Finite Group Databasebeta

← #11904445

Subgroups — #11904445

Order 1152.

3255 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3#10596287C211yesmaximal, characteristic, complemented
4C3×#5816C211yesmaximal, characteristic, complemented
5#10595428C214yesmaximal, complemented
6#10595427C214yesmaximal, complemented
7#10595358C214yesmaximal, complemented
8#10595357C214yesmaximal, complemented
9#10595062C214yesmaximal, complemented
10D3×#929C214yesmaximal, complemented
11#10595023C211yesmaximal, characteristic, complemented
12#10595022C211yesmaximal, characteristic, complemented
13#10594982C211yesmaximal, characteristic, complemented
14#87273—31nomaximal
15#86354—31nomaximal
16C22×C32×Q8C2211yescharacteristic, complemented
17C2×#3828C2211yescharacteristic
18C2×C3×#239—28no—
19C2×C3×#239C2214yescomplemented
20C2×C3×#239C2214yescomplemented
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2212yescomplemented
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×C3×C4×D3C2212yescomplemented
26C2×D3×#67C2214yes—
27#64307—28no—
28C2×#3802C2212yescomplemented
29C2×D3×D12C2212yescomplemented
30C2×#3796C2212yescomplemented
31C2×#3795C2212yescomplemented
32#64156C2212yescomplemented
33#64155C2214yescomplemented
34#64153C2212yescomplemented
35#64138C2214yescomplemented
36#64135C2211yescharacteristic, complemented
37C3×#947C2212yescomplemented
38C3×#946C2214yescomplemented
39C3×#944C2212yescomplemented
40C3×#929C2214yescomplemented
41C3×#926C2211yescharacteristic, complemented
42#63977C2212yescomplemented
43#63976C2212yescomplemented
44D3×#217C2214yescomplemented
45#63966C2212yescomplemented
46#63961C2212yescomplemented
47#63922C2218yescomplemented
48D3×(C2×D3)⋊C4C2218yescomplemented
49#63909C2212yescomplemented
50#63908C2212yescomplemented
51#63905C2218yescomplemented
52C4×#626C2214yescomplemented
53C4×#625C2214yescomplemented
54#63898C2214yescomplemented
55Dic3×D12C2214yescomplemented
56#63886C2218yescomplemented
57#63885C2218yescomplemented
58#63884C2218yescomplemented
59D3×Dic3⋊C4C2218yescomplemented
60#63857C2212yescomplemented
61#63856C2212yescomplemented
62#63850C2218yescomplemented
63C22×C3×#41—31no—
64C2×#1009—31no—
65C22×#239D311yescharacteristic, complemented
66C2×#1004—31no—
67C3×#536—31no—
68#5829—34no—
69#5829—34no—
70#5828—31no—
71#5824—34no—
72#5824—34no—
73#5816—31no—
74#5816—31no—
75#5816—61no—
76#5816D311yescharacteristic, complemented
77#5804—34no—
78#5798—31no—
79#5791—31no—
80#5791—31no—
81C2×#929—34no—
82#5726—34no—
83#5676—34no—
84#5653—34no—
85D3×#123—34no—
86#5631—34no—
87#5630—34no—
88#5524—31no—
89#5521—31no—
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×D32C2314yes—
93C2×C32×Q8—24no—
94C2×C32×Q8C2312yes—
95C2×C32×Q8C2312yes—
96C22×C32×C4C2312yes—
97C22×C32×C4C2311yescharacteristic
98C2×#638C2312yes—
99#3828—24no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2312yes—
102C2×#634C2311yescharacteristic
103C2×C3×#67C2312yes—
104C22×C3×Dic3C2311yescharacteristic
105C3×#239—216no—
106C3×#239—216no—
107C3×#235—24no—
108C2×C3×D12—28no—
109C2×C3×D12D418yescomplemented
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2318yes—
112C2×C3×D12C2312yes—
113C2×C3×D12C2312yes—
114C2×C3×C4×D3—28no—
115C2×C3×C4×D3—24no—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2318yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6C2311yescharacteristic
121D3×#67—216no—
122C2×#626C2314yes—
123C2×#626C2314yes—
124C2×#625C2314yes—
125C2×#625C2314yes—
126C2×D3×Dic3C2314yes—
127C2×D3×Dic3C2318yes—
128#3802—28no—
129D3×D12—28no—
130#3796—28no—
131#3795—28no—
132#3757C2312yes—
133#3752C2318yes—
134C4⋊(C3⋊Dic3)C2312yes—
135#3750C2318yes—
136C4×C3⋊Dic3C2312yes—
137C3×#217C2312yes—
138C3×(C2×D3)⋊C4C2318yes—
139C3×C4⋊Dic3C2312yes—
140C3×Dic3⋊C4C2318yes—
141C3×C4×Dic3C2312yes—
142#3724C2314yes—
143Dic3⋊Dic3C2314yes—
144#3722C2314yes—
145(C2×D3)⋊Dic3C2318yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2314yes—
149#3485—91noSylow
150C2×C3×#41—34no—
151C2×C3×#41—34no—
152C2×C3×#41—31no—
153C2×C3×#41—68no—
154C22×C3×Q8—21no—
155C22×C3×Q8C2×D311yescharacteristic, complemented
156C22×C3×Q8C2×D311yescharacteristic, complemented
157C22×C3×D4—31no—
158C22×C3×D4—32no—
159C23×C3×C4—32no—
160C23×C3×C4—31no—
161C22×#67—34no—
162#1009—68no—
163C2×#239—28no—
164C2×#239—32no—
165C2×#239C2×D314yescomplemented
166C2×#239C2×D314yescomplemented
167#1004—68no—
168C2×#237—32no—
169C2×#237—32no—
170C2×D3×D4—34no—
171C2×D3×D4—32no—
172C2×D3×D4—32no—
173C2×D3×D4—32no—
174C2×#235—31no—
175C2×#235—31no—
176C2×#235—32no—
177C2×#235—61no—
178C2×#235C2×D311yescharacteristic
179C22×D12—32no—
180C22×D12C2×D311yescharacteristic
181C22×D12C2×D312yescomplemented
182C22×C4×D3C2×D312yescomplemented
183C22×C4×D3C2×D311yescharacteristic, complemented
184C3×C4⋊Q8—32no—
185C3×#124—32no—
186C3×#123—34no—
187C3×C22⋊Q8—34no—
188C3×#117—31no—
189#953—32no—
190#953—32no—
191C2×#217—34no—
192#947—32no—
193#947—32no—
194#947—62no—
195#947C2×D312yescomplemented
196#946—34no—
197#946—34no—
198#946—32no—
199#946—64no—
200#946C2×D314yescomplemented
201#944—32no—
202#944—32no—
203#944—62no—
204#944C2×D312yescomplemented
205#939—38no—
206#939—38no—
207#938—32no—
208#937—32no—
209#937—38no—
210#935—32no—
211#935—38no—
212D4×Dic3—34no—
213D4×Dic3—34no—
214#930—32no—
215#930—32no—
216#929—34no—
217#929—34no—
218#929—32no—
219#929—32no—
220#929—38no—
221#929—38no—
222#929—64no—
223#929C2×D314yescomplemented
224C4×#67—34no—
225C4×#67—34no—
226C4×#67—34no—
227C2×(C2×D3)⋊C4—38no—
228#926—31no—
229#926—31no—
230#926—61no—
231#926C2×D311yescharacteristic, complemented
232#924—32no—
233#924—32no—
234C2×Dic3⋊C4—38no—
235#897—32no—
236#895—38no—
237#895—32no—
238#894—38no—
239#894—38no—
240#893—34no—
241D3×C4⋊C4—38no—
242#886—32no—
243#884—38no—
244#883—38no—
245#882—32no—
246#882—38no—
247D3×C22⋊C4—34no—
248D3×C22⋊C4—38no—
249C4×D12—34no—
250C4×D12—34no—
251C23×C32C2411yescharacteristic
252C22×C3⋊D3C2412yes—
253C22×C3×D3—22no—
254C22×C3×D3—44no—
255C22×C3×D3—42no—
256C22×C3×D3C2×D418yes—
257C22×C3×D3C2412yes—
258C22×C3×D3C2412yes—
259C22×C3×D3C2414yes—
260C2×D32—28no—
261C2×D32—48no—
262C32×Q8—24no—
263C32×Q8—24no—
264C2×C32×C4—24no—
265C2×C32×C4C2×D414yes—
266C2×C32×C4C2414yes—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269#638—24no—
270C2×C3⋊Dic3C2414yes—
271C2×C3⋊Dic3C2412yes—
272C4⋊(C3⋊D3)—22no—
273C4×C3⋊D3—24no—
274#634—22no—
275C3×#67—24no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3C2414yes—
278C2×C3×Dic3C2412yes—
279C2×C3×Dic3C2412yes—
280C3×D12—216no—
281C3×D12—22no—
282C3×D12C2×D418yes—
283C3×D12C2×D418yes—
284C3×C4×D3—216no—
285C3×C4×D3—24no—
286C3×C4×D3—24no—
287C3×C4×D3—24no—
288C3×Dic6—22no—
289#626—28no—
290#626—44no—
291#625—28no—
292#625—44no—
293D3×Dic3—28no—
294D3×Dic3—48no—
295C2×H(5,𝔽2)—91no—
296C22×#41—31no—
297#547—94no—
298#547—94no—
299#546—94no—
300#546—94no—
301#536—31no—
302#536—91no—
303#534—94no—
304#525—91no—
305#525—91no—
306C2×#123—94no—
307#518—91no—
308C24×C3—32no—
309C24×C3—31no—
310C23×D3—34no—
311C23×D3—34no—
312C23×D3C22×D311yescharacteristic
313C23×D3C22×D312yes—
314C3×#41—616no—
315C3×#41—616no—
316C3×#41—64no—
317C2×C3×Q8—24no—
318C2×C3×Q8—24no—
319C2×C3×Q8—22no—
320C2×C3×Q8—22no—
321C2×C3×Q8—31no—
322C2×C3×Q8—44no—
323C2×C3×Q8C22×D312yes—
324C2×C3×Q8C22×D312yes—
325C2×C3×Q8C22×D312yes—
326C2×C3×Q8C22×D312yes—
327C2×C3×D4—32no—
328C2×C3×D4—38no—
329C2×C3×D4—32no—
330C2×C3×D4—32no—
331C2×C3×D4—38no—
332C2×C3×D4—31no—
333C2×C3×D4—68no—
334C22×C3×C4—21no—
335C22×C3×C4—22no—
336C22×C3×C4—31no—
337C22×C3×C4—38no—
338C22×C3×C4—32no—
339C22×C3×C4—32no—
340C22×C3×C4—32no—
341C22×C3×C4—68no—
342C22×C3×C4—64no—
343C22×C3×C4C22×D312yes—
344C22×C3×C4C22×D312yes—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C2×#67—32no—
348C2×#67—32no—
349C2×#67—34no—
350C2×#67—34no—
351C2×#67—34no—
352C2×#67—34no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—62no—
356C2×#67—616no—
357C2×#67C22×D312yes—
358C22×Dic3—34no—
359C22×Dic3—38no—
360C22×Dic3C22×D311yescharacteristic
361#239—216no—
362#239—216no—
363#239—68no—
364#237—68no—
365#237—68no—
366D3×D4—68no—
367D3×D4—68no—
368D3×D4—616no—
369D3×D4—68no—
370#235—24no—
371#235—64no—
372#235—64no—
373#235—68no—
374#235—124no—
375C2×D12—28no—
376C2×D12—34no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—34no—
380C2×D12—61no—
381C2×D12—68no—
382C2×D12#6718yescomplemented
383C2×D12C22×D318yes—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D312yes—
386C2×D12C22×D312yes—
387C2×C4×D3—28no—
388C2×C4×D3—24no—
389C2×C4×D3—34no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3—38no—
393C2×C4×D3—62no—
394C2×C4×D3C22×D312yes—
395C2×C4×D3C22×D318yes—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D312yes—
398C2×Dic6—31no—
399C2×Dic6—31no—
400C2×Dic6—61no—
401C2×Dic6C22×D311yescharacteristic
402C3×C4⋊C4—38no—
403C3×C4⋊C4—32no—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—38no—
406C3×C42—32no—
407#217—32no—
408#217—32no—
409#217—34no—
410#217—34no—
411#217—34no—
412#217—38no—
413#217—62no—
414#217C22×D312yes—
415(C2×D3)⋊C4—38no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—38no—
420(C2×D3)⋊C4—38no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—68no—
424(C2×D3)⋊C4C22×D318yes—
425C4⋊Dic3—32no—
426C4⋊Dic3—32no—
427C4⋊Dic3—34no—
428C4⋊Dic3—62no—
429C4⋊Dic3C22×D312yes—
430Dic3⋊C4—38no—
431Dic3⋊C4—38no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—68no—
436Dic3⋊C4C22×D318yes—
437C4×Dic3—32no—
438C4×Dic3—32no—
439C4×Dic3—62no—
440C4×Dic3C22×D312yes—
441C22×C32—22no—
442C22×C32C22×D412yes—
443C22×C32C2511yescharacteristic
444C2×C3⋊D3—22no—
445C2×C3⋊D3—24no—
446C2×C3×D3—28no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—24no—
451C2×C3×D3—22no—
452C2×C3×D3—48no—
453C2×C3×D3—44no—
454C2×C3×D3C22×D418yes—
455D32—88no—
456C32×C4—24no—
457C32×C4C22×D412yes—
458C32×C4C22×D412yes—
459C3⋊Dic3—22no—
460C3⋊Dic3—24no—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—24no—
464H(5,𝔽2)—188no—
465C2×#41—34no—
466C2×#41—34no—
467C2×#41—31no—
468C2×#41—68no—
469C2×#41—92no—
470C2×#41—92no—
471C2×#41—91no—
472C22×Q8D3211yescharacteristic, complemented
473C22×D4—31no—
474C22×D4—32no—
475C22×D4—92no—
476C22×D4—92no—
477C22×D4—94no—
478C23×C4—32no—
479C23×C4—31no—
480C4⋊Q8—32no—
481C4⋊Q8—92no—
482#124—32no—
483#124—92no—
484#123—34no—
485#123—92no—
486#123—98no—
487#123—98no—
488#123—98no—
489#123—92no—
490#123—94no—
491C22⋊Q8—34no—
492C22⋊Q8—92no—
493C22⋊Q8—92no—
494C22⋊Q8—94no—
495#121—98no—
496#121—92no—
497#121—98no—
498#121—92no—
499#120—98no—
500#120—92no—
501#120—92no—
502C4×D4—94no—
503C4×D4—94no—
504C4×D4—94no—
505C4×D4—94no—
506#117—31no—
507#117—91no—
508C2×C4⋊C4—98no—
509C2×C22⋊C4—98no—
510C2×C22⋊C4—94no—
511C23×C3—21no—
512C23×C3—34no—
513C23×C3—38no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—62no—
517C23×C3—124no—
518C23×C3—122no—
519C23×C3C23×D311yescharacteristic
520C23×C3C23×D311yescharacteristic
521C22×D3—22no—
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—44no—
525C22×D3—42no—
526C22×D3—62no—
527C22×D3—68no—
528C22×D3—68no—
529C22×D3—128no—
530C22×D3—128no—
531C22×D3C2×#6718yes—
532C22×D3C23×D312yes—
533C22×D3C23×D312yes—
534C22×D3C23×D314yes—
535C3×Q8—24no—
536C3×Q8—24no—
537C3×Q8—24no—
538C3×Q8—24no—
539C3×Q8—44no—
540C3×Q8—44no—
541C3×Q8—62no—
542C3×D4—38no—
543C3×D4—38no—
544C3×D4—616no—
545C3×D4—64no—
546C3×D4—62no—
547C2×C3×C4—24no—
548C2×C3×C4—24no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—24no—
552C2×C3×C4—24no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—34no—
556C2×C3×C4—44no—
557C2×C3×C4—616no—
558C2×C3×C4—62no—
559C2×C3×C4—64no—
560C2×C3×C4—64no—
561C2×C3×C4—64no—
562C2×C3×C4D3×D414yes—
563C2×C3×C4C2×#6714yes—
564C2×C3×C4C23×D314yes—
565C2×C3×C4C23×D314yes—
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570#67—24no—
571#67—68no—
572#67—68no—
573#67—64no—
574#67—64no—
575#67—68no—
576#67—124no—
577#67—124no—
578#67—124no—
579#67—124no—
580C2×Dic3—22no—
581C2×Dic3—34no—
582C2×Dic3—34no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—64no—
586C2×Dic3—62no—
587C2×Dic3—68no—
588C2×Dic3—128no—
589C2×Dic3C23×D314yes—
590C2×Dic3C23×D312yes—
591C2×Dic3C23×D312yes—
592D12—216no—
593D12—22no—
594D12—68no—
595D12—62no—
596D12—62no—
597D12—122no—
598D12—124no—
599D12C2×#6718yes—
600D12C2×#6718yes—
601C4×D3—216no—
602C4×D3—24no—
603C4×D3—24no—
604C4×D3—24no—
605C4×D3—68no—
606C4×D3—64no—
607C4×D3—64no—
608C4×D3—124no—
609C4×D3—128no—
610Dic6—22no—
611Dic6—62no—
612Dic6—62no—
613Dic6—122no—
614C2×C32—22no—
615C2×C32C23×D411yescharacteristic
616C2×C32#58512yes—
617C3⋊D3—42no—
618C3×D3—28no—
619C3×D3—42no—
620C3×D3—42no—
621C24—32no—
622C24—31no—
623C24—94no—
624#41—616no—
625#41—616no—
626#41—64no—
627#41—188no—
628#41—188no—
629#41—184no—
630C2×Q8—24no—
631C2×Q8—31no—
632C2×Q8—91no—
633C2×Q8C2×D3212yes—
634C2×Q8C2×D3212yes—
635C2×D4—32no—
636C2×D4—32no—
637C2×D4—32no—
638C2×D4—38no—
639C2×D4—31no—
640C2×D4—38no—
641C2×D4—68no—
642C2×D4—94no—
643C2×D4—94no—
644C2×D4—94no—
645C2×D4—92no—
646C2×D4—94no—
647C2×D4—91no—
648C2×D4—188no—
649C2×D4—188no—
650C2×D4—1816no—
651C22×C4—31no—
652C22×C4—38no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—68no—
657C22×C4—64no—
658C22×C4—94no—
659C22×C4—98no—
660C22×C4—92no—
661C22×C4C2×D3212yes—
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—38no—
664C4⋊C4—32no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—98no—
668C4⋊C4—92no—
669C22⋊C4—32no—
670C22⋊C4—38no—
671C22⋊C4—94no—
672C22⋊C4—94no—
673C22⋊C4—98no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4—92no—
677C22⋊C4—98no—
678C42—32no—
679C42—92no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—38no—
685C22×C3—42no—
686C22×C3—68no—
687C22×C3—62no—
688C22×C3—64no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—128no—
693C22×C3—124no—
694C22×C3C2×D3×D412yes—
695C22×C3C22×#6712yes—
696C22×C3C24×D311yescharacteristic
697C22×C3C24×D311yescharacteristic
698C2×D3—28no—
699C2×D3—22no—
700C2×D3—22no—
701C2×D3—22no—
702C2×D3—24no—
703C2×D3—22no—
704C2×D3—48no—
705C2×D3—44no—
706C2×D3—62no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—62no—
710C2×D3—122no—
711C2×D3—124no—
712C2×D3—248no—
713C2×D3—248no—
714C2×D3C22×#6718yes—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—44no—
720C3×C4—62no—
721C3×C4—64no—
722C3×C4—62no—
723C3×C4C2×D3×D412yes—
724C3×C4C2×D3×D412yes—
725C3×C4C22×#6712yes—
726C3×C4C22×#6712yes—
727Dic3—22no—
728Dic3—24no—
729Dic3—22no—
730Dic3—62no—
731Dic3—64no—
732Dic3—64no—
733Dic3—62no—
734Dic3—122no—
735Dic3—124no—
736C32#348511yescharacteristic, complemented, Sylow
737C23—34no—
738C23—38no—
739C23—32no—
740C23—32no—
741C23—62no—
742C23—92no—
743C23—124no—
744C23—122no—
745C23—188no—
746C23—368no—
747C23C22×D3211yescharacteristic
748Q8—24no—
749Q8—24no—
750Q8—62no—
751Q8—182no—
752D4—38no—
753D4—38no—
754D4—616no—
755D4—64no—
756D4—62no—
757D4—188no—
758D4—188no—
759D4—184no—
760D4—182no—
761D4—364no—
762D4—364no—
763C2×C4—24no—
764C2×C4—34no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—616no—
768C2×C4—62no—
769C2×C4—64no—
770C2×C4—64no—
771C2×C4—64no—
772C2×C4—94no—
773C2×C4—92no—
774C2×C4—188no—
775C2×C4—184no—
776C2×C4—368no—
777C2×C4D3×#6714yes—
778C2×C4C22×D3214yes—
779C2×C4C22×D3211yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C2×C3—22no—
782C2×C3—22no—
783C2×C3—22no—
784C2×C3—21no—
785C2×C3—42no—
786C2×C3—68no—
787C2×C3—122no—
788C2×C3—122no—
789C2×C3C22×D3×D411yescharacteristic
790C2×C3#596412yes—
791C2×C3#596812yes—
792C2×C3C23×#6711yescharacteristic
793D3—28no—
794D3—42no—
795D3—42no—
796D3—122no—
797D3—122no—
798D3—242no—
799C22—22no—
800C22—38no—
801C22—68no—
802C22—62no—
803C22—62no—
804C22—64no—
805C22—62no—
806C22—62no—
807C22—128no—
808C22—124no—
809C22—184no—
810C22—182no—
811C22—728no—
812C22C2×D3×#6712yes—
813C22C23×D3211yescharacteristic
814C4—24no—
815C4—64no—
816C4—62no—
817C4—62no—
818C4—184no—
819C4—182no—
820C4C2×D3×#6712yes—
821C4C2×D3×#6712yes—
822C3—21no—
823C3#8635411yescharacteristic, complemented
824C3#8727311yescharacteristic, complemented
825C2—22no—
826C2—68no—
827C2—122no—
828C2—122no—
829C2—362no—
830C2#1059668812yes—
831C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C2×#64307C2semidirect
3. #10596287C2semidirect
4. C3×#5816C2semidirect
5. #10595428C2semidirect
6. #10595427C2semidirect
7. #10595358C2semidirect
8. #10595357C2semidirect
9. #10595062C2semidirect
10. D3×#929C2semidirect
11. #10595023C2semidirect
12. #10595022C2semidirect
13. #10594982C2semidirect
16. C22×C32×Q8C22semidirect
19. C2×C3×#239C22semidirect
20. C2×C3×#239C22semidirect
23. C22×C3×D12C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×C3×C4×D3C22semidirect
28. C2×#3802C22semidirect
29. C2×D3×D12C22semidirect
30. C2×#3796C22semidirect
31. C2×#3795C22semidirect
32. #64156C22semidirect
33. #64155C22semidirect
34. #64153C22semidirect
35. #64138C22semidirect
36. #64135C22semidirect
37. C3×#947C22semidirect
38. C3×#946C22semidirect
39. C3×#944C22semidirect
40. C3×#929C22semidirect
41. C3×#926C22semidirect
42. #63977C22semidirect
43. #63976C22semidirect
44. D3×#217C22semidirect
45. #63966C22semidirect
46. #63961C22semidirect
47. #63922C22semidirect
48. D3×(C2×D3)⋊C4C22semidirect
49. #63909C22semidirect
50. #63908C22semidirect
51. #63905C22semidirect
52. C4×#626C22semidirect
53. C4×#625C22semidirect
54. #63898C22semidirect
55. Dic3×D12C22semidirect
56. #63886C22semidirect
57. #63885C22semidirect
58. #63884C22semidirect
59. D3×Dic3⋊C4C22semidirect
60. #63857C22semidirect
61. #63856C22semidirect
62. #63850C22semidirect
65. C22×#239D3semidirect
76. #5816D3semidirect
109. C2×C3×D12D4semidirect
155. C22×C3×Q8C2×D3semidirect
156. C22×C3×Q8C2×D3semidirect
165. C2×#239C2×D3semidirect
166. C2×#239C2×D3semidirect
181. C22×D12C2×D3semidirect
182. C22×C4×D3C2×D3semidirect
183. C22×C4×D3C2×D3semidirect
195. #947C2×D3semidirect
200. #946C2×D3semidirect
204. #944C2×D3semidirect
223. #929C2×D3semidirect
231. #926C2×D3semidirect
382. C2×D12#67semidirect
472. C22×Q8D32semidirect
736. C32#3485semidirect
823. C3#86354semidirect
824. C3#87273semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×#643072
#105962872
C3×#58162
#105954282
#105954272
#105953582
#105953572
#105950622
D3×#9292
#105950232
#105950222
#105949822
#872733
#863543