Finite Group Databasebeta

← #11904442

Subgroups — #11904442

Order 1152.

3285 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3#10595995C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5521C211yesmaximal, characteristic, complemented
6#10595034C211yesmaximal, characteristic, complemented
7#10594866C211yesmaximal, characteristic, complemented
8#10594629C214yesmaximal, complemented
9#10594381C214yesmaximal, complemented
10#10594291C214yesmaximal, complemented
11D3×#886C214yesmaximal, complemented
12#10594005C214yesmaximal, complemented
13#10593896C214yesmaximal, complemented
14#86354—31nomaximal
15#85858—31nomaximal
16C2×#3828C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic, complemented
21C2×D3×#67C2214yes—
22C22×#626C2212yescomplemented
23C22×D3×Dic3C2212yescomplemented
24#64307—28no—
25C2×#3802C2212yescomplemented
26C2×D3×D12C2212yescomplemented
27C2×#3796—28no—
28C2×#3796C2214yescomplemented
29C2×#3796C2214yescomplemented
30C2×#3796C2212yescomplemented
31C2×#3795C2212yescomplemented
32C32×#117C2211yescharacteristic, complemented
33#64106C2212yescomplemented
34#64104C2212yescomplemented
35#64095C2212yescomplemented
36#64091C2212yescomplemented
37C4×C4⋊(C3⋊D3)C2214yescomplemented
38C3×#926C2211yescharacteristic, complemented
39C3×#897C2214yescomplemented
40C3×#893C2214yescomplemented
41C3×#886C2214yescomplemented
42C3×D3×C22⋊C4C2214yescomplemented
43C3×#875C2212yescomplemented
44C3×C4×D12C2214yescomplemented
45C3×#869C2212yescomplemented
46#63981C2212yescomplemented
47#63966C2214yescomplemented
48#63962C2212yescomplemented
49#63923C2218yescomplemented
50D3×(C2×D3)⋊C4C2218yescomplemented
51#63916C2212yescomplemented
52#63909C2218yescomplemented
53#63906C2218yescomplemented
54C4×#626C2214yescomplemented
55#63891C2218yescomplemented
56#63890C2218yescomplemented
57#63890C2218yescomplemented
58D3×C4⋊Dic3C2218yescomplemented
59#63871C2214yescomplemented
60#63871C2212yescomplemented
61#63866C2212yescomplemented
62#63864C2212yescomplemented
63C2×#1009—31no—
64C22×#239—31no—
65C2×#1004—31no—
66C22×#237—31no—
67C3×#536—31no—
68C3×#518—31no—
69#5828—31no—
70#5816—31no—
71#5726—34no—
72#5676—34no—
73#5653—34no—
74D3×#123—34no—
75#5631—34no—
76#5630—34no—
77#5555—34no—
78#5555—34no—
79#5554—34no—
80#5554—34no—
81#5526—31no—
82#5526D311yescharacteristic, complemented
83#5524—31no—
84#5524—31no—
85#5524—31no—
86#5524—61no—
87#5521D311yescharacteristic, complemented
88#5493—34no—
89C2×#886—34no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×D32C2314yes—
93C22×C32×C4C2311yescharacteristic
94C2×#638C2312yes—
95C22×C3⋊Dic3C2311yescharacteristic
96#3828—24no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2314yes—
99C2×C4×C3⋊D3—24no—
100C2×C4×C3⋊D3C2312yes—
101C2×C4×C3⋊D3C2312yes—
102C2×C4×C3⋊D3C2312yes—
103C2×#634C2311yescharacteristic
104C2×C3×#67C2312yes—
105C22×C3×Dic3C2312yes—
106C3×#235—24no—
107C2×C3×D12D418yescomplemented
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2312yes—
110C2×C3×D12C2312yes—
111C2×C3×C4×D3C2312yes—
112C2×C3×C4×D3C2318yes—
113C2×C3×Dic6—24no—
114C2×C3×Dic6C2312yes—
115C2×C3×Dic6C2312yes—
116C2×C3×Dic6C2311yescharacteristic
117D3×#67—216no—
118C2×#626—28no—
119C2×#626C2318yes—
120C2×#626C2314yes—
121C2×#626C2314yes—
122C2×#625C2314yes—
123C2×D3×Dic3—28no—
124C2×D3×Dic3C2314yes—
125C2×D3×Dic3C2318yes—
126#3802—28no—
127D3×D12—28no—
128#3796—216no—
129#3796—216no—
130#3796—28no—
131#3795—28no—
132C32×C4⋊C4C2312yes—
133C32×C22⋊C4C2312yes—
134C32×C42C2312yes—
135#3752C2314yes—
136#3752C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138C3×#217C2312yes—
139C3×(C2×D3)⋊C4C2318yes—
140C3×(C2×D3)⋊C4C2318yes—
141C3×C4⋊Dic3C2318yes—
142C3×C4⋊Dic3C2312yes—
143C3×C4×Dic3C2312yes—
144Dic3⋊Dic3C2318yes—
145Dic3⋊Dic3C2314yes—
146#3722C2318yes—
147#3722C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149#3485—91noSylow
150C2×C3×#41—31no—
151C22×C3×Q8—31no—
152C22×C3×D4—31no—
153C22×#67—34no—
154C22×#67—32no—
155C23×Dic3—32no—
156#1009—68no—
157C2×#239—34no—
158C2×#239—34no—
159C2×#239—32no—
160C2×#239—68no—
161#1004—68no—
162C2×#237—32no—
163C2×#237—34no—
164C2×#237—34no—
165C2×#237—32no—
166C2×#237—68no—
167C2×D3×D4—34no—
168C2×D3×D4—32no—
169C2×D3×D4—32no—
170C2×D3×D4—32no—
171C2×#235—31no—
172C2×#235—31no—
173C2×#235—32no—
174C2×#235—61no—
175C2×#235C2×D311yescharacteristic
176C22×D12—32no—
177C22×D12—32no—
178C22×D12C2×D311yescharacteristic
179C22×C4×D3—32no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—61no—
183C22×Dic6C2×D311yescharacteristic, complemented
184C3×C4⋊Q8—32no—
185C3×#124—32no—
186C3×#123—34no—
187C3×C22⋊Q8—34no—
188C3×C4×D4—34no—
189C3×C4×D4—34no—
190C3×#117—21no—
191C3×#117—31no—
192C3×#117C2×D311yescharacteristic, complemented
193C3×#117C2×D311yescharacteristic, complemented
194C2×C3×C22⋊C4—34no—
195#947—32no—
196#946—34no—
197#946—32no—
198#944—32no—
199#938—32no—
200#937—32no—
201#935—32no—
202#930—38no—
203#930—38no—
204#929—34no—
205C4×#67—34no—
206C2×(C2×D3)⋊C4—38no—
207#926C2×D311yescharacteristic, complemented
208C2×C4⋊Dic3—38no—
209#897—32no—
210#897—34no—
211#897—32no—
212#897—32no—
213#897—62no—
214#897C2×D314yescomplemented
215#895—32no—
216#895—38no—
217#895—32no—
218#895—32no—
219#895—62no—
220#894—38no—
221#894—38no—
222#893C2×D314yescomplemented
223D3×C4⋊C4—38no—
224#886—32no—
225#886—34no—
226#886—32no—
227#886—32no—
228#886—38no—
229#886—38no—
230#886—38no—
231#886—62no—
232#886C2×D314yescomplemented
233#884—38no—
234#883—38no—
235#882—32no—
236#882—32no—
237#882—32no—
238#882—38no—
239#882—38no—
240#882—62no—
241D3×C22⋊C4—38no—
242D3×C22⋊C4C2×D314yescomplemented
243#875—32no—
244#875C2×D312yescomplemented
245C4×D12—34no—
246C4×D12—34no—
247C4×D12—34no—
248C4×D12—64no—
249C4×D12C2×D314yescomplemented
250#869—32no—
251#869C2×D312yescomplemented
252C23×C32C2411yescharacteristic
253C22×C3⋊D3—22no—
254C22×C3⋊D3—42no—
255C22×C3⋊D3C2412yes—
256C22×C3⋊D3C2412yes—
257C22×C3×D3—44no—
258C22×C3×D3C2×D418yes—
259C22×C3×D3C2412yes—
260C22×C3×D3C2414yes—
261C2×D32—28no—
262C2×D32—48no—
263C2×C32×C4C2×D414yes—
264C2×C32×C4C2414yes—
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—24no—
268C2×C3⋊Dic3—22no—
269C2×C3⋊Dic3C2412yes—
270C2×C3⋊Dic3C2412yes—
271C4⋊(C3⋊D3)—22no—
272C4⋊(C3⋊D3)—44no—
273C4×C3⋊D3—24no—
274C4×C3⋊D3—24no—
275C4×C3⋊D3—24no—
276#634—22no—
277C3×#67—24no—
278C2×C3×Dic3—24no—
279C2×C3×Dic3C2414yes—
280C2×C3×Dic3C2412yes—
281C2×C3×Dic3C2414yes—
282C3×D12—22no—
283C3×D12C2×D418yes—
284C3×D12C2×D418yes—
285C3×C4×D3—24no—
286C3×C4×D3—48no—
287C3×Dic6—24no—
288C3×Dic6—24no—
289C3×Dic6—22no—
290#626—216no—
291#626—28no—
292#626—44no—
293#625—28no—
294D3×Dic3—28no—
295D3×Dic3—216no—
296C2×H(5,𝔽2)—91no—
297C22×#41—91no—
298#547—94no—
299#547—94no—
300#546—94no—
301#546—94no—
302#536—31no—
303#536—91no—
304#534—94no—
305#525—91no—
306#525—91no—
307C2×#123—94no—
308#518—31no—
309C24×C3—32no—
310C23×D3—31no—
311C23×D3—31no—
312C23×D3—34no—
313C23×D3—34no—
314C23×D3—61no—
315C23×D3C22×D312yes—
316C3×#41—64no—
317C2×C3×Q8—32no—
318C2×C3×Q8—32no—
319C2×C3×Q8—31no—
320C2×C3×Q8—64no—
321C2×C3×D4—32no—
322C2×C3×D4—38no—
323C2×C3×D4—32no—
324C2×C3×D4—32no—
325C2×C3×D4—31no—
326C22×C3×C4—21no—
327C22×C3×C4—32no—
328C22×C3×C4—32no—
329C22×C3×C4—38no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—32no—
333C2×#67—32no—
334C2×#67—34no—
335C2×#67—34no—
336C2×#67—38no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—62no—
340C2×#67—68no—
341C2×#67—616no—
342C2×#67C22×D312yes—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—34no—
346C22×Dic3—38no—
347C22×Dic3—61no—
348C22×Dic3—68no—
349C22×Dic3C22×D312yes—
350#239—616no—
351#239—616no—
352#239—68no—
353#237—616no—
354#237—616no—
355#237—68no—
356#237—68no—
357D3×D4—68no—
358D3×D4—68no—
359D3×D4—616no—
360D3×D4—68no—
361#235—24no—
362#235—64no—
363#235—64no—
364#235—68no—
365#235—124no—
366C2×D12—38no—
367C2×D12—34no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—34no—
371C2×D12—34no—
372C2×D12—34no—
373C2×D12—64no—
374C2×D12—61no—
375C2×D12—68no—
376C2×D12—68no—
377C2×D12D1218yescomplemented
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D312yes—
380C2×D12C22×D312yes—
381C2×C4×D3—38no—
382C2×C4×D3—34no—
383C2×C4×D3—32no—
384C2×C4×D3—32no—
385C2×C4×D3—32no—
386C2×C4×D3—32no—
387C2×C4×D3—32no—
388C2×C4×D3—32no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—68no—
393C2×C4×D3—64no—
394C2×C4×D3—64no—
395C2×C4×D3—124no—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D318yes—
398C2×Dic6—24no—
399C2×Dic6—31no—
400C2×Dic6—31no—
401C2×Dic6—61no—
402C2×Dic6C22×D312yes—
403C2×Dic6C22×D311yescharacteristic
404C2×Dic6C22×D312yes—
405C3×C4⋊C4—22no—
406C3×C4⋊C4—38no—
407C3×C4⋊C4—32no—
408C3×C4⋊C4C22×D312yes—
409C3×C4⋊C4C22×D312yes—
410C3×C22⋊C4—22no—
411C3×C22⋊C4—32no—
412C3×C22⋊C4—38no—
413C3×C22⋊C4—38no—
414C3×C22⋊C4C22×D312yes—
415C3×C22⋊C4C22×D312yes—
416C3×C42—22no—
417C3×C42—32no—
418C3×C42C22×D312yes—
419C3×C42C22×D312yes—
420#217—34no—
421#217C22×D312yes—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—38no—
429(C2×D3)⋊C4—38no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—64no—
432(C2×D3)⋊C4—64no—
433(C2×D3)⋊C4C22×D318yes—
434(C2×D3)⋊C4C22×D318yes—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—38no—
438C4⋊Dic3—34no—
439C4⋊Dic3—64no—
440C4⋊Dic3C22×D318yes—
441C4⋊Dic3C22×D312yes—
442Dic3⋊C4—38no—
443Dic3⋊C4—34no—
444C4×Dic3C22×D312yes—
445C22×C32—22no—
446C22×C32C22×D412yes—
447C22×C32C2511yescharacteristic
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—24no—
453C2×C3⋊D3—44no—
454C2×C3×D3—28no—
455C2×C3×D3—22no—
456C2×C3×D3—24no—
457C2×C3×D3—48no—
458C2×C3×D3C22×D418yes—
459D32—88no—
460C32×C4—24no—
461C32×C4C22×D412yes—
462C32×C4C22×D412yes—
463C3⋊Dic3—22no—
464C3⋊Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3—22no—
467C3×Dic3—24no—
468H(5,𝔽2)—188no—
469C2×#41—31no—
470C2×#41—92no—
471C2×#41—94no—
472C2×#41—94no—
473C2×#41—92no—
474C2×#41—91no—
475C2×#41—188no—
476C22×Q8—31no—
477C22×D4—31no—
478C22×D4—92no—
479C22×D4—92no—
480C22×D4—92no—
481C22×D4—94no—
482C23×C4—92no—
483C23×C4—91no—
484C4⋊Q8—32no—
485C4⋊Q8—92no—
486#124—32no—
487#124—92no—
488#123—34no—
489#123—98no—
490#123—98no—
491#123—98no—
492#123—94no—
493#123—92no—
494#123—92no—
495C22⋊Q8—34no—
496C22⋊Q8—92no—
497C22⋊Q8—94no—
498C22⋊Q8—92no—
499#121—98no—
500#121—98no—
501#121—92no—
502#121—92no—
503#120—98no—
504#120—92no—
505#120—92no—
506C4×D4—34no—
507C4×D4—34no—
508C4×D4—94no—
509C4×D4—94no—
510#117—31no—
511#117D3211yescharacteristic, complemented
512C2×C4⋊C4—98no—
513C2×C22⋊C4—34no—
514C2×C22⋊C4—98no—
515C23×C3—21no—
516C23×C3—34no—
517C23×C3—38no—
518C23×C3—32no—
519C23×C3—124no—
520C23×C3C23×D311yescharacteristic
521C23×C3C23×D311yescharacteristic
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—32no—
525C22×D3—32no—
526C22×D3—44no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—68no—
530C22×D3—62no—
531C22×D3—62no—
532C22×D3—68no—
533C22×D3—122no—
534C22×D3—128no—
535C22×D3—128no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—124no—
539C22×D3C2×D1218yes—
540C22×D3C23×D312yes—
541C22×D3C23×D314yes—
542C3×Q8—64no—
543C3×Q8—64no—
544C3×Q8—62no—
545C3×D4—38no—
546C3×D4—38no—
547C3×D4—64no—
548C3×D4—62no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—24no—
552C2×C3×C4—24no—
553C2×C3×C4—34no—
554C2×C3×C4—32no—
555C2×C3×C4—34no—
556C2×C3×C4—64no—
557C2×C3×C4—64no—
558C2×C3×C4—128no—
559C2×C3×C4C2×D1214yes—
560C2×C3×C4D3×D414yes—
561C2×C3×C4C23×D314yes—
562C2×C3×C4C23×D314yes—
563C2×C3×C4C23×D311yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567#67—24no—
568#67—68no—
569#67—616no—
570#67—68no—
571#67—64no—
572#67—64no—
573#67—68no—
574#67—124no—
575#67—124no—
576C2×Dic3—24no—
577C2×Dic3—32no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—616no—
584C2×Dic3—68no—
585C2×Dic3—62no—
586C2×Dic3—62no—
587C2×Dic3—122no—
588C2×Dic3C23×D314yes—
589C2×Dic3C23×D312yes—
590C2×Dic3C23×D314yes—
591D12—22no—
592D12—68no—
593D12—616no—
594D12—62no—
595D12—62no—
596D12—122no—
597D12—124no—
598D12—124no—
599D12—128no—
600D12—124no—
601D12C2×D1218yes—
602D12C2×D1218yes—
603C4×D3—24no—
604C4×D3—48no—
605C4×D3—616no—
606C4×D3—68no—
607C4×D3—64no—
608C4×D3—64no—
609C4×D3—64no—
610C4×D3—64no—
611C4×D3—64no—
612C4×D3—64no—
613C4×D3—124no—
614C4×D3—124no—
615C4×D3—124no—
616Dic6—24no—
617Dic6—24no—
618Dic6—22no—
619Dic6—62no—
620Dic6—62no—
621Dic6—122no—
622C2×C32—22no—
623C2×C32C23×D411yescharacteristic
624C2×C32#58512yes—
625C3⋊D3—42no—
626C3⋊D3—42no—
627C3×D3—28no—
628C3×D3—42no—
629C24—32no—
630C24—94no—
631C24—91no—
632#41—64no—
633#41—188no—
634#41—1816no—
635#41—1816no—
636#41—188no—
637#41—184no—
638C2×Q8—32no—
639C2×Q8—32no—
640C2×Q8—31no—
641C2×Q8—64no—
642C2×Q8—91no—
643C2×D4—32no—
644C2×D4—32no—
645C2×D4—32no—
646C2×D4—31no—
647C2×D4—38no—
648C2×D4—98no—
649C2×D4—94no—
650C2×D4—94no—
651C2×D4—94no—
652C2×D4—92no—
653C2×D4—91no—
654C2×D4—94no—
655C2×D4—188no—
656C2×D4—188no—
657C2×D4—188no—
658C2×D4—1816no—
659C22×C4—32no—
660C22×C4—32no—
661C22×C4—38no—
662C22×C4—98no—
663C22×C4—94no—
664C22×C4—91no—
665C22×C4—92no—
666C22×C4—92no—
667C22×C4—92no—
668C22×C4—188no—
669C22×C4—184no—
670C22×C4C2×D3211yescharacteristic
671C4⋊C4—38no—
672C4⋊C4—32no—
673C4⋊C4—94no—
674C4⋊C4—98no—
675C4⋊C4—94no—
676C4⋊C4C2×D3212yes—
677C22⋊C4—32no—
678C22⋊C4—38no—
679C22⋊C4—38no—
680C22⋊C4—98no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4C2×D3212yes—
686C42—32no—
687C42C2×D3212yes—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—21no—
692C22×C3—38no—
693C22×C3—42no—
694C22×C3—68no—
695C22×C3—62no—
696C22×C3—64no—
697C22×C3—128no—
698C22×C3C22×D1212yes—
699C22×C3C2×D3×D412yes—
700C22×C3C24×D311yescharacteristic
701C22×C3C24×D311yescharacteristic
702C2×D3—28no—
703C2×D3—22no—
704C2×D3—24no—
705C2×D3—48no—
706C2×D3—64no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—64no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—64no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—122no—
720C2×D3—124no—
721C2×D3—124no—
722C2×D3—124no—
723C2×D3—128no—
724C2×D3—248no—
725C2×D3—248no—
726C2×D3C22×D1218yes—
727C3×C4—24no—
728C3×C4—24no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—44no—
732C3×C4—62no—
733C3×C4—64no—
734C3×C4—64no—
735C3×C4C22×D1212yes—
736C3×C4C22×D1212yes—
737C3×C4C2×D3×D412yes—
738C3×C4C2×D3×D412yes—
739Dic3—24no—
740Dic3—22no—
741Dic3—24no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—62no—
746Dic3—122no—
747Dic3—122no—
748C32#348511yescharacteristic, complemented, Sylow
749C23—34no—
750C23—38no—
751C23—32no—
752C23—92no—
753C23—92no—
754C23—124no—
755C23—188no—
756C23—182no—
757C23—362no—
758C23—368no—
759C23C22×D3211yescharacteristic
760Q8—64no—
761Q8—64no—
762Q8—62no—
763Q8—182no—
764D4—38no—
765D4—38no—
766D4—64no—
767D4—62no—
768D4—188no—
769D4—1816no—
770D4—188no—
771D4—184no—
772D4—182no—
773D4—364no—
774D4—364no—
775C2×C4—34no—
776C2×C4—34no—
777C2×C4—32no—
778C2×C4—64no—
779C2×C4—64no—
780C2×C4—92no—
781C2×C4—92no—
782C2×C4—128no—
783C2×C4—1816no—
784C2×C4—188no—
785C2×C4—182no—
786C2×C4—184no—
787C2×C4—184no—
788C2×C4—184no—
789C2×C4D3×D1214yes—
790C2×C4C22×D3214yes—
791C2×C4C22×D3211yescharacteristic
792C2×C4C22×D3211yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—22no—
797C2×C3—42no—
798C2×C3—68no—
799C2×C3—122no—
800C2×C3C23×D1211yescharacteristic
801C2×C3C22×D3×D411yescharacteristic
802C2×C3#596612yes—
803C2×C3#596812yes—
804D3—28no—
805D3—42no—
806D3—124no—
807D3—122no—
808D3—122no—
809D3—122no—
810D3—122no—
811D3—242no—
812C22—22no—
813C22—38no—
814C22—68no—
815C22—62no—
816C22—64no—
817C22—128no—
818C22—182no—
819C22—182no—
820C22—182no—
821C22—182no—
822C22—184no—
823C22—364no—
824C22—728no—
825C22C2×D3×D1212yes—
826C22C23×D3211yescharacteristic
827C4—24no—
828C4—62no—
829C4—64no—
830C4—64no—
831C4—182no—
832C4—182no—
833C4C2×D3×D1212yes—
834C4C2×D3×D1212yes—
835C3—21no—
836C3#8585811yescharacteristic, complemented
837C3#8635411yescharacteristic, complemented
838C2—22no—
839C2—68no—
840C2—122no—
841C2—362no—
842C2—362no—
843C2C22×D3×D1211yescharacteristic
844C2#1059669812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C22×#3796C2semidirect
3. #10595995C2semidirect
4. C3×#5526C2semidirect
5. C3×#5521C2semidirect
6. #10595034C2semidirect
7. #10594866C2semidirect
8. #10594629C2semidirect
9. #10594381C2semidirect
10. #10594291C2semidirect
11. D3×#886C2semidirect
12. #10594005C2semidirect
13. #10593896C2semidirect
17. C22×C4×C3⋊D3C22semidirect
20. C22×C3×Dic6C22semidirect
22. C22×#626C22semidirect
23. C22×D3×Dic3C22semidirect
25. C2×#3802C22semidirect
26. C2×D3×D12C22semidirect
28. C2×#3796C22semidirect
29. C2×#3796C22semidirect
30. C2×#3796C22semidirect
31. C2×#3795C22semidirect
32. C32×#117C22semidirect
33. #64106C22semidirect
34. #64104C22semidirect
35. #64095C22semidirect
36. #64091C22semidirect
37. C4×C4⋊(C3⋊D3)C22semidirect
38. C3×#926C22semidirect
39. C3×#897C22semidirect
40. C3×#893C22semidirect
41. C3×#886C22semidirect
42. C3×D3×C22⋊C4C22semidirect
43. C3×#875C22semidirect
44. C3×C4×D12C22semidirect
45. C3×#869C22semidirect
46. #63981C22semidirect
47. #63966C22semidirect
48. #63962C22semidirect
49. #63923C22semidirect
50. D3×(C2×D3)⋊C4C22semidirect
51. #63916C22semidirect
52. #63909C22semidirect
53. #63906C22semidirect
54. C4×#626C22semidirect
55. #63891C22semidirect
56. #63890C22semidirect
57. #63890C22semidirect
58. D3×C4⋊Dic3C22semidirect
59. #63871C22semidirect
60. #63871C22semidirect
61. #63866C22semidirect
62. #63864C22semidirect
82. #5526D3semidirect
87. #5521D3semidirect
107. C2×C3×D12D4semidirect
183. C22×Dic6C2×D3semidirect
192. C3×#117C2×D3semidirect
193. C3×#117C2×D3semidirect
207. #926C2×D3semidirect
214. #897C2×D3semidirect
222. #893C2×D3semidirect
232. #886C2×D3semidirect
242. D3×C22⋊C4C2×D3semidirect
244. #875C2×D3semidirect
249. C4×D12C2×D3semidirect
251. #869C2×D3semidirect
377. C2×D12D12semidirect
511. #117D32semidirect
748. C32#3485semidirect
836. C3#85858semidirect
837. C3#86354semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C22×#37962
#105959952
C3×#55262
C3×#55212
#105950342
#105948662
#105946292
#105943812
#105942912
D3×#8862
#105940052
#105938962
#863543
#858583