Finite Group Databasebeta

← C2×#10595398 #11901163

Subgroups — C2×#10595398 #11901163

Order 1152.

3441 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×C3×#239C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64155C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595398C2116yesmaximal, direct product factor
6C2×#63916C211yesmaximal, characteristic, complemented
7C2×#63908C211yesmaximal, characteristic, complemented
8C2×#63906C212yesmaximal, complemented
9C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63886C212yesmaximal, complemented
11C2×#63885C212yesmaximal, complemented
12C2×#63851C212yesmaximal, complemented
13C2×#5833—31nomaximal
14C2×#5629—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#239—28no—
18C2×C3×#239C2218yescomplemented
19C22×C3×D12C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2212yes—
28C22×#625C2211yescharacteristic
29C22×#625C2212yes—
30C22×D3×Dic3C2212yes—
31C2×#3798—28no—
32C2×#3798C2218yescomplemented
33#64155C2218yescomplemented
34C2×#3752C2212yes—
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×#3750C2212yes—
37C3×#946C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63916C2218yescomplemented
45#63908C2218yescomplemented
46#63906C22116yescomplemented
47D3×C4⋊Dic3C2218yescomplemented
48#63886C22116yescomplemented
49#63885C22116yescomplemented
50#63851C22116yescomplemented
51C22×C3×#41—31no—
52C22×#239D311yescharacteristic, complemented
53C22×#235—31no—
54C22×#235—31no—
55C2×C3×C22⋊Q8—31no—
56#5833—316no—
57C2×#946—31no—
58C2×#946—31no—
59C2×#946—61no—
60C2×#946D311yescharacteristic, complemented
61C2×#939—32no—
62C2×#939—32no—
63C2×#938—31no—
64C2×#938—31no—
65C2×#930—31no—
66C2×#930—32no—
67C22×C4⋊Dic3—31no—
68C2×#924—32no—
69#5629—316no—
70C2×#896—32no—
71C2×#895—32no—
72C2×#895—31no—
73C2×D3×C4⋊C4—31no—
74C2×#884—32no—
75C2×#884—32no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C2×C32×Q8—24no—
81C2×C32×Q8C2314yes—
82C22×C32×C4C2312yes—
83C22×C32×C4C2311yescharacteristic
84C22×C3⋊Dic3C2312yes—
85C22×C3⋊Dic3C2311yescharacteristic
86C2×C4×C3⋊D3—24no—
87C2×C4×C3⋊D3C2314yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C3×#239—232no—
92C2×C3×D12—28no—
93C2×C3×D12—24no—
94C2×C3×D12C2318yes—
95C2×C3×D12C2314yes—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3—28no—
98C2×C3×C4×D3D418yescomplemented
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2318yes—
101C2×C3×C4×D3C2314yes—
102C2×#627—24no—
103C2×#627C2314yes—
104C2×#626—24no—
105C2×#626—24no—
106C2×#626—44no—
107C2×#626C2314yes—
108C2×#626C2314yes—
109C2×#626C2318yes—
110C2×#625—24no—
111C2×#625—44no—
112C2×#625C2314yes—
113C2×#625C2318yes—
114C2×D3×Dic3—44no—
115C2×D3×Dic3C2318yes—
116#3798—232no—
117#3752C2318yes—
118C4⋊(C3⋊Dic3)C2314yes—
119#3750C2318yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×C4⋊Dic3C2314yes—
122C3×Dic3⋊C4C2318yes—
123Dic3⋊Dic3C2318yes—
124(C2×D3)⋊Dic3C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C2×#537—91noSylow
127C2×C3×#41—38no—
128C2×C3×#41—68no—
129C22×C3×Q8—21no—
130C22×C3×Q8C2×D311yescharacteristic
131C22×C3×Q8C2×D311yescharacteristic
132C22×C3×D4—31no—
133C22×C3×D4—32no—
134C23×C3×C4—31no—
135C23×C3×C4—31no—
136C23×C3×C4—32no—
137C22×#67—31no—
138C22×#67—31no—
139C22×#67—32no—
140C22×#67—32no—
141C22×#67—31no—
142C22×#67—31no—
143C22×#67—32no—
144C23×Dic3—32no—
145C2×#239—28no—
146C2×#239C2×D318yescomplemented
147C2×#235—38no—
148C2×#235—38no—
149C2×#235—68no—
150C2×#235—68no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12—32no—
154C22×D12C2×D312yes—
155C22×D12C2×D311yescharacteristic
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—32no—
159C22×C4×D3—61no—
160C22×C4×D3C2×D311yescharacteristic
161C22×C4×D3C2×D312yes—
162C22×C4×D3C2×D311yescharacteristic
163C22×Dic6—31no—
164C22×Dic6—31no—
165C3×C22⋊Q8—38no—
166C2×C3×C4⋊C4—32no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—32no—
169C2×#217—32no—
170C2×#217—32no—
171#946—38no—
172#946—38no—
173#946—68no—
174#946C2×D318yescomplemented
175#939—316no—
176#939—316no—
177#938—38no—
178#938—38no—
179#930—38no—
180#930—316no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—32no—
183C2×(C2×D3)⋊C4—32no—
184C2×(C2×D3)⋊C4—32no—
185C2×(C2×D3)⋊C4—62no—
186C2×(C2×D3)⋊C4C2×D312yes—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—32no—
190C2×C4⋊Dic3—38no—
191C2×C4⋊Dic3—61no—
192C2×C4⋊Dic3C2×D311yescharacteristic
193#924—316no—
194C2×Dic3⋊C4—32no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4—62no—
198C2×Dic3⋊C4C2×D312yes—
199#896—316no—
200#895—316no—
201#895—38no—
202D3×C4⋊C4—38no—
203#884—316no—
204#884—316no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3C2412yes—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—24no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3C2×D414yes—
219C22×C3×D3C2414yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2412yes—
222C32×Q8—28no—
223C2×C32×C4—24no—
224C2×C32×C4C2×D414yes—
225C2×C32×C4C2414yes—
226C2×C32×C4C2412yes—
227C2×C3⋊Dic3—22no—
228C2×C3⋊Dic3—24no—
229C2×C3⋊Dic3C2412yes—
230C2×C3⋊Dic3C2414yes—
231C4×C3⋊D3—28no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3C2×D414yes—
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2412yes—
238C3×D12—216no—
239C3×D12—28no—
240C3×C4×D3—28no—
241C3×C4×D3—216no—
242C3×C4×D3C2×D4116yescomplemented
243#627—28no—
244#626—28no—
245#626—28no—
246#626—48no—
247#625—28no—
248#625—48no—
249D3×Dic3—48no—
250C22×#41—31no—
251C22×#41—91no—
252#537—916no—
253C2×C22⋊Q8—31no—
254C2×C22⋊Q8—92no—
255C2×C22⋊Q8—91no—
256C2×#121—92no—
257C2×#121—92no—
258C2×#121—91no—
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×D312yes—
269C23×D3C22×D311yescharacteristic
270C23×D3C22×D311yescharacteristic
271C3×#41—632no—
272C2×C3×Q8—24no—
273C2×C3×Q8—24no—
274C2×C3×Q8—24no—
275C2×C3×Q8—44no—
276C2×C3×Q8C22×D314yes—
277C2×C3×Q8C22×D314yes—
278C2×C3×D4—34no—
279C2×C3×D4—38no—
280C2×C3×D4—68no—
281C2×C3×D4—64no—
282C22×C3×C4—21no—
283C22×C3×C4—22no—
284C22×C3×C4—31no—
285C22×C3×C4—38no—
286C22×C3×C4—34no—
287C22×C3×C4—32no—
288C22×C3×C4—31no—
289C22×C3×C4—38no—
290C22×C3×C4—34no—
291C22×C3×C4—68no—
292C22×C3×C4—64no—
293C22×C3×C4C22×D312yes—
294C22×C3×C4C22×D312yes—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C2×#67—34no—
298C2×#67—34no—
299C2×#67—38no—
300C2×#67—38no—
301C2×#67—34no—
302C2×#67—34no—
303C2×#67—38no—
304C2×#67—64no—
305C2×#67—64no—
306C2×#67—64no—
307C2×#67—64no—
308C2×#67—124no—
309C2×#67—124no—
310C2×#67—124no—
311C22×Dic3—32no—
312C22×Dic3—31no—
313C22×Dic3—31no—
314C22×Dic3—32no—
315C22×Dic3—38no—
316C22×Dic3—61no—
317C22×Dic3—62no—
318C22×Dic3—124no—
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D312yes—
321C22×Dic3C22×D311yescharacteristic
322#239—232no—
323#235—632no—
324#235—632no—
325C2×D12—28no—
326C2×D12—24no—
327C2×D12—34no—
328C2×D12—34no—
329C2×D12—38no—
330C2×D12—64no—
331C2×D12—64no—
332C2×D12—124no—
333C2×D12C22×D318yes—
334C2×D12C22×D314yes—
335C2×C4×D3—24no—
336C2×C4×D3—28no—
337C2×C4×D3—34no—
338C2×C4×D3—34no—
339C2×C4×D3—38no—
340C2×C4×D3—64no—
341C2×C4×D3—64no—
342C2×C4×D3—64no—
343C2×C4×D3—124no—
344C2×C4×D3—124no—
345C2×C4×D3#6718yescomplemented
346C2×C4×D3C22×D318yes—
347C2×C4×D3C22×D314yes—
348C2×C4×D3C22×D314yes—
349C2×Dic6—34no—
350C2×Dic6—34no—
351C2×Dic6—64no—
352C2×Dic6—64no—
353C3×C4⋊C4—34no—
354C3×C4⋊C4—38no—
355C3×C22⋊C4—38no—
356#217—38no—
357#217—38no—
358(C2×D3)⋊C4—38no—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—68no—
363(C2×D3)⋊C4C22×D318yes—
364C4⋊Dic3—34no—
365C4⋊Dic3—34no—
366C4⋊Dic3—38no—
367C4⋊Dic3—64no—
368C4⋊Dic3C22×D314yes—
369Dic3⋊C4—38no—
370Dic3⋊C4—38no—
371Dic3⋊C4—38no—
372Dic3⋊C4—68no—
373Dic3⋊C4C22×D318yes—
374C22×C32C22×D412yes—
375C22×C32H(5,𝔽2)12yes—
376C22×C322−1+412yes—
377C22×C32C2511yescharacteristic
378C2×C3⋊D3—22no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—22no—
381C2×C3⋊D3—44no—
382C2×C3×D3—28no—
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—24no—
387C2×C3×D3—22no—
388C2×C3×D3—24no—
389C2×C3×D3—22no—
390C2×C3×D3—24no—
391C2×C3×D3—48no—
392C2×C3×D3—44no—
393C2×C3×D3C22×D414yes—
394C32×C4—24no—
395C32×C4C22×D414yes—
396C3⋊Dic3—22no—
397C3⋊Dic3—24no—
398C3×Dic3—22no—
399C3×Dic3—24no—
400C3×Dic3C22×D414yes—
401C2×#41—38no—
402C2×#41—68no—
403C2×#41—98no—
404C2×#41—188no—
405C22×Q8—91no—
406C22×Q8D3211yescharacteristic
407C22×D4—32no—
408C22×D4—31no—
409C22×D4—91no—
410C22×D4—91no—
411C22×D4—92no—
412C22×D4—91no—
413C22×D4—92no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—32no—
417C23×C4—92no—
418C23×C4—91no—
419C22⋊Q8—38no—
420C22⋊Q8—916no—
421C22⋊Q8—98no—
422#121—916no—
423#121—916no—
424#121—98no—
425#121—916no—
426#121—98no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—32no—
429C2×C4⋊C4—98no—
430C2×C4⋊C4—92no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—92no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C23×C3—21no—
438C23×C3—34no—
439C23×C3—32no—
440C23×C3—34no—
441C23×C3—32no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—62no—
447C23×C3—64no—
448C23×C3—62no—
449C23×C3—62no—
450C23×C3C23×D311yescharacteristic
451C23×C3C23×D311yescharacteristic
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—24no—
457C22×D3—22no—
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—32no—
461C22×D3—32no—
462C22×D3—62no—
463C22×D3—64no—
464C22×D3—62no—
465C22×D3—62no—
466C22×D3—62no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3C2×#6714yes—
473C22×D3C23×D314yes—
474C22×D3C23×D312yes—
475C22×D3C23×D312yes—
476C3×Q8—28no—
477C3×Q8—28no—
478C3×Q8—48no—
479C3×D4—616no—
480C3×D4—68no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—34no—
487C2×C3×C4—32no—
488C2×C3×C4—316no—
489C2×C3×C4—34no—
490C2×C3×C4—32no—
491C2×C3×C4—44no—
492C2×C3×C4—616no—
493C2×C3×C4—64no—
494C2×C3×C4—62no—
495C2×C3×C4—68no—
496C2×C3×C4D3×D414yes—
497C2×C3×C4C2×#6714yes—
498C2×C3×C4C23×D314yes—
499C2×C3×C4C23×D314yes—
500C2×C3×C4C23×D312yes—
501C2×C3×C4C23×D312yes—
502#67—68no—
503#67—68no—
504#67—68no—
505#67—68no—
506#67—128no—
507#67—128no—
508#67—128no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—34no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—34no—
515C2×Dic3—62no—
516C2×Dic3—64no—
517C2×Dic3—62no—
518C2×Dic3—64no—
519C2×Dic3—64no—
520C2×Dic3—62no—
521C2×Dic3—122no—
522C2×Dic3—124no—
523C2×Dic3—128no—
524C2×Dic3C2×#6714yes—
525C2×Dic3C23×D312yes—
526C2×Dic3C23×D314yes—
527C2×Dic3C23×D312yes—
528D12—216no—
529D12—28no—
530D12—68no—
531D12—68no—
532D12—128no—
533C4×D3—28no—
534C4×D3—216no—
535C4×D3—68no—
536C4×D3—68no—
537C4×D3—128no—
538C4×D3—128no—
539C4×D3C2×#67116yescomplemented
540Dic6—68no—
541Dic6—68no—
542C2×C32#53714yescomplemented
543C2×C32C23×D411yescharacteristic
544C2×C32C2×H(5,𝔽2)11yescharacteristic
545C2×C32C2×2−1+411yescharacteristic
546C3⋊D3—42no—
547C3×D3—24no—
548C3×D3—42no—
549C3×D3—44no—
550C24—31no—
551C24—31no—
552C24—32no—
553C24—91no—
554#41—632no—
555#41—1832no—
556C2×Q8—24no—
557C2×Q8—94no—
558C2×Q8—184no—
559C2×Q8C2×D3214yes—
560C2×D4—38no—
561C2×D4—34no—
562C2×D4—68no—
563C2×D4—64no—
564C2×D4—94no—
565C2×D4—94no—
566C2×D4—98no—
567C2×D4—94no—
568C2×D4—98no—
569C2×D4—184no—
570C2×D4—184no—
571C2×D4—184no—
572C2×D4—364no—
573C2×D4—364no—
574C22×C4—31no—
575C22×C4—34no—
576C22×C4—38no—
577C22×C4—32no—
578C22×C4—31no—
579C22×C4—34no—
580C22×C4—38no—
581C22×C4—68no—
582C22×C4—64no—
583C22×C4—98no—
584C22×C4—92no—
585C22×C4—91no—
586C22×C4—94no—
587C22×C4—184no—
588C22×C4—364no—
589C22×C4C2×D3212yes—
590C22×C4C2×D3211yescharacteristic
591C4⋊C4—34no—
592C4⋊C4—38no—
593C4⋊C4—98no—
594C4⋊C4—94no—
595C4⋊C4—98no—
596C22⋊C4—38no—
597C22⋊C4—98no—
598C22⋊C4—98no—
599C22⋊C4—98no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—34no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—68no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—124no—
615C22×C3—128no—
616C22×C3C2×D3×D412yes—
617C22×C3#100712yes—
618C22×C3#100912yes—
619C22×C3#100912yes—
620C22×C3#101012yes—
621C22×C3C22×#6712yes—
622C22×C3C24×D311yescharacteristic
623C22×C3C24×D311yescharacteristic
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—28no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—24no—
630C2×D3—22no—
631C2×D3—24no—
632C2×D3—24no—
633C2×D3—48no—
634C2×D3—44no—
635C2×D3—64no—
636C2×D3—62no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—122no—
643C2×D3—122no—
644C2×D3—128no—
645C2×D3—124no—
646C2×D3—124no—
647C2×D3C22×#6714yes—
648C3×C4—24no—
649C3×C4—24no—
650C3×C4—24no—
651C3×C4—34no—
652C3×C4—44no—
653C3×C4—64no—
654C3×C4—62no—
655C3×C4C2×D3×D414yes—
656C3×C4C22×#6714yes—
657Dic3—22no—
658Dic3—24no—
659Dic3—62no—
660Dic3—64no—
661Dic3—64no—
662Dic3—62no—
663Dic3—122no—
664Dic3—124no—
665Dic3C22×#6714yes—
666C32C2×#53711yescharacteristic, complemented, Sylow
667C23—34no—
668C23—32no—
669C23—32no—
670C23—34no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—64no—
675C23—64no—
676C23—62no—
677C23—64no—
678C23—62no—
679C23—92no—
680C23—182no—
681C23—182no—
682C23—182no—
683C23C22×D3211yescharacteristic
684Q8—28no—
685Q8—188no—
686D4—616no—
687D4—68no—
688D4—188no—
689D4—188no—
690D4—188no—
691D4—368no—
692D4—368no—
693C2×C4—24no—
694C2×C4—34no—
695C2×C4—32no—
696C2×C4—316no—
697C2×C4—34no—
698C2×C4—32no—
699C2×C4—616no—
700C2×C4—64no—
701C2×C4—62no—
702C2×C4—68no—
703C2×C4—94no—
704C2×C4—92no—
705C2×C4—184no—
706C2×C4—182no—
707C2×C4—188no—
708C2×C4—368no—
709C2×C4D3×#6714yes—
710C2×C4C22×D3214yes—
711C2×C4C22×D3212yes—
712C2×C3—24no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—64no—
717C2×C3—124no—
718C2×C3—122no—
719C2×C3#562914yescomplemented
720C2×C3#583314yescomplemented
721C2×C3C22×D3×D411yescharacteristic
722C2×C3C2×#100711yescharacteristic
723C2×C3C2×#100911yescharacteristic
724C2×C3C2×#100911yescharacteristic
725C2×C3C2×#101011yescharacteristic
726C2×C3C23×#6711yescharacteristic
727D3—24no—
728D3—42no—
729D3—44no—
730D3—124no—
731D3—122no—
732D3—122no—
733C22—34no—
734C22—68no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—64no—
739C22—64no—
740C22—62no—
741C22—64no—
742C22—62no—
743C22—128no—
744C22—124no—
745C22—182no—
746C22—182no—
747C22—182no—
748C22—364no—
749C22#6431512yes—
750C22#6432012yes—
751C22C2×D3×#6712yes—
752C22C23×D3211yescharacteristic
753C4—24no—
754C4—34no—
755C4—64no—
756C4—62no—
757C4—184no—
758C4—182no—
759C4C2×D3×#6714yes—
760C3—21no—
761C3C2×#562911yescharacteristic, complemented
762C3C2×#583311yescharacteristic, complemented
763C2—64no—
764C2—124no—
765C2—122no—
766C2—362no—
767C2#1059539814yesdirect product factor
768C2C2×#6431511yescharacteristic
769C2C2×#6432011yescharacteristic
770C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×#3798C2semidirect
3. C2×#64155C2semidirect
4. C2×C3×#946C2semidirect
5. #10595398C2direct (N × H)
6. C2×#63916C2semidirect
7. C2×#63908C2semidirect
8. C2×#63906C2semidirect
9. C2×D3×C4⋊Dic3C2semidirect
10. C2×#63886C2semidirect
11. C2×#63885C2semidirect
12. C2×#63851C2semidirect
18. C2×C3×#239C22semidirect
32. C2×#3798C22semidirect
33. #64155C22semidirect
37. C3×#946C22semidirect
44. #63916C22semidirect
45. #63908C22semidirect
46. #63906C22semidirect
47. D3×C4⋊Dic3C22semidirect
48. #63886C22semidirect
49. #63885C22semidirect
50. #63851C22semidirect
52. C22×#239D3semidirect
60. C2×#946D3semidirect
98. C2×C3×C4×D3D4semidirect
146. C2×#239C2×D3semidirect
174. #946C2×D3semidirect
242. C3×C4×D3C2×D4semidirect
345. C2×C4×D3#67semidirect
539. C4×D3C2×#67semidirect
542. C2×C32#537semidirect
666. C32C2×#537semidirect
719. C2×C3#5629semidirect
720. C2×C3#5833semidirect
761. C3C2×#5629semidirect
762. C3C2×#5833semidirect
767. C2#10595398direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×#37982
C2×#641552
C2×C3×#9462
#105953982
C2×#639162
C2×#639082
C2×#639062
C2×D3×C4⋊Dic32
C2×#638862
C2×#638852
C2×#638512
C2×#58333
C2×#56293