Finite Group Databasebeta

← C2×#10594803 #11902671

Subgroups — C2×#10594803 #11902671

Order 1152.

3349 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×Dic6C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63964C212yesmaximal, complemented
6C2×#63952C212yesmaximal
7C2×#63888C212yesmaximal, complemented
8C2×#63873C211yesmaximal, characteristic, complemented
9C2×#63871C211yesmaximal, characteristic, complemented
10C2×#63843C211yesmaximal, characteristic, complemented
11C2×#63839C212yesmaximal, complemented
12#10594803C2116yesmaximal, direct product factor
13C2×Q8×#67—31nomaximal
14C2×#5632—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C22×C3×Dic6—28no—
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yes—
23C22×C3×Dic6C2211yescharacteristic
24C22×C3×Dic6C2218yescomplemented
25C22×#627C2212yes—
26C22×#624C2212yes—
27C2×#3797—28no—
28C2×#3797C2218yescomplemented
29C2×#3757C2211yescharacteristic
30C4×#638C2218yes—
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C3×#217C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C3×#924C2218yescomplemented
37C2×C3×Dic3⋊C4C2212yes—
38C2×#3724C2212yes—
39C2×#3724C2212yes—
40C2×Dic3⋊Dic3C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42#63964C22116yescomplemented
43C2×#3722C2212yes—
44C2×Dic32C2212yes—
45#63952C22116yes—
46#63888C22116yescomplemented
47#63873C2218yescomplemented
48#63871C2218yescomplemented
49#63843C2218yescomplemented
50#63839C22116yescomplemented
51C23×C3×Q8—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C23×Dic6D311yescharacteristic, complemented
55C2×C3×C22⋊Q8—31no—
56Q8×#67—316no—
57C2×#946—31no—
58C2×#946—32no—
59C2×Q8×Dic3—31no—
60C2×#944—31no—
61C2×#944—31no—
62C2×#944—32no—
63C2×C4×#67—31no—
64C2×C4×#67—31no—
65C2×C4×#67—32no—
66C2×C4×#67—61no—
67C2×#924—32no—
68C2×#924D311yescharacteristic, complemented
69#5632—316no—
70C2×#897—31no—
71C2×#896—32no—
72C2×#888—32no—
73C2×#887—31no—
74C2×#67⋊C4—32no—
75C2×#878—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C22×C32×C4—24no—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2314yes—
81C22×C32×C4C2311yescharacteristic
82C2×#638Q818yescomplemented
83C2×#638C2314yes—
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2311yescharacteristic
87C2×C4×C3⋊D3—24no—
88C2×C4×C3⋊D3C2314yes—
89C22×C3×Dic3—28no—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2318yes—
94C22×C3×Dic3C2312yes—
95C2×C3×Dic6—24no—
96C2×C3×Dic6—24no—
97C2×C3×Dic6—28no—
98C2×C3×Dic6—232no—
99C2×C3×Dic6D418yescomplemented
100C2×C3×Dic6C2314yes—
101C2×C3×Dic6C2318yes—
102C2×C3×Dic6C2314yes—
103C2×C3×Dic6C2314yes—
104C2×#627—28no—
105C2×#627C2318yes—
106C2×#624—28no—
107C2×#624C2318yes—
108#3797—232no—
109#3757C2314yes—
110#3752C2314yes—
111#3750C2314yes—
112C4×C3⋊Dic3C2314yes—
113C3×#217C2318yes—
114C3×C4⋊Dic3C2314yes—
115C3×Dic3⋊C4C2318yes—
116#3724C2318yes—
117#3724C2318yes—
118Dic3⋊Dic3C2318yes—
119Dic3⋊Dic3C2318yes—
120#3722C2318yes—
121Dic32C2318yes—
122C2×D4×Q8—91noSylow
123C22×C3×Q8—31no—
124C22×C3×Q8—31no—
125C22×C3×Q8—32no—
126C22×C3×Q8—31no—
127C22×C3×Q8—38no—
128C22×C3×Q8—68no—
129C23×C3×C4—21no—
130C23×C3×C4—32no—
131C23×C3×C4C2×D311yescharacteristic
132C23×C3×C4C2×D311yescharacteristic
133C22×#67—31no—
134C22×#67—31no—
135C22×#67—61no—
136C23×Dic3C2×D312yes—
137C2×D3×Q8—38no—
138C2×D3×Q8—38no—
139C2×D3×Q8—68no—
140C2×D3×Q8—68no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—32no—
144C22×C4×D3—32no—
145C22×C4×D3—61no—
146C22×Dic6—28no—
147C22×Dic6—32no—
148C22×Dic6—32no—
149C22×Dic6C2×D312yes—
150C22×Dic6C2×D311yescharacteristic
151C22×Dic6C2×D311yescharacteristic
152C22×Dic6C2×D311yescharacteristic
153C22×Dic6C2×D318yescomplemented
154C3×C22⋊Q8—38no—
155C2×C3×C4⋊C4—32no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C22⋊C4—32no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—61no—
161C2×#217C2×D312yes—
162#946—38no—
163#946—316no—
164Q8×Dic3—38no—
165#944—38no—
166#944—38no—
167#944—316no—
168C4×#67—38no—
169C4×#67—38no—
170C4×#67—316no—
171C4×#67—68no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—61no—
177C2×C4⋊Dic3—32no—
178C2×C4⋊Dic3—32no—
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924—316no—
181#924C2×D318yescomplemented
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4—32no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—61no—
191C2×Dic3⋊C4C2×D312yes—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—32no—
195C2×C4×Dic3—32no—
196C2×C4×Dic3—61no—
197#897—38no—
198#896—316no—
199#888—316no—
200#887—38no—
201#67⋊C4—316no—
202#878—316no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32C2×Q814yescomplemented
206C23×C32C2412yes—
207C23×C32C2411yescharacteristic
208C22×C3⋊D3—22no—
209C22×C3⋊D3—22no—
210C22×C3⋊D3C2×Q814yescomplemented
211C22×C3⋊D3C2412yes—
212C2×C32×C4—22no—
213C2×C32×C4—28no—
214C2×C32×C4C2×D414yes—
215C2×C32×C4C2412yes—
216C2×C32×C4C2412yes—
217#638C2×Q8116yescomplemented
218C2×C3⋊Dic3—22no—
219C2×C3⋊Dic3—22no—
220C2×C3⋊Dic3C2×Q814yescomplemented
221C2×C3⋊Dic3C2412yes—
222C2×C3⋊Dic3C2412yes—
223C2×C3⋊Dic3C2412yes—
224C4×C3⋊D3—28no—
225C2×C3×Dic3—24no—
226C2×C3×Dic3—24no—
227C2×C3×Dic3—24no—
228C2×C3×Dic3—216no—
229C2×C3×Dic3C2×D418yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2414yes—
232C2×C3×Dic3C2414yes—
233C2×C3×Dic3C2414yes—
234C3×Dic6—28no—
235C3×Dic6—28no—
236C3×Dic6—216no—
237C3×Dic6C2×D4116yescomplemented
238#627—216no—
239#624—216no—
240C23×Q8—31no—
241C23×Q8—91no—
242D4×Q8—916no—
243C2×C4⋊Q8—92no—
244C2×C4⋊Q8—91no—
245C2×C22⋊Q8—31no—
246C2×C22⋊Q8—92no—
247C2×C22⋊Q8—92no—
248C2×C22⋊Q8—91no—
249C2×C4×Q8—91no—
250C2×C4×D4—92no—
251C2×C4×D4—91no—
252C24×C3—21no—
253C24×C3C22×D311yescharacteristic
254C24×C3C22×D311yescharacteristic
255C23×D3—31no—
256C23×D3—31no—
257C23×D3—61no—
258C2×C3×Q8—38no—
259C2×C3×Q8—34no—
260C2×C3×Q8—38no—
261C2×C3×Q8—34no—
262C2×C3×Q8—34no—
263C2×C3×Q8—68no—
264C2×C3×Q8—632no—
265C2×C3×Q8—64no—
266C2×C3×Q8—64no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—24no—
272C22×C3×C4—32no—
273C22×C3×C4—32no—
274C22×C3×C4—32no—
275C22×C3×C4—32no—
276C22×C3×C4—38no—
277C22×C3×C4—44no—
278C22×C3×C4—68no—
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D314yes—
282C22×C3×C4C22×D314yes—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C2×#67—38no—
286C2×#67—38no—
287C2×#67—34no—
288C2×#67—34no—
289C2×#67—64no—
290C2×#67—68no—
291C22×Dic3—28no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3C22×D318yes—
302C22×Dic3C22×D312yes—
303C22×Dic3C22×D312yes—
304C22×Dic3C22×D312yes—
305C22×Dic3C22×D312yes—
306D3×Q8—632no—
307D3×Q8—632no—
308C2×C4×D3—34no—
309C2×C4×D3—34no—
310C2×C4×D3—38no—
311C2×C4×D3—38no—
312C2×C4×D3—64no—
313C2×C4×D3—68no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—68no—
317C2×C4×D3—124no—
318C2×Dic6—24no—
319C2×Dic6—24no—
320C2×Dic6—28no—
321C2×Dic6—232no—
322C2×Dic6—38no—
323C2×Dic6—38no—
324C2×Dic6—68no—
325C2×Dic6—68no—
326C2×Dic6#6718yescomplemented
327C2×Dic6C22×D318yes—
328C2×Dic6C22×D314yes—
329C2×Dic6C22×D314yes—
330C2×Dic6C22×D314yes—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—38no—
333C3×C22⋊C4—38no—
334#217—34no—
335#217—34no—
336#217—64no—
337#217C22×D318yes—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—38no—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—64no—
343C4⋊Dic3—38no—
344C4⋊Dic3—38no—
345C4⋊Dic3C22×D314yes—
346Dic3⋊C4—34no—
347Dic3⋊C4—34no—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4—64no—
355Dic3⋊C4C22×D318yes—
356C4×Dic3—34no—
357C4×Dic3—34no—
358C4×Dic3—38no—
359C4×Dic3—38no—
360C4×Dic3—64no—
361C22×C32—28no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32C22×D412yes—
365C22×C32C22×Q812yes—
366C22×C32C22×Q814yescomplemented
367C22×C322−1+412yes—
368C22×C32C2511yescharacteristic
369C2×C3⋊D3—28no—
370C2×C3⋊D3—22no—
371C2×C3⋊D3—22no—
372C2×C3⋊D3C22×Q814yescomplemented
373C32×C4—22no—
374C32×C4C22×D414yes—
375C3⋊Dic3—22no—
376C3⋊Dic3—22no—
377C3⋊Dic3C22×Q814yescomplemented
378C3×Dic3—24no—
379C3×Dic3—24no—
380C3×Dic3—24no—
381C3×Dic3C22×D418yes—
382C22×Q8—31no—
383C22×Q8—31no—
384C22×Q8—32no—
385C22×Q8—31no—
386C22×Q8—38no—
387C22×Q8—68no—
388C22×Q8—92no—
389C22×Q8—98no—
390C22×Q8—188no—
391C22×D4—91no—
392C23×C4—32no—
393C23×C4—92no—
394C23×C4—91no—
395C23×C4D3211yescharacteristic
396C4⋊Q8—916no—
397C4⋊Q8—98no—
398C22⋊Q8—38no—
399C22⋊Q8—916no—
400C22⋊Q8—916no—
401C22⋊Q8—98no—
402C4×Q8—98no—
403C4×D4—916no—
404C4×D4—98no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—92no—
408C2×C4⋊C4—92no—
409C2×C4⋊C4—92no—
410C2×C4⋊C4—92no—
411C2×C4⋊C4—91no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—92no—
414C2×C22⋊C4—91no—
415C2×C22⋊C4—91no—
416C2×C42—92no—
417C2×C42—91no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—21no—
424C23×C3—24no—
425C23×C3—42no—
426C23×C3—42no—
427C23×C3D3×Q814yescomplemented
428C23×C3D3×Q814yescomplemented
429C23×C3C23×D312yes—
430C23×C3C23×D312yes—
431C23×C3C23×D311yescharacteristic
432C23×C3C23×D311yescharacteristic
433C22×D3—34no—
434C22×D3—34no—
435C22×D3—32no—
436C22×D3—32no—
437C22×D3—64no—
438C22×D3—62no—
439C22×D3—62no—
440C22×D3—62no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—122no—
444C22×D3—122no—
445C3×Q8—316no—
446C3×Q8—616no—
447C3×Q8—68no—
448C3×Q8—68no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—28no—
452C2×C3×C4—28no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—38no—
457C2×C3×C4—34no—
458C2×C3×C4—34no—
459C2×C3×C4—34no—
460C2×C3×C4—34no—
461C2×C3×C4—48no—
462C2×C3×C4—42no—
463C2×C3×C4—616no—
464C2×C3×C4—64no—
465C2×C3×C4—64no—
466C2×C3×C4—64no—
467C2×C3×C4D3×D414yes—
468C2×C3×C4C2×#6714yes—
469C2×C3×C4C23×D312yes—
470C2×C3×C4C23×D312yes—
471C2×C3×C4C23×D312yes—
472C2×C3×C4C23×D312yes—
473#67—316no—
474#67—316no—
475#67—616no—
476C2×Dic3—24no—
477C2×Dic3—24no—
478C2×Dic3—24no—
479C2×Dic3—216no—
480C2×Dic3—34no—
481C2×Dic3—34no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—32no—
487C2×Dic3—32no—
488C2×Dic3—64no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—122no—
497C2×Dic3—122no—
498C2×Dic3C2×#6718yes—
499C2×Dic3C23×D314yes—
500C2×Dic3C23×D314yes—
501C2×Dic3C23×D314yes—
502C2×Dic3C23×D314yes—
503C4×D3—616no—
504C4×D3—68no—
505C4×D3—68no—
506C4×D3—616no—
507C4×D3—128no—
508Dic6—28no—
509Dic6—28no—
510Dic6—216no—
511Dic6—616no—
512Dic6—616no—
513Dic6C2×#67116yescomplemented
514C2×C32—24no—
515C2×C32D4×Q814yescomplemented
516C2×C32C23×D411yescharacteristic
517C2×C32C23×Q811yescharacteristic
518C2×C32C2×2−1+411yescharacteristic
519C3⋊D3—24no—
520C24—91no—
521C24C2×D3211yescharacteristic
522C2×Q8—34no—
523C2×Q8—34no—
524C2×Q8—38no—
525C2×Q8—34no—
526C2×Q8—38no—
527C2×Q8—68no—
528C2×Q8—632no—
529C2×Q8—64no—
530C2×Q8—64no—
531C2×Q8—98no—
532C2×Q8—188no—
533C2×Q8—1832no—
534C2×D4—94no—
535C2×D4—98no—
536C22×C4—24no—
537C22×C4—32no—
538C22×C4—38no—
539C22×C4—32no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—68no—
543C22×C4—98no—
544C22×C4—91no—
545C22×C4—91no—
546C22×C4—91no—
547C22×C4—94no—
548C22×C4—188no—
549C22×C4—184no—
550C22×C4C2×D3214yes—
551C22×C4C2×D3211yescharacteristic
552C22×C4C2×D3211yescharacteristic
553C4⋊C4—34no—
554C4⋊C4—38no—
555C4⋊C4—98no—
556C4⋊C4—98no—
557C4⋊C4—98no—
558C4⋊C4—98no—
559C4⋊C4—94no—
560C22⋊C4—38no—
561C22⋊C4—98no—
562C22⋊C4—94no—
563C22⋊C4—94no—
564C42—98no—
565C42—94no—
566C22×C3—28no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—28no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—21no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—48no—
580C22×C3C2×D3×D412yes—
581C22×C3C2×D3×Q812yes—
582C22×C3C2×D3×Q812yes—
583C22×C3C2×D3×Q814yescomplemented
584C22×C3C2×D3×Q814yescomplemented
585C22×C3#100712yes—
586C22×C3#101012yes—
587C22×C3C22×#6712yes—
588C22×C3C24×D311yescharacteristic
589C22×C3C24×D311yescharacteristic
590C2×D3—34no—
591C2×D3—34no—
592C2×D3—64no—
593C2×D3—68no—
594C2×D3—62no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—68no—
599C2×D3—122no—
600C2×D3—122no—
601C2×D3—128no—
602C3×C4—22no—
603C3×C4—22no—
604C3×C4—24no—
605C3×C4—38no—
606C3×C4—42no—
607C3×C4—64no—
608C3×C4—64no—
609C3×C4—64no—
610C3×C4C2×D3×D414yes—
611C3×C4C22×#6714yes—
612Dic3—24no—
613Dic3—24no—
614Dic3—24no—
615Dic3—34no—
616Dic3—34no—
617Dic3—64no—
618Dic3—62no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—122no—
623Dic3—122no—
624Dic3C22×#6718yes—
625C32C2×D4×Q811yescharacteristic, complemented, Sylow
626C23—22no—
627C23—22no—
628C23—94no—
629C23—92no—
630C23—182no—
631C23—182no—
632C23#379714yescomplemented
633C23C22×D3212yes—
634C23C22×D3211yescharacteristic
635Q8—316no—
636Q8—616no—
637Q8—68no—
638Q8—68no—
639Q8—1816no—
640D4—916no—
641C2×C4—22no—
642C2×C4—28no—
643C2×C4—38no—
644C2×C4—34no—
645C2×C4—34no—
646C2×C4—34no—
647C2×C4—34no—
648C2×C4—616no—
649C2×C4—64no—
650C2×C4—64no—
651C2×C4—64no—
652C2×C4—94no—
653C2×C4—92no—
654C2×C4—92no—
655C2×C4—92no—
656C2×C4—1816no—
657C2×C4—182no—
658C2×C4—182no—
659C2×C4—188no—
660C2×C4D3×#6714yes—
661C2×C4C22×D3212yes—
662C2×C4C22×D3212yes—
663C2×C3—24no—
664C2×C3—24no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—24no—
669C2×C3—44no—
670C2×C3#563214yescomplemented
671C2×C3Q8×#6714yescomplemented
672C2×C3C22×D3×D411yescharacteristic
673C2×C3C22×D3×Q811yescharacteristic
674C2×C3C22×D3×Q811yescharacteristic
675C2×C3C2×#100711yescharacteristic
676C2×C3C2×#101011yescharacteristic
677C2×C3C23×#6711yescharacteristic
678D3—64no—
679D3—64no—
680D3—124no—
681C22—22no—
682C22—22no—
683C22—28no—
684C22—94no—
685C22—182no—
686C22—182no—
687C22—188no—
688C22#6429712yes—
689C22C2×#379712yes—
690C22C2×#379714yescomplemented
691C22C2×D3×#6712yes—
692C22C23×D3211yescharacteristic
693C4—22no—
694C4—38no—
695C4—64no—
696C4—64no—
697C4—64no—
698C4—94no—
699C4—182no—
700C4—182no—
701C4C2×D3×#6714yes—
702C3—21no—
703C3C2×#563211yescharacteristic, complemented
704C3C2×Q8×#6711yescharacteristic, complemented
705C2—24no—
706C2—184no—
707C2#1059480314yesdirect product factor
708C2C2×#6429711yescharacteristic
709C2C22×#379711yescharacteristic
710C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×Dic6C2semidirect
2. C22×#3797C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63964C2semidirect
7. C2×#63888C2semidirect
8. C2×#63873C2semidirect
9. C2×#63871C2semidirect
10. C2×#63843C2semidirect
11. C2×#63839C2semidirect
12. #10594803C2direct (N × H)
24. C22×C3×Dic6C22semidirect
28. C2×#3797C22semidirect
36. C3×#924C22semidirect
42. #63964C22semidirect
46. #63888C22semidirect
47. #63873C22semidirect
48. #63871C22semidirect
49. #63843C22semidirect
50. #63839C22semidirect
54. C23×Dic6D3semidirect
68. C2×#924D3semidirect
82. C2×#638Q8semidirect
99. C2×C3×Dic6D4semidirect
153. C22×Dic6C2×D3semidirect
181. #924C2×D3semidirect
205. C23×C32C2×Q8semidirect
210. C22×C3⋊D3C2×Q8semidirect
217. #638C2×Q8semidirect
220. C2×C3⋊Dic3C2×Q8semidirect
237. C3×Dic6C2×D4semidirect
326. C2×Dic6#67semidirect
366. C22×C32C22×Q8semidirect
372. C2×C3⋊D3C22×Q8semidirect
377. C3⋊Dic3C22×Q8semidirect
427. C23×C3D3×Q8semidirect
428. C23×C3D3×Q8semidirect
513. Dic6C2×#67semidirect
515. C2×C32D4×Q8semidirect
583. C22×C3C2×D3×Q8semidirect
584. C22×C3C2×D3×Q8semidirect
625. C32C2×D4×Q8semidirect
632. C23#3797semidirect
670. C2×C3#5632semidirect
671. C2×C3Q8×#67semidirect
690. C22C2×#3797semidirect
703. C3C2×#5632semidirect
704. C3C2×Q8×#67semidirect
707. C2#10594803direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×Dic62
C22×#37972
C2×C4×#6382
C2×C3×#9242
C2×#639642
C2×#639522
C2×#638882
C2×#638732
C2×#638712
C2×#638432
C2×#638392
#105948032
C2×Q8×#673
C2×#56323