Finite Group Databasebeta

← C2×#10594528 #11901164

Subgroups — C2×#10594528 #11901164

Order 1152.

3489 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#895C211yesmaximal, characteristic, complemented
6C2×#63916C212yesmaximal, complemented
7C2×#63912C212yesmaximal, complemented
8C2×#63908C211yesmaximal, characteristic, complemented
9C2×#63899C212yesmaximal, complemented
10C2×#63885C212yesmaximal, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12#10594528C2116yesmaximal, direct product factor
13C2×#5629—31nomaximal
14C2×#5608—31nomaximal
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C3×D12C2211yescharacteristic
18C22×C3×D12C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2212yes—
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#625C2212yes—
28C22×D3×Dic3C2212yes—
29C2×#3798—28no—
30C2×#3798C2218yescomplemented
31C2×#3796—28no—
32C2×#3796C2218yescomplemented
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3750C2212yes—
36C4⋊C4×C3⋊D3C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×C4⋊Dic3C2212yes—
40C3×#897C2218yescomplemented
41C3×#895C2218yescomplemented
42C2×#3724C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63916C22116yescomplemented
46#63912C22116yescomplemented
47#63908C2218yescomplemented
48#63899C22116yescomplemented
49#63885C22116yescomplemented
50#63856C2218yescomplemented
51C22×#239—31no—
52C22×#237—31no—
53C22×#235—31no—
54C22×#235—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×#121—31no—
57C2×#946—31no—
58C2×#939—32no—
59C2×#938—31no—
60C2×#938—32no—
61C2×#930—31no—
62C2×#924—31no—
63#5629—316no—
64#5608—316no—
65C2×#897D311yescharacteristic, complemented
66C2×#896—32no—
67C2×#895—32no—
68C2×#895D311yescharacteristic, complemented
69C2×D3×C4⋊C4—31no—
70C2×D3×C4⋊C4—31no—
71C2×D3×C4⋊C4—61no—
72C2×#884—32no—
73C2×#884—32no—
74C2×#884—32no—
75C2×#878—32no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2312yes—
83C22×C3⋊Dic3C2311yescharacteristic
84C2×C4×C3⋊D3—44no—
85C2×C4×C3⋊D3D418yescomplemented
86C2×C4×C3⋊D3C2318yes—
87C2×C4×C3⋊D3C2314yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×D12—24no—
92C2×C3×D12—44no—
93C2×C3×D12C2314yes—
94C2×C3×D12C2318yes—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3C2314yes—
98C2×C3×C4×D3C2314yes—
99C2×C3×Dic6—24no—
100C2×C3×Dic6C2314yes—
101C2×#627—24no—
102C2×#627C2314yes—
103C2×#626—28no—
104C2×#626—24no—
105C2×#626—24no—
106C2×#626C2318yes—
107C2×#626C2314yes—
108C2×#626C2314yes—
109C2×#625—24no—
110C2×#625—44no—
111C2×#625C2314yes—
112C2×#625C2318yes—
113C2×D3×Dic3—28no—
114C2×D3×Dic3C2318yes—
115#3798—232no—
116#3796—232no—
117C32×C4⋊C4C2314yes—
118C4⋊(C3⋊Dic3)C2314yes—
119#3750C2318yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×(C2×D3)⋊C4C2318yes—
122C3×C4⋊Dic3C2318yes—
123#3724C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C2×#537—91noSylow
127C22×C3×Q8—31no—
128C22×C3×D4—31no—
129C22×C3×D4—32no—
130C23×C3×C4—31no—
131C23×C3×C4—31no—
132C22×#67—31no—
133C22×#67—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—31no—
137C22×#67—31no—
138C22×#67—32no—
139C23×Dic3—32no—
140C2×#239—38no—
141C2×#239—68no—
142C2×#237—38no—
143C2×#237—68no—
144C2×#235—38no—
145C2×#235—38no—
146C2×#235—68no—
147C2×#235—68no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—32no—
151C22×D12C2×D311yescharacteristic
152C22×D12C2×D312yes—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—32no—
158C22×C4×D3—61no—
159C22×C4×D3—62no—
160C22×C4×D3C2×D311yescharacteristic
161C22×C4×D3C2×D311yescharacteristic
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6C2×D311yescharacteristic
165C3×C22⋊Q8—38no—
166C3×#121—38no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—32no—
169C2×C3×C4⋊C4C2×D311yescharacteristic
170C2×C3×C4⋊C4C2×D311yescharacteristic
171C2×C3×C22⋊C4—32no—
172C2×C3×C22⋊C4—32no—
173C2×#217—32no—
174C2×#217—32no—
175#946—38no—
176#939—316no—
177#938—38no—
178#938—316no—
179#930—38no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4C2×D312yes—
183C2×(C2×D3)⋊C4C2×D312yes—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187C2×C4⋊Dic3C2×D312yes—
188#924—38no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4—32no—
192C2×Dic3⋊C4—32no—
193C2×Dic3⋊C4—62no—
194#897C2×D318yescomplemented
195#896—316no—
196#895—316no—
197#895C2×D318yescomplemented
198D3×C4⋊C4—38no—
199D3×C4⋊C4—38no—
200D3×C4⋊C4—68no—
201#884—316no—
202#884—316no—
203#884—316no—
204#878—316no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3C2×D414yes—
209C22×C3⋊D3C2412yes—
210C22×C3×D3—24no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—24no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3C2412yes—
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C2×C32×C4—24no—
223C2×C32×C4C2×D414yes—
224C2×C32×C4C2414yes—
225C2×C32×C4C2412yes—
226C2×C3⋊Dic3—24no—
227C2×C3⋊Dic3C2×D414yes—
228C2×C3⋊Dic3C2414yes—
229C2×C3⋊Dic3C2412yes—
230C4×C3⋊D3—48no—
231C4×C3⋊D3C2×D4116yescomplemented
232C2×C3×Dic3—24no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2412yes—
238C3×D12—28no—
239C3×D12—48no—
240C3×C4×D3—28no—
241C3×C4×D3—28no—
242C3×Dic6—28no—
243#627—28no—
244#626—216no—
245#626—28no—
246#626—28no—
247#625—28no—
248#625—48no—
249D3×Dic3—216no—
250C22×#41—91no—
251C22×#41—91no—
252#537—916no—
253C2×C22⋊Q8—31no—
254C2×C22⋊Q8—92no—
255C2×C22⋊Q8—91no—
256C2×#121—31no—
257C2×#121—92no—
258C2×#121—92no—
259C2×#121—92no—
260C2×#121—91no—
261C22×C4⋊C4—91no—
262C24×C3—31no—
263C24×C3—32no—
264C24×C3—31no—
265C23×D3—31no—
266C23×D3—31no—
267C23×D3—61no—
268C23×D3C22×D311yescharacteristic
269C23×D3C22×D312yes—
270C23×D3C22×D311yescharacteristic
271C2×C3×Q8—34no—
272C2×C3×Q8—64no—
273C2×C3×D4—34no—
274C2×C3×D4—38no—
275C2×C3×D4—64no—
276C2×C3×D4—124no—
277C22×C3×C4—21no—
278C22×C3×C4—22no—
279C22×C3×C4—31no—
280C22×C3×C4—32no—
281C22×C3×C4—31no—
282C22×C3×C4—34no—
283C22×C3×C4—34no—
284C22×C3×C4—64no—
285C22×C3×C4—64no—
286C22×C3×C4C22×D312yes—
287C22×C3×C4C22×D312yes—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C2×#67—34no—
291C2×#67—34no—
292C2×#67—38no—
293C2×#67—38no—
294C2×#67—34no—
295C2×#67—38no—
296C2×#67—34no—
297C2×#67—64no—
298C2×#67—64no—
299C2×#67—68no—
300C2×#67—64no—
301C2×#67—64no—
302C2×#67—124no—
303C2×#67—124no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—32no—
307C22×Dic3—32no—
308C22×Dic3—38no—
309C22×Dic3—61no—
310C22×Dic3—62no—
311C22×Dic3—68no—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D312yes—
314C22×Dic3C22×D311yescharacteristic
315#239—632no—
316#237—632no—
317#235—632no—
318#235—632no—
319C2×D12—24no—
320C2×D12—34no—
321C2×D12—38no—
322C2×D12—34no—
323C2×D12—44no—
324C2×D12—64no—
325C2×D12—64no—
326C2×D12—68no—
327C2×D12C22×D314yes—
328C2×D12C22×D318yes—
329C2×C4×D3—24no—
330C2×C4×D3—24no—
331C2×C4×D3—38no—
332C2×C4×D3—38no—
333C2×C4×D3—34no—
334C2×C4×D3—34no—
335C2×C4×D3—38no—
336C2×C4×D3—38no—
337C2×C4×D3—38no—
338C2×C4×D3—64no—
339C2×C4×D3—68no—
340C2×C4×D3—68no—
341C2×C4×D3—68no—
342C2×C4×D3—124no—
343C2×C4×D3—124no—
344C2×C4×D3—128no—
345C2×C4×D3C22×D314yes—
346C2×C4×D3C22×D314yes—
347C2×Dic6—24no—
348C2×Dic6—34no—
349C2×Dic6—34no—
350C2×Dic6—64no—
351C2×Dic6—64no—
352C2×Dic6C22×D314yes—
353C3×C4⋊C4—24no—
354C3×C4⋊C4—38no—
355C3×C4⋊C4C22×D314yes—
356C3×C4⋊C4C22×D314yes—
357C3×C22⋊C4—38no—
358C3×C22⋊C4—38no—
359#217—38no—
360#217—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4C22×D318yes—
364(C2×D3)⋊C4C22×D318yes—
365C4⋊Dic3—34no—
366C4⋊Dic3—34no—
367C4⋊Dic3—64no—
368C4⋊Dic3C22×D318yes—
369Dic3⋊C4—38no—
370Dic3⋊C4—38no—
371Dic3⋊C4—38no—
372Dic3⋊C4—38no—
373Dic3⋊C4—68no—
374C22×C32C22×D412yes—
375C22×C32H(5,𝔽2)12yes—
376C22×C322−1+412yes—
377C22×C32C2511yescharacteristic
378C2×C3⋊D3—28no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—22no—
381C2×C3⋊D3C22×D414yes—
382C2×C3×D3—24no—
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—24no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—24no—
391C2×C3×D3—48no—
392C2×C3×D3—44no—
393C2×C3×D3—44no—
394C32×C4—24no—
395C32×C4C22×D414yes—
396C3⋊Dic3—24no—
397C3⋊Dic3C22×D414yes—
398C3×Dic3—24no—
399C3×Dic3—22no—
400C3×Dic3—22no—
401C2×#41—98no—
402C2×#41—98no—
403C2×#41—188no—
404C2×#41—188no—
405C22×Q8—31no—
406C22×Q8—91no—
407C22×D4—31no—
408C22×D4—32no—
409C22×D4—91no—
410C22×D4—92no—
411C22×D4—91no—
412C22×D4—91no—
413C22×D4—92no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—92no—
417C23×C4—91no—
418C23×C4—92no—
419C22⋊Q8—38no—
420C22⋊Q8—916no—
421C22⋊Q8—98no—
422#121—38no—
423#121—916no—
424#121—916no—
425#121—916no—
426#121—98no—
427C2×C4⋊C4—32no—
428C2×C4⋊C4—92no—
429C2×C4⋊C4—92no—
430C2×C4⋊C4—91no—
431C2×C4⋊C4—98no—
432C2×C4⋊C4D3211yescharacteristic
433C2×C22⋊C4—32no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C23×C3—21no—
438C23×C3—32no—
439C23×C3—34no—
440C23×C3—32no—
441C23×C3—64no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—64no—
447C23×C3—64no—
448C23×C3—62no—
449C23×C3—62no—
450C23×C3C23×D311yescharacteristic
451C23×C3C23×D311yescharacteristic
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—24no—
455C22×D3—22no—
456C22×D3—24no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—24no—
461C22×D3—34no—
462C22×D3—34no—
463C22×D3—32no—
464C22×D3—32no—
465C22×D3—64no—
466C22×D3—62no—
467C22×D3—64no—
468C22×D3—64no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3C23×D312yes—
474C22×D3C23×D314yes—
475C22×D3C23×D312yes—
476C3×Q8—68no—
477C3×D4—68no—
478C3×D4—128no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—32no—
485C2×C3×C4—34no—
486C2×C3×C4—32no—
487C2×C3×C4—44no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—64no—
491C2×C3×C4—68no—
492C2×C3×C4—68no—
493C2×C3×C4D3×D414yes—
494C2×C3×C4D3×D414yes—
495C2×C3×C4C23×D314yes—
496C2×C3×C4C23×D314yes—
497C2×C3×C4C23×D312yes—
498C2×C3×C4C23×D312yes—
499#67—68no—
500#67—68no—
501#67—616no—
502#67—68no—
503#67—68no—
504#67—128no—
505#67—128no—
506C2×Dic3—24no—
507C2×Dic3—22no—
508C2×Dic3—22no—
509C2×Dic3—34no—
510C2×Dic3—34no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—34no—
514C2×Dic3—34no—
515C2×Dic3—64no—
516C2×Dic3—62no—
517C2×Dic3—64no—
518C2×Dic3—616no—
519C2×Dic3—64no—
520C2×Dic3—64no—
521C2×Dic3—124no—
522C2×Dic3C23×D312yes—
523C2×Dic3C23×D314yes—
524C2×Dic3C23×D312yes—
525D12—28no—
526D12—48no—
527D12—68no—
528D12—68no—
529D12—616no—
530C4×D3—28no—
531C4×D3—28no—
532C4×D3—316no—
533C4×D3—316no—
534C4×D3—616no—
535C4×D3—616no—
536C4×D3—128no—
537C4×D3—128no—
538C4×D3—1216no—
539Dic6—28no—
540Dic6—68no—
541Dic6—68no—
542C2×C32#53714yescomplemented
543C2×C32C23×D411yescharacteristic
544C2×C32C2×H(5,𝔽2)11yescharacteristic
545C2×C32C2×2−1+411yescharacteristic
546C3⋊D3—24no—
547C3×D3—44no—
548C3×D3—42no—
549C3×D3—42no—
550C24—31no—
551C24—32no—
552C24—31no—
553C24—91no—
554#41—1832no—
555#41—1832no—
556C2×Q8—34no—
557C2×Q8—64no—
558C2×Q8—94no—
559C2×Q8—184no—
560C2×D4—34no—
561C2×D4—38no—
562C2×D4—64no—
563C2×D4—94no—
564C2×D4—98no—
565C2×D4—94no—
566C2×D4—94no—
567C2×D4—98no—
568C2×D4—124no—
569C2×D4—184no—
570C2×D4—184no—
571C2×D4—188no—
572C2×D4—184no—
573C2×D4—364no—
574C22×C4—31no—
575C22×C4—32no—
576C22×C4—31no—
577C22×C4—34no—
578C22×C4—34no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—98no—
582C22×C4—91no—
583C22×C4—94no—
584C22×C4—98no—
585C22×C4—92no—
586C22×C4—98no—
587C22×C4—188no—
588C22×C4—364no—
589C22×C4C2×D3212yes—
590C22×C4C2×D3211yescharacteristic
591C4⋊C4—38no—
592C4⋊C4—98no—
593C4⋊C4—98no—
594C4⋊C4—94no—
595C4⋊C4C2×D3214yes—
596C22⋊C4—38no—
597C22⋊C4—38no—
598C22⋊C4—98no—
599C22⋊C4—98no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—64no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—124no—
614C22×C3—128no—
615C22×C3—124no—
616C22×C3C2×D3×D412yes—
617C22×C3C2×D3×D412yes—
618C22×C3#100412yes—
619C22×C3#100712yes—
620C22×C3#100912yes—
621C22×C3#101012yes—
622C22×C3C24×D311yescharacteristic
623C22×C3C24×D311yescharacteristic
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—24no—
627C2×D3—22no—
628C2×D3—24no—
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—22no—
632C2×D3—24no—
633C2×D3—34no—
634C2×D3—34no—
635C2×D3—44no—
636C2×D3—48no—
637C2×D3—44no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—616no—
642C2×D3—62no—
643C2×D3—62no—
644C2×D3—62no—
645C2×D3—62no—
646C2×D3—68no—
647C2×D3—68no—
648C3×C4—24no—
649C3×C4—24no—
650C3×C4—24no—
651C3×C4—44no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—64no—
655C3×C4C2×D3×D414yes—
656C3×C4C2×D3×D414yes—
657Dic3—24no—
658Dic3—22no—
659Dic3—22no—
660Dic3—34no—
661Dic3—34no—
662Dic3—64no—
663Dic3—64no—
664Dic3—64no—
665Dic3—124no—
666C32C2×#53711yescharacteristic, complemented, Sylow
667C23—32no—
668C23—34no—
669C23—32no—
670C23—62no—
671C23—62no—
672C23—64no—
673C23—62no—
674C23—64no—
675C23—62no—
676C23—62no—
677C23—64no—
678C23—62no—
679C23—94no—
680C23—92no—
681C23—182no—
682C23—182no—
683C23C22×D3211yescharacteristic
684Q8—68no—
685Q8—188no—
686D4—68no—
687D4—128no—
688D4—188no—
689D4—188no—
690D4—1816no—
691D4—188no—
692D4—368no—
693C2×C4—24no—
694C2×C4—32no—
695C2×C4—34no—
696C2×C4—32no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—68no—
701C2×C4—68no—
702C2×C4—94no—
703C2×C4—92no—
704C2×C4—916no—
705C2×C4—94no—
706C2×C4—1816no—
707C2×C4—184no—
708C2×C4—368no—
709C2×C4#380214yes—
710C2×C4C22×D3214yes—
711C2×C4C22×D3212yes—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—24no—
716C2×C3—122no—
717C2×C3—124no—
718C2×C3—122no—
719C2×C3#560814yescomplemented
720C2×C3#562914yescomplemented
721C2×C3C22×D3×D411yescharacteristic
722C2×C3C22×D3×D411yescharacteristic
723C2×C3C2×#100411yescharacteristic
724C2×C3C2×#100711yescharacteristic
725C2×C3C2×#100911yescharacteristic
726C2×C3C2×#101011yescharacteristic
727D3—42no—
728D3—44no—
729D3—42no—
730D3—68no—
731D3—64no—
732D3—64no—
733C22—62no—
734C22—62no—
735C22—64no—
736C22—62no—
737C22—64no—
738C22—62no—
739C22—62no—
740C22—64no—
741C22—62no—
742C22—94no—
743C22—124no—
744C22—124no—
745C22—128no—
746C22—182no—
747C22—182no—
748C22—188no—
749C22C2×#380212yes—
750C22#6431412yes—
751C22#6431512yes—
752C22C23×D3211yescharacteristic
753C4—24no—
754C4—62no—
755C4—62no—
756C4—64no—
757C4—94no—
758C4—184no—
759C4C2×#380214yes—
760C3—21no—
761C3C2×#560811yescharacteristic, complemented
762C3C2×#562911yescharacteristic, complemented
763C2—122no—
764C2—122no—
765C2—124no—
766C2—184no—
767C2#1059452814yesdirect product factor
768C2C22×#380211yescharacteristic
769C2C2×#6431411yescharacteristic
770C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3798C2semidirect
2. C22×#3796C2semidirect
3. C2×C4⋊C4×C3⋊D3C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#895C2semidirect
6. C2×#63916C2semidirect
7. C2×#63912C2semidirect
8. C2×#63908C2semidirect
9. C2×#63899C2semidirect
10. C2×#63885C2semidirect
11. C2×#63856C2semidirect
12. #10594528C2direct (N × H)
30. C2×#3798C22semidirect
32. C2×#3796C22semidirect
36. C4⋊C4×C3⋊D3C22semidirect
40. C3×#897C22semidirect
41. C3×#895C22semidirect
45. #63916C22semidirect
46. #63912C22semidirect
47. #63908C22semidirect
48. #63899C22semidirect
49. #63885C22semidirect
50. #63856C22semidirect
65. C2×#897D3semidirect
68. C2×#895D3semidirect
85. C2×C4×C3⋊D3D4semidirect
194. #897C2×D3semidirect
197. #895C2×D3semidirect
231. C4×C3⋊D3C2×D4semidirect
542. C2×C32#537semidirect
666. C32C2×#537semidirect
719. C2×C3#5608semidirect
720. C2×C3#5629semidirect
761. C3C2×#5608semidirect
762. C3C2×#5629semidirect
767. C2#10594528direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37982
C22×#37962
C2×C4⋊C4×C3⋊D32
C2×C3×#8972
C2×C3×#8952
C2×#639162
C2×#639122
C2×#639082
C2×#638992
C2×#638852
C2×#638562
#105945282
C2×#56293
C2×#56083