Finite Group Databasebeta

← #11904570

Subgroups — #11904570

Order 1152.

3205 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3#10595987C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5524C211yesmaximal, characteristic, complemented
6#10595040C211yesmaximal, characteristic, complemented
7#10595022C211yesmaximal, characteristic, complemented
8#10594527C214yesmaximal, complemented
9#10594525C214yesmaximal, complemented
10#10594192C214yesmaximal, complemented
11#10594082C214yesmaximal, complemented
12#10593906C214yesmaximal, complemented
13#10593905C214yesmaximal, complemented
14#86315—31nomaximal
15#86023—31nomaximal
16C22×#634C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#625C2212yes—
22C2×#3805C2214yes—
23C22×D3×Dic3C2212yes—
24#64298—28no—
25C2×#3795—28no—
26C2×#3795C2214yes—
27C2×#3795C2214yes—
28C2×#3795C2212yescomplemented
29C2×#3795C2212yescomplemented
30C2×D3×Dic6C2212yescomplemented
31C2×D3×Dic6C2212yescomplemented
32C32×#117C2211yescharacteristic
33#64135C2211yescharacteristic
34#64096C2214yescomplemented
35#64086C2214yes—
36C4×#634C2214yescomplemented
37C3×#897C2212yescomplemented
38C3×#895C2212yescomplemented
39C3×#895C2214yescomplemented
40C3×#886C2212yes—
41C3×#882C2214yes—
42C3×#882C2212yes—
43C3×#875C2212yescomplemented
44C3×#874C2212yescomplemented
45C3×C4×D12C2214yescomplemented
46#63976C2214yes—
47#63976C2212yes—
48#63961C2212yes—
49#63915C2218yescomplemented
50#63914C2218yescomplemented
51#63914C2212yescomplemented
52#63908C2214yescomplemented
53#63908C2212yescomplemented
54#63902C2218yescomplemented
55C4×#625C2214yescomplemented
56#63899C2218yescomplemented
57#63898C2218yescomplemented
58#63885C2218yescomplemented
59#63885C2218yescomplemented
60#63885C2218yescomplemented
61#63863C2212yescomplemented
62#63856C2212yescomplemented
63C2×#1010—31no—
64C2×#1010—31no—
65C22×#237—31no—
66C22×#235—31no—
67C3×#535—31no—
68C3×#525—31no—
69#5830—31no—
70#5828—31no—
71#5805—31no—
72#5791—31no—
73#5718—34no—
74#5677—34no—
75#5656—34no—
76#5633—34no—
77#5599—34no—
78#5599—34no—
79#5598—34no—
80#5592—34no—
81#5592—34no—
82#5586—34no—
83#5553—34no—
84#5552—34no—
85#5525D311yescharacteristic, complemented
86#5524D311yescharacteristic, complemented
87#5516—31no—
88#5516—31no—
89#5516—61no—
90C23×C3×D3C2312yes—
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2312yes—
94C2×#634D418yescomplemented
95C2×#634C2312yes—
96C2×#634C2312yes—
97C2×C3×#67C2312yes—
98C2×C3×#67C2312yes—
99C22×C3×Dic3C2311yescharacteristic
100C3×#235—24no—
101C3×#235—24no—
102C2×C3×D12—24no—
103C2×C3×D12C2312yes—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2312yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2318yes—
108C2×C3×D12C2314yes—
109C2×C3×C4×D3—24no—
110C2×C3×C4×D3C2312yes—
111C2×C3×C4×D3C2312yes—
112C2×C3×C4×D3C2312yes—
113C2×C3×C4×D3C2312yes—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×#627C2314yes—
117C2×#625—28no—
118C2×#625C2318yes—
119C2×#625C2314yes—
120C2×#625C2314yes—
121C2×#625C2318yes—
122#3805—216no—
123C2×D3×Dic3—28no—
124C2×D3×Dic3C2314yes—
125C2×D3×Dic3C2314yes—
126C2×D3×Dic3C2318yes—
127#3795—216no—
128#3795—216no—
129#3795—28no—
130#3795—28no—
131D3×Dic6—28no—
132D3×Dic6—28no—
133C32×C4⋊C4C2312yes—
134C32×C22⋊C4C2312yes—
135C32×C42C2312yes—
136#3757C2312yes—
137C4⋊(C3⋊Dic3)C2312yes—
138#3750C2318yes—
139C4×C3⋊Dic3C2318yes—
140C4×C3⋊Dic3C2312yes—
141C3×(C2×D3)⋊C4C2318yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×C4⋊Dic3C2314yes—
145#3724C2314yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2318yes—
148(C2×D3)⋊Dic3C2314yes—
149#3487—91noSylow
150C2×C3×#41—31no—
151C2×C3×#41—31no—
152C22×C3×D4—31no—
153C23×C3×C4—31no—
154C22×#67—32no—
155C22×#67—32no—
156C23×Dic3—32no—
157#1010—68no—
158#1010—68no—
159C2×D3×Q8—32no—
160C2×D3×Q8—32no—
161C2×#237—34no—
162C2×#237—34no—
163C2×#237—34no—
164C2×#237—34no—
165C2×#237—32no—
166C2×#237—32no—
167C2×#237—68no—
168C2×#235—34no—
169C2×#235—34no—
170C2×#235—32no—
171C2×#235—32no—
172C2×#235—68no—
173C2×#235C2×D311yescharacteristic
174C2×#235C2×D311yescharacteristic
175C22×D12C2×D311yescharacteristic
176C22×C4×D3—32no—
177C22×C4×D3C2×D311yescharacteristic
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6—32no—
181C22×Dic6—32no—
182C22×Dic6—61no—
183C3×#127—32no—
184C3×#124—32no—
185C3×#123—32no—
186C3×C22⋊Q8—32no—
187C3×#121—34no—
188C3×#121—32no—
189C3×#120—34no—
190C3×#120—32no—
191C3×C4×D4—34no—
192C3×#117—21no—
193C3×#117C2×D311yescharacteristic
194C3×#117C2×D311yescharacteristic
195#953—32no—
196#953—34no—
197#947—32no—
198#946—32no—
199#940—38no—
200#940—32no—
201#940—38no—
202#940—32no—
203#939—38no—
204#939—38no—
205#939—38no—
206#938—34no—
207#938—32no—
208#937—34no—
209#937—32no—
210#936—32no—
211#935—32no—
212D4×Dic3—38no—
213#930—32no—
214#930—34no—
215#929—32no—
216C4×#67—34no—
217C4×#67—34no—
218#926—31no—
219#926—31no—
220#926—61no—
221#924—32no—
222#897C2×D312yescomplemented
223#896—38no—
224#895C2×D314yescomplemented
225#895C2×D312yescomplemented
226#893—38no—
227#887—34no—
228#887—34no—
229#887—64no—
230#886C2×D312yes—
231#885—38no—
232#885—38no—
233#884—38no—
234#884—38no—
235#884—38no—
236#882C2×D314yes—
237#882C2×D312yes—
238#67⋊C4—38no—
239#67⋊C4—38no—
240#878—38no—
241#877—34no—
242#877—34no—
243#877—64no—
244#875C2×D312yescomplemented
245#874C2×D312yescomplemented
246C4×D12C2×D314yescomplemented
247C4×Dic6—34no—
248C4×Dic6—34no—
249C4×Dic6—64no—
250C23×C32C2411yescharacteristic
251C22×C3×D3—24no—
252C22×C3×D3—22no—
253C22×C3×D3—42no—
254C22×C3×D3—44no—
255C22×C3×D3C2414yes—
256C22×C3×D3C2412yes—
257C22×C3×D3C2412yes—
258C22×C3×D3C2412yes—
259C2×C32×C4C2×D414yes—
260C2×C32×C4C2414yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2411yescharacteristic
263C2×C3⋊Dic3C2×D418yes—
264C2×C3⋊Dic3C2414yes—
265C2×C3⋊Dic3C2414yes—
266#634C2×D418yes—
267#634C2×D418yes—
268C3×#67—24no—
269C3×#67—24no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3C2412yes—
272C2×C3×Dic3C2412yes—
273C2×C3×Dic3C2412yes—
274C3×D12—24no—
275C3×D12—24no—
276C3×D12—22no—
277C3×D12—22no—
278C3×D12—44no—
279C3×D12—48no—
280C3×C4×D3—24no—
281C3×C4×D3—24no—
282C3×C4×D3—24no—
283C3×C4×D3—24no—
284C3×Dic6—22no—
285C3×Dic6—22no—
286#627—28no—
287#625—28no—
288#625—216no—
289#625—48no—
290#625—44no—
291D3×Dic3—28no—
292D3×Dic3—28no—
293D3×Dic3—216no—
294C2×2−1+4—91no—
295C22×#41—91no—
296#550—94no—
297#550—94no—
298#548—94no—
299#548—94no—
300#535—31no—
301#535—94no—
302#535—91no—
303#525—31no—
304#525—94no—
305#525—91no—
306#519—91no—
307C24×C3—32no—
308C24×C3—31no—
309C23×D3C22×D312yes—
310C23×D3C22×D311yescharacteristic
311C3×#41—64no—
312C3×#41—64no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×D4—32no—
316C2×C3×D4—32no—
317C2×C3×D4—32no—
318C2×C3×D4—32no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—38no—
322C2×C3×D4—34no—
323C2×C3×D4—64no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—32no—
327C22×C3×C4—32no—
328C22×C3×C4—32no—
329C22×C3×C4—32no—
330C22×C3×C4—64no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—34no—
334C2×#67—38no—
335C2×#67—38no—
336C2×#67—34no—
337C2×#67—38no—
338C2×#67—38no—
339C2×#67—34no—
340C2×#67—34no—
341C2×#67—68no—
342C2×#67—68no—
343C2×#67C22×D312yes—
344C2×#67C22×D312yes—
345C22×Dic3—32no—
346C22×Dic3—32no—
347C22×Dic3—38no—
348C22×Dic3—34no—
349C22×Dic3—34no—
350C22×Dic3—62no—
351C22×Dic3—68no—
352C22×Dic3C22×D311yescharacteristic
353D3×Q8—68no—
354D3×Q8—68no—
355#237—616no—
356#237—616no—
357#237—68no—
358#237—68no—
359#237—616no—
360#237—616no—
361#235—24no—
362#235—24no—
363#235—616no—
364#235—616no—
365#235—68no—
366#235—68no—
367C2×D12—24no—
368C2×D12C22×D311yescharacteristic
369C2×D12C22×D312yes—
370C2×D12C22×D311yescharacteristic
371C2×D12C22×D312yes—
372C2×D12C22×D314yes—
373C2×D12C22×D318yes—
374C2×C4×D3—24no—
375C2×C4×D3—34no—
376C2×C4×D3—38no—
377C2×C4×D3—34no—
378C2×C4×D3—68no—
379C2×C4×D3C22×D312yes—
380C2×C4×D3C22×D312yes—
381C2×C4×D3C22×D312yes—
382C2×C4×D3C22×D312yes—
383C2×Dic6—38no—
384C2×Dic6—38no—
385C2×Dic6—32no—
386C2×Dic6—32no—
387C2×Dic6—32no—
388C2×Dic6—32no—
389C2×Dic6—34no—
390C2×Dic6—34no—
391C2×Dic6—62no—
392C2×Dic6—62no—
393C2×Dic6—68no—
394C2×Dic6—68no—
395C2×Dic6—68no—
396C2×Dic6C22×D311yescharacteristic
397C2×Dic6C22×D311yescharacteristic
398C3×C4⋊C4—22no—
399C3×C4⋊C4—34no—
400C3×C4⋊C4C22×D312yes—
401C3×C4⋊C4C22×D312yes—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—38no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4C22×D312yes—
407C3×C22⋊C4C22×D312yes—
408C3×C42—22no—
409C3×C42C22×D312yes—
410C3×C42C22×D312yes—
411#217—32no—
412#217—32no—
413#217—38no—
414#217—34no—
415#217—34no—
416#217—62no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—38no—
420(C2×D3)⋊C4C22×D314yes—
421(C2×D3)⋊C4C22×D314yes—
422(C2×D3)⋊C4C22×D318yes—
423C4⋊Dic3—32no—
424C4⋊Dic3—32no—
425C4⋊Dic3—62no—
426C4⋊Dic3C22×D314yes—
427Dic3⋊C4—38no—
428Dic3⋊C4—38no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—68no—
432C4×Dic3—38no—
433C4×Dic3—38no—
434C4×Dic3—32no—
435C4×Dic3—32no—
436C4×Dic3—68no—
437C4×Dic3—62no—
438C22×C32—22no—
439C22×C32C22×D412yes—
440C22×C32C2511yescharacteristic
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—24no—
444C2×C3×D3—22no—
445C2×C3×D3—24no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D3—28no—
449C2×C3×D3—22no—
450C2×C3×D3—48no—
451C2×C3×D3—44no—
452C32×C4—24no—
453C32×C4C22×D412yes—
454C32×C4C22×D412yes—
455C3⋊Dic3—24no—
456C3⋊Dic3C22×D418yes—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—22no—
4602−1+4—188no—
461C2×#41—31no—
462C2×#41—31no—
463C2×#41—94no—
464C2×#41—94no—
465C2×#41—92no—
466C2×#41—92no—
467C2×#41—94no—
468C2×#41—188no—
469C22×Q8—92no—
470C22×Q8—92no—
471C22×Q8—91no—
472C22×D4—31no—
473C22×D4—92no—
474C23×C4—31no—
475C23×C4—92no—
476#127—32no—
477#127—92no—
478#127—98no—
479#124—32no—
480#124—98no—
481#124—92no—
482#123—32no—
483#123—92no—
484C22⋊Q8—32no—
485C22⋊Q8—98no—
486C22⋊Q8—92no—
487#121—32no—
488#121—34no—
489#121—98no—
490#121—98no—
491#121—98no—
492#121—92no—
493#121—94no—
494#120—32no—
495#120—34no—
496#120—92no—
497#120—94no—
498C4×Q8—94no—
499C4×Q8—94no—
500C4×D4—34no—
501C4×D4—98no—
502C4×D4—98no—
503C4×D4—94no—
504#117—91no—
505#117—94no—
506#117D3211yescharacteristic
507C23×C3—21no—
508C23×C3—34no—
509C23×C3—32no—
510C23×C3—32no—
511C23×C3—32no—
512C23×C3—64no—
513C23×C3—62no—
514C23×C3—124no—
515C23×C3—122no—
516C23×C3C23×D311yescharacteristic
517C23×C3C23×D311yescharacteristic
518C22×D3—22no—
519C22×D3—24no—
520C22×D3—42no—
521C22×D3—44no—
522C22×D3C23×D314yes—
523C22×D3C23×D312yes—
524C22×D3C23×D312yes—
525C22×D3C23×D312yes—
526C3×Q8—62no—
527C3×Q8—62no—
528C3×D4—64no—
529C3×D4—64no—
530C3×D4—64no—
531C3×D4—64no—
532C3×D4—62no—
533C3×D4—62no—
534C3×D4—128no—
535C3×D4—124no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—62no—
544C2×C3×C4—64no—
545C2×C3×C4—64no—
546C2×C3×C4—64no—
547C2×C3×C4—64no—
548C2×C3×C4D3×D414yes—
549C2×C3×C4D3×D414yes—
550C2×C3×C4C23×D314yes—
551C2×C3×C4C23×D314yes—
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—24no—
557#67—24no—
558#67—616no—
559#67—68no—
560#67—68no—
561#67—616no—
562#67—128no—
563#67—124no—
564#67—124no—
565#67—128no—
566C2×Dic3—22no—
567C2×Dic3—38no—
568C2×Dic3—38no—
569C2×Dic3—34no—
570C2×Dic3—34no—
571C2×Dic3—34no—
572C2×Dic3—34no—
573C2×Dic3—68no—
574C2×Dic3—64no—
575C2×Dic3—64no—
576C2×Dic3—68no—
577C2×Dic3—68no—
578C2×Dic3—616no—
579C2×Dic3C23×D312yes—
580C2×Dic3C23×D312yes—
581C2×Dic3C23×D312yes—
582D12—24no—
583D12—24no—
584D12—22no—
585D12—22no—
586D12—44no—
587D12—48no—
588C4×D3—24no—
589C4×D3—24no—
590C4×D3—24no—
591C4×D3—24no—
592C4×D3—616no—
593C4×D3—68no—
594C4×D3—68no—
595Dic6—22no—
596Dic6—22no—
597Dic6—38no—
598Dic6—38no—
599Dic6—38no—
600Dic6—38no—
601Dic6—68no—
602Dic6—68no—
603Dic6—68no—
604Dic6—68no—
605C2×C32—22no—
606C2×C32C23×D411yescharacteristic
607C2×C32#58512yes—
608C3×D3—42no—
609C3×D3—42no—
610C3×D3—42no—
611C3×D3—44no—
612C24—31no—
613C24—32no—
614#41—64no—
615#41—64no—
616#41—1816no—
617#41—1816no—
618#41—188no—
619#41—188no—
620#41—1816no—
621C2×Q8—31no—
622C2×Q8—31no—
623C2×Q8—94no—
624C2×Q8—92no—
625C2×Q8—92no—
626C2×Q8—98no—
627C2×Q8—188no—
628C2×Q8—188no—
629C2×D4—32no—
630C2×D4—32no—
631C2×D4—32no—
632C2×D4—31no—
633C2×D4—32no—
634C2×D4—31no—
635C2×D4—34no—
636C2×D4—38no—
637C2×D4—64no—
638C2×D4—98no—
639C2×D4—94no—
640C2×D4—94no—
641C2×D4—98no—
642C2×D4—188no—
643C22×C4—31no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—32no—
648C22×C4—64no—
649C22×C4—94no—
650C22×C4—94no—
651C22×C4—98no—
652C22×C4—92no—
653C22×C4—188no—
654C22×C4C2×D3211yescharacteristic
655C4⋊C4—34no—
656C4⋊C4—94no—
657C4⋊C4—98no—
658C4⋊C4—92no—
659C4⋊C4C2×D3212yes—
660C22⋊C4—34no—
661C22⋊C4—34no—
662C22⋊C4—38no—
663C22⋊C4—94no—
664C22⋊C4—94no—
665C22⋊C4—98no—
666C22⋊C4—92no—
667C22⋊C4C2×D3212yes—
668C42—98no—
669C42—92no—
670C42C2×D3212yes—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—21no—
675C22×C3—42no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—64no—
679C22×C3—62no—
680C22×C3—64no—
681C22×C3—68no—
682C22×C3—64no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—128no—
686C22×C3—124no—
687C22×C3C2×D3×D412yes—
688C22×C3C2×D3×D412yes—
689C22×C3C24×D311yescharacteristic
690C22×C3C24×D311yescharacteristic
691C2×D3—22no—
692C2×D3—22no—
693C2×D3—22no—
694C2×D3—24no—
695C2×D3—22no—
696C2×D3—24no—
697C2×D3—22no—
698C2×D3—24no—
699C2×D3—28no—
700C2×D3—44no—
701C2×D3—48no—
702C3×C4—24no—
703C3×C4—24no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—44no—
707C3×C4—62no—
708C3×C4—62no—
709C3×C4—62no—
710C3×C4C2×D3×D412yes—
711C3×C4C2×D3×D412yes—
712C3×C4C2×D3×D412yes—
713C3×C4C2×D3×D412yes—
714Dic3—22no—
715Dic3—22no—
716Dic3—22no—
717Dic3—38no—
718Dic3—38no—
719Dic3—68no—
720Dic3—64no—
721Dic3—64no—
722Dic3—124no—
723C32#348711yescharacteristic, complemented, Sylow
724C23—32no—
725C23—34no—
726C23—32no—
727C23—32no—
728C23—62no—
729C23—64no—
730C23—122no—
731C23—124no—
732C23C22×D3211yescharacteristic
733Q8—62no—
734Q8—62no—
735Q8—98no—
736Q8—98no—
737Q8—188no—
738D4—64no—
739D4—64no—
740D4—64no—
741D4—64no—
742D4—62no—
743D4—62no—
744D4—128no—
745D4—124no—
746D4—1816no—
747D4—188no—
748D4—364no—
749D4—368no—
750C2×C4—32no—
751C2×C4—32no—
752C2×C4—32no—
753C2×C4—62no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—64no—
757C2×C4—64no—
758C2×C4—98no—
759C2×C4—94no—
760C2×C4—94no—
761C2×C4—1816no—
762C2×C4—188no—
763C2×C4—188no—
764C2×C4#380214yes—
765C2×C4C22×D3214yes—
766C2×C4C22×D3211yescharacteristic
767C2×C4C22×D3211yescharacteristic
768C2×C3—22no—
769C2×C3—22no—
770C2×C3—21no—
771C2×C3—22no—
772C2×C3—42no—
773C2×C3—124no—
774C2×C3—122no—
775C2×C3—122no—
776C2×C3—122no—
777C2×C3C22×D3×D411yescharacteristic
778C2×C3C22×D3×D411yescharacteristic
779C2×C3#596412yes—
780C2×C3#596612yes—
781D3—42no—
782D3—42no—
783D3—44no—
784D3—42no—
785C22—22no—
786C22—62no—
787C22—62no—
788C22—62no—
789C22—64no—
790C22—64no—
791C22—62no—
792C22—64no—
793C22—68no—
794C22—62no—
795C22—124no—
796C22—128no—
797C22C2×#380212yes—
798C22C23×D3211yescharacteristic
799C4—24no—
800C4—62no—
801C4—62no—
802C4—62no—
803C4—98no—
804C4—184no—
805C4C2×#380212yes—
806C4C2×#380212yes—
807C3—21no—
808C3#8602311yescharacteristic, complemented
809C3#8631511yescharacteristic, complemented
810C2—22no—
811C2—122no—
812C2—124no—
813C2—122no—
814C2—122no—
815C2C22×#380211yescharacteristic
816C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64298C2semidirect
2. C22×#3795C2semidirect
3. #10595987C2semidirect
4. C3×#5525C2semidirect
5. C3×#5524C2semidirect
6. #10595040C2semidirect
7. #10595022C2semidirect
8. #10594527C2semidirect
9. #10594525C2semidirect
10. #10594192C2semidirect
11. #10594082C2semidirect
12. #10593906C2semidirect
13. #10593905C2semidirect
28. C2×#3795C22semidirect
29. C2×#3795C22semidirect
30. C2×D3×Dic6C22semidirect
31. C2×D3×Dic6C22semidirect
34. #64096C22semidirect
36. C4×#634C22semidirect
37. C3×#897C22semidirect
38. C3×#895C22semidirect
39. C3×#895C22semidirect
43. C3×#875C22semidirect
44. C3×#874C22semidirect
45. C3×C4×D12C22semidirect
49. #63915C22semidirect
50. #63914C22semidirect
51. #63914C22semidirect
52. #63908C22semidirect
53. #63908C22semidirect
54. #63902C22semidirect
55. C4×#625C22semidirect
56. #63899C22semidirect
57. #63898C22semidirect
58. #63885C22semidirect
59. #63885C22semidirect
60. #63885C22semidirect
61. #63863C22semidirect
62. #63856C22semidirect
85. #5525D3semidirect
86. #5524D3semidirect
94. C2×#634D4semidirect
222. #897C2×D3semidirect
224. #895C2×D3semidirect
225. #895C2×D3semidirect
244. #875C2×D3semidirect
245. #874C2×D3semidirect
246. C4×D12C2×D3semidirect
723. C32#3487semidirect
808. C3#86023semidirect
809. C3#86315semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C22×#37952
#105959872
C3×#55252
C3×#55242
#105950402
#105950222
#105945272
#105945252
#105941922
#105940822
#105939062
#105939052
#863153
#860233