Finite Group Databasebeta

← #11904429

Subgroups — #11904429

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
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C3×#5791C211yesmaximal, characteristic, complemented
5#10595524C214yesmaximal, complemented
6#10595070C214yesmaximal, complemented
7#10595067C214yesmaximal, complemented
8D3×#929C214yesmaximal, complemented
9#10594982C211yesmaximal, characteristic, complemented
10#10594890C214yesmaximal, complemented
11#10594887C214yesmaximal, complemented
12#10594866C211yesmaximal, characteristic, complemented
13#10594855C211yesmaximal, characteristic, complemented
14#87273—31nomaximal
15#86040—31nomaximal
16C23×C32×C4C2211yescharacteristic, complemented
17C2×#3828C2211yescharacteristic
18C22×C3×#67C2212yescomplemented
19C2×C3×#235—28no—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2214yescomplemented
22C2×C3×#235C2214yescomplemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2212yescomplemented
25C22×C3×Dic6C2211yescharacteristic, complemented
26C2×D3×#67C2214yes—
27#64307—28no—
28C2×#3802C2212yescomplemented
29C2×D3×D12C2212yescomplemented
30C2×#3796C2212yescomplemented
31C2×#3795C2212yescomplemented
32#64162C2212yescomplemented
33#64139C2212yescomplemented
34#64138C2212yescomplemented
35C4×#638C2214yescomplemented
36#64135C2211yescharacteristic, complemented
37#64133C2212yescomplemented
38C3×#953C2212yescomplemented
39C3×#930C2212yescomplemented
40C3×#929C2212yescomplemented
41C3×C4×#67C2214yescomplemented
42C3×#926C2211yescharacteristic, complemented
43C3×#924C2212yescomplemented
44#63983C2218yescomplemented
45#63971C2218yescomplemented
46#63970C2218yescomplemented
47#63969C2218yescomplemented
48D3×#217C2214yescomplemented
49#63966C2214yescomplemented
50#63961C2214yescomplemented
51D3×(C2×D3)⋊C4C2218yescomplemented
52#63905C2218yescomplemented
53#63898C2214yescomplemented
54Dic3×D12C2214yescomplemented
55D3×Dic3⋊C4C2218yescomplemented
56#63873C2212yescomplemented
57#63871C2214yescomplemented
58#63866C2212yescomplemented
59#63864C2212yescomplemented
60#63863C2212yescomplemented
61#63856C2214yescomplemented
62#63850C2218yescomplemented
63C22×C3×#41—31no—
64C2×#1009—31no—
65C2×#1004—31no—
66C22×#235D311yescharacteristic, complemented
67C3×#525—31no—
68#5829—34no—
69#5829—34no—
70#5825—31no—
71#5824—34no—
72#5824—34no—
73#5816—31no—
74#5816—31no—
75#5804—34no—
76#5798—31no—
77#5791—31no—
78#5791—31no—
79#5791—61no—
80#5791D311yescharacteristic, complemented
81C2×#929—34no—
82D3×#123—34no—
83#5631—34no—
84#5612—34no—
85#5589—34no—
86#5551—34no—
87#5550—34no—
88#5526—31no—
89#5521—31no—
90C24×C32C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×D32C2314yes—
93C22×C32×C4—24no—
94C22×C32×C4C2312yes—
95C22×C32×C4C2312yes—
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638C2312yes—
99C2×#638C2314yes—
100#3828—24no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3C2312yes—
103C2×#634C2311yescharacteristic
104C2×C3×#67—28no—
105C2×C3×#67C2312yes—
106C2×C3×#67C2318yes—
107C2×C3×#67C2314yes—
108C22×C3×Dic3C2312yes—
109C3×#235—24no—
110C3×#235—216no—
111C3×#235—216no—
112C2×C3×D12D418yescomplemented
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2312yes—
115C2×C3×D12C2312yes—
116C2×C3×C4×D3—28no—
117C2×C3×C4×D3C2312yes—
118C2×C3×C4×D3C2318yes—
119C2×C3×Dic6—24no—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2312yes—
122C2×C3×Dic6C2312yes—
123D3×#67—216no—
124C2×#626C2314yes—
125C2×#625C2314yes—
126C2×D3×Dic3C2314yes—
127C2×D3×Dic3C2318yes—
128#3802—28no—
129D3×D12—28no—
130#3796—28no—
131#3795—28no—
132#3757C2314yes—
133#3757C2312yes—
134#3752C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136#3750C2314yes—
137C4×C3⋊Dic3C2312yes—
138C3×#217C2314yes—
139C3×#217C2312yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×C4⋊Dic3C2312yes—
142C3×Dic3⋊C4C2314yes—
143C3×C4×Dic3C2312yes—
144#3724C2318yes—
145Dic3⋊Dic3C2318yes—
146#3722C2318yes—
147(C2×D3)⋊Dic3C2318yes—
148(C2×D3)⋊Dic3C2318yes—
149#3485—91noSylow
150C2×C3×#41—31no—
151C2×C3×#41—34no—
152C2×C3×#41—34no—
153C2×C3×#41—68no—
154C22×C3×Q8—31no—
155C22×C3×D4—32no—
156C22×C3×D4—31no—
157C23×C3×C4—21no—
158C23×C3×C4—32no—
159C23×C3×C4C2×D311yescharacteristic, complemented
160C23×C3×C4C2×D311yescharacteristic, complemented
161C22×#67—34no—
162C22×#67C2×D312yescomplemented
163#1009—68no—
164C2×#239—32no—
165#1004—68no—
166C2×#237—32no—
167C2×#237—32no—
168C2×D3×D4—34no—
169C2×D3×D4—32no—
170C2×D3×D4—32no—
171C2×D3×D4—32no—
172C2×#235—28no—
173C2×#235—31no—
174C2×#235—31no—
175C2×#235—32no—
176C2×#235—61no—
177C2×#235C2×D311yescharacteristic
178C2×#235C2×D314yescomplemented
179C2×#235C2×D314yescomplemented
180C22×D12—32no—
181C22×D12C2×D311yescharacteristic
182C22×C4×D3C2×D312yescomplemented
183C22×Dic6C2×D311yescharacteristic, complemented
184C3×#123—32no—
185C3×C22⋊Q8—32no—
186C3×#121—32no—
187C3×#120—32no—
188C3×C4×D4—34no—
189C3×#117—31no—
190#953—32no—
191#953—32no—
192#953—62no—
193#953C2×D312yescomplemented
194C2×#217—34no—
195#947—32no—
196#947—32no—
197#946—34no—
198#946—34no—
199#944—32no—
200#944—32no—
201#944—32no—
202#939—38no—
203#939—38no—
204#938—38no—
205#937—38no—
206#937—38no—
207#936—32no—
208#935—34no—
209#935—38no—
210D4×Dic3—34no—
211D4×Dic3—34no—
212#930—32no—
213#930—32no—
214#930—62no—
215#930C2×D312yescomplemented
216#929—32no—
217#929—32no—
218#929—34no—
219#929—34no—
220#929—38no—
221#929—38no—
222#929—62no—
223#929C2×D312yescomplemented
224C4×#67—34no—
225C4×#67—34no—
226C4×#67—64no—
227C4×#67C2×D314yescomplemented
228C2×(C2×D3)⋊C4—38no—
229#926—31no—
230#926—31no—
231#926—61no—
232#926C2×D311yescharacteristic, complemented
233#924—32no—
234#924—32no—
235#924—34no—
236#924—62no—
237#924C2×D312yescomplemented
238C2×Dic3⋊C4—38no—
239#897—34no—
240#894—38no—
241#893—34no—
242D3×C4⋊C4—38no—
243#886—34no—
244#884—38no—
245#883—38no—
246#883—38no—
247D3×C22⋊C4—34no—
248D3×C22⋊C4—38no—
249#875—32no—
250C4×D12—34no—
251#869—32no—
252C23×C32—22no—
253C23×C32—42no—
254C23×C32C2412yes—
255C23×C32C2411yescharacteristic
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×C4—22no—
264C2×C32×C4—24no—
265C2×C32×C4—24no—
266C2×C32×C4C2×D414yes—
267C2×C32×C4C2412yes—
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270#638—24no—
271#638—44no—
272C2×C3⋊Dic3C2414yes—
273C2×C3⋊Dic3C2412yes—
274C4⋊(C3⋊D3)—22no—
275C4×C3⋊D3—24no—
276#634—22no—
277C3×#67—24no—
278C3×#67—216no—
279C3×#67—44no—
280C2×C3×Dic3—24no—
281C2×C3×Dic3C2414yes—
282C2×C3×Dic3C2414yes—
283C2×C3×Dic3C2412yes—
284C3×D12—22no—
285C3×D12C2×D418yes—
286C3×D12C2×D418yes—
287C3×C4×D3—216no—
288C3×C4×D3—24no—
289C3×Dic6—22no—
290C3×Dic6—24no—
291C3×Dic6—24no—
292#626—28no—
293#625—28no—
294D3×Dic3—28no—
295D3×Dic3—48no—
296C2×H(5,𝔽2)—91no—
297C22×#41—31no—
298#547—94no—
299#547—94no—
300#546—94no—
301#546—94no—
302#536—91no—
303#536—91no—
304#534—94no—
305#525—31no—
306#525—91no—
307C2×#123—94no—
308#518—91no—
309C24×C3—21no—
310C24×C3—32no—
311C24×C3C22×D311yescharacteristic
312C24×C3C22×D311yescharacteristic
313C23×D3—34no—
314C23×D3—34no—
315C23×D3C22×D312yes—
316C3×#41—616no—
317C3×#41—616no—
318C3×#41—64no—
319C2×C3×Q8—31no—
320C2×C3×Q8—32no—
321C2×C3×Q8—32no—
322C2×C3×Q8—64no—
323C2×C3×D4—32no—
324C2×C3×D4—38no—
325C2×C3×D4—34no—
326C2×C3×D4—38no—
327C2×C3×D4—32no—
328C2×C3×D4—32no—
329C2×C3×D4—31no—
330C2×C3×D4—68no—
331C22×C3×C4—24no—
332C22×C3×C4—24no—
333C22×C3×C4—21no—
334C22×C3×C4—22no—
335C22×C3×C4—22no—
336C22×C3×C4—21no—
337C22×C3×C4—32no—
338C22×C3×C4—38no—
339C22×C3×C4—32no—
340C22×C3×C4—44no—
341C22×C3×C4—68no—
342C22×C3×C4C22×D312yes—
343C22×C3×C4C22×D312yes—
344C22×C3×C4C22×D312yes—
345C22×C3×C4C22×D312yes—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—28no—
351C2×#67—32no—
352C2×#67—32no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—64no—
359C2×#67—62no—
360C2×#67—616no—
361C2×#67C22×D318yes—
362C2×#67C22×D312yes—
363C2×#67C22×D314yes—
364C22×Dic3—34no—
365C22×Dic3—38no—
366C22×Dic3C22×D312yes—
367#239—68no—
368#237—68no—
369#237—68no—
370D3×D4—68no—
371D3×D4—68no—
372D3×D4—616no—
373D3×D4—68no—
374#235—24no—
375#235—216no—
376#235—216no—
377#235—64no—
378#235—64no—
379#235—68no—
380#235—124no—
381C2×D12—34no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—61no—
385C2×D12—68no—
386C2×D12#6718yescomplemented
387C2×D12C22×D311yescharacteristic
388C2×D12C22×D312yes—
389C2×D12C22×D312yes—
390C2×C4×D3—28no—
391C2×C4×D3—34no—
392C2×C4×D3—32no—
393C2×C4×D3—32no—
394C2×C4×D3—38no—
395C2×C4×D3—62no—
396C2×C4×D3C22×D318yes—
397C2×C4×D3C22×D312yes—
398C2×Dic6—24no—
399C2×Dic6—31no—
400C2×Dic6—31no—
401C2×Dic6—61no—
402C2×Dic6C22×D312yes—
403C2×Dic6C22×D312yes—
404C2×Dic6C22×D311yescharacteristic
405C3×C4⋊C4—34no—
406C3×C4⋊C4—32no—
407C3×C22⋊C4—32no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C42—32no—
411#217—32no—
412#217—34no—
413#217—34no—
414#217—32no—
415#217—38no—
416#217—38no—
417#217—64no—
418#217—62no—
419#217C22×D314yes—
420#217C22×D312yes—
421(C2×D3)⋊C4—38no—
422(C2×D3)⋊C4—38no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—38no—
426(C2×D3)⋊C4—38no—
427(C2×D3)⋊C4—64no—
428(C2×D3)⋊C4C22×D314yes—
429C4⋊Dic3—32no—
430C4⋊Dic3—32no—
431C4⋊Dic3—38no—
432C4⋊Dic3—62no—
433C4⋊Dic3C22×D312yes—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—38no—
437Dic3⋊C4—38no—
438Dic3⋊C4—38no—
439Dic3⋊C4—64no—
440Dic3⋊C4C22×D314yes—
441C4×Dic3—32no—
442C4×Dic3—32no—
443C4×Dic3—62no—
444C4×Dic3C22×D312yes—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—44no—
450C22×C32C22×D412yes—
451C22×C32C2511yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—24no—
454C2×C3×D3—28no—
455C2×C3×D3—22no—
456C2×C3×D3—24no—
457C2×C3×D3—48no—
458C2×C3×D3C22×D418yes—
459D32—88no—
460C32×C4—22no—
461C32×C4C22×D412yes—
462C32×C4C22×D412yes—
463C3⋊Dic3—22no—
464C3⋊Dic3—24no—
465C3×Dic3—22no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468H(5,𝔽2)—188no—
469C2×#41—31no—
470C2×#41—34no—
471C2×#41—34no—
472C2×#41—68no—
473C2×#41—92no—
474C2×#41—92no—
475C2×#41—91no—
476C22×Q8—31no—
477C22×D4—32no—
478C22×D4—31no—
479C22×D4—92no—
480C22×D4—92no—
481C22×D4—94no—
482C23×C4—32no—
483C23×C4D3211yescharacteristic, complemented
484C4⋊Q8—92no—
485C4⋊Q8—92no—
486#124—92no—
487#124—92no—
488#123—32no—
489#123—94no—
490#123—98no—
491#123—98no—
492#123—98no—
493#123—94no—
494#123—92no—
495C22⋊Q8—32no—
496C22⋊Q8—94no—
497C22⋊Q8—94no—
498C22⋊Q8—92no—
499#121—32no—
500#121—98no—
501#121—98no—
502#121—92no—
503#120—32no—
504#120—98no—
505#120—92no—
506C4×D4—34no—
507C4×D4—94no—
508C4×D4—94no—
509C4×D4—94no—
510#117—31no—
511#117—91no—
512C2×C4⋊C4—98no—
513C2×C22⋊C4—98no—
514C2×C22⋊C4—94no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—22no—
518C23×C3—21no—
519C23×C3—34no—
520C23×C3—38no—
521C23×C3—32no—
522C23×C3—42no—
523C23×C3—42no—
524C23×C3—42no—
525C23×C3—44no—
526C23×C3—124no—
527C23×C3C23×D312yes—
528C23×C3C23×D312yes—
529C23×C3C23×D311yescharacteristic
530C23×C3C23×D311yescharacteristic
531C22×D3—32no—
532C22×D3—32no—
533C22×D3—44no—
534C22×D3—62no—
535C22×D3—68no—
536C22×D3—68no—
537C22×D3—128no—
538C22×D3—128no—
539C22×D3C2×#6718yes—
540C22×D3C23×D312yes—
541C22×D3C23×D314yes—
542C3×Q8—64no—
543C3×Q8—64no—
544C3×Q8—62no—
545C3×D4—38no—
546C3×D4—38no—
547C3×D4—616no—
548C3×D4—64no—
549C3×D4—62no—
550C3×D4—124no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—24no—
554C2×C3×C4—24no—
555C2×C3×C4—24no—
556C2×C3×C4—24no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—24no—
561C2×C3×C4—34no—
562C2×C3×C4—32no—
563C2×C3×C4—34no—
564C2×C3×C4—44no—
565C2×C3×C4—44no—
566C2×C3×C4—42no—
567C2×C3×C4—616no—
568C2×C3×C4—64no—
569C2×C3×C4—64no—
570C2×C3×C4D3×D414yes—
571C2×C3×C4C2×#6714yes—
572C2×C3×C4C23×D312yes—
573C2×C3×C4C23×D312yes—
574C2×C3×C4C23×D311yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—24no—
579#67—216no—
580#67—44no—
581#67—68no—
582#67—68no—
583#67—64no—
584#67—64no—
585#67—68no—
586#67—124no—
587#67—124no—
588#67—124no—
589#67—128no—
590C2×Dic3—24no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—64no—
596C2×Dic3—62no—
597C2×Dic3—68no—
598C2×Dic3—128no—
599C2×Dic3C23×D314yes—
600C2×Dic3C23×D312yes—
601C2×Dic3C23×D314yes—
602D12—22no—
603D12—68no—
604D12—62no—
605D12—62no—
606D12—122no—
607D12C2×#6718yes—
608D12C2×#6718yes—
609C4×D3—216no—
610C4×D3—24no—
611C4×D3—68no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—124no—
615C4×D3—128no—
616Dic6—22no—
617Dic6—24no—
618Dic6—24no—
619Dic6—62no—
620Dic6—62no—
621Dic6—122no—
622C2×C32—22no—
623C2×C32—42no—
624C2×C32C23×D411yescharacteristic
625C2×C32#58512yes—
626C3⋊D3—42no—
627C3×D3—28no—
628C3×D3—42no—
629C24—32no—
630C24—94no—
631C24C2×D3211yescharacteristic
632#41—616no—
633#41—616no—
634#41—64no—
635#41—188no—
636#41—188no—
637#41—184no—
638C2×Q8—31no—
639C2×Q8—32no—
640C2×Q8—32no—
641C2×Q8—64no—
642C2×Q8—91no—
643C2×D4—32no—
644C2×D4—38no—
645C2×D4—34no—
646C2×D4—32no—
647C2×D4—32no—
648C2×D4—31no—
649C2×D4—38no—
650C2×D4—68no—
651C2×D4—94no—
652C2×D4—94no—
653C2×D4—92no—
654C2×D4—94no—
655C2×D4—91no—
656C2×D4—188no—
657C2×D4—188no—
658C2×D4—1816no—
659C22×C4—24no—
660C22×C4—32no—
661C22×C4—38no—
662C22×C4—32no—
663C22×C4—68no—
664C22×C4—94no—
665C22×C4—98no—
666C22×C4—92no—
667C22×C4C2×D3212yes—
668C22×C4C2×D3212yes—
669C22×C4C2×D3211yescharacteristic
670C22×C4C2×D3211yescharacteristic
671C4⋊C4—34no—
672C4⋊C4—32no—
673C4⋊C4—98no—
674C4⋊C4—98no—
675C4⋊C4—94no—
676C4⋊C4—92no—
677C22⋊C4—32no—
678C22⋊C4—34no—
679C22⋊C4—34no—
680C22⋊C4—98no—
681C22⋊C4—98no—
682C22⋊C4—98no—
683C22⋊C4—92no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C42—32no—
687C42—92no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—24no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—21no—
699C22×C3—38no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—48no—
706C22×C3—68no—
707C22×C3—64no—
708C22×C3—62no—
709C22×C3—128no—
710C22×C3C2×D3×D412yes—
711C22×C3C22×#6712yes—
712C22×C3C24×D311yescharacteristic
713C22×C3C24×D311yescharacteristic
714C2×D3—28no—
715C2×D3—22no—
716C2×D3—24no—
717C2×D3—48no—
718C2×D3—62no—
719C2×D3—64no—
720C2×D3—64no—
721C2×D3—62no—
722C2×D3—122no—
723C2×D3—124no—
724C2×D3—248no—
725C2×D3—248no—
726C2×D3C22×#6718yes—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—42no—
732C3×C4—64no—
733C3×C4—64no—
734C3×C4—62no—
735C3×C4C2×D3×D412yes—
736C3×C4C2×D3×D412yes—
737C3×C4C22×#6712yes—
738C3×C4C22×#6712yes—
739Dic3—22no—
740Dic3—24no—
741Dic3—24no—
742Dic3—62no—
743Dic3—64no—
744Dic3—64no—
745Dic3—62no—
746Dic3—122no—
747Dic3—124no—
748C32#348511yescharacteristic, complemented, Sylow
749C23—22no—
750C23—34no—
751C23—38no—
752C23—32no—
753C23—42no—
754C23—92no—
755C23—124no—
756C23—188no—
757C23—368no—
758C23C22×D3212yes—
759C23C22×D3211yescharacteristic
760Q8—64no—
761Q8—64no—
762Q8—62no—
763Q8—182no—
764D4—38no—
765D4—38no—
766D4—616no—
767D4—64no—
768D4—62no—
769D4—124no—
770D4—188no—
771D4—188no—
772D4—184no—
773D4—182no—
774D4—364no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—34no—
779C2×C4—32no—
780C2×C4—34no—
781C2×C4—616no—
782C2×C4—64no—
783C2×C4—64no—
784C2×C4—94no—
785C2×C4—92no—
786C2×C4—188no—
787C2×C4—184no—
788C2×C4—368no—
789C2×C4D3×#6714yes—
790C2×C4C22×D3212yes—
791C2×C4C22×D3211yescharacteristic
792C2×C4C22×D3211yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—22no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—44no—
799C2×C3—42no—
800C2×C3—42no—
801C2×C3—68no—
802C2×C3—122no—
803C2×C3C22×D3×D411yescharacteristic
804C2×C3#596412yes—
805C2×C3#596412yes—
806C2×C3C23×#6711yescharacteristic
807D3—28no—
808D3—42no—
809D3—122no—
810D3—122no—
811D3—242no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—38no—
817C22—44no—
818C22—68no—
819C22—64no—
820C22—62no—
821C22—128no—
822C22—184no—
823C22—182no—
824C22—728no—
825C22C2×D3×#6712yes—
826C22C23×D3211yescharacteristic
827C4—22no—
828C4—64no—
829C4—64no—
830C4—62no—
831C4—184no—
832C4—182no—
833C4C2×D3×#6712yes—
834C4C2×D3×#6712yes—
835C3—21no—
836C3#8604011yescharacteristic, complemented
837C3#8727311yescharacteristic, complemented
838C2—22no—
839C2—42no—
840C2—68no—
841C2—122no—
842C2—362no—
843C2#1059666912yes—
844C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×#64307C2semidirect
3. #10596262C2semidirect
4. C3×#5791C2semidirect
5. #10595524C2semidirect
6. #10595070C2semidirect
7. #10595067C2semidirect
8. D3×#929C2semidirect
9. #10594982C2semidirect
10. #10594890C2semidirect
11. #10594887C2semidirect
12. #10594866C2semidirect
13. #10594855C2semidirect
16. C23×C32×C4C22semidirect
18. C22×C3×#67C22semidirect
21. C2×C3×#235C22semidirect
22. C2×C3×#235C22semidirect
24. C22×C3×C4×D3C22semidirect
25. C22×C3×Dic6C22semidirect
28. C2×#3802C22semidirect
29. C2×D3×D12C22semidirect
30. C2×#3796C22semidirect
31. C2×#3795C22semidirect
32. #64162C22semidirect
33. #64139C22semidirect
34. #64138C22semidirect
35. C4×#638C22semidirect
36. #64135C22semidirect
37. #64133C22semidirect
38. C3×#953C22semidirect
39. C3×#930C22semidirect
40. C3×#929C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#926C22semidirect
43. C3×#924C22semidirect
44. #63983C22semidirect
45. #63971C22semidirect
46. #63970C22semidirect
47. #63969C22semidirect
48. D3×#217C22semidirect
49. #63966C22semidirect
50. #63961C22semidirect
51. D3×(C2×D3)⋊C4C22semidirect
52. #63905C22semidirect
53. #63898C22semidirect
54. Dic3×D12C22semidirect
55. D3×Dic3⋊C4C22semidirect
56. #63873C22semidirect
57. #63871C22semidirect
58. #63866C22semidirect
59. #63864C22semidirect
60. #63863C22semidirect
61. #63856C22semidirect
62. #63850C22semidirect
66. C22×#235D3semidirect
80. #5791D3semidirect
112. C2×C3×D12D4semidirect
159. C23×C3×C4C2×D3semidirect
160. C23×C3×C4C2×D3semidirect
162. C22×#67C2×D3semidirect
178. C2×#235C2×D3semidirect
179. C2×#235C2×D3semidirect
182. C22×C4×D3C2×D3semidirect
183. C22×Dic6C2×D3semidirect
193. #953C2×D3semidirect
215. #930C2×D3semidirect
223. #929C2×D3semidirect
227. C4×#67C2×D3semidirect
232. #926C2×D3semidirect
237. #924C2×D3semidirect
386. C2×D12#67semidirect
483. C23×C4D32semidirect
748. C32#3485semidirect
836. C3#86040semidirect
837. C3#87273semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#643072
#105962622
C3×#57912
#105955242
#105950702
#105950672
D3×#9292
#105949822
#105948902
#105948872
#105948662
#105948552
#872733
#860403