Finite Group Databasebeta

← C2×#83900 #11662003

Subgroups — C2×#83900 #11662003

Order 768.

2874 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#135C211yesmaximal, characteristic, complemented
2C2×#5832C211yesmaximal, characteristic, complemented
3C2×Dic3×#41C211yesmaximal, characteristic, complemented
4C22×#950C211yesmaximal, characteristic, complemented
5C2×#5233C211yesmaximal, characteristic, complemented
6#83900C2116yesmaximal, direct product factor
7C2×#5185C211yesmaximal, characteristic, complemented
8C2×#5182C211yesmaximal, characteristic, complemented
9C2×#5166C211yesmaximal, characteristic, complemented
10C2×#5163C211yesmaximal, characteristic, complemented
11C2×#5165C211yesmaximal, characteristic, complemented
12C2×#5162C211yesmaximal, characteristic, complemented
13C2×#5153C211yesmaximal, characteristic, complemented
14C2×#5150C211yesmaximal, characteristic, complemented
15C2×#5113C211yesmaximal, characteristic, complemented
16C22×Dic3⋊C8C211yesmaximal, characteristic, complemented
17C2×#3035—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×C3×#41C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C2×C3×#135—28no—
22C2×C3×#135C2218yescomplemented
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C23×C3×C8C2211yescharacteristic
28#5832—24no—
29#5832C2218yescomplemented
30Dic3×#41—24no—
31Dic3×#41C2218yescomplemented
32C2×#950—28no—
33C2×#950C2218yescomplemented
34C2×#947C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic
36C2×Q8×Dic3C2211yescharacteristic
37C2×#944C2211yescharacteristic
38C22×#216C2211yescharacteristic
39C22×#215C2211yescharacteristic
40C2×#940C2211yescharacteristic
41C2×#939—21no—
42C2×#939—21no—
43C2×#936C2211yescharacteristic
44C2×D4×Dic3—21no—
45C2×D4×Dic3—21no—
46C2×D4×Dic3C2211yescharacteristic
47C2×D4×Dic3C2211yescharacteristic
48C22×#214C2211yescharacteristic
49C22×#213C2211yescharacteristic
50C2×C4×#67—21no—
51C2×C4×#67—21no—
52C2×#926—21no—
53C2×#926C2211yescharacteristic
54C22×C4×Dic3—21no—
55C22×C4×Dic3C2211yescharacteristic
56C23×C3⋊C8C2211yescharacteristic
57#5233C2218yescomplemented
58C2×#835C2211yescharacteristic
59C2×#835C2211yescharacteristic
60C2×#832C2211yescharacteristic
61C2×#832C2211yescharacteristic
62#5185C2218yescomplemented
63#5182C2218yescomplemented
64#5166C2218yescomplemented
65#5165C2218yescomplemented
66#5163C2218yescomplemented
67#5162C2218yescomplemented
68#5153C2218yescomplemented
69#5150C2218yescomplemented
70#5113C2218yescomplemented
71C2×#821C2211yescharacteristic
72C2×#821C2211yescharacteristic
73C2×#816C2211yescharacteristic
74C2×#816C2211yescharacteristic
75C2×Dic3⋊C8C2211yescharacteristic
76C2×Dic3⋊C8C2211yescharacteristic
77C2×Dic3⋊C8C2211yescharacteristic
78C2×Dic3⋊C8C2211yescharacteristic
79C2×Dic3⋊C8C2218yescomplemented
80C22×#135—31no—
81C22×#135D311yescharacteristic, complemented
82C2×#532—31no—
83C2×C4×#41—31no—
84#3035—316no—
85C2×#464—31no—
86C2×#464—31no—
87C2×#462—31no—
88C2×#460—31no—
89C2×#463—31no—
90C2×#463—31no—
91C2×#461—31no—
92C2×#459—31no—
93C22×C4⋊C8—31no—
94C2×#416—31no—
95C2×#416—31no—
96C2×C3×#41—22no—
97C2×C3×#41—22no—
98C2×C3×#41—24no—
99C2×C3×#41—24no—
100C2×C3×#41—24no—
101C2×C3×#41D418yescomplemented
102C2×C3×#41C2314yes—
103C2×C3×#41C2314yes—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4—21no—
107C22×C3×D4—21no—
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C22×#67—21no—
114C22×#67—21no—
115C22×#67—21no—
116C23×Dic3—21no—
117C23×Dic3—21no—
118C23×Dic3D411yescharacteristic
119C23×Dic3D411yescharacteristic
120C2×#235—22no—
121C2×#235—24no—
122C2×#235—24no—
123C2×#235C2314yes—
124C22×D12C2311yescharacteristic
125C22×C4×D3—21no—
126C22×Dic6C2311yescharacteristic
127C3×#135—232no—
128C2×C3×Q16—24no—
129C2×C3×Q16C2314yes—
130C2×C3×SD16—24no—
131C2×C3×SD16—24no—
132C2×C3×SD16C2314yes—
133C2×C3×SD16C2314yes—
134C2×C3×D8—24no—
135C2×C3×D8C2314yes—
136C22×C3×C8—24no—
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C22×C3×C8C2314yes—
140C2×#217—21no—
141C2×#217—21no—
142C2×#217—21no—
143C2×#217—21no—
144C2×#217—21no—
145#950—232no—
146#947—22no—
147#947C2314yes—
148Q8×Dic3—22no—
149Q8×Dic3—22no—
150Q8×Dic3C2314yes—
151Q8×Dic3C2314yes—
152#944—22no—
153#944C2314yes—
154C2×#216—24no—
155C2×#216C2314yes—
156C2×#215—24no—
157C2×#215C2314yes—
158#940—22no—
159#940C2314yes—
160#939—28no—
161#939—28no—
162#936—22no—
163#936C2314yes—
164D4×Dic3—28no—
165D4×Dic3—28no—
166D4×Dic3—22no—
167D4×Dic3—22no—
168D4×Dic3C2314yes—
169D4×Dic3C2314yes—
170C2×#214—24no—
171C2×#214C2314yes—
172C2×#213—24no—
173C2×#213C2314yes—
174C4×#67—28no—
175C4×#67—28no—
176C2×(C2×D3)⋊C4—21no—
177C2×(C2×D3)⋊C4—21no—
178#926—22no—
179#926—28no—
180#926C2314yes—
181C2×C4⋊Dic3—21no—
182C2×C4⋊Dic3—21no—
183C2×C4⋊Dic3C2311yescharacteristic
184C2×C4⋊Dic3C2311yescharacteristic
185C2×Dic3⋊C4—21no—
186C2×Dic3⋊C4—21no—
187C2×C4×Dic3—21no—
188C2×C4×Dic3—21no—
189C2×C4×Dic3—21no—
190C2×C4×Dic3—28no—
191C2×C4×Dic3D411yescharacteristic
192C2×C4×Dic3D411yescharacteristic
193C2×C4×Dic3D414yes—
194C2×C4×Dic3C2311yescharacteristic
195C2×C4×Dic3C2311yescharacteristic
196C2×C4×Dic3C2314yes—
197C22×C3⋊C8—24no—
198C22×C3⋊C8C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200C22×C3⋊C8C2314yes—
201#835C2314yes—
202#835C2314yes—
203#832C2314yes—
204#832C2314yes—
205#821C2314yes—
206#821C2314yes—
207#816C2314yes—
208#816C2314yes—
209Dic3⋊C8C2314yes—
210Dic3⋊C8C2314yes—
211Dic3⋊C8C2314yes—
212Dic3⋊C8C2314yes—
213C22×#41—31no—
214C22×#41C2×D311yescharacteristic
215C22×#41C2×D311yescharacteristic
216C2×#135—28no—
217C2×#135—38no—
218C2×#135—68no—
219C2×#135C2×D318yescomplemented
220C22×Q16—31no—
221C22×Q16C2×D311yescharacteristic
222C22×SD16—31no—
223C22×SD16—31no—
224C22×SD16C2×D311yescharacteristic
225C22×SD16C2×D311yescharacteristic
226C22×D8—31no—
227C22×D8C2×D311yescharacteristic
228C23×C8—31no—
229C23×C8C2×D311yescharacteristic
230#532—38no—
231#532—64no—
232C2×C4⋊Q8—31no—
233C2×#127—31no—
234C2×#124—31no—
235C2×#124—31no—
236C2×#121—61no—
237C2×#121—61no—
238C4×#41—38no—
239C4×#41—64no—
240C2×C4×Q8—31no—
241C2×C4×Q8—31no—
242C2×C4×D4—31no—
243C2×C4×D4—31no—
244C2×C4×D4—61no—
245C2×C4×D4—61no—
246C2×C4×D4—61no—
247C2×C4×D4—61no—
248C2×#117—31no—
249C2×#117—61no—
250C22×C42—31no—
251C22×C42—61no—
252#464—38no—
253#464—38no—
254#463—38no—
255#463—38no—
256#462—38no—
257#461—38no—
258#460—38no—
259#459—38no—
260C2×C4⋊C8—31no—
261C2×C4⋊C8—31no—
262C2×C4⋊C8—31no—
263C2×C4⋊C8—31no—
264C2×C4⋊C8—38no—
265#416—38no—
266#416—38no—
267C2×#103—31no—
268C2×#103—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C24×C3—21no—
276C24×C3—21no—
277C24×C3C2×D411yescharacteristic
278C23×D3—21no—
279C3×#41—216no—
280C3×#41—28no—
281C3×#41—28no—
282C3×#41—28no—
283C3×#41—48no—
284C3×#41C2×D4116yescomplemented
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×Q8—22no—
290C2×C3×Q8C2×D414yes—
291C2×C3×Q8C2412yes—
292C2×C3×Q8C2412yes—
293C2×C3×D4—28no—
294C2×C3×D4—24no—
295C2×C3×D4—24no—
296C2×C3×D4—21no—
297C2×C3×D4—22no—
298C2×C3×D4—21no—
299C2×C3×D4—22no—
300C2×C3×D4—22no—
301C2×C3×D4—44no—
302C2×C3×D4C2×D414yes—
303C2×C3×D4C2412yes—
304C2×C3×D4C2412yes—
305C22×C3×C4—21no—
306C22×C3×C4—28no—
307C22×C3×C4—24no—
308C22×C3×C4—21no—
309C22×C3×C4—24no—
310C22×C3×C4—44no—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D414yes—
314C22×C3×C4#4114yes—
315C22×C3×C4C2411yescharacteristic
316C22×C3×C4C2412yes—
317C2×#67—24no—
318C2×#67—24no—
319C2×#67—24no—
320C2×#67—44no—
321C2×#67—44no—
322C2×#67—44no—
323C22×Dic3—24no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—24no—
328C22×Dic3—24no—
329C22×Dic3—42no—
330C22×Dic3—44no—
331C22×Dic3—44no—
332C22×Dic3C2×D411yescharacteristic
333C22×Dic3C2×D411yescharacteristic
334C22×Dic3C2×D411yescharacteristic
335C22×Dic3C2×D414yes—
336C22×Dic3C2×D414yes—
337C22×Dic3C2×D411yescharacteristic
338#235—28no—
339#235—28no—
340#235—48no—
341C2×D12—22no—
342C2×D12—22no—
343C2×D12—21no—
344C2×D12C2412yes—
345C2×C4×D3—24no—
346C2×C4×D3—44no—
347C2×Dic6—22no—
348C2×Dic6—22no—
349C2×Dic6—21no—
350C2×Dic6C2412yes—
351C3×Q16—28no—
352C3×SD16—28no—
353C3×SD16—28no—
354C3×D8—28no—
355C2×C3×C8—22no—
356C2×C3×C8—22no—
357C2×C3×C8—28no—
358C2×C3×C8C2412yes—
359C2×C3×C8C2412yes—
360#217—24no—
361#217—24no—
362#217—24no—
363#217—24no—
364#217—24no—
365#216—28no—
366#215—28no—
367#214—28no—
368#213—28no—
369(C2×D3)⋊C4—24no—
370(C2×D3)⋊C4—24no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—24no—
374C4⋊Dic3—24no—
375C4⋊Dic3C2412yes—
376C4⋊Dic3C2412yes—
377Dic3⋊C4—24no—
378Dic3⋊C4—24no—
379C4×Dic3—24no—
380C4×Dic3—24no—
381C4×Dic3—24no—
382C4×Dic3C2×D414yes—
383C4×Dic3C2×D414yes—
384C4×Dic3C2×D412yes—
385C4×Dic3C2×D412yes—
386C4×Dic3C2412yes—
387C4×Dic3C2412yes—
388C2×C3⋊C8—22no—
389C2×C3⋊C8—22no—
390C2×C3⋊C8—28no—
391C2×C3⋊C8C2412yes—
392C2×C3⋊C8C2412yes—
393C2×#41—22no—
394C2×#41—22no—
395C2×#41—24no—
396C2×#41—24no—
397C2×#41—24no—
398C2×#41—34no—
399C2×#41—62no—
400C2×#41—64no—
401C2×#41—64no—
402C2×#41#6718yescomplemented
403C2×#41C22×D314yes—
404C2×#41C22×D314yes—
405C22×Q8—31no—
406C22×Q8C22×D311yescharacteristic
407C22×Q8C22×D311yescharacteristic
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—31no—
411C22×D4—61no—
412C22×D4—61no—
413C22×D4—61no—
414C22×D4C22×D311yescharacteristic
415C22×D4C22×D311yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—61no—
421C23×C4—61no—
422C23×C4—61no—
423C23×C4C22×D311yescharacteristic
424#135—232no—
425#135—632no—
426C2×Q16—24no—
427C2×Q16—34no—
428C2×Q16—64no—
429C2×Q16C22×D314yes—
430C2×SD16—24no—
431C2×SD16—24no—
432C2×SD16—34no—
433C2×SD16—34no—
434C2×SD16—64no—
435C2×SD16—64no—
436C2×SD16C22×D314yes—
437C2×SD16C22×D314yes—
438C2×D8—24no—
439C2×D8—34no—
440C2×D8—64no—
441C2×D8C22×D314yes—
442C22×C8—24no—
443C22×C8—31no—
444C22×C8—31no—
445C22×C8—34no—
446C22×C8—64no—
447C22×C8C22×D311yescharacteristic
448C22×C8C22×D311yescharacteristic
449C22×C8C22×D314yes—
450C4⋊Q8—34no—
451C4⋊Q8—62no—
452#127—34no—
453#127—62no—
454#124—34no—
455#124—34no—
456#124—62no—
457#124—62no—
458#121—68no—
459#121—68no—
460C4×Q8—34no—
461C4×Q8—34no—
462C4×Q8—62no—
463C4×Q8—62no—
464C4×D4—34no—
465C4×D4—34no—
466C4×D4—68no—
467C4×D4—68no—
468C4×D4—62no—
469C4×D4—62no—
470C4×D4—68no—
471C4×D4—68no—
472#117—34no—
473#117—68no—
474#117—62no—
475C2×C4⋊C4—31no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—61no—
478C2×C4⋊C4—61no—
479C2×C4⋊C4—61no—
480C2×C4⋊C4—61no—
481C2×C22⋊C4—61no—
482C2×C22⋊C4—61no—
483C2×C22⋊C4—61no—
484C2×C22⋊C4—61no—
485C2×C22⋊C4—61no—
486C2×C22⋊C4—61no—
487C2×C22⋊C4—61no—
488C2×C42—34no—
489C2×C42—31no—
490C2×C42—31no—
491C2×C42—31no—
492C2×C42—31no—
493C2×C42—34no—
494C2×C42—68no—
495C2×C42—61no—
496C2×C42—61no—
497C2×C42—61no—
498C4⋊C8—34no—
499C4⋊C8—34no—
500C4⋊C8—34no—
501C4⋊C8—34no—
502#103—34no—
503#103—34no—
504#103—34no—
505#103—34no—
506#102—34no—
507#102—34no—
508#102—34no—
509#102—34no—
510C23×C3—22no—
511C23×C3—22no—
512C23×C3—24no—
513C23×C3—22no—
514C23×C3—22no—
515C23×C3—42no—
516C23×C3—42no—
517C23×C3—42no—
518C23×C3—42no—
519C23×C3—42no—
520C23×C3#12114yes—
521C23×C3C22×D412yes—
522C23×C3C22×D411yescharacteristic
523C22×D3—22no—
524C22×D3—42no—
525C22×D3—42no—
526C22×D3—42no—
527C3×Q8—24no—
528C3×Q8—22no—
529C3×Q8—22no—
530C3×Q8—22no—
531C3×Q8—42no—
532C3×Q8C22×D414yes—
533C3×D4—216no—
534C3×D4—24no—
535C3×D4—22no—
536C3×D4—22no—
537C3×D4—22no—
538C3×D4—48no—
539C3×D4—42no—
540C3×D4C22×D414yes—
541C2×C3×C4—24no—
542C2×C3×C4—22no—
543C2×C3×C4—216no—
544C2×C3×C4—22no—
545C2×C3×C4—42no—
546C2×C3×C4—48no—
547C2×C3×C4#12114yes—
548C2×C3×C4#12118yes—
549C2×C3×C4C22×D412yes—
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D412yes—
552C2×C3×C4C22×D414yes—
553C2×C3×C4C2×#4112yes—
554C2×C3×C4C2×#4114yes—
555C2×C3×C4C2511yescharacteristic
556#67—48no—
557#67—48no—
558#67—48no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—28no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—44no—
567C2×Dic3—48no—
568C2×Dic3—42no—
569C2×Dic3—42no—
570C2×Dic3—42no—
571C2×Dic3—48no—
572C2×Dic3#13514yescomplemented
573C2×Dic3C22×D412yes—
574C2×Dic3C22×D412yes—
575C2×Dic3C22×D412yes—
576C2×Dic3C22×D412yes—
577D12—22no—
578D12—22no—
579D12—42no—
580C4×D3—48no—
581Dic6—22no—
582Dic6—22no—
583Dic6—42no—
584C3×C8—22no—
585C3×C8—22no—
586C3⋊C8—22no—
587C3⋊C8—22no—
588C24—21no—
589C24—21no—
590C24—61no—
591C24D3×D411yescharacteristic
592#41—216no—
593#41—28no—
594#41—28no—
595#41—28no—
596#41—48no—
597#41—68no—
598#41—68no—
599#41—128no—
600#41C2×#67116yescomplemented
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—32no—
607C2×Q8—61no—
608C2×Q8—62no—
609C2×Q8—62no—
610C2×Q8C2×#6714yes—
611C2×Q8C23×D312yes—
612C2×Q8C23×D312yes—
613C2×D4—28no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—32no—
622C2×D4—44no—
623C2×D4—64no—
624C2×D4—64no—
625C2×D4—64no—
626C2×D4—61no—
627C2×D4—62no—
628C2×D4—62no—
629C2×D4—124no—
630C2×D4—124no—
631C2×D4—124no—
632C2×D4C2×#6714yes—
633C2×D4C23×D312yes—
634C2×D4C23×D312yes—
635C22×C4—21no—
636C22×C4—28no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—34no—
645C22×C4—34no—
646C22×C4—44no—
647C22×C4—64no—
648C22×C4—64no—
649C22×C4—64no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—64no—
654C22×C4—124no—
655C22×C4—122no—
656C22×C4—124no—
657C22×C4—124no—
658C22×C4D3×D412yes—
659C22×C4D3×D411yescharacteristic
660C22×C4#23714yes—
661C22×C4C2×#6714yes—
662C22×C4C23×D311yescharacteristic
663C22×C4C23×D312yes—
664Q16—28no—
665Q16—68no—
666SD16—28no—
667SD16—28no—
668SD16—68no—
669SD16—68no—
670D8—28no—
671D8—68no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—28no—
675C2×C8—32no—
676C2×C8—32no—
677C2×C8—62no—
678C2×C8—62no—
679C2×C8—68no—
680C2×C8C23×D312yes—
681C2×C8C23×D312yes—
682C4⋊C4—32no—
683C4⋊C4—32no—
684C4⋊C4—64no—
685C4⋊C4—64no—
686C4⋊C4—64no—
687C4⋊C4—64no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C22⋊C4—64no—
691C22⋊C4—64no—
692C22⋊C4—64no—
693C22⋊C4—64no—
694C22⋊C4—64no—
695C22⋊C4—64no—
696C22⋊C4—64no—
697C42—34no—
698C42—34no—
699C42—32no—
700C42—32no—
701C42—32no—
702C42—32no—
703C42—64no—
704C42—64no—
705C42—64no—
706C22×C3—28no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—24no—
710C22×C3—48no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—84no—
717C22×C3C2×#12114yes—
718C22×C3C2×#12112yes—
719C22×C3C2×#13512yes—
720C22×C3#57512yes—
721C22×C3C23×D411yescharacteristic
722C2×D3—42no—
723C2×D3—42no—
724C2×D3—42no—
725C2×D3—84no—
726C3×C4—24no—
727C3×C4—42no—
728C3×C4C2×#12112yes—
729C3×C4C2×#12114yes—
730C3×C4C23×D411yescharacteristic
731C3×C4C22×#4111yescharacteristic
732Dic3—22no—
733Dic3—22no—
734Dic3—22no—
735Dic3—42no—
736Dic3—42no—
737Dic3—42no—
738Dic3C2×#13514yescomplemented
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—22no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—62no—
750C23—122no—
751C23—122no—
752C23—122no—
753C23#93914yes—
754C23C2×D3×D412yes—
755C23C2×D3×D411yescharacteristic
756Q8—22no—
757Q8—24no—
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—62no—
762Q8—62no—
763Q8—122no—
764Q8C22×#6714yes—
765D4—216no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—24no—
770D4—48no—
771D4—42no—
772D4—62no—
773D4—62no—
774D4—128no—
775D4—128no—
776D4—128no—
777D4—122no—
778D4C22×#6714yes—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—216no—
782C2×C4—22no—
783C2×C4—32no—
784C2×C4—34no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—32no—
788C2×C4—42no—
789C2×C4—48no—
790C2×C4—68no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—128no—
798C2×C4—124no—
799C2×C4—128no—
800C2×C4—122no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—128no—
804C2×C4#93914yes—
805C2×C4#93918yes—
806C2×C4C2×D3×D412yes—
807C2×C4C2×D3×D411yescharacteristic
808C2×C4C2×#23712yes—
809C2×C4C2×#23714yes—
810C2×C4C22×#6712yes—
811C2×C4C22×#6714yes—
812C2×C4C24×D311yescharacteristic
813C8—22no—
814C8—22no—
815C8—62no—
816C8—62no—
817C2×C3—24no—
818C2×C3—44no—
819C2×C3—82no—
820C2×C3#303514yescomplemented
821C2×C3C22×#12111yescharacteristic
822C2×C3C22×#13511yescharacteristic
823C2×C3C2×#57511yescharacteristic
824D3—82no—
825C22—22no—
826C22—22no—
827C22—28no—
828C22—24no—
829C22—42no—
830C22—42no—
831C22—48no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—84no—
836C22—122no—
837C22—122no—
838C22—122no—
839C22—244no—
840C22D3×#13512yes—
841C22#576812yes—
842C22C2×#93914yes—
843C22C2×#93912yes—
844C22C22×D3×D411yescharacteristic
845C4—24no—
846C4—34no—
847C4—42no—
848C4—62no—
849C4—62no—
850C4—62no—
851C4—122no—
852C4—122no—
853C4—122no—
854C4C2×#93914yes—
855C4C2×#93912yes—
856C4C22×#23711yescharacteristic
857C4C23×#6711yescharacteristic
858C3C2×#303511yescharacteristic, complemented, Sylow
859C2—24no—
860C2—44no—
861C2—82no—
862C2—242no—
863C2#8390014yesdirect product factor
864C2C2×D3×#13511yescharacteristic
865C2C2×#576811yescharacteristic
866C2C22×#93911yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#135C2
socleC23×C3C22×D4
hypercenterC22×#135D3
hypocenterC3C2×#3035
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×C3×#135C2semidirect
2. C2×#5832C2semidirect
3. C2×Dic3×#41C2semidirect
4. C22×#950C2semidirect
5. C2×#5233C2semidirect
6. #83900C2direct (N × H)
7. C2×#5185C2semidirect
8. C2×#5182C2semidirect
9. C2×#5166C2semidirect
10. C2×#5163C2semidirect
11. C2×#5165C2semidirect
12. C2×#5162C2semidirect
13. C2×#5153C2semidirect
14. C2×#5150C2semidirect
15. C2×#5113C2semidirect
16. C22×Dic3⋊C8C2semidirect
22. C2×C3×#135C22semidirect
29. #5832C22semidirect
31. Dic3×#41C22semidirect
33. C2×#950C22semidirect
57. #5233C22semidirect
62. #5185C22semidirect
63. #5182C22semidirect
64. #5166C22semidirect
65. #5165C22semidirect
66. #5163C22semidirect
67. #5162C22semidirect
68. #5153C22semidirect
69. #5150C22semidirect
70. #5113C22semidirect
79. C2×Dic3⋊C8C22semidirect
81. C22×#135D3semidirect
101. C2×C3×#41D4semidirect
219. C2×#135C2×D3semidirect
284. C3×#41C2×D4semidirect
402. C2×#41#67semidirect
572. C2×Dic3#135semidirect
600. #41C2×#67semidirect
738. Dic3C2×#135semidirect
820. C2×C3#3035semidirect
858. C3C2×#3035semidirect
863. C2#83900direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1352
C2×#58322
C2×Dic3×#412
C22×#9502
C2×#52332
#839002
C2×#51852
C2×#51822
C2×#51662
C2×#51632
C2×#51652
C2×#51622
C2×#51532
C2×#51502
C2×#51132
C22×Dic3⋊C82
C2×#30353