Finite Group Databasebeta

← C2×D3×#950 #11918612

Subgroups — C2×D3×#950 #11918612

Order 1152.

3141 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5D3×#950C2116yesmaximal, direct product factor
6C2×#63949C211yesmaximal, characteristic, complemented
7C2×#63947C211yesmaximal, characteristic, complemented
8C2×D3×#216C211yesmaximal, characteristic, complemented
9C2×D3×#215C211yesmaximal, characteristic, complemented
10C2×#63935C211yesmaximal, characteristic, complemented
11C2×#63933C211yesmaximal, characteristic, complemented
12C2×D3×#214C211yesmaximal, characteristic, complemented
13C2×D3×#213C211yesmaximal, characteristic, complemented
14C2×#63829C211yesmaximal, characteristic, complemented
15C2×#63822C211yesmaximal, characteristic, complemented
16C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
17C22×#950—31nomaximal
18C2×D3×#135—31nomaximal
19C2×C32×#41C2211yescharacteristic, complemented
20C2×#3828C2211yescharacteristic, complemented
21C3×D3×#41—24no—
22C3×D3×#41C2218yescomplemented
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×#237—21no—
26C2×C3×#237C2211yescharacteristic, complemented
27C2×C3×D3×D4—21no—
28C2×C3×D3×D4C2211yescharacteristic
29C2×C3×#235—21no—
30C2×C3×#235C2211yescharacteristic, complemented
31C2×C3×#235C2211yescharacteristic, complemented
32C22×C3×C4×D3—21no—
33C22×C3×C4×D3C2211yescharacteristic
34C2×D3×#67—21no—
35C2×#3804—21no—
36D3×#235—24no—
37D3×#235C2218yescomplemented
38C2×D3×D12C2211yescharacteristic
39C2×C4×D32—21no—
40C2×#3799C2211yescharacteristic, complemented
41C2×#3798—21no—
42C2×#3795C2211yescharacteristic, complemented
43C2×D3×Dic6C2211yescharacteristic
44#64159C2218yescomplemented
45C2×#3756C2211yescharacteristic, complemented
46C2×#3755C2211yescharacteristic, complemented
47C2×#3754C2211yescharacteristic, complemented
48C2×#3753C2211yescharacteristic, complemented
49C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×#950C2218yescomplemented
51C2×C3×#216C2211yescharacteristic, complemented
52C2×C3×#215C2211yescharacteristic, complemented
53C2×C3×#214C2211yescharacteristic, complemented
54C2×C3×#213C2211yescharacteristic, complemented
55C22×C3×C3⋊C8C2211yescharacteristic, complemented
56#63949C2218yescomplemented
57#63947C2218yescomplemented
58D3×#216C2218yescomplemented
59D3×#215C2218yescomplemented
60#63935C2218yescomplemented
61#63933C2218yescomplemented
62D3×#214C2218yescomplemented
63D3×#213C2218yescomplemented
64C2×#3719C2211yescharacteristic, complemented
65C2×#3718C2211yescharacteristic, complemented
66C2×#3717C2211yescharacteristic, complemented
67#63829C2218yescomplemented
68C2×#3716C2211yescharacteristic, complemented
69C2×#3715C2211yescharacteristic, complemented
70C2×#3715C2211yescharacteristic, complemented
71C2×#3714C2211yescharacteristic, complemented
72#63822C2218yescomplemented
73C2×#3713C2211yescharacteristic, complemented
74C2×D3×C3⋊C8C2211yescharacteristic
75C2×D3×C3⋊C8C2211yescharacteristic
76C2×D3×C3⋊C8C2218yescomplemented
77C2×D3×C3⋊C8C2211yescharacteristic, complemented
78C2×D3×C3⋊C8C2211yescharacteristic, complemented
79C22×C3×#41—31no—
80C2×D3×#41—31no—
81C2×D3×#41D311yescharacteristic, complemented
82C22×#235—31no—
83C2×C3×#135—31no—
84C2×#950—31no—
85C2×#950—31no—
86C2×#950—31no—
87C2×#950—31no—
88C2×#950—316no—
89C2×#950—31no—
90C2×#950—31no—
91C2×#950—31no—
92C2×#950—31no—
93C2×#950—31no—
94C2×#950—61no—
95C2×#950D311yescharacteristic, direct product factor
96C22×#216—31no—
97C22×#215—31no—
98C22×#214—31no—
99C22×#213—31no—
100C23×C3⋊C8—31no—
101D3×#135—316no—
102C2×#919—31no—
103C2×D3×Q16—31no—
104C2×#916—31no—
105C2×#916—31no—
106C2×D3×SD16—31no—
107C2×D3×SD16—31no—
108C2×#912—31no—
109C2×D3×D8—31no—
110C2×#904—31no—
111C22×D3×C8—31no—
112C23×C3×D3—21no—
113C23×C3×D3D411yescharacteristic
114C22×D32—21no—
115C32×#41—22no—
116C32×#41C2314yescomplemented
117C2×C32×Q8C2311yescharacteristic
118C2×C32×D4—21no—
119C2×C32×D4C2311yescharacteristic
120C22×C32×C4—21no—
121C22×C32×C4C2311yescharacteristic
122C2×#638—21no—
123#3828—22no—
124#3828C2314yescomplemented
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3—21no—
127C2×#634C2311yescharacteristic
128C2×C3×#67—21no—
129C2×C3×#67—21no—
130C2×C3×#67—21no—
131C2×C3×#67—21no—
132C22×C3×Dic3—21no—
133C22×C3×Dic3D411yescharacteristic
134C3×#239—22no—
135C3×#239C2314yescomplemented
136C3×D3×Q8—22no—
137C3×D3×Q8C2314yes—
138C3×#237—28no—
139C3×#237—22no—
140C3×#237C2314yescomplemented
141C3×D3×D4—28no—
142C3×D3×D4—22no—
143C3×D3×D4C2314yes—
144C3×#235—22no—
145C3×#235—22no—
146C3×#235—28no—
147C3×#235C2314yescomplemented
148C3×#235C2314yescomplemented
149C2×C3×D12—21no—
150C2×C3×D12C2311yescharacteristic
151C2×C3×D12C2311yescharacteristic
152C2×C3×C4×D3—21no—
153C2×C3×C4×D3—21no—
154C2×C3×C4×D3—21no—
155C2×C3×C4×D3—21no—
156C2×C3×C4×D3—28no—
157C2×C3×C4×D3D411yescharacteristic
158C2×C3×C4×D3D411yescharacteristic
159C2×C3×C4×D3D414yes—
160C2×C3×C4×D3C2311yescharacteristic
161C2×C3×C4×D3C2311yescharacteristic
162C2×C3×C4×D3C2314yes—
163C2×C3×Dic6—21no—
164C2×C3×Dic6C2311yescharacteristic
165C2×C3×Dic6C2311yescharacteristic
166D3×#67—28no—
167C2×#627—21no—
168C2×#626—21no—
169C2×#626—21no—
170C2×#625—21no—
171C2×#624—21no—
172#3804—28no—
173C2×D3×Dic3—21no—
174C2×D3×Dic3—21no—
175D3×D12—22no—
176D3×D12C2314yes—
177C4×D32—28no—
178#3799—22no—
179#3799C2314yescomplemented
180#3798—28no—
181#3795—22no—
182#3795C2314yescomplemented
183D3×Dic6—22no—
184D3×Dic6C2314yes—
185#3756C2314yescomplemented
186#3755C2314yescomplemented
187#3754C2314yescomplemented
188#3753C2314yescomplemented
189C2×C3⋊(C3⋊C8)C2311yescharacteristic
190C2×C3⋊(C3⋊C8)C2311yescharacteristic
191C2×C3⋊(C3⋊C8)C2314yescomplemented
192C3×#216C2314yescomplemented
193C3×#215C2314yescomplemented
194C3×#214C2314yescomplemented
195C3×#213C2314yescomplemented
196C2×C3×C3⋊C8C2311yescharacteristic
197C2×C3×C3⋊C8C2311yescharacteristic
198C2×C3×C3⋊C8C2314yescomplemented
199#3719C2314yescomplemented
200#3718C2314yescomplemented
201#3717C2314yescomplemented
202#3716C2314yescomplemented
203#3715C2314yescomplemented
204#3715C2314yescomplemented
205#3714C2314yescomplemented
206#3713C2314yescomplemented
207D3×C3⋊C8C2314yes—
208D3×C3⋊C8C2314yes—
209D3×C3⋊C8C2314yescomplemented
210D3×C3⋊C8C2314yescomplemented
211C22×#135—91noSylow
212C2×C3×#41—21no—
213C2×C3×#41—38no—
214C2×C3×#41—31no—
215C2×C3×#41—31no—
216C2×C3×#41—31no—
217C2×C3×#41—31no—
218C2×C3×#41—61no—
219C2×C3×#41—61no—
220C2×C3×#41—64no—
221C2×C3×#41C2×D311yescharacteristic, complemented
222C2×C3×#41C2×D311yescharacteristic, complemented
223C22×C3×Q8—31no—
224C22×C3×D4—31no—
225C22×C3×D4—61no—
226C23×C3×C4—31no—
227C23×C3×C4—61no—
228C22×#67—61no—
229D3×#41—24no—
230D3×#41—38no—
231D3×#41—64no—
232D3×#41C2×D318yescomplemented
233C2×#239—31no—
234C2×#239C2×D311yescharacteristic, complemented
235C2×D3×Q8—31no—
236C2×D3×Q8C2×D311yescharacteristic
237C2×#237—21no—
238C2×#237—31no—
239C2×#237—61no—
240C2×#237C2×D311yescharacteristic, complemented
241C2×D3×D4—21no—
242C2×D3×D4—31no—
243C2×D3×D4—61no—
244C2×D3×D4C2×D311yescharacteristic
245C2×#235—21no—
246C2×#235—31no—
247C2×#235—31no—
248C2×#235—38no—
249C2×#235—31no—
250C2×#235—31no—
251C2×#235—61no—
252C2×#235—61no—
253C2×#235—64no—
254C2×#235—61no—
255C2×#235—61no—
256C2×#235C2×D311yescharacteristic, complemented
257C2×#235C2×D311yescharacteristic, complemented
258C22×D12—31no—
259C22×C4×D3—21no—
260C22×C4×D3—61no—
261C22×C4×D3—61no—
262C22×C4×D3C2×D311yescharacteristic
263C22×Dic6—31no—
264C3×#135—38no—
265C2×C3×Q16—31no—
266C2×C3×SD16—31no—
267C2×C3×SD16—31no—
268C2×C3×D8—31no—
269C22×C3×C8—31no—
270#950—38no—
271#950—38no—
272#950—38no—
273#950—38no—
274#950—38no—
275#950—38no—
276#950—38no—
277#950—38no—
278#950—38no—
279#950—68no—
280#950C2×D318yesdirect product factor
281C2×#216—31no—
282C2×#216—31no—
283C2×#216—31no—
284C2×#216—31no—
285C2×#216—38no—
286C2×#216—31no—
287C2×#216—61no—
288C2×#216C2×D311yescharacteristic, complemented
289C2×#215—31no—
290C2×#215—31no—
291C2×#215—31no—
292C2×#215—31no—
293C2×#215—38no—
294C2×#215—31no—
295C2×#215—61no—
296C2×#215C2×D311yescharacteristic, complemented
297C2×#214—31no—
298C2×#214—31no—
299C2×#214—31no—
300C2×#214—31no—
301C2×#214—38no—
302C2×#214—31no—
303C2×#214—61no—
304C2×#214C2×D311yescharacteristic, complemented
305C2×#213—31no—
306C2×#213—31no—
307C2×#213—31no—
308C2×#213—31no—
309C2×#213—38no—
310C2×#213—31no—
311C2×#213—61no—
312C2×#213C2×D311yescharacteristic, complemented
313C22×C3⋊C8—31no—
314C22×C3⋊C8—31no—
315C22×C3⋊C8—31no—
316C22×C3⋊C8—31no—
317C22×C3⋊C8—31no—
318C22×C3⋊C8—31no—
319C22×C3⋊C8—38no—
320C22×C3⋊C8—61no—
321C22×C3⋊C8C2×D311yescharacteristic, complemented
322#919—38no—
323D3×Q16—38no—
324#916—38no—
325#916—38no—
326D3×SD16—38no—
327D3×SD16—38no—
328#912—38no—
329D3×D8—38no—
330C2×Dic12—31no—
331#904—38no—
332C2×D24—31no—
333C2×#204—31no—
334C2×#204—31no—
335C2×D3×C8—31no—
336C2×D3×C8—31no—
337C2×D3×C8—31no—
338C2×D3×C8—31no—
339C2×D3×C8—38no—
340C23×C32—21no—
341C23×C32C2×D411yescharacteristic
342C22×C3⋊D3—21no—
343C22×C3×D3—24no—
344C22×C3×D3—21no—
345C22×C3×D3—21no—
346C22×C3×D3—24no—
347C22×C3×D3—44no—
348C22×C3×D3C2×D411yescharacteristic
349C22×C3×D3C2×D414yes—
350C22×C3×D3C2×D411yescharacteristic
351C2×D32—24no—
352C2×D32—44no—
353C32×Q8—21no—
354C32×Q8C2412yes—
355C32×D4—24no—
356C32×D4—21no—
357C32×D4C2412yes—
358C2×C32×C4—21no—
359C2×C32×C4—24no—
360C2×C32×C4C2×D411yescharacteristic
361C2×C32×C4C2×D412yes—
362C2×C32×C4C2411yescharacteristic
363C2×C32×C4C2412yes—
364#638—24no—
365C2×C3⋊Dic3—21no—
366C4⋊(C3⋊D3)—21no—
367C4⋊(C3⋊D3)C2412yes—
368C4×C3⋊D3—24no—
369#634—21no—
370#634C2412yes—
371C3×#67—24no—
372C3×#67—24no—
373C3×#67—24no—
374C3×#67—24no—
375C2×C3×Dic3—21no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—24no—
378C2×C3×Dic3C2×D411yescharacteristic
379C2×C3×Dic3C2×D414yes—
380C2×C3×Dic3C2×D411yescharacteristic
381C3×D12—24no—
382C3×D12—21no—
383C3×D12—21no—
384C3×D12C2412yes—
385C3×D12C2412yes—
386C3×C4×D3—24no—
387C3×C4×D3—24no—
388C3×C4×D3—24no—
389C3×C4×D3—24no—
390C3×C4×D3C2×D412yes—
391C3×C4×D3C2×D412yes—
392C3×C4×D3C2×D414yes—
393C3×C4×D3C2×D414yes—
394C3×C4×D3C2412yes—
395C3×C4×D3C2412yes—
396C3×Dic6—21no—
397C3×Dic6—21no—
398C3×Dic6—24no—
399C3×Dic6C2412yes—
400C3×Dic6C2412yes—
401#627—24no—
402#626—24no—
403#626—24no—
404#625—24no—
405#624—24no—
406D3×Dic3—24no—
407D3×Dic3—24no—
408C3⋊(C3⋊C8)C2412yes—
409C3⋊(C3⋊C8)C2412yes—
410C3×C3⋊C8C2412yes—
411C3×C3⋊C8C2412yes—
412C22×#41—31no—
413C22×#41—91no—
414C2×#135—31no—
415C2×#135—91no—
416C2×#135—91no—
417C2×#135—91no—
418C2×#135—91no—
419C2×#135—91no—
420C2×#135—916no—
421C2×#135—91no—
422C2×#135—91no—
423C22×Q16—91no—
424C22×SD16—91no—
425C22×SD16—91no—
426C22×D8—91no—
427C23×C8—91no—
428C24×C3—31no—
429C24×C3—61no—
430C23×D3—21no—
431C23×D3—61no—
432C23×D3—61no—
433C23×D3#6711yescharacteristic
434C3×#41—22no—
435C3×#41—22no—
436C3×#41—24no—
437C3×#41—34no—
438C3×#41—34no—
439C3×#41—34no—
440C3×#41—34no—
441C3×#41—42no—
442C3×#41—68no—
443C3×#41—68no—
444C3×#41—62no—
445C3×#41—62no—
446C3×#41—62no—
447C3×#41—62no—
448C3×#41C22×D314yescomplemented
449C3×#41C22×D314yescomplemented
450C2×C3×Q8—21no—
451C2×C3×Q8—34no—
452C2×C3×Q8—31no—
453C2×C3×Q8—31no—
454C2×C3×Q8—61no—
455C2×C3×Q8—62no—
456C2×C3×Q8C22×D311yescharacteristic
457C2×C3×Q8C22×D311yescharacteristic
458C2×C3×D4—21no—
459C2×C3×D4—21no—
460C2×C3×D4—21no—
461C2×C3×D4—34no—
462C2×C3×D4—31no—
463C2×C3×D4—31no—
464C2×C3×D4—41no—
465C2×C3×D4—61no—
466C2×C3×D4—62no—
467C2×C3×D4—61no—
468C2×C3×D4—68no—
469C2×C3×D4—61no—
470C2×C3×D4—61no—
471C2×C3×D4—61no—
472C2×C3×D4C22×D311yescharacteristic
473C2×C3×D4C22×D311yescharacteristic
474C22×C3×C4—21no—
475C22×C3×C4—21no—
476C22×C3×C4—21no—
477C22×C3×C4—31no—
478C22×C3×C4—31no—
479C22×C3×C4—34no—
480C22×C3×C4—31no—
481C22×C3×C4—31no—
482C22×C3×C4—31no—
483C22×C3×C4—34no—
484C22×C3×C4—41no—
485C22×C3×C4—61no—
486C22×C3×C4—68no—
487C22×C3×C4—61no—
488C22×C3×C4—61no—
489C22×C3×C4—61no—
490C22×C3×C4—61no—
491C22×C3×C4C22×D311yescharacteristic
492C22×C3×C4C22×D311yescharacteristic
493C2×#67—21no—
494C2×#67—21no—
495C2×#67—21no—
496C2×#67—21no—
497C2×#67—61no—
498C2×#67—68no—
499C2×#67—61no—
500C2×#67—61no—
501C2×#67—61no—
502C2×#67—61no—
503C2×#67—61no—
504C2×#67—121no—
505C22×Dic3—21no—
506C22×Dic3—61no—
507C22×Dic3—61no—
508C22×Dic3#6711yescharacteristic
509#239—22no—
510#239—34no—
511#239—62no—
512#239C22×D314yescomplemented
513D3×Q8—22no—
514D3×Q8—34no—
515D3×Q8—62no—
516D3×Q8C22×D314yes—
517#237—28no—
518#237—22no—
519#237—34no—
520#237—68no—
521#237—62no—
522#237C22×D314yescomplemented
523D3×D4—28no—
524D3×D4—22no—
525D3×D4—34no—
526D3×D4—68no—
527D3×D4—62no—
528D3×D4C22×D314yes—
529#235—22no—
530#235—22no—
531#235—28no—
532#235—34no—
533#235—34no—
534#235—34no—
535#235—34no—
536#235—64no—
537#235—62no—
538#235—68no—
539#235—62no—
540#235—68no—
541#235—62no—
542#235—62no—
543#235—68no—
544#235—122no—
545#235C22×D314yescomplemented
546#235C22×D314yescomplemented
547C2×D12—21no—
548C2×D12—31no—
549C2×D12—31no—
550C2×D12—34no—
551C2×D12—61no—
552C2×D12—62no—
553C2×D12—61no—
554C2×D12—61no—
555C2×D12C22×D311yescharacteristic
556C2×D12C22×D311yescharacteristic
557C2×C4×D3—21no—
558C2×C4×D3—21no—
559C2×C4×D3—21no—
560C2×C4×D3—21no—
561C2×C4×D3—28no—
562C2×C4×D3—68no—
563C2×C4×D3—61no—
564C2×C4×D3—61no—
565C2×C4×D3—61no—
566C2×C4×D3—61no—
567C2×C4×D3—61no—
568C2×C4×D3—61no—
569C2×C4×D3—68no—
570C2×C4×D3—121no—
571C2×C4×D3#6711yescharacteristic
572C2×C4×D3#6711yescharacteristic
573C2×C4×D3#6714yes—
574C2×C4×D3C22×D311yescharacteristic
575C2×C4×D3C22×D311yescharacteristic
576C2×C4×D3C22×D314yes—
577C2×Dic6—21no—
578C2×Dic6—31no—
579C2×Dic6—31no—
580C2×Dic6—34no—
581C2×Dic6—61no—
582C2×Dic6—62no—
583C2×Dic6—61no—
584C2×Dic6—61no—
585C2×Dic6C22×D311yescharacteristic
586C2×Dic6C22×D311yescharacteristic
587C3×Q16—34no—
588C3×SD16—34no—
589C3×SD16—34no—
590C3×D8—34no—
591C2×C3×C8—31no—
592C2×C3×C8—31no—
593C2×C3×C8—34no—
594#216—34no—
595#216—34no—
596#216—34no—
597#216—34no—
598#216—34no—
599#216—64no—
600#216C22×D314yescomplemented
601#215—34no—
602#215—34no—
603#215—34no—
604#215—34no—
605#215—34no—
606#215—64no—
607#215C22×D314yescomplemented
608#214—34no—
609#214—34no—
610#214—34no—
611#214—34no—
612#214—34no—
613#214—64no—
614#214C22×D314yescomplemented
615#213—34no—
616#213—34no—
617#213—34no—
618#213—34no—
619#213—34no—
620#213—64no—
621#213C22×D314yescomplemented
622C2×C3⋊C8—31no—
623C2×C3⋊C8—31no—
624C2×C3⋊C8—34no—
625C2×C3⋊C8—31no—
626C2×C3⋊C8—31no—
627C2×C3⋊C8—34no—
628C2×C3⋊C8—34no—
629C2×C3⋊C8—34no—
630C2×C3⋊C8—34no—
631C2×C3⋊C8—34no—
632C2×C3⋊C8—61no—
633C2×C3⋊C8—61no—
634C2×C3⋊C8—64no—
635C2×C3⋊C8C22×D311yescharacteristic
636C2×C3⋊C8C22×D311yescharacteristic
637C2×C3⋊C8C22×D314yescomplemented
638Dic12—34no—
639D24—34no—
640#204—34no—
641#204—34no—
642D3×C8—34no—
643D3×C8—34no—
644D3×C8—34no—
645D3×C8—34no—
646C22×C32—22no—
647C22×C32—22no—
648C22×C32—42no—
649C22×C32C22×D412yes—
650C22×C32C22×D411yescharacteristic
651C2×C3⋊D3—22no—
652C2×C3⋊D3—42no—
653C2×C3×D3—22no—
654C2×C3×D3—28no—
655C2×C3×D3—22no—
656C2×C3×D3—22no—
657C2×C3×D3—42no—
658C2×C3×D3—42no—
659C2×C3×D3—48no—
660C2×C3×D3#13514yescomplemented
661C2×C3×D3C22×D412yes—
662C2×C3×D3C22×D412yes—
663D32—48no—
664C32×C4—22no—
665C32×C4C22×D411yescharacteristic
666C32×C4C22×D412yes—
667C32×C4C2511yescharacteristic
668C3⋊Dic3—22no—
669C3×Dic3—22no—
670C3×Dic3—22no—
671C3×Dic3C22×D412yes—
672C3×Dic3C22×D412yes—
673C2×#41—38no—
674C2×#41—31no—
675C2×#41—31no—
676C2×#41—31no—
677C2×#41—31no—
678C2×#41—61no—
679C2×#41—61no—
680C2×#41—64no—
681C2×#41—91no—
682C2×#41—91no—
683C2×#41—98no—
684C2×#41—91no—
685C2×#41—181no—
686C2×#41—181no—
687C2×#41—184no—
688C2×#41D3211yescharacteristic, complemented
689C22×Q8—31no—
690C22×Q8—91no—
691C22×D4—31no—
692C22×D4—61no—
693C22×D4—91no—
694C22×D4—181no—
695C23×C4—31no—
696C23×C4—61no—
697C23×C4—181no—
698#135—38no—
699#135—98no—
700#135—98no—
701#135—98no—
702#135—98no—
703#135—98no—
704#135—98no—
705#135—98no—
706C2×Q16—31no—
707C2×Q16—91no—
708C2×Q16—98no—
709C2×Q16—91no—
710C2×Q16—91no—
711C2×SD16—31no—
712C2×SD16—31no—
713C2×SD16—91no—
714C2×SD16—91no—
715C2×SD16—98no—
716C2×SD16—98no—
717C2×SD16—91no—
718C2×SD16—91no—
719C2×SD16—91no—
720C2×SD16—91no—
721C2×D8—31no—
722C2×D8—91no—
723C2×D8—98no—
724C2×D8—91no—
725C2×D8—91no—
726C22×C8—31no—
727C22×C8—91no—
728C22×C8—91no—
729C22×C8—91no—
730C22×C8—91no—
731C22×C8—98no—
732C22×C8—91no—
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—21no—
736C23×C3—31no—
737C23×C3—34no—
738C23×C3—31no—
739C23×C3—41no—
740C23×C3—64no—
741C23×C3—64no—
742C23×C3—61no—
743C23×C3—61no—
744C23×C3—124no—
745C23×C3D3×D411yescharacteristic
746C23×C3C2×#6711yescharacteristic
747C22×D3—24no—
748C22×D3—21no—
749C22×D3—21no—
750C22×D3—24no—
751C22×D3—44no—
752C22×D3—64no—
753C22×D3—61no—
754C22×D3—61no—
755C22×D3—64no—
756C22×D3—121no—
757C22×D3—124no—
758C22×D3—124no—
759C22×D3C2×#6711yescharacteristic
760C22×D3C2×#6714yes—
761C22×D3C2×#6711yescharacteristic
762C3×Q8—21no—
763C3×Q8—21no—
764C3×Q8—22no—
765C3×Q8—32no—
766C3×Q8—32no—
767C3×Q8—41no—
768C3×Q8—64no—
769C3×Q8—61no—
770C3×Q8—61no—
771C3×Q8C23×D312yes—
772C3×Q8C23×D312yes—
773C3×D4—24no—
774C3×D4—24no—
775C3×D4—21no—
776C3×D4—21no—
777C3×D4—22no—
778C3×D4—32no—
779C3×D4—32no—
780C3×D4—41no—
781C3×D4—44no—
782C3×D4—64no—
783C3×D4—64no—
784C3×D4—64no—
785C3×D4—64no—
786C3×D4—64no—
787C3×D4—61no—
788C3×D4—61no—
789C3×D4C23×D312yes—
790C3×D4C23×D312yes—
791C2×C3×C4—21no—
792C2×C3×C4—21no—
793C2×C3×C4—24no—
794C2×C3×C4—24no—
795C2×C3×C4—21no—
796C2×C3×C4—22no—
797C2×C3×C4—22no—
798C2×C3×C4—21no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—34no—
802C2×C3×C4—32no—
803C2×C3×C4—34no—
804C2×C3×C4—34no—
805C2×C3×C4—32no—
806C2×C3×C4—32no—
807C2×C3×C4—32no—
808C2×C3×C4—44no—
809C2×C3×C4—41no—
810C2×C3×C4—64no—
811C2×C3×C4—64no—
812C2×C3×C4—64no—
813C2×C3×C4—61no—
814C2×C3×C4—61no—
815C2×C3×C4—64no—
816C2×C3×C4—64no—
817C2×C3×C4D3×D412yes—
818C2×C3×C4D3×D411yescharacteristic
819C2×C3×C4C2×#6712yes—
820C2×C3×C4C2×#6711yescharacteristic
821C2×C3×C4C23×D311yescharacteristic
822C2×C3×C4C23×D312yes—
823C2×C3×C4C23×D311yescharacteristic
824C2×C3×C4C23×D312yes—
825#67—24no—
826#67—24no—
827#67—24no—
828#67—24no—
829#67—64no—
830#67—64no—
831#67—64no—
832#67—64no—
833#67—64no—
834#67—64no—
835#67—124no—
836C2×Dic3—21no—
837C2×Dic3—21no—
838C2×Dic3—24no—
839C2×Dic3—64no—
840C2×Dic3—61no—
841C2×Dic3—61no—
842C2×Dic3—64no—
843C2×Dic3—121no—
844C2×Dic3C2×#6711yescharacteristic
845C2×Dic3C2×#6711yescharacteristic
846C2×Dic3C2×#6714yes—
847D12—24no—
848D12—21no—
849D12—21no—
850D12—32no—
851D12—32no—
852D12—62no—
853D12—64no—
854D12—64no—
855D12—61no—
856D12—61no—
857D12—121no—
858D12C23×D312yes—
859D12C23×D312yes—
860C4×D3—24no—
861C4×D3—24no—
862C4×D3—24no—
863C4×D3—24no—
864C4×D3—64no—
865C4×D3—64no—
866C4×D3—64no—
867C4×D3—64no—
868C4×D3—64no—
869C4×D3—64no—
870C4×D3—124no—
871C4×D3C2×#6714yes—
872C4×D3C2×#6714yes—
873C4×D3C2×#6712yes—
874C4×D3C2×#6712yes—
875C4×D3C23×D312yes—
876C4×D3C23×D312yes—
877Dic6—21no—
878Dic6—21no—
879Dic6—24no—
880Dic6—32no—
881Dic6—32no—
882Dic6—62no—
883Dic6—64no—
884Dic6—61no—
885Dic6—61no—
886Dic6—64no—
887Dic6—121no—
888Dic6C23×D312yes—
889Dic6C23×D312yes—
890C3×C8—32no—
891C3×C8—32no—
892C3⋊C8—32no—
893C3⋊C8—32no—
894C3⋊C8—32no—
895C3⋊C8—32no—
896C3⋊C8—62no—
897C3⋊C8—62no—
898C3⋊C8C23×D312yes—
899C3⋊C8C23×D312yes—
900C2×C32—22no—
901C2×C32—42no—
902C2×C32C2×#13512yescomplemented
903C2×C32C23×D411yescharacteristic
904C3⋊D3—42no—
905C3×D3—22no—
906C3×D3—42no—
907C3×D3—42no—
908C3×D3C2×#13514yescomplemented
909C24—31no—
910C24—61no—
911C24—181no—
912#41—22no—
913#41—34no—
914#41—34no—
915#41—34no—
916#41—34no—
917#41—68no—
918#41—68no—
919#41—62no—
920#41—62no—
921#41—62no—
922#41—62no—
923#41—94no—
924#41—94no—
925#41—94no—
926#41—188no—
927#41—188no—
928#41—182no—
929#41—182no—
930#41—182no—
931#41C2×D3214yescomplemented
932C2×Q8—34no—
933C2×Q8—31no—
934C2×Q8—31no—
935C2×Q8—61no—
936C2×Q8—62no—
937C2×Q8—94no—
938C2×Q8—91no—
939C2×Q8—181no—
940C2×Q8—182no—
941C2×Q8C2×D3211yescharacteristic
942C2×D4—21no—
943C2×D4—34no—
944C2×D4—31no—
945C2×D4—31no—
946C2×D4—61no—
947C2×D4—62no—
948C2×D4—61no—
949C2×D4—68no—
950C2×D4—61no—
951C2×D4—61no—
952C2×D4—61no—
953C2×D4—94no—
954C2×D4—91no—
955C2×D4—182no—
956C2×D4—181no—
957C2×D4—181no—
958C2×D4—188no—
959C2×D4—181no—
960C2×D4—181no—
961C2×D4C2×D3211yescharacteristic
962C22×C4—21no—
963C22×C4—31no—
964C22×C4—31no—
965C22×C4—31no—
966C22×C4—34no—
967C22×C4—34no—
968C22×C4—31no—
969C22×C4—31no—
970C22×C4—61no—
971C22×C4—68no—
972C22×C4—61no—
973C22×C4—61no—
974C22×C4—61no—
975C22×C4—61no—
976C22×C4—181no—
977C22×C4—188no—
978C22×C4—181no—
979C22×C4—181no—
980C22×C4—181no—
981C22×C4C2×D3211yescharacteristic
982Q16—34no—
983Q16—94no—
984Q16—94no—
985Q16—94no—
986SD16—34no—
987SD16—34no—
988SD16—94no—
989SD16—94no—
990SD16—94no—
991SD16—94no—
992SD16—94no—
993SD16—94no—
994D8—34no—
995D8—94no—
996D8—94no—
997D8—94no—
998C2×C8—31no—
999C2×C8—31no—
1000C2×C8—34no—
1001C2×C8—94no—
1002C2×C8—94no—
1003C2×C8—94no—
1004C2×C8—94no—
1005C2×C8—91no—
1006C2×C8—91no—
1007C2×C8—94no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—21no—
1013C22×C3—22no—
1014C22×C3—32no—
1015C22×C3—34no—
1016C22×C3—32no—
1017C22×C3—42no—
1018C22×C3—42no—
1019C22×C3—42no—
1020C22×C3—42no—
1021C22×C3—68no—
1022C22×C3—62no—
1023C22×C3—62no—
1024C22×C3—62no—
1025C22×C3—82no—
1026C22×C3—128no—
1027C22×C3—122no—
1028C22×C3—122no—
1029C22×C3C2×D3×D412yes—
1030C22×C3C2×D3×D411yescharacteristic
1031C22×C3C22×#6712yes—
1032C22×C3C22×#6711yescharacteristic
1033C2×D3—22no—
1034C2×D3—28no—
1035C2×D3—22no—
1036C2×D3—22no—
1037C2×D3—42no—
1038C2×D3—42no—
1039C2×D3—48no—
1040C2×D3—62no—
1041C2×D3—62no—
1042C2×D3—122no—
1043C2×D3—128no—
1044C2×D3—122no—
1045C2×D3—122no—
1046C2×D3—128no—
1047C2×D3—242no—
1048C2×D3#95014yesdirect product factor
1049C2×D3C22×#6712yes—
1050C2×D3C22×#6712yes—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—21no—
1054C3×C4—22no—
1055C3×C4—21no—
1056C3×C4—32no—
1057C3×C4—32no—
1058C3×C4—42no—
1059C3×C4—62no—
1060C3×C4—62no—
1061C3×C4C2×D3×D411yescharacteristic
1062C3×C4C2×D3×D412yes—
1063C3×C4C22×#6711yescharacteristic
1064C3×C4C22×#6712yes—
1065C3×C4C24×D311yescharacteristic
1066C3×C4C24×D311yescharacteristic
1067Dic3—22no—
1068Dic3—22no—
1069Dic3—62no—
1070Dic3—62no—
1071Dic3—122no—
1072Dic3C22×#6712yes—
1073Dic3C22×#6712yes—
1074C32C22×#13511yescharacteristic, complemented, Sylow
1075C23—21no—
1076C23—31no—
1077C23—34no—
1078C23—31no—
1079C23—64no—
1080C23—64no—
1081C23—61no—
1082C23—61no—
1083C23—124no—
1084C23—184no—
1085C23—181no—
1086C23—364no—
1087C23D3×#6711yescharacteristic
1088Q8—21no—
1089Q8—32no—
1090Q8—32no—
1091Q8—64no—
1092Q8—61no—
1093Q8—61no—
1094Q8—92no—
1095Q8—184no—
1096Q8—181no—
1097Q8C22×D3212yes—
1098D4—24no—
1099D4—21no—
1100D4—32no—
1101D4—32no—
1102D4—64no—
1103D4—64no—
1104D4—64no—
1105D4—64no—
1106D4—64no—
1107D4—61no—
1108D4—61no—
1109D4—92no—
1110D4—184no—
1111D4—184no—
1112D4—184no—
1113D4—184no—
1114D4—181no—
1115D4C22×D3212yes—
1116C2×C4—21no—
1117C2×C4—24no—
1118C2×C4—31no—
1119C2×C4—31no—
1120C2×C4—34no—
1121C2×C4—34no—
1122C2×C4—32no—
1123C2×C4—32no—
1124C2×C4—34no—
1125C2×C4—32no—
1126C2×C4—32no—
1127C2×C4—64no—
1128C2×C4—64no—
1129C2×C4—64no—
1130C2×C4—61no—
1131C2×C4—61no—
1132C2×C4—64no—
1133C2×C4—64no—
1134C2×C4—184no—
1135C2×C4—184no—
1136C2×C4—184no—
1137C2×C4—181no—
1138C2×C4—184no—
1139C2×C4D3×#6712yes—
1140C2×C4D3×#6711yescharacteristic
1141C2×C4C22×D3211yescharacteristic
1142C2×C4C22×D3212yes—
1143C8—32no—
1144C8—32no—
1145C8—92no—
1146C8—92no—
1147C2×C3—22no—
1148C2×C3—22no—
1149C2×C3—21no—
1150C2×C3—22no—
1151C2×C3—34no—
1152C2×C3—42no—
1153C2×C3—42no—
1154C2×C3—42no—
1155C2×C3—62no—
1156C2×C3—82no—
1157C2×C3—122no—
1158C2×C3—122no—
1159C2×C3D3×#13512yescomplemented
1160C2×C3C2×#95012yescomplemented
1161C2×C3C22×D3×D411yescharacteristic
1162C2×C3C23×#6711yescharacteristic
1163D3—22no—
1164D3—42no—
1165D3—42no—
1166D3—122no—
1167D3—122no—
1168D3—242no—
1169D3C2×#95014yesdirect product factor
1170C22—22no—
1171C22—22no—
1172C22—32no—
1173C22—34no—
1174C22—32no—
1175C22—42no—
1176C22—68no—
1177C22—62no—
1178C22—62no—
1179C22—62no—
1180C22—128no—
1181C22—122no—
1182C22—122no—
1183C22—182no—
1184C22—368no—
1185C22—362no—
1186C22C2×D3×#6712yes—
1187C22C2×D3×#6711yescharacteristic
1188C4—22no—
1189C4—32no—
1190C4—32no—
1191C4—62no—
1192C4—62no—
1193C4—182no—
1194C4C2×D3×#6712yes—
1195C4C2×D3×#6711yescharacteristic
1196C4C23×D3211yescharacteristic
1197C3—21no—
1198C3C2×D3×#13511yescharacteristic, complemented
1199C3C22×#95011yescharacteristic, complemented
1200C2—22no—
1201C2—34no—
1202C2—42no—
1203C2—62no—
1204C2—122no—
1205C2—122no—
1206C2—362no—
1207C2D3×#95012yesdirect product factor
1208C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C22×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×D3×#235C2semidirect
3. C2×#64159C2semidirect
4. C2×C3×#950C2semidirect
5. D3×#950C2direct (N × H)
6. C2×#63949C2semidirect
7. C2×#63947C2semidirect
8. C2×D3×#216C2semidirect
9. C2×D3×#215C2semidirect
10. C2×#63935C2semidirect
11. C2×#63933C2semidirect
12. C2×D3×#214C2semidirect
13. C2×D3×#213C2semidirect
14. C2×#63829C2semidirect
15. C2×#63822C2semidirect
16. C22×D3×C3⋊C8C2semidirect
19. C2×C32×#41C22semidirect
20. C2×#3828C22semidirect
22. C3×D3×#41C22semidirect
23. C2×C3×#239C22semidirect
26. C2×C3×#237C22semidirect
30. C2×C3×#235C22semidirect
31. C2×C3×#235C22semidirect
37. D3×#235C22semidirect
40. C2×#3799C22semidirect
42. C2×#3795C22semidirect
44. #64159C22semidirect
45. C2×#3756C22semidirect
46. C2×#3755C22semidirect
47. C2×#3754C22semidirect
48. C2×#3753C22semidirect
49. C22×C3⋊(C3⋊C8)C22semidirect
50. C3×#950C22semidirect
51. C2×C3×#216C22semidirect
52. C2×C3×#215C22semidirect
53. C2×C3×#214C22semidirect
54. C2×C3×#213C22semidirect
55. C22×C3×C3⋊C8C22semidirect
56. #63949C22semidirect
57. #63947C22semidirect
58. D3×#216C22semidirect
59. D3×#215C22semidirect
60. #63935C22semidirect
61. #63933C22semidirect
62. D3×#214C22semidirect
63. D3×#213C22semidirect
64. C2×#3719C22semidirect
65. C2×#3718C22semidirect
66. C2×#3717C22semidirect
67. #63829C22semidirect
68. C2×#3716C22semidirect
69. C2×#3715C22semidirect
70. C2×#3715C22semidirect
71. C2×#3714C22semidirect
72. #63822C22semidirect
73. C2×#3713C22semidirect
76. C2×D3×C3⋊C8C22semidirect
77. C2×D3×C3⋊C8C22semidirect
78. C2×D3×C3⋊C8C22semidirect
81. C2×D3×#41D3semidirect
95. C2×#950D3direct (N × H)
116. C32×#41C23semidirect
124. #3828C23semidirect
135. C3×#239C23semidirect
140. C3×#237C23semidirect
147. C3×#235C23semidirect
148. C3×#235C23semidirect
179. #3799C23semidirect
182. #3795C23semidirect
185. #3756C23semidirect
186. #3755C23semidirect
187. #3754C23semidirect
188. #3753C23semidirect
191. C2×C3⋊(C3⋊C8)C23semidirect
192. C3×#216C23semidirect
193. C3×#215C23semidirect
194. C3×#214C23semidirect
195. C3×#213C23semidirect
198. C2×C3×C3⋊C8C23semidirect
199. #3719C23semidirect
200. #3718C23semidirect
201. #3717C23semidirect
202. #3716C23semidirect
203. #3715C23semidirect
204. #3715C23semidirect
205. #3714C23semidirect
206. #3713C23semidirect
209. D3×C3⋊C8C23semidirect
210. D3×C3⋊C8C23semidirect
221. C2×C3×#41C2×D3semidirect
222. C2×C3×#41C2×D3semidirect
232. D3×#41C2×D3semidirect
234. C2×#239C2×D3semidirect
240. C2×#237C2×D3semidirect
256. C2×#235C2×D3semidirect
257. C2×#235C2×D3semidirect
280. #950C2×D3direct (N × H)
288. C2×#216C2×D3semidirect
296. C2×#215C2×D3semidirect
304. C2×#214C2×D3semidirect
312. C2×#213C2×D3semidirect
321. C22×C3⋊C8C2×D3semidirect
448. C3×#41C22×D3semidirect
449. C3×#41C22×D3semidirect
512. #239C22×D3semidirect
522. #237C22×D3semidirect
545. #235C22×D3semidirect
546. #235C22×D3semidirect
600. #216C22×D3semidirect
607. #215C22×D3semidirect
614. #214C22×D3semidirect
621. #213C22×D3semidirect
637. C2×C3⋊C8C22×D3semidirect
660. C2×C3×D3#135semidirect
688. C2×#41D32semidirect
902. C2×C32C2×#135semidirect
908. C3×D3C2×#135semidirect
931. #41C2×D32semidirect
1048. C2×D3#950direct (N × H)
1074. C32C22×#135semidirect
1159. C2×C3D3×#135semidirect
1160. C2×C3C2×#950semidirect
1169. D3C2×#950direct (N × H)
1198. C3C2×D3×#135semidirect
1199. C3C22×#950semidirect
1207. C2D3×#950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×D3×#2352
C2×#641592
C2×C3×#9502
D3×#9502
C2×#639492
C2×#639472
C2×D3×#2162
C2×D3×#2152
C2×#639352
C2×#639332
C2×D3×#2142
C2×D3×#2132
C2×#638292
C2×#638222
C22×D3×C3⋊C82
C22×#9503
C2×D3×#1353