Finite Group Databasebeta

← #11884487

Subgroups — #11884487

Order 1152.

1092 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2#10595427C211yesmaximal, characteristic, complemented
3#10595236C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592875C211yesmaximal, characteristic, complemented
6C3×#5174C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10591579C211yesmaximal, characteristic, complemented
10#10591515C211yesmaximal, characteristic, complemented
11#10591452C211yesmaximal, characteristic, complemented
12#10591433C211yesmaximal, characteristic, complemented
13#10590832C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590722C211yesmaximal, characteristic, complemented
16#83922—31nomaximal
17#80836—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic
24C2×#3755C2211yescharacteristic, complemented
25#64149C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic
27C2×#3745C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#938C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#916—24no—
33C2×C3×#204C2211yescharacteristic
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic, complemented
36#63979—21no—
37#63978—21no—
38#63958—21no—
39#63952—21no—
40#63922—21no—
41D3×(C2×D3)⋊C4—21no—
42#63909C2211yescharacteristic
43#63909C2211yescharacteristic, complemented
44C4×#625C2211yescharacteristic
45#63898C2211yescharacteristic
46#63886—21no—
47#63850—21no—
48#63843C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63794—24no—
52#63642C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5834—31no—
65#5829—31no—
66C2×#916D311yescharacteristic, complemented
67C2×#914—31no—
68C2×#908—31no—
69#5630—31no—
70#5599—31no—
71C3×#468—31no—
72#5238—31no—
73#5238—31no—
74#5187—31no—
75#5185—31no—
76#5176—31no—
77#5176—31no—
78#5176—61no—
79#5174D311yescharacteristic, complemented
80#5164—31no—
81#5156—31no—
82#5150—31no—
83#5127—31no—
84#5115—31no—
85#5111—31no—
86#5047—31no—
87#5036—31no—
88#4889—31no—
89#4883—31no—
90#4810—31no—
91#4798—31no—
92#4786—31no—
93#4781—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×#239—22no—
105C3×#239—41no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×D12—21no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625D411yescharacteristic
119C2×#624—21no—
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3799—22no—
124#3799—41no—
125C32×SD16—22no—
126C2×C32×C8C2311yescharacteristic
127#3755—41no—
128#3753—41no—
129#3752—21no—
130#3752—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3745—22no—
134C3×#217—21no—
135C3×#216—22no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204D414yescomplemented
144C3×ΓL(1,𝔽25)—22no—
145C3×D3×C8—22no—
146#3724D411yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152(C2×D3)⋊Dic3D411yescharacteristic
153Dic32—21no—
154#3717—22no—
155#3714—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#237C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—21no—
168C2×C3×SD16—31no—
169C2×C3×SD16C2×D311yescharacteristic, complemented
170C2×C3×SD16C2×D311yescharacteristic, complemented
171C2×C3×D8—31no—
172C2×C3×M16—31no—
173C22×C3×C8—31no—
174C3×C22⋊Q8—31no—
175C3×#121—31no—
176#947—31no—
177#947—31no—
178#947—61no—
179#946C2×D311yescharacteristic
180Q8×Dic3—31no—
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—61no—
186#940—31no—
187#940—31no—
188#940—61no—
189#940—61no—
190#940—61no—
191#939—61no—
192#939—61no—
193#938—61no—
194#938C2×D311yescharacteristic
195#937—61no—
196D4×Dic3—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213C2×D311yescharacteristic
202#930—31no—
203#930—31no—
204#930—61no—
205#929—61no—
206C4×#67—31no—
207C4×#67—31no—
208C4×#67—61no—
209C2×(C2×D3)⋊C4—61no—
210#916—24no—
211#914—64no—
212#908—64no—
213C2×D24—31no—
214C2×D24—31no—
215C2×D24—31no—
216C2×D24—61no—
217C2×#204—31no—
218C2×#204C2×D311yescharacteristic
219C2×ΓL(1,𝔽25)C2×D311yescharacteristic
220C2×D3×C8C2×D311yescharacteristic, complemented
221#895—31no—
222#895—31no—
223#895—61no—
224#894—61no—
225#893—31no—
226#887—31no—
227#884—61no—
228#882—61no—
229#67⋊C4—61no—
230D3×C22⋊C4—61no—
231C3×#107—31no—
232C3×#103—31no—
233C3×#102—31no—
234#835—31no—
235#835C2×D311yescharacteristic, complemented
236#832—31no—
237#832C2×D311yescharacteristic, complemented
238#830—31no—
239#830—31no—
240#821—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244#818C2×D311yescharacteristic, complemented
245#815—31no—
246#815—31no—
247#815—61no—
248Dic3⋊C8—31no—
249Dic3⋊C8—31no—
250#810—31no—
251#809—31no—
252#809—31no—
253#809—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269#638—42no—
270#638—81no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C3×#67—42no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6C2×D412yes—
295#626—42no—
296#626—42no—
297#626—81no—
298#626—81no—
299#625—41no—
300#624—42no—
301D3×Dic3—81no—
302C32×C8C2×D412yes—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—31no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—31no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—31no—
345C2×#67—31no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—121no—
355C2×#67—121no—
356C22×Dic3—21no—
357C22×Dic3—61no—
358#239—22no—
359#239—41no—
360#239—62no—
361#239—121no—
362#237—22no—
363#237—41no—
364D3×D4—62no—
365D3×D4—121no—
366#235—62no—
367#235—121no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—62no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—121no—
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3C22×D311yescharacteristic
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6C22×D311yescharacteristic
389C3×Q16—62no—
390C3×SD16—22no—
391C3×SD16—22no—
392C3×SD16—34no—
393C3×SD16—42no—
394C3×D8—62no—
395C3×M16—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407#217—21no—
408#217—31no—
409#217—31no—
410#217—61no—
411#216—22no—
412#215—62no—
413#215—121no—
414#215—121no—
415#215—122no—
416#213—22no—
417#213—62no—
418#213—121no—
419#213—121no—
420#213—122no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—121no—
434(C2×D3)⋊C4—121no—
435C4⋊Dic3—61no—
436C4⋊Dic3C22×D311yescharacteristic
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—31no—
440Dic3⋊C4—31no—
441Dic3⋊C4—61no—
442C4×Dic3—31no—
443C4×Dic3—31no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452D24—62no—
453D24—62no—
454D24—62no—
455D24—122no—
456#204—62no—
457#204#6714yescomplemented
458ΓL(1,𝔽25)—22no—
459D3×C8—22no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—22no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—41no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—21no—
484C3⋊Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—22no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—31no—
492C2×#41—91no—
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16D3211yescharacteristic, complemented
501C2×D8—31no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—31no—
507#127—91no—
508#127—181no—
509#124—91no—
510#123—181no—
511C22⋊Q8—31no—
512#121—31no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—91no—
520C4×D4—91no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—31no—
525C4⋊C8—91no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—31no—
538C23×C3—31no—
539C23×C3—41no—
540C23×C3—61no—
541C22×D3—21no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—121no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—241no—
553C22×D3—241no—
554C22×D3D3×D411yescharacteristic
555C22×D3D3×D411yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—32no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—61no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—32no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—61no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—241no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—42no—
593#67—81no—
594#67—122no—
595#67—122no—
596#67—121no—
597#67—121no—
598#67—122no—
599#67—122no—
600#67—242no—
601#67—241no—
602#67—241no—
603#67—241no—
604#67—241no—
605#67—242no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—42no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—241no—
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619D12—21no—
620D12—42no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—121no—
630D12—121no—
631D12—121no—
632D12—121no—
633D12—122no—
634D12—122no—
635D12—241no—
636D12—241no—
637D12C2×#6712yes—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—42no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—241no—
646Dic6—21no—
647Dic6C2×#6712yes—
648C3×C8—22no—
649C3×C8—61no—
650C3×C8—61no—
651C3×C8D3×D412yes—
652C3×C8C2×#6712yes—
653C3⋊C8—21no—
654C3⋊C8—21no—
655C3⋊C8—62no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C2×C32—81no—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57611yescharacteristic
662C3⋊D3—81no—
663C3⋊D3—81no—
664C3×D3—41no—
665C3×D3—42no—
666C3×D3—41no—
667C24—181no—
668#41—62no—
669#41—62no—
670#41—121no—
671#41—121no—
672#41—182no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8C2×D3211yescharacteristic
676C2×D4—31no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—182no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—361no—
691C2×D4C2×D3211yescharacteristic
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—181no—
697C22×C4—181no—
698Q16—62no—
699SD16—22no—
700SD16—34no—
701SD16—182no—
702SD16—361no—
703D8—62no—
704D8—182no—
705D8—182no—
706D8—361no—
707M16—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8—91no—
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—91no—
721C22⋊C4—91no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C42—91no—
728C42—181no—
729C22×C3—21no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—62no—
742C22×C3—61no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—21no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—244no—
778C2×D3—244no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—61no—
784C3×C4—62no—
785C3×C4—61no—
786C3×C4—81no—
787C3×C4—121no—
788C3×C4—121no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4#100911yescharacteristic
792C3×C4C22×#6711yescharacteristic
793Dic3—22no—
794Dic3—21no—
795Dic3—21no—
796Dic3—41no—
797Dic3—41no—
798Dic3—61no—
799Dic3—61no—
800Dic3—61no—
801Dic3—61no—
802Dic3—121no—
803Dic3—121no—
804C32#326811yescharacteristic, complemented, Sylow
805C23—21no—
806C23—31no—
807C23—31no—
808C23—61no—
809C23—181no—
810C23—181no—
811C23—362no—
812C23—362no—
813C23—721no—
814Q8—21no—
815Q8—21no—
816Q8—32no—
817Q8—61no—
818D4—21no—
819D4—21no—
820D4—32no—
821D4—61no—
822D4—122no—
823D4—122no—
824D4—181no—
825D4—181no—
826D4—181no—
827D4—181no—
828D4—241no—
829D4—362no—
830D4—362no—
831D4—362no—
832D4—361no—
833D4—721no—
834D4—721no—
835D4—721no—
836C2×C4—21no—
837C2×C4—31no—
838C2×C4—31no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—91no—
847C2×C4—91no—
848C2×C4—122no—
849C2×C4—122no—
850C2×C4—362no—
851C2×C4—721no—
852C2×C4C22×D3211yescharacteristic
853C8—61no—
854C8—61no—
855C8—181no—
856C8D3×#6712yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—81no—
861C2×C3—81no—
862C2×C3—122no—
863C2×C3—121no—
864C2×C3—121no—
865C2×C3—161no—
866C2×C3#560911yescharacteristic
867C2×C3#576811yescharacteristic
868C2×C3#576911yescharacteristic
869C2×C3#577411yescharacteristic
870C2×C3#577711yescharacteristic
871C2×C3D4×#6711yescharacteristic
872D3—41no—
873D3—41no—
874D3—42no—
875D3—241no—
876D3—241no—
877D3—241no—
878D3—241no—
879D3—481no—
880D3—481no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—62no—
891C22—121no—
892C22—121no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—724no—
900C22D32×D411yescharacteristic
901C4—41no—
902C4—61no—
903C4—61no—
904C4—62no—
905C4—121no—
906C4—121no—
907C4—181no—
908C4—181no—
909C4#6431411yescharacteristic
910C4C2×D3×#6711yescharacteristic
911C3—21no—
912C3#8083611yescharacteristic, complemented
913C3#8392211yescharacteristic, complemented
914C2—81no—
915C2—121no—
916C2—121no—
917C2—122no—
918C2—721no—
919C2—721no—
920C2#1059474611yescharacteristic
921C2#1059475511yescharacteristic
922C2#1059528811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. #10595427C2semidirect
3. #10595236C2semidirect
4. C2×#63794C2semidirect
5. #10592875C2semidirect
6. C3×#5174C2semidirect
7. #10591657C2semidirect
8. #10591588C2semidirect
9. #10591579C2semidirect
10. #10591515C2semidirect
11. #10591452C2semidirect
12. #10591433C2semidirect
13. #10590832C2semidirect
14. #10590779C2semidirect
15. #10590722C2semidirect
19. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
24. C2×#3755C22semidirect
25. #64149C22semidirect
29. C2×C3×#216C22semidirect
35. C2×C3×D3×C8C22semidirect
43. #63909C22semidirect
48. #63843C22semidirect
52. #63642C22semidirect
53. C3×#835C22semidirect
54. C3×#832C22semidirect
55. C3×#818C22semidirect
56. #63572C22semidirect
57. #63565C22semidirect
59. #63564C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#916D3semidirect
79. #5174D3semidirect
143. C3×#204D4semidirect
161. C2×#237C2×D3semidirect
169. C2×C3×SD16C2×D3semidirect
170. C2×C3×SD16C2×D3semidirect
181. C2×#216C2×D3semidirect
220. C2×D3×C8C2×D3semidirect
235. #835C2×D3semidirect
237. #832C2×D3semidirect
244. #818C2×D3semidirect
457. #204#67semidirect
500. C2×SD16D32semidirect
804. C32#3268semidirect
912. C3#80836semidirect
913. C3#83922semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105954272
#105952362
C2×#637942
#105928752
C3×#51742
#105916572
#105915882
#105915792
#105915152
#105914522
#105914332
#105908322
#105907792
#105907222
#839223
#808363