3C2212yes—
23Q8×C3⋊Dic3C2212yescomplemented
24D4×C3⋊Dic3C2214yes—
25D4×C3⋊Dic3C2212yescomplemented
26#64135C2211yescharacteristic
27#64135C2212yescomplemented
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C4×C3⋊Dic3C2212yescomplemented
30C3×#947C2211yescharacteristic, complemented
31C3×#946C2212yes—
32C3×#944C2211yescharacteristic, complemented
33C3×#940C2211yescharacteristic, complemented
34C3×#939C2214yes—
35C3×#938C2212yes—
36C3×#937C2212yes—
37C3×#936C2211yescharacteristic, complemented
38C3×#935C2212yes—
39C3×C4×#67C2214yes—
40C3×C4×#67C2214yescomplemented
41C3×#926C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43#63976C2212yes—
44#67⋊Dic3C2214yes—
45#67⋊Dic3C2214yes—
46#67⋊Dic3C2214yescomplemented
47#63970C2214yes—
48#63969C2214yes—
49#63964C2214yes—
50#63961C2212yes—
51#63959C2214yescomplemented
52#63957C2214yescomplemented
53#63956C2214yescomplemented
54C2×Dic32C2212yes—
55#63918C2212yescomplemented
56C4×#627C2214yescomplemented
57#63908C2212yes—
58#63902C2214yes—
59C4×#625C2214yes—
60#63898C2212yescomplemented
61#63893C2214yes—
62#63891C2214yes—
63#63878C2214yes—
64#63878C2214yescomplemented
65C4×D3×Dic3C2212yes—
66C4×D3×Dic3C2212yes—
67C4×D3×Dic3C2212yes—
68C4×D3×Dic3C2212yes—
69C4×D3×Dic3C2212yescomplemented
70#63869C2212yescomplemented
71#63861C2214yescomplemented
72#63856C2212yes—
73#63855C2212yescomplemented
74#63845C2214yescomplemented
75#63843C2212yescomplemented
76#63838C2214yescomplemented
77C3×#532—31no—
78C3×#525—31no—
79#5832D311yescharacteristic, complemented
80#5828—31no—
81#5828D311yescharacteristic, complemented
82Dic3×#41—31no—
83Dic3×#41—31no—
84Dic3×#41—31no—
85Dic3×#41—61no—
86#5791—31no—
87C22×C4×Dic3—31no—
88#5728—32no—
89#5716—32no—
90#5680—32no—
91#5680—32no—
92#5649—34no—
93#5624—32no—
94#5622—32no—
95#5606—34no—
96#5600—32no—
97#5600—34no—
98#5596—32no—
99#5586—34no—
100#5557—34no—
101#5538—34no—
102C4×#237—34no—
103C4×#237—34no—
104#5522—31no—
105#5517—31no—
106C2×C42×D3—31no—
107#5470—31no—
108C23×C3×D3C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2311yescharacteristic
113C22×C32×C4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C22×C3⋊Dic3C2312yes—
116C22×C3⋊Dic3C2314yes—
117C2×C3×#67C2314yes—
118C2×C3×#67C2314yes—
119C2×C3×#67C2312yes—
120C22×C3×Dic3C2312yes—
121C22×C3×Dic3C2311yescharacteristic
122C3×#235—24no—
123C2×C3×D12C2311yescharacteristic
124C2×C3×C4×D3—24no—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×C4×D3C2312yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×#627C2314yes—
130C2×#625C2314yes—
131#3805—216no—
132C2×D3×Dic3—28no—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2314yes—
137C2×D3×Dic3C2312yes—
138#3757C2312yes—
139#3757C2314yes—
140C4⋊(C3⋊Dic3)C2314yes—
141C4⋊(C3⋊Dic3)C2312yes—
142C4×C3⋊Dic3C2314yes—
143C4×C3⋊Dic3C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2312yes—
147C3×#217C2312yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×C4⋊Dic3C2312yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2311yescharacteristic
157C3×C4×Dic3C2311yescharacteristic
158C3×C4×Dic3C2312yes—
159#3724C2314yes—
160#3724C2314yes—
161Dic3⋊Dic3C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167Dic32C2312yes—
168Dic32C2314yes—
169Dic32C2312yes—
170Dic32C2312yes—
171Dic32C2312yes—
172#3444—91noSylow
173C2×C3×#41—21no—
174C2×C3×#41—31no—
175C2×C3×#41C2×D311yescharacteristic
176C2×C3×#41C2×D311yescharacteristic
177C23×C3×C4—31no—
178C23×Dic3—32no—
179C2×#237—34no—
180C2×#237—34no—
181C2×#235C2×D311yescharacteristic
182C22×C4×D3—32no—
183C22×C4×D3C2×D311yescharacteristic
184C3×C4⋊Q8—31no—
185C3×#127—31no—
186C3×#124—31no—
187C3×#124—31no—
188C3×#123—32no—
189C3×C22⋊Q8—32no—
190C3×#121—32no—
191C3×#121—34no—
192C3×#120—32no—
193C3×C4×D4—34no—
194C3×C4×D4—34no—
195C3×#117—31no—
196C2×C3×C42—31no—
197#953—32no—
198#947C2×D311yescharacteristic, complemented
199#946—32no—
200#946C2×D312yes—
201Q8×Dic3—32no—
202Q8×Dic3—32no—
203Q8×Dic3—32no—
204Q8×Dic3—62no—
205#944C2×D311yescharacteristic, complemented
206#940C2×D311yescharacteristic, complemented
207#939—34no—
208#939C2×D314yes—
209#938—34no—
210#938—32no—
211#938C2×D312yes—
212#937—32no—
213#937C2×D312yes—
214#936—34no—
215#936C2×D311yescharacteristic, complemented
216#935—32no—
217#935—34no—
218#935C2×D312yes—
219D4×Dic3—34no—
220D4×Dic3—32no—
221D4×Dic3—34no—
222D4×Dic3—32no—
223D4×Dic3—34no—
224D4×Dic3—34no—
225D4×Dic3—34no—
226D4×Dic3—32no—
227D4×Dic3—64no—
228D4×Dic3—62no—
229#930—32no—
230#929—32no—
231C4×#67—34no—
232C4×#67—34no—
233C4×#67C2×D314yes—
234C4×#67C2×D314yescomplemented
235#926—31no—
236#926—31no—
237#926—32no—
238#926—32no—
239#926—32no—
240#926—61no—
241#926—62no—
242#926C2×D311yescharacteristic
243#924—32no—
244#924—34no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—32no—
248C2×C4×Dic3—32no—
249C2×C4×Dic3—32no—
250C2×C4×Dic3—32no—
251C2×C4×Dic3—32no—
252C2×C4×Dic3—32no—
253C2×C4×Dic3—32no—
254C2×C4×Dic3—32no—
255C2×C4×Dic3—32no—
256C2×C4×Dic3—61no—
257C2×C4×Dic3—62no—
258C2×C4×Dic3C2×D311yescharacteristic
259#898—34no—
260#897—34no—
261#893—32no—
262#892—34no—
263#892—34no—
264#890—34no—
265#890—32no—
266#889—34no—
267#888—32no—
268#887—32no—
269#887—34no—
270#887—34no—
271#886—34no—
272#885—34no—
273#883—34no—
274#883—34no—
275#67⋊C4—34no—
276#67⋊C4—34no—
277#67⋊C4—34no—
278#67⋊C4—34no—
279#67⋊C4—34no—
280#879—34no—
281#879—34no—
282#879—34no—
283#878—34no—
284#878—34no—
285#877—34no—
286#877—34no—
287#877—34no—
288#877—34no—
289#872—32no—
290C42×D3—32no—
291C42×D3—32no—
292C42×D3—32no—
293C42×D3—32no—
294C42×D3—32no—
295#870—32no—
296#869—32no—
297C4×Dic6—34no—
298C4×Dic6—34no—
299C23×C32C2412yes—
300C23×C32C2411yescharacteristic
301C22×C3×D3—22no—
302C22×C3×D3—24no—
303C22×C3×D3C2412yes—
304C22×C3×D3C2412yes—
305C32×Q8—22no—
306C32×D4—24no—
307C32×D4—22no—
308C2×C32×C4—24no—
309C2×C32×C4#4114yescomplemented
310C2×C32×C4C2412yes—
311C2×C32×C4C2411yescharacteristic
312C2×C32×C4C2411yescharacteristic
313C2×C3⋊Dic3—24no—
314C2×C3⋊Dic3—28no—
315C2×C3⋊Dic3C2412yes—
316C2×C3⋊Dic3C2414yes—
317C2×C3⋊Dic3C2412yes—
318C3×#67—24no—
319C3×#67—28no—
320C3×#67—28no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—24no—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2414yes—
327C2×C3×Dic3C2412yes—
328C3×D12—22no—
329C3×C4×D3—24no—
330C3×C4×D3—24no—
331C3×C4×D3—24no—
332C3×Dic6—22no—
333#627—28no—
334#625—28no—
335D3×Dic3—24no—
336D3×Dic3—24no—
337D3×Dic3—28no—
338D3×Dic3—24no—
339D3×Dic3#4118yescomplemented
340#533—91no—
341#533—92no—
342#532—31no—
343#532—92no—
344#529—94no—
345#529—94no—
346#529—92no—
347#529—92no—
348#525—31no—
349#525—94no—
350#525—91no—
351C4×#41—91no—
352C4×#41—94no—
353C4×#41—91no—
354C22×C42—91no—
355C24×C3—31no—
356C23×D3C22×D311yescharacteristic
357C3×#41—28no—
358C3×#41—24no—
359C3×#41—24no—
360C3×#41—64no—
361C2×C3×Q8—21no—
362C2×C3×Q8—31no—
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×Q8C22×D311yescharacteristic
365C2×C3×D4—22no—
366C2×C3×D4—21no—
367C2×C3×D4—32no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—31no—
371C2×C3×D4C22×D312yes—
372C2×C3×D4C22×D311yescharacteristic
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C22×D312yes—
375C22×C3×C4—22no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—32no—
379C22×C3×C4—32no—
380C22×C3×C4—32no—
381C22×C3×C4—32no—
382C22×C3×C4—64no—
383C22×C3×C4C22×D312yes—
384C22×C3×C4C22×D312yes—
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C2×#67—34no—
388C2×#67—34no—
389C2×#67C22×D312yes—
390C2×#67C22×D314yes—
391C2×#67C22×D314yes—
392C22×Dic3—32no—
393C22×Dic3—34no—
394C22×Dic3—34no—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—34no—
398C22×Dic3—32no—
399C22×Dic3—32no—
400C22×Dic3—32no—
401C22×Dic3—62no—
402C22×Dic3—64no—
403C22×Dic3—68no—
404C22×Dic3C22×D312yes—
405C22×Dic3C22×D311yescharacteristic
406#237—616no—
407#237—616no—
408#235—24no—
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—24no—
411C2×C4×D3—32no—
412C2×C4×D3—32no—
413C2×C4×D3—32no—
414C2×C4×D3—32no—
415C2×C4×D3—34no—
416C2×C4×D3—68no—
417C2×C4×D3C22×D312yes—
418C2×C4×D3C22×D312yes—
419C2×C4×D3C22×D312yes—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6C22×D311yescharacteristic
423C3×C4⋊C4—32no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—32no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C42—32no—
432C3×C42—32no—
433C3×C42—31no—
434C3×C42—31no—
435#217—32no—
436#217—34no—
437#217—34no—
438#217—32no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—62no—
443#217—64no—
444#217C22×D314yes—
445#217C22×D314yes—
446#217C22×D312yes—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4C22×D314yes—
451(C2×D3)⋊C4C22×D314yes—
452C4⋊Dic3—32no—
453C4⋊Dic3—34no—
454C4⋊Dic3—34no—
455C4⋊Dic3—32no—
456C4⋊Dic3—34no—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3—62no—
460C4⋊Dic3—64no—
461C4⋊Dic3C22×D312yes—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4C22×D314yes—
470Dic3⋊C4C22×D314yes—
471C4×Dic3—32no—
472C4×Dic3—32no—
473C4×Dic3—31no—
474C4×Dic3—31no—
475C4×Dic3—31no—
476C4×Dic3—32no—
477C4×Dic3—31no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—32no—
481C4×Dic3—32no—
482C4×Dic3—32no—
483C4×Dic3—32no—
484C4×Dic3—32no—
485C4×Dic3—34no—
486C4×Dic3—32no—
487C4×Dic3—34no—
488C4×Dic3—32no—
489C4×Dic3—32no—
490C4×Dic3—32no—
491C4×Dic3—61no—
492C4×Dic3—61no—
493C4×Dic3—62no—
494C4×Dic3—62no—
495C4×Dic3—64no—
496C4×Dic3C22×D312yes—
497C4×Dic3C22×D312yes—
498C4×Dic3C22×D311yescharacteristic
499C4×Dic3C22×D311yescharacteristic
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—24no—
503C22×C32C2×#4112yes—
504C22×C32C2511yescharacteristic
505C2×C3×D3—28no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—24no—
509C2×C3×D3—22no—
510C2×C3×D3C2×#4114yes—
511C32×C4—22no—
512C32×C4C2×#4112yes—
513C32×C4C2×#4112yes—
514C3⋊Dic3—22no—
515C3⋊Dic3—24no—
516C3⋊Dic3C2×#4114yes—
517C3×Dic3—22no—
518C3×Dic3—24no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3C2×#4114yes—
522C2×#41—31no—
523C2×#41—94no—
524C2×#41D3211yescharacteristic
525C23×C4—31no—
526C23×C4—92no—
527C4⋊Q8—31no—
528C4⋊Q8—92no—
529#127—31no—
530#126—94no—
531#126—94no—
532#125—92no—
533#125—94no—
534#124—31no—
535#124—31no—
536#124—94no—
537#123—32no—
538#123—94no—
539#123—94no—
540#123—92no—
541C22⋊Q8—32no—
542C22⋊Q8—94no—
543C22⋊Q8—94no—
544C22⋊Q8—92no—
545#121—32no—
546#121—34no—
547#121—92no—
548#121—94no—
549#120—32no—
550#120—92no—
551C4×Q8—94no—
552C4×Q8—94no—
553C4×Q8—92no—
554C4×Q8—92no—
555C4×D4—34no—
556C4×D4—34no—
557C4×D4—94no—
558C4×D4—94no—
559C4×D4—94no—
560C4×D4—94no—
561C4×D4—92no—
562C4×D4—94no—
563C4×D4—94no—
564C4×D4—92no—
565#117—31no—
566#117—92no—
567#117—94no—
568#117—94no—
569#117—94no—
570#117—91no—
571#117—92no—
572C2×C42—31no—
573C2×C42—92no—
574C2×C42—92no—
575C2×C42—92no—
576C2×C42—92no—
577C2×C42—92no—
578C2×C42—92no—
579C2×C42—92no—
580C2×C42—91no—
581C23×C3—22no—
582C23×C3—21no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—64no—
586C23×C3—62no—
587C23×C3C23×D312yes—
588C23×C3C23×D312yes—
589C23×C3C23×D311yescharacteristic
590C23×C3C23×D311yescharacteristic
591C22×D3—22no—
592C22×D3—24no—
593C22×D3C23×D312yes—
594C22×D3C23×D312yes—
595C3×Q8—24no—
596C3×Q8—22no—
597C3×Q8—22no—
598C3×Q8—62no—
599C3×D4—28no—
600C3×D4—24no—
601C3×D4—24no—
602C3×D4—24no—
603C3×D4—22no—
604C3×D4—22no—
605C3×D4—68no—
606C3×D4—68no—
607C3×D4—64no—
608C3×D4—62no—
609C2×C3×C4—28no—
610C2×C3×C4—24no—
611C2×C3×C4—24no—
612C2×C3×C4—22no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—24no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—34no—
621C2×C3×C4—64no—
622C2×C3×C4—62no—
623C2×C3×C4—64no—
624C2×C3×C4—64no—
625C2×C3×C4—64no—
626C2×C3×C4#23714yescomplemented
627C2×C3×C4#23714yescomplemented
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D311yescharacteristic
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D311yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634#67—24no—
635#67—28no—
636#67—28no—
637#67—68no—
638#67—68no—
639C2×Dic3—22no—
640C2×Dic3—24no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—38no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—34no—
647C2×Dic3—34no—
648C2×Dic3—62no—
649C2×Dic3—62no—
650C2×Dic3—64no—
651C2×Dic3—68no—
652C2×Dic3—64no—
653C2×Dic3—64no—
654C2×Dic3—64no—
655C2×Dic3—68no—
656C2×Dic3—68no—
657C2×Dic3—64no—
658C2×Dic3—64no—
659C2×Dic3—124no—
660C2×Dic3—128no—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D314yes—
665C2×Dic3C23×D312yes—
666D12—22no—
667C4×D3—24no—
668C4×D3—24no—
669C4×D3—24no—
670C4×D3—38no—
671C4×D3—64no—
672C4×D3—68no—
673C4×D3—64no—
674C4×D3—64no—
675Dic6—22no—
676Dic6—68no—
677Dic6—68no—
678C2×C32—22no—
679C2×C32—42no—
680C2×C32C22×#4111yescharacteristic
681C2×C32C22×#4112yes—
682C3×D3—24no—
683C3×D3—42no—
684C24—31no—
685#41—24no—
686#41—64no—
687#41—1816no—
688C2×Q8—31no—
689C2×Q8—94no—
690C2×Q8C2×D3211yescharacteristic
691C2×D4—34no—
692C2×D4—34no—
693C2×D4—32no—
694C2×D4—31no—
695C2×D4—94no—
696C2×D4C2×D3212yes—
697C2×D4C2×D3211yescharacteristic
698C22×C4—32no—
699C22×C4—31no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—64no—
704C22×C4—92no—
705C22×C4—92no—
706C22×C4—92no—
707C22×C4—92no—
708C22×C4—94no—
709C22×C4—92no—
710C22×C4—94no—
711C22×C4—188no—
712C22×C4C2×D3212yes—
713C22×C4C2×D3211yescharacteristic
714C4⋊C4—32no—
715C4⋊C4—34no—
716C4⋊C4—34no—
717C4⋊C4—94no—
718C4⋊C4—94no—
719C4⋊C4—94no—
720C4⋊C4—94no—
721C4⋊C4—94no—
722C4⋊C4—92no—
723C4⋊C4—94no—
724C22⋊C4—32no—
725C22⋊C4—34no—
726C22⋊C4—34no—
727C22⋊C4—34no—
728C22⋊C4—34no—
729C22⋊C4—94no—
730C22⋊C4—94no—
731C22⋊C4—94no—
732C22⋊C4—92no—
733C22⋊C4—94no—
734C42—31no—
735C42—31no—
736C42—32no—
737C42—32no—
738C42—92no—
739C42—92no—
740C42—92no—
741C42—92no—
742C42—94no—
743C42—92no—
744C42—94no—
745C42—91no—
746C42—91no—
747C42—92no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—24no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—24no—
754C22×C3—24no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—34no—
758C22×C3—42no—
759C22×C3—44no—
760C22×C3—68no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—64no—
765C22×C3C2×#23712yes—
766C22×C3C2×#23712yes—
767C22×C3C24×D311yescharacteristic
768C22×C3C24×D311yescharacteristic
769C2×D3—28no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—24no—
774C2×D3D3×#4114yes—
775C3×C4—24no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—34no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—64no—
784C3×C4—62no—
785C3×C4C2×#23712yes—
786C3×C4C2×#23712yes—
787C3×C4C2×#23712yes—
788C3×C4C2×#23712yes—
789Dic3—22no—
790Dic3—22no—
791Dic3—24no—
792Dic3—22no—
793Dic3—34no—
794Dic3—34no—
795Dic3—64no—
796Dic3—64no—
797Dic3—64no—
798Dic3—62no—
799Dic3—62no—
800Dic3—122no—
801Dic3—124no—
802Dic3D3×#4114yes—
803C32#344411yescharacteristic, complemented, Sylow
804C23—32no—
805C23—32no—
806C23—64no—
807C23—62no—
808C23C22×D3212yes—
809C23C22×D3211yescharacteristic
810Q8—22no—
811Q8—62no—
812Q8—188no—
813D4—24no—
814D4—22no—
815D4—68no—
816D4—68no—
817D4—64no—
818D4—62no—
819D4—188no—
820C2×C4—24no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—34no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—64no—
827C2×C4—62no—
828C2×C4—64no—
829C2×C4—64no—
830C2×C4—64no—
831C2×C4—98no—
832C2×C4—92no—
833C2×C4—92no—
834C2×C4—94no—
835C2×C4—184no—
836C2×C4—184no—
837C2×C4—188no—
838C2×C4—184no—
839C2×C4—184no—
840C2×C4—188no—
841C2×C4#380514yescomplemented
842C2×C4C22×D3212yes—
843C2×C4C22×D3211yescharacteristic
844C2×C4C22×D3211yescharacteristic
845C2×C3—22no—
846C2×C3—22no—
847C2×C3—22no—
848C2×C3—21no—
849C2×C3—42no—
850C2×C3—44no—
851C2×C3—42no—
852C2×C3—42no—
853C2×C3—64no—
854C2×C3—122no—
855C2×C3C22×#23711yescharacteristic
856C2×C3C22×#23711yescharacteristic
857C2×C3C2×D3×#4112yes—
858C2×C3C2×D3×#4112yes—
859D3—24no—
860D3—42no—
861C22—22no—
862C22—24no—
863C22—22no—
864C22—34no—
865C22—68no—
866C22—62no—
867C22—62no—
868C22—64no—
869C22—62no—
870C22C2×#380512yes—
871C22C23×D3211yescharacteristic
872C4—22no—
873C4—34no—
874C4—62no—
875C4—64no—
876C4—62no—
877C4—62no—
878C4—94no—
879C4—182no—
880C4—184no—
881C4C2×#380512yes—
882C4C2×#380512yes—
883C3—21no—
884C3#8601811yescharacteristic, complemented
885C3#8621911yescharacteristic, complemented
886C2—22no—
887C2—42no—
888C2—64no—
889C2—122no—
890C2D32×#4112yes—
891C2C22×#380511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
2. C3×#5832C2semidirect
3. C3×#5828C2semidirect
4. #10595377C2semidirect
5. #10595368C2semidirect
6. #10595202C2semidirect
7. #10595173C2semidirect
8. #10595133C2semidirect
9. #10595130C2semidirect
10. #10595049C2semidirect
11. #10595022C2semidirect
12. #10594958C2semidirect
13. #10594934C2semidirect
14. C4×#3805C2semidirect
15. C2×C4×D3×Dic3C2semidirect
23. Q8×C3⋊Dic3C22semidirect
25. D4×C3⋊Dic3C22semidirect
27. #64135C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
30. C3×#947C22semidirect
32. C3×#944C22semidirect
33. C3×#940C22semidirect
37. C3×#936C22semidirect
40. C3×C4×#67C22semidirect
46. #67⋊Dic3C22semidirect
51. #63959C22semidirect
52. #63957C22semidirect
53. #63956C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
60. #63898C22semidirect
64. #63878C22semidirect
69. C4×D3×Dic3C22semidirect
70. #63869C22semidirect
71. #63861C22semidirect
73. #63855C22semidirect
74. #63845C22semidirect
75. #63843C22semidirect
76. #63838C22semidirect
79. #5832D3semidirect
81. #5828D3semidirect
198. #947C2×D3semidirect
205. #944C2×D3semidirect
206. #940C2×D3semidirect
215. #936C2×D3semidirect
234. C4×#67C2×D3semidirect
309. C2×C32×C4#41semidirect
339. D3×Dic3#41semidirect
626. C2×C3×C4#237semidirect
627. C2×C3×C4#237semidirect
803. C32#3444semidirect
841. C2×C4#3805semidirect
884. C3#86018semidirect
885. C3#86219semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
C3×#58322
C3×#58282
#105953772
#105953682
#105952022
#105951732
#105951332
#105951302
#105950492
#105950222
#105949582
#105949342
C4×#38052
C2×C4×D3×Dic32
#862193
#860183