Finite Group Databasebeta

← #11904441

Subgroups — #11904441

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
1C2×C3×#1009C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3#10596296C211yesmaximal, characteristic, complemented
4C3×#5828C211yesmaximal, characteristic, complemented
5#10595357C214yesmaximal, complemented
6#10595230C214yesmaximal, complemented
7#10595228C214yesmaximal, complemented
8D3×#935C214yesmaximal, complemented
9#10595022C211yesmaximal, characteristic, complemented
10#10594982C211yesmaximal, characteristic, complemented
11#10594887C214yesmaximal, complemented
12#10594886C214yesmaximal, complemented
13#10594856C211yesmaximal, characteristic, complemented
14#87280—31nomaximal
15#86040—31nomaximal
16C2×C32×#41C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C3×#1009—28no—
19C2×C3×#239C2212yescomplemented
20C2×C3×D3×D4C2214yes—
21C2×C3×D3×D4C2212yescomplemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2212yescomplemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2212yescomplemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#625C2212yescomplemented
28C22×D3×Dic3C2212yescomplemented
29C2×#3795—28no—
30C2×#3795C2214yescomplemented
31C2×#3795C2214yescomplemented
32#64153C2212yescomplemented
33#64145C2212yescomplemented
34#64144C2214yescomplemented
35#64135C2211yescharacteristic, complemented
36#64133C2214yescomplemented
37C3×#946C2212yescomplemented
38C3×#938C2212yescomplemented
39C3×#937C2212yescomplemented
40C3×#935C2212yescomplemented
41C3×C4×#67C2214yescomplemented
42C3×#926C2211yescharacteristic, complemented
43#63976C2218yescomplemented
44#63976C2212yescomplemented
45#63970C2218yescomplemented
46#63969C2218yescomplemented
47D3×#217C2218yescomplemented
48D3×#217C2214yescomplemented
49#63962C2214yescomplemented
50#63961C2212yescomplemented
51#63908C2212yescomplemented
52#63905C2218yescomplemented
53C4×#625C2214yescomplemented
54#63898C2214yescomplemented
55Dic3×D12C2214yescomplemented
56#63885C2218yescomplemented
57#63884C2218yescomplemented
58D3×Dic3⋊C4C2218yescomplemented
59#63866C2212yescomplemented
60#63860C2212yescomplemented
61#63857C2214yescomplemented
62#63856C2212yescomplemented
63C2×C3×H(5,𝔽2)—31no—
64C2×#1009D311yescharacteristic, complemented
65C22×#237—31no—
66C22×#235—31no—
67C3×#525—31no—
68#5828—31no—
69#5828D311yescharacteristic, complemented
70#5825—31no—
71#5825—31no—
72#5825—31no—
73#5825—61no—
74#5824—34no—
75#5824—34no—
76#5806—34no—
77#5806—34no—
78#5804—34no—
79#5798—31no—
80C2×#935—34no—
81#5791—31no—
82D3×#123—34no—
83#5631—34no—
84#5612—34no—
85#5589—34no—
86#5551—34no—
87#5550—34no—
88#5526—31no—
89#5521—31no—
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2314yes—
92C23×C3×D3C2312yes—
93C32×#41—24no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2312yes—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2312yes—
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3C2312yes—
100C2×#634—24no—
101C2×#634C2312yes—
102C2×#634C2312yes—
103C2×C3×#67C2312yes—
104C2×C3×#67C2314yes—
105C2×C3×#67C2314yes—
106C22×C3×Dic3C2311yescharacteristic
107C3×#239—28no—
108C3×D3×D4—216no—
109C3×D3×D4—28no—
110C3×#235—24no—
111C3×#235—28no—
112C2×C3×D12—28no—
113C2×C3×D12D418yescomplemented
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2314yes—
116C2×C3×D12C2312yes—
117C2×C3×D12C2312yes—
118C2×C3×C4×D3—24no—
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2312yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2314yes—
123C2×C3×Dic6C2311yescharacteristic
124C2×#625—28no—
125C2×#625C2318yes—
126C2×#625C2314yes—
127C2×D3×Dic3—28no—
128C2×D3×Dic3C2318yes—
129C2×D3×Dic3C2318yes—
130#3795—216no—
131#3795—216no—
132#3757C2318yes—
133#3757C2312yes—
134C4⋊(C3⋊Dic3)C2312yes—
135#3750C2318yes—
136C4×C3⋊Dic3C2312yes—
137C3×#217C2312yes—
138C3×#217C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×C4⋊Dic3C2312yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2312yes—
143#3724C2314yes—
144Dic3⋊Dic3C2318yes—
145(C2×D3)⋊Dic3C2314yes—
146(C2×D3)⋊Dic3C2318yes—
147(C2×D3)⋊Dic3C2314yes—
148(C2×D3)⋊Dic3C2318yes—
149#3485—91noSylow
150C3×H(5,𝔽2)—68no—
151C2×C3×#41—21no—
152C2×C3×#41—32no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41C2×D311yescharacteristic
156C2×C3×#41C2×D311yescharacteristic
157C22×C3×D4—34no—
158C22×C3×D4—32no—
159C22×C3×D4—31no—
160C22×C3×D4—32no—
161C23×C3×C4—31no—
162C22×#67—32no—
163C22×#67—32no—
164C23×Dic3—32no—
165#1009—28no—
166C2×#239C2×D312yescomplemented
167C2×#237—34no—
168C2×#237—34no—
169C2×#237—68no—
170C2×D3×D4C2×D314yes—
171C2×D3×D4C2×D312yescomplemented
172C2×#235—34no—
173C2×#235—34no—
174C2×#235—68no—
175C2×#235C2×D311yescharacteristic
176C2×#235C2×D312yescomplemented
177C22×D12C2×D311yescharacteristic
178C22×D12C2×D312yescomplemented
179C22×C4×D3—32no—
180C22×C4×D3C2×D311yescharacteristic, complemented
181C22×Dic6—31no—
182C22×Dic6—31no—
183C22×Dic6—61no—
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—38no—
192C2×#217—34no—
193C2×#217—38no—
194#946—32no—
195#946C2×D312yescomplemented
196#944—32no—
197#944—32no—
198#944—32no—
199#944—62no—
200#939—38no—
201#939—38no—
202#938—38no—
203#938—32no—
204#938C2×D312yescomplemented
205#937—32no—
206#937—38no—
207#937C2×D312yescomplemented
208#936—32no—
209#936—32no—
210#936—32no—
211#936—62no—
212#935—34no—
213#935—34no—
214#935—32no—
215#935—34no—
216#935—38no—
217#935—38no—
218#935—64no—
219#935C2×D312yescomplemented
220D4×Dic3—34no—
221D4×Dic3—34no—
222#930—32no—
223#929—32no—
224#929—38no—
225C4×#67—34no—
226C4×#67—34no—
227C4×#67C2×D314yescomplemented
228#926—31no—
229#926—31no—
230#926—61no—
231#926C2×D311yescharacteristic, complemented
232#924—34no—
233#924—34no—
234#924—32no—
235#924—34no—
236#924—64no—
237C2×Dic3⋊C4—38no—
238#897—34no—
239#894—38no—
240#893—34no—
241D3×C4⋊C4—38no—
242#886—34no—
243#884—38no—
244#883—38no—
245#883—38no—
246D3×C22⋊C4—34no—
247D3×C22⋊C4—38no—
248#875—32no—
249C4×D12—34no—
250#869—32no—
251C23×C32C2412yes—
252C23×C32C2411yescharacteristic
253C22×C3×D3—22no—
254C22×C3×D3—28no—
255C22×C3×D3—44no—
256C22×C3×D3—42no—
257C22×C3×D3—48no—
258C22×C3×D3C2×D418yes—
259C22×C3×D3C2412yes—
260C22×C3×D3C2412yes—
261C22×C3×D3C2414yes—
262C32×Q8—22no—
263C32×D4—24no—
264C32×D4—22no—
265C2×C32×C4—24no—
266C2×C32×C4C2×D414yes—
267C2×C32×C4C2412yes—
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—24no—
271C2×C3⋊Dic3C2414yes—
272C2×C3⋊Dic3C2414yes—
273#634—24no—
274#634—24no—
275C3×#67—24no—
276C3×#67—28no—
277C3×#67—44no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3C2414yes—
280C2×C3×Dic3C2412yes—
281C2×C3×Dic3C2412yes—
282C3×D12—28no—
283C3×D12—22no—
284C3×D12C2×D418yes—
285C3×D12C2×D418yes—
286C3×C4×D3—28no—
287C3×C4×D3—24no—
288C3×C4×D3—24no—
289C3×C4×D3—24no—
290C3×Dic6—22no—
291#625—216no—
292#625—44no—
293D3×Dic3—216no—
294D3×Dic3—48no—
295C2×H(5,𝔽2)—31no—
296C22×#41—91no—
297#547—94no—
298#547—94no—
299#546—94no—
300#546—94no—
301#536—91no—
302#536—91no—
303#534—94no—
304#525—31no—
305#525—91no—
306C2×#123—94no—
307#518—91no—
308C24×C3—32no—
309C24×C3—34no—
310C24×C3—31no—
311C23×D3C22×D314yes—
312C23×D3C22×D311yescharacteristic
313C23×D3C22×D312yes—
314C3×#41—24no—
315C3×#41—24no—
316C3×#41—44no—
317C3×#41—68no—
318C3×#41—68no—
319C3×#41—64no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—22no—
325C2×C3×D4—21no—
326C2×C3×D4—32no—
327C2×C3×D4—34no—
328C2×C3×D4—34no—
329C2×C3×D4—38no—
330C2×C3×D4—32no—
331C2×C3×D4—32no—
332C2×C3×D4—34no—
333C2×C3×D4—31no—
334C2×C3×D4—68no—
335C2×C3×D4—68no—
336C2×C3×D4—616no—
337C2×C3×D4C22×D312yes—
338C2×C3×D4C22×D312yes—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4—31no—
344C22×C3×C4—34no—
345C22×C3×C4—32no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C22×C3×C4—64no—
349C22×C3×C4C22×D312yes—
350C22×C3×C4C22×D312yes—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—38no—
354C2×#67—38no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—68no—
358C2×#67—68no—
359C2×#67C22×D314yes—
360C2×#67C22×D312yes—
361C2×#67C22×D314yes—
362C22×Dic3—32no—
363C22×Dic3—32no—
364C22×Dic3—38no—
365C22×Dic3—38no—
366C22×Dic3—62no—
367C22×Dic3—68no—
368C22×Dic3C22×D311yescharacteristic
369#239—28no—
370#237—616no—
371#237—616no—
372D3×D4—216no—
373D3×D4—28no—
374#235—24no—
375#235—28no—
376#235—616no—
377#235—616no—
378C2×D12—28no—
379C2×D12#6718yescomplemented
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D314yes—
382C2×D12C22×D312yes—
383C2×D12C22×D312yes—
384C2×C4×D3—24no—
385C2×C4×D3—38no—
386C2×C4×D3—38no—
387C2×C4×D3—68no—
388C2×C4×D3C22×D314yes—
389C2×C4×D3C22×D312yes—
390C2×C4×D3C22×D312yes—
391C2×C4×D3C22×D312yes—
392C2×Dic6—32no—
393C2×Dic6—32no—
394C2×Dic6—32no—
395C2×Dic6—32no—
396C2×Dic6—62no—
397C2×Dic6—62no—
398C2×Dic6—64no—
399C2×Dic6—64no—
400C2×Dic6—124no—
401C2×Dic6C22×D311yescharacteristic
402C3×C4⋊C4—34no—
403C3×C4⋊C4—32no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—32no—
406C3×C22⋊C4—34no—
407C3×C42—32no—
408#217—32no—
409#217—38no—
410#217—38no—
411#217—32no—
412#217—34no—
413#217—38no—
414#217—34no—
415#217—38no—
416#217—68no—
417#217—62no—
418#217C22×D312yes—
419#217C22×D314yes—
420(C2×D3)⋊C4—38no—
421(C2×D3)⋊C4—38no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4C22×D314yes—
425C4⋊Dic3—32no—
426C4⋊Dic3—32no—
427C4⋊Dic3—38no—
428C4⋊Dic3—62no—
429C4⋊Dic3C22×D312yes—
430Dic3⋊C4—38no—
431Dic3⋊C4—38no—
432Dic3⋊C4—34no—
433Dic3⋊C4—38no—
434Dic3⋊C4—34no—
435Dic3⋊C4—68no—
436Dic3⋊C4C22×D314yes—
437C4×Dic3—32no—
438C4×Dic3—32no—
439C4×Dic3—62no—
440C4×Dic3C22×D312yes—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—24no—
444C22×C32C22×D412yes—
445C22×C32C2511yescharacteristic
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×D3—88no—
455C2×C3×D3C22×D418yes—
456C32×C4—22no—
457C32×C4C22×D412yes—
458C32×C4C22×D412yes—
459C3⋊Dic3—24no—
460C3⋊Dic3—24no—
461C3×Dic3—22no—
462C3×Dic3—22no—
463C3×Dic3—24no—
464H(5,𝔽2)—68no—
465C2×#41—32no—
466C2×#41—31no—
467C2×#41—32no—
468C2×#41—94no—
469C2×#41—94no—
470C2×#41—188no—
471C2×#41D3211yescharacteristic
472C22×Q8—91no—
473C22×D4—34no—
474C22×D4—32no—
475C22×D4—31no—
476C22×D4—32no—
477C22×D4—92no—
478C23×C4—31no—
479C23×C4—92no—
480C4⋊Q8—92no—
481C4⋊Q8—92no—
482#124—92no—
483#124—92no—
484#123—32no—
485#123—98no—
486#123—94no—
487#123—98no—
488#123—98no—
489#123—92no—
490#123—94no—
491C22⋊Q8—32no—
492C22⋊Q8—94no—
493C22⋊Q8—92no—
494C22⋊Q8—94no—
495#121—32no—
496#121—98no—
497#121—92no—
498#121—98no—
499#120—32no—
500#120—92no—
501#120—98no—
502C4×D4—34no—
503C4×D4—94no—
504C4×D4—94no—
505C4×D4—94no—
506#117—31no—
507#117—91no—
508C2×C4⋊C4—98no—
509C2×C22⋊C4—94no—
510C2×C22⋊C4—98no—
511C23×C3—21no—
512C23×C3—22no—
513C23×C3—34no—
514C23×C3—38no—
515C23×C3—32no—
516C23×C3—32no—
517C23×C3—68no—
518C23×C3—62no—
519C23×C3—124no—
520C23×C3—122no—
521C23×C3—128no—
522C23×C3C23×D312yes—
523C23×C3C23×D312yes—
524C23×C3C23×D311yescharacteristic
525C23×C3C23×D311yescharacteristic
526C22×D3—22no—
527C22×D3—28no—
528C22×D3—44no—
529C22×D3—42no—
530C22×D3—48no—
531C22×D3C2×#6718yes—
532C22×D3C23×D312yes—
533C22×D3C23×D312yes—
534C22×D3C23×D314yes—
535C3×Q8—22no—
536C3×Q8—22no—
537C3×Q8—42no—
538C3×Q8—62no—
539C3×D4—24no—
540C3×D4—24no—
541C3×D4—22no—
542C3×D4—22no—
543C3×D4—38no—
544C3×D4—38no—
545C3×D4—42no—
546C3×D4—44no—
547C3×D4—68no—
548C3×D4—68no—
549C3×D4—64no—
550C3×D4—62no—
551C3×D4—124no—
552C2×C3×C4—24no—
553C2×C3×C4—24no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—22no—
557C2×C3×C4—24no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—34no—
561C2×C3×C4—44no—
562C2×C3×C4—68no—
563C2×C3×C4—62no—
564C2×C3×C4—64no—
565C2×C3×C4—64no—
566C2×C3×C4—64no—
567C2×C3×C4D3×D414yes—
568C2×C3×C4C2×#6714yes—
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C23×D311yescharacteristic
575#67—24no—
576#67—28no—
577#67—44no—
578#67—616no—
579#67—616no—
580#67—124no—
581#67—124no—
582C2×Dic3—22no—
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—34no—
586C2×Dic3—34no—
587C2×Dic3—64no—
588C2×Dic3—64no—
589C2×Dic3—616no—
590C2×Dic3—64no—
591C2×Dic3—64no—
592C2×Dic3—124no—
593C2×Dic3—128no—
594C2×Dic3C23×D314yes—
595C2×Dic3C23×D312yes—
596C2×Dic3C23×D312yes—
597D12—28no—
598D12—22no—
599D12C2×#6718yes—
600D12C2×#6718yes—
601C4×D3—28no—
602C4×D3—24no—
603C4×D3—24no—
604C4×D3—24no—
605C4×D3—616no—
606C4×D3—128no—
607Dic6—22no—
608Dic6—64no—
609Dic6—64no—
610Dic6—64no—
611Dic6—64no—
612Dic6—124no—
613Dic6—124no—
614C2×C32—22no—
615C2×C32—42no—
616C2×C32C23×D411yescharacteristic
617C2×C32#58512yes—
618C3×D3—28no—
619C3×D3—42no—
620C3×D3—42no—
621C24—32no—
622C24—34no—
623C24—31no—
624#41—24no—
625#41—68no—
626#41—68no—
627#41—64no—
628#41—1816no—
629#41—1816no—
630C2×Q8—31no—
631C2×Q8—92no—
632C2×Q8—92no—
633C2×Q8—184no—
634C2×Q8C2×D3211yescharacteristic
635C2×D4—32no—
636C2×D4—34no—
637C2×D4—34no—
638C2×D4—32no—
639C2×D4—32no—
640C2×D4—34no—
641C2×D4—31no—
642C2×D4—38no—
643C2×D4—68no—
644C2×D4—68no—
645C2×D4—616no—
646C2×D4—98no—
647C2×D4—94no—
648C2×D4—188no—
649C2×D4C2×D3212yes—
650C2×D4C2×D3211yescharacteristic
651C22×C4—31no—
652C22×C4—34no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—64no—
657C22×C4—98no—
658C22×C4—98no—
659C22×C4—92no—
660C22×C4—188no—
661C22×C4C2×D3212yes—
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—32no—
665C4⋊C4—94no—
666C4⋊C4—98no—
667C4⋊C4—98no—
668C4⋊C4—92no—
669C22⋊C4—32no—
670C22⋊C4—34no—
671C22⋊C4—34no—
672C22⋊C4—94no—
673C22⋊C4—98no—
674C22⋊C4—98no—
675C22⋊C4—94no—
676C22⋊C4—92no—
677C22⋊C4—98no—
678C42—32no—
679C42—92no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—38no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—44no—
692C22×C3—68no—
693C22×C3—62no—
694C22×C3—64no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—128no—
699C22×C3—124no—
700C22×C3—248no—
701C22×C3C2×D3×D412yes—
702C22×C3C22×#6712yes—
703C22×C3C24×D311yescharacteristic
704C22×C3C24×D311yescharacteristic
705C2×D3—28no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—24no—
710C2×D3—22no—
711C2×D3—48no—
712C2×D3—44no—
713C2×D3—88no—
714C2×D3C22×#6718yes—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—42no—
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—64no—
731Dic3—64no—
732Dic3—64no—
733Dic3—64no—
734Dic3—124no—
735Dic3—124no—
736C32#348511yescharacteristic, complemented, Sylow
737C23—34no—
738C23—38no—
739C23—32no—
740C23—32no—
741C23—68no—
742C23—62no—
743C23—124no—
744C23—122no—
745C23—128no—
746C23C22×D3212yes—
747C23C22×D3211yescharacteristic
748Q8—22no—
749Q8—62no—
750Q8—184no—
751Q8—184no—
752D4—24no—
753D4—22no—
754D4—38no—
755D4—38no—
756D4—68no—
757D4—68no—
758D4—64no—
759D4—62no—
760D4—124no—
761D4—1816no—
762D4—364no—
763C2×C4—24no—
764C2×C4—34no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—68no—
768C2×C4—62no—
769C2×C4—64no—
770C2×C4—64no—
771C2×C4—64no—
772C2×C4—94no—
773C2×C4—94no—
774C2×C4—1816no—
775C2×C4—184no—
776C2×C4—368no—
777C2×C4D3×#6714yes—
778C2×C4C22×D3212yes—
779C2×C4C22×D3211yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C2×C3—22no—
782C2×C3—22no—
783C2×C3—22no—
784C2×C3—21no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—42no—
788C2×C3—68no—
789C2×C3—82no—
790C2×C3—122no—
791C2×C3—122no—
792C2×C3C22×D3×D411yescharacteristic
793C2×C3#596412yes—
794C2×C3#596612yes—
795C2×C3C23×#6711yescharacteristic
796D3—28no—
797D3—42no—
798D3—42no—
799C22—22no—
800C22—24no—
801C22—22no—
802C22—38no—
803C22—68no—
804C22—62no—
805C22—62no—
806C22—64no—
807C22—62no—
808C22—62no—
809C22—128no—
810C22—124no—
811C22—248no—
812C22C2×D3×#6712yes—
813C22C23×D3211yescharacteristic
814C4—22no—
815C4—64no—
816C4—62no—
817C4—62no—
818C4—184no—
819C4—184no—
820C4C2×D3×#6712yes—
821C4C2×D3×#6712yes—
822C3—21no—
823C3#8604011yescharacteristic, complemented
824C3#8728011yescharacteristic, complemented
825C2—22no—
826C2—42no—
827C2—68no—
828C2—122no—
829C2—122no—
830C2#1059669612yes—
831C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1009C2semidirect
2. C22×#3795C2semidirect
3. #10596296C2semidirect
4. C3×#5828C2semidirect
5. #10595357C2semidirect
6. #10595230C2semidirect
7. #10595228C2semidirect
8. D3×#935C2semidirect
9. #10595022C2semidirect
10. #10594982C2semidirect
11. #10594887C2semidirect
12. #10594886C2semidirect
13. #10594856C2semidirect
17. C22×#634C22semidirect
19. C2×C3×#239C22semidirect
21. C2×C3×D3×D4C22semidirect
23. C2×C3×#235C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×#625C22semidirect
28. C22×D3×Dic3C22semidirect
30. C2×#3795C22semidirect
31. C2×#3795C22semidirect
32. #64153C22semidirect
33. #64145C22semidirect
34. #64144C22semidirect
35. #64135C22semidirect
36. #64133C22semidirect
37. C3×#946C22semidirect
38. C3×#938C22semidirect
39. C3×#937C22semidirect
40. C3×#935C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#926C22semidirect
43. #63976C22semidirect
44. #63976C22semidirect
45. #63970C22semidirect
46. #63969C22semidirect
47. D3×#217C22semidirect
48. D3×#217C22semidirect
49. #63962C22semidirect
50. #63961C22semidirect
51. #63908C22semidirect
52. #63905C22semidirect
53. C4×#625C22semidirect
54. #63898C22semidirect
55. Dic3×D12C22semidirect
56. #63885C22semidirect
57. #63884C22semidirect
58. D3×Dic3⋊C4C22semidirect
59. #63866C22semidirect
60. #63860C22semidirect
61. #63857C22semidirect
62. #63856C22semidirect
64. C2×#1009D3semidirect
69. #5828D3semidirect
113. C2×C3×D12D4semidirect
166. C2×#239C2×D3semidirect
171. C2×D3×D4C2×D3semidirect
176. C2×#235C2×D3semidirect
178. C22×D12C2×D3semidirect
180. C22×C4×D3C2×D3semidirect
195. #946C2×D3semidirect
204. #938C2×D3semidirect
207. #937C2×D3semidirect
219. #935C2×D3semidirect
227. C4×#67C2×D3semidirect
231. #926C2×D3semidirect
379. C2×D12#67semidirect
736. C32#3485semidirect
823. C3#86040semidirect
824. C3#87280semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C22×#37952
#105962962
C3×#58282
#105953572
#105952302
#105952282
D3×#9352
#105950222
#105949822
#105948872
#105948862
#105948562
#872803
#860403