Finite Group Databasebeta

← #11904573

Subgroups — #11904573

Order 1152.

3237 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C3×#5791C211yesmaximal, characteristic, complemented
5#10595513C214yesmaximal, complemented
6#10595042C211yesmaximal, characteristic, complemented
7#10595040C211yesmaximal, characteristic, complemented
8#10595007C214yesmaximal, complemented
9#10595006C214yesmaximal, complemented
10#10594899C214yesmaximal, complemented
11#10594896C214yesmaximal, complemented
12#10594830C214yesmaximal, complemented
13#10594818C211yesmaximal, characteristic, complemented
14#87274—31nomaximal
15#86023—31nomaximal
16C23×C32×C4C2211yescharacteristic
17C2×#3828C2211yescharacteristic
18C22×C3×#67C2212yes—
19C2×C3×#235—28no—
20C2×C3×#235C2214yes—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2214yes—
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2212yes—
25C22×C3×Dic6C2211yescharacteristic
26C2×#3804C2214yes—
27C2×#3799C2212yescomplemented
28C2×#3797C2212yescomplemented
29#64297—28no—
30C2×#3796C2212yescomplemented
31C2×D3×Dic6C2212yescomplemented
32#64162C2212yes—
33#64139C2212yescomplemented
34#64138C2212yes—
35C4×#638C2214yescomplemented
36#64135C2211yescharacteristic
37#64133C2212yescomplemented
38C3×#953C2212yes—
39C3×#930C2212yescomplemented
40C3×#929C2212yes—
41C3×C4×#67C2214yescomplemented
42C3×#926C2211yescharacteristic
43C3×#924C2212yescomplemented
44#63979C2218yescomplemented
45#63977C2214yes—
46#63976C2214yes—
47#63970C2218yescomplemented
48#63959C2218yescomplemented
49#63958C2218yescomplemented
50#63955C2214yes—
51#63916C2214yescomplemented
52#63914C2212yescomplemented
53#63911C2212yescomplemented
54#63908C2214yescomplemented
55#63906C2218yescomplemented
56#63904C2218yescomplemented
57#63879C2218yescomplemented
58#63863C2212yescomplemented
59#63860C2212yescomplemented
60#63851C2218yescomplemented
61#63843C2214yescomplemented
62Dic3×Dic6C2214yescomplemented
63C22×C3×#41—31no—
64C2×#1010—31no—
65C2×#1007—31no—
66C22×#235D311yescharacteristic, complemented
67C3×#525—31no—
68#5834—34no—
69#5834—34no—
70#5831—34no—
71#5831—34no—
72#5830—31no—
73#5812—31no—
74#5805—31no—
75#5805—34no—
76#5805—31no—
77#5791—31no—
78#5791—31no—
79#5791—34no—
80#5791—61no—
81#5791D311yescharacteristic, complemented
82#5656—34no—
83#5633—34no—
84#5599—34no—
85#5592—34no—
86#5553—34no—
87#5552—34no—
88#5525—31no—
89#5516—31no—
90C24×C32C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×C32×C4—24no—
93C22×C32×C4C2312yes—
94C22×C32×C4C2312yes—
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638C2312yes—
98C2×#638C2314yes—
99#3828—24no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3C2312yes—
102C2×#634C2311yescharacteristic
103C2×C3×#67—28no—
104C2×C3×#67C2312yes—
105C2×C3×#67C2318yes—
106C2×C3×#67C2314yes—
107C22×C3×Dic3C2312yes—
108C3×#235—24no—
109C3×#235—216no—
110C3×#235—216no—
111C2×C3×D12—24no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2312yes—
114C2×C3×D12C2312yes—
115C2×C3×C4×D3—28no—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2318yes—
118C2×C3×Dic6D418yescomplemented
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2312yes—
122C2×#627C2314yes—
123C2×#626C2314yes—
124C2×#626C2318yes—
125C2×#625C2318yes—
126C2×#624C2314yes—
127#3804—216no—
128C2×D3×Dic3C2314yes—
129#3799—28no—
130#3797—28no—
131#3796—28no—
132D3×Dic6—28no—
133#3757C2314yes—
134#3757C2312yes—
135#3752C2314yes—
136C4⋊(C3⋊Dic3)C2312yes—
137#3750C2314yes—
138C4×C3⋊Dic3C2312yes—
139C3×#217C2314yes—
140C3×#217C2312yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×C4⋊Dic3C2312yes—
143C3×Dic3⋊C4C2314yes—
144C3×C4×Dic3C2312yes—
145Dic3⋊Dic3C2318yes—
146(C2×D3)⋊Dic3C2318yes—
147(C2×D3)⋊Dic3C2318yes—
148Dic32C2318yes—
149#3487—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
160C23×C3×C4C2×D311yescharacteristic
161C22×#67C2×D312yes—
162#1010—68no—
163#1007—68no—
164C2×#239—32no—
165C2×#239—32no—
166C2×D3×Q8—32no—
167C2×D3×Q8—32no—
168C2×D3×Q8—32no—
169C2×#237—34no—
170C2×#237—32no—
171C2×#235—28no—
172C2×#235—31no—
173C2×#235—31no—
174C2×#235—34no—
175C2×#235—32no—
176C2×#235—61no—
177C2×#235C2×D314yes—
178C2×#235C2×D314yes—
179C2×#235C2×D311yescharacteristic
180C22×D12C2×D311yescharacteristic
181C22×C4×D3C2×D312yes—
182C22×Dic6—32no—
183C22×Dic6C2×D311yescharacteristic
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—34no—
193#953—34no—
194#953—62no—
195#953C2×D312yes—
196#947—32no—
197Q8×Dic3—34no—
198Q8×Dic3—34no—
199#940—38no—
200#940—38no—
201#940—32no—
202#940—32no—
203#940—32no—
204#939—38no—
205#938—38no—
206#938—34no—
207#938—38no—
208#938—34no—
209#937—34no—
210#936—32no—
211#936—38no—
212#936—32no—
213#930—32no—
214#930—32no—
215#930—34no—
216#930—38no—
217#930—62no—
218#930C2×D312yescomplemented
219#929—32no—
220#929—32no—
221#929—62no—
222#929C2×D312yes—
223C4×#67—34no—
224C4×#67—34no—
225C4×#67—38no—
226C4×#67—38no—
227C4×#67—64no—
228C4×#67C2×D314yescomplemented
229#926—31no—
230#926—31no—
231#926—34no—
232#926—61no—
233#926C2×D311yescharacteristic
234#924—32no—
235#924—32no—
236#924—38no—
237#924—62no—
238#924C2×D312yescomplemented
239#896—38no—
240#895—34no—
241#893—38no—
242#887—34no—
243#885—38no—
244#884—38no—
245#884—38no—
246#882—34no—
247#67⋊C4—38no—
248#877—34no—
249#875—32no—
250#874—32no—
251C4×Dic6—34no—
252C23×C32—22no—
253C23×C32—42no—
254C23×C32C2412yes—
255C23×C32C2411yescharacteristic
256C22×C3⋊D3C2412yes—
257C22×C3×D3—24no—
258C22×C3×D3—44no—
259C22×C3×D3C2414yes—
260C22×C3×D3C2412yes—
261C2×C32×C4—22no—
262C2×C32×C4—24no—
263C2×C32×C4—24no—
264C2×C32×C4C2×D414yes—
265C2×C32×C4C2412yes—
266C2×C32×C4C2411yescharacteristic
267C2×C32×C4C2411yescharacteristic
268#638—24no—
269#638—44no—
270C2×C3⋊Dic3C2414yes—
271C2×C3⋊Dic3C2412yes—
272C4⋊(C3⋊D3)—22no—
273C4×C3⋊D3—24no—
274#634—22no—
275C3×#67—24no—
276C3×#67—216no—
277C3×#67—44no—
278C2×C3×Dic3C2×D418yes—
279C2×C3×Dic3C2414yes—
280C2×C3×Dic3C2412yes—
281C2×C3×Dic3C2414yes—
282C3×D12—22no—
283C3×D12—24no—
284C3×D12—24no—
285C3×C4×D3—24no—
286C3×C4×D3—216no—
287C3×Dic6—22no—
288C3×Dic6C2×D418yes—
289C3×Dic6C2×D418yes—
290#627—28no—
291#626—28no—
292#626—48no—
293#625—48no—
294#624—28no—
295D3×Dic3—28no—
296C2×2−1+4—91no—
297C22×#41—31no—
298#550—94no—
299#550—94no—
300#548—94no—
301#548—94no—
302#535—91no—
303#535—94no—
304#535—91no—
305#525—31no—
306#525—94no—
307#525—91no—
308#519—91no—
309C24×C3—21no—
310C24×C3—32no—
311C24×C3C22×D311yescharacteristic
312C24×C3C22×D311yescharacteristic
313C23×D3C22×D312yes—
314C3×#41—616no—
315C3×#41—616no—
316C3×#41—64no—
317C2×C3×Q8—38no—
318C2×C3×Q8—32no—
319C2×C3×Q8—32no—
320C2×C3×Q8—31no—
321C2×C3×D4—38no—
322C2×C3×D4—32no—
323C2×C3×D4—34no—
324C2×C3×D4—32no—
325C2×C3×D4—32no—
326C2×C3×D4—31no—
327C2×C3×D4—68no—
328C2×C3×D4—64no—
329C22×C3×C4—24no—
330C22×C3×C4—24no—
331C22×C3×C4—21no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—21no—
335C22×C3×C4—32no—
336C22×C3×C4—38no—
337C22×C3×C4—32no—
338C22×C3×C4—44no—
339C22×C3×C4—68no—
340C22×C3×C4C22×D312yes—
341C22×C3×C4C22×D312yes—
342C22×C3×C4C22×D312yes—
343C22×C3×C4C22×D312yes—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—28no—
349C2×#67—32no—
350C2×#67—32no—
351C2×#67—34no—
352C2×#67—34no—
353C2×#67—38no—
354C2×#67—38no—
355C2×#67—34no—
356C2×#67—38no—
357C2×#67—64no—
358C2×#67—62no—
359C2×#67C22×D318yes—
360C2×#67C22×D312yes—
361C2×#67C22×D314yes—
362C22×Dic3—34no—
363C22×Dic3C22×D312yes—
364#239—68no—
365#239—68no—
366D3×Q8—68no—
367D3×Q8—68no—
368D3×Q8—68no—
369#237—616no—
370#237—68no—
371#235—24no—
372#235—216no—
373#235—216no—
374#235—616no—
375#235—64no—
376#235—64no—
377#235—68no—
378#235—124no—
379C2×D12—24no—
380C2×D12—34no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—38no—
384C2×D12—61no—
385C2×D12C22×D312yes—
386C2×D12C22×D312yes—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—28no—
389C2×C4×D3—34no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—62no—
395C2×C4×D3C22×D318yes—
396C2×C4×D3C22×D312yes—
397C2×Dic6—31no—
398C2×Dic6—31no—
399C2×Dic6—34no—
400C2×Dic6—34no—
401C2×Dic6—61no—
402C2×Dic6—68no—
403C2×Dic6#6718yescomplemented
404C2×Dic6C22×D311yescharacteristic
405C2×Dic6C22×D312yes—
406C2×Dic6C22×D312yes—
407C3×C4⋊C4—32no—
408C3×C4⋊C4—34no—
409C3×C22⋊C4—32no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C42—32no—
413#217—32no—
414#217—34no—
415#217—34no—
416#217—32no—
417#217—38no—
418#217—38no—
419#217—64no—
420#217—62no—
421#217C22×D314yes—
422#217C22×D312yes—
423(C2×D3)⋊C4—38no—
424(C2×D3)⋊C4—38no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
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—64no—
438Dic3⋊C4C22×D314yes—
439C4×Dic3—32no—
440C4×Dic3—32no—
441C4×Dic3—38no—
442C4×Dic3—38no—
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—22no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—28no—
458C2×C3×D3—48no—
459C32×C4—22no—
460C32×C4C22×D412yes—
461C32×C4C22×D412yes—
462C3⋊Dic3—22no—
463C3⋊Dic3—24no—
464C3×Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3C22×D418yes—
4672−1+4—188no—
468C2×#41—31no—
469C2×#41—34no—
470C2×#41—34no—
471C2×#41—68no—
472C2×#41—94no—
473C2×#41—92no—
474C2×#41—92no—
475C2×#41—91no—
476C22×Q8—31no—
477C22×Q8—92no—
478C22×Q8—92no—
479C22×D4—32no—
480C22×D4—31no—
481C23×C4—32no—
482C23×C4D3211yescharacteristic
483#127—92no—
484#127—98no—
485#127—92no—
486#124—92no—
487#124—98no—
488#124—92no—
489#123—32no—
490#123—92no—
491C22⋊Q8—32no—
492C22⋊Q8—98no—
493C22⋊Q8—92no—
494#121—32no—
495#121—98no—
496#121—98no—
497#121—94no—
498#121—94no—
499#121—98no—
500#121—92no—
501#120—32no—
502#120—94no—
503#120—94no—
504#120—92no—
505C4×Q8—94no—
506C4×Q8—94no—
507C4×D4—34no—
508C4×D4—98no—
509C4×D4—98no—
510C4×D4—94no—
511#117—31no—
512#117—94no—
513#117—91no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—21no—
518C23×C3—34no—
519C23×C3—32no—
520C23×C3—42no—
521C23×C3—42no—
522C23×C3—42no—
523C23×C3—44no—
524C23×C3—64no—
525C23×C3—124no—
526C23×C3C23×D312yes—
527C23×C3C23×D312yes—
528C23×C3C23×D311yescharacteristic
529C23×C3C23×D311yescharacteristic
530C22×D3—24no—
531C22×D3—32no—
532C22×D3—32no—
533C22×D3—44no—
534C22×D3—62no—
535C22×D3C23×D314yes—
536C22×D3C23×D312yes—
537C3×Q8—38no—
538C3×Q8—38no—
539C3×Q8—62no—
540C3×D4—616no—
541C3×D4—64no—
542C3×D4—64no—
543C3×D4—64no—
544C3×D4—62no—
545C3×D4—124no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—24no—
549C2×C3×C4—24no—
550C2×C3×C4—24no—
551C2×C3×C4—24no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—22no—
555C2×C3×C4—24no—
556C2×C3×C4—38no—
557C2×C3×C4—34no—
558C2×C3×C4—34no—
559C2×C3×C4—32no—
560C2×C3×C4—44no—
561C2×C3×C4—44no—
562C2×C3×C4—42no—
563C2×C3×C4—616no—
564C2×C3×C4—64no—
565C2×C3×C4D3×D414yes—
566C2×C3×C4C2×#6714yes—
567C2×C3×C4C23×D312yes—
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—24no—
574#67—216no—
575#67—44no—
576#67—64no—
577#67—64no—
578#67—68no—
579#67—124no—
580#67—128no—
581#67—128no—
582#67—128no—
583#67—124no—
584#67—124no—
585#67—128no—
586C2×Dic3—34no—
587C2×Dic3—34no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—64no—
591C2×Dic3—62no—
592C2×Dic3—68no—
593C2×Dic3C2×#6718yes—
594C2×Dic3C23×D314yes—
595C2×Dic3C23×D312yes—
596C2×Dic3C23×D314yes—
597D12—22no—
598D12—24no—
599D12—24no—
600D12—68no—
601D12—62no—
602D12—62no—
603D12—122no—
604D12—128no—
605C4×D3—24no—
606C4×D3—216no—
607C4×D3—68no—
608C4×D3—68no—
609C4×D3—64no—
610C4×D3—64no—
611C4×D3—68no—
612C4×D3—124no—
613Dic6—22no—
614Dic6—68no—
615Dic6—62no—
616Dic6—62no—
617Dic6—68no—
618Dic6—122no—
619Dic6C2×#6718yes—
620Dic6C2×#6718yes—
621C2×C32—22no—
622C2×C32—42no—
623C2×C32C23×D411yescharacteristic
624C2×C32#58512yes—
625C3⋊D3—42no—
626C3×D3—42no—
627C3×D3—44no—
628C24—32no—
629C24C2×D3211yescharacteristic
630#41—616no—
631#41—616no—
632#41—64no—
633#41—1816no—
634#41—188no—
635#41—188no—
636#41—184no—
637C2×Q8—32no—
638C2×Q8—32no—
639C2×Q8—31no—
640C2×Q8—38no—
641C2×Q8—94no—
642C2×Q8—91no—
643C2×Q8—188no—
644C2×Q8—188no—
645C2×D4—32no—
646C2×D4—38no—
647C2×D4—34no—
648C2×D4—31no—
649C2×D4—32no—
650C2×D4—32no—
651C2×D4—68no—
652C2×D4—64no—
653C2×D4—94no—
654C2×D4—98no—
655C2×D4—92no—
656C2×D4—98no—
657C2×D4—94no—
658C2×D4—91no—
659C22×C4—24no—
660C22×C4—32no—
661C22×C4—32no—
662C22×C4—38no—
663C22×C4—68no—
664C22×C4—94no—
665C22×C4—94no—
666C22×C4—92no—
667C22×C4C2×D3212yes—
668C22×C4C2×D3212yes—
669C22×C4C2×D3211yescharacteristic
670C22×C4C2×D3211yescharacteristic
671C4⋊C4—32no—
672C4⋊C4—34no—
673C4⋊C4—98no—
674C4⋊C4—92no—
675C4⋊C4—94no—
676C22⋊C4—32no—
677C22⋊C4—34no—
678C22⋊C4—34no—
679C22⋊C4—98no—
680C22⋊C4—98no—
681C22⋊C4—92no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C42—32no—
685C42—98no—
686C42—92no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—21no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—44no—
702C22×C3—44no—
703C22×C3—48no—
704C22×C3—64no—
705C22×C3—64no—
706C22×C3—68no—
707C22×C3—62no—
708C22×C3—128no—
709C22×C3C2×D3×D412yes—
710C22×C3C22×#6712yes—
711C22×C3C24×D311yescharacteristic
712C22×C3C24×D311yescharacteristic
713C2×D3—22no—
714C2×D3—28no—
715C2×D3—24no—
716C2×D3—24no—
717C2×D3—48no—
718C2×D3—62no—
719C2×D3—64no—
720C2×D3—64no—
721C2×D3—62no—
722C2×D3—122no—
723C2×D3—124no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—38no—
729C3×C4—42no—
730C3×C4—64no—
731C3×C4—62no—
732C3×C4C2×D3×D412yes—
733C3×C4C2×D3×D412yes—
734C3×C4C22×#6712yes—
735C3×C4C22×#6712yes—
736Dic3—22no—
737Dic3—24no—
738Dic3—62no—
739Dic3—64no—
740Dic3—64no—
741Dic3—62no—
742Dic3—122no—
743Dic3—124no—
744Dic3C22×#6718yes—
745C32#348711yescharacteristic, complemented, Sylow
746C23—22no—
747C23—32no—
748C23—34no—
749C23—42no—
750C23—64no—
751C23—92no—
752C23—124no—
753C23C22×D3212yes—
754C23C22×D3211yescharacteristic
755Q8—38no—
756Q8—38no—
757Q8—62no—
758Q8—188no—
759Q8—182no—
760D4—616no—
761D4—64no—
762D4—64no—
763D4—64no—
764D4—62no—
765D4—124no—
766D4—188no—
767D4—184no—
768D4—182no—
769D4—368no—
770D4—364no—
771D4—368no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—38no—
776C2×C4—34no—
777C2×C4—34no—
778C2×C4—32no—
779C2×C4—616no—
780C2×C4—64no—
781C2×C4—94no—
782C2×C4—92no—
783C2×C4—188no—
784C2×C4—188no—
785C2×C4—184no—
786C2×C4D3×#6714yes—
787C2×C4C22×D3212yes—
788C2×C4C22×D3211yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C2×C3—22no—
791C2×C3—22no—
792C2×C3—22no—
793C2×C3—21no—
794C2×C3—42no—
795C2×C3—44no—
796C2×C3—42no—
797C2×C3—42no—
798C2×C3—124no—
799C2×C3—122no—
800C2×C3C22×D3×D411yescharacteristic
801C2×C3#596412yes—
802C2×C3#596412yes—
803C2×C3C23×#6711yescharacteristic
804D3—42no—
805D3—44no—
806D3—122no—
807D3—122no—
808D3—242no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—44no—
814C22—64no—
815C22—68no—
816C22—64no—
817C22—62no—
818C22—128no—
819C22—184no—
820C22—182no—
821C22C2×D3×#6712yes—
822C22C23×D3211yescharacteristic
823C4—22no—
824C4—38no—
825C4—64no—
826C4—62no—
827C4—184no—
828C4—182no—
829C4C2×D3×#6712yes—
830C4C2×D3×#6712yes—
831C3—21no—
832C3#8602311yescharacteristic, complemented
833C3#8727411yescharacteristic, complemented
834C2—22no—
835C2—42no—
836C2—124no—
837C2—122no—
838C2—362no—
839C2#1059666912yes—
840C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3487
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×#64297C2semidirect
3. #10596262C2semidirect
4. C3×#5791C2semidirect
5. #10595513C2semidirect
6. #10595042C2semidirect
7. #10595040C2semidirect
8. #10595007C2semidirect
9. #10595006C2semidirect
10. #10594899C2semidirect
11. #10594896C2semidirect
12. #10594830C2semidirect
13. #10594818C2semidirect
27. C2×#3799C22semidirect
28. C2×#3797C22semidirect
30. C2×#3796C22semidirect
31. C2×D3×Dic6C22semidirect
33. #64139C22semidirect
35. C4×#638C22semidirect
37. #64133C22semidirect
39. C3×#930C22semidirect
41. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
44. #63979C22semidirect
47. #63970C22semidirect
48. #63959C22semidirect
49. #63958C22semidirect
51. #63916C22semidirect
52. #63914C22semidirect
53. #63911C22semidirect
54. #63908C22semidirect
55. #63906C22semidirect
56. #63904C22semidirect
57. #63879C22semidirect
58. #63863C22semidirect
59. #63860C22semidirect
60. #63851C22semidirect
61. #63843C22semidirect
62. Dic3×Dic6C22semidirect
66. C22×#235D3semidirect
81. #5791D3semidirect
118. C2×C3×Dic6D4semidirect
218. #930C2×D3semidirect
228. C4×#67C2×D3semidirect
238. #924C2×D3semidirect
403. C2×Dic6#67semidirect
745. C32#3487semidirect
832. C3#86023semidirect
833. C3#87274semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#642972
#105962622
C3×#57912
#105955132
#105950422
#105950402
#105950072
#105950062
#105948992
#105948962
#105948302
#105948182
#872743
#860233