Finite Group Databasebeta

← C2×#10595357 #11902557

Subgroups — C2×#10595357 #11902557

Order 1152.

3409 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64153C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5#10595357C2116yesmaximal, direct product factor
6C2×#63905C212yesmaximal, complemented
7C2×C4×#625C211yesmaximal, characteristic, complemented
8C2×#63898C211yesmaximal, characteristic, complemented
9C2×#63885C212yesmaximal, complemented
10C2×#63884C212yesmaximal, complemented
11C2×D3×Dic3⋊C4C212yesmaximal, complemented
12C2×#63857C211yesmaximal, characteristic, complemented
13C2×#5824—31nomaximal
14C2×#5631—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C2×C3×#239—28no—
18C2×C3×#239C2218yescomplemented
19C22×C3×D12C2212yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2212yes—
24C22×#625C2212yes—
25C22×#625C2211yescharacteristic
26C22×D3×Dic3C2212yes—
27C22×D3×Dic3C2212yes—
28C2×#3795—28no—
29C2×#3795C2218yescomplemented
30#64153C2218yescomplemented
31C2×#3750C2212yes—
32C2×#3750C2212yes—
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C3×#946C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2212yes—
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2212yes—
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44#63905C22116yescomplemented
45C4×#625C2218yescomplemented
46#63898C2218yescomplemented
47#63885C22116yescomplemented
48#63884C22116yescomplemented
49D3×Dic3⋊C4C22116yescomplemented
50#63857C2218yescomplemented
51C22×C3×#41—31no—
52C22×#239D311yescharacteristic, complemented
53C22×#237—31no—
54C22×#235—31no—
55C2×C3×C22⋊Q8—31no—
56#5824—316no—
57C2×#946D311yescharacteristic, complemented
58C2×#944—31no—
59C2×#944—31no—
60C2×#944—61no—
61C2×#939—32no—
62C2×#935—32no—
63C2×D4×Dic3—31no—
64C2×#929—32no—
65C2×C4×#67—31no—
66C2×C4×#67—31no—
67C2×#924—31no—
68C22×Dic3⋊C4—32no—
69#5631—316no—
70C2×#897—31no—
71C2×#894—32no—
72C2×#893—31no—
73C2×D3×C4⋊C4—32no—
74C2×#884—32no—
75C2×#883—32no—
76C23×C3×D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C2×C32×Q8—24no—
80C2×C32×Q8C2314yes—
81C22×C32×C4C2312yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3⋊Dic3C2312yes—
84C22×C3⋊Dic3C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C2×#634—24no—
87C2×#634C2314yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C3×#239—232no—
92C2×C3×D12—28no—
93C2×C3×D12D418yescomplemented
94C2×C3×D12C2318yes—
95C2×C3×D12C2314yes—
96C2×C3×C4×D3—28no—
97C2×C3×C4×D3—24no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2314yes—
101C2×C3×C4×D3C2318yes—
102C2×#625—28no—
103C2×#625—24no—
104C2×#625C2318yes—
105C2×#625C2314yes—
106C2×D3×Dic3—28no—
107C2×D3×Dic3—28no—
108C2×D3×Dic3C2318yes—
109C2×D3×Dic3C2318yes—
110#3795—232no—
111#3750C2318yes—
112#3750C2318yes—
113C4×C3⋊Dic3C2314yes—
114C3×(C2×D3)⋊C4C2318yes—
115C3×C4⋊Dic3C2314yes—
116C3×Dic3⋊C4C2318yes—
117#3724C2314yes—
118Dic3⋊Dic3C2318yes—
119(C2×D3)⋊Dic3C2318yes—
120(C2×D3)⋊Dic3C2314yes—
121(C2×D3)⋊Dic3C2318yes—
122(C2×D3)⋊Dic3C2314yes—
123C2×#547—91noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—21no—
127C22×C3×Q8C2×D311yescharacteristic
128C22×C3×Q8C2×D311yescharacteristic
129C22×C3×D4—31no—
130C22×C3×D4—32no—
131C23×C3×C4—31no—
132C23×C3×C4—32no—
133C23×C3×C4—31no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—31no—
137C22×#67—31no—
138C23×Dic3—32no—
139C23×Dic3—32no—
140C2×#239—28no—
141C2×#239C2×D318yescomplemented
142C2×#237—38no—
143C2×#237—68no—
144C2×#235—38no—
145C2×#235—68no—
146C22×D12C2×D312yes—
147C22×D12C2×D311yescharacteristic
148C22×C4×D3—32no—
149C22×C4×D3—32no—
150C22×C4×D3C2×D311yescharacteristic
151C22×C4×D3C2×D312yes—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—31no—
154C22×Dic6—31no—
155C22×Dic6—61no—
156C3×C22⋊Q8—38no—
157C2×C3×C4⋊C4—32no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—32no—
160C2×#217—31no—
161C2×#217—32no—
162C2×#217—31no—
163C2×#217—32no—
164#946C2×D318yescomplemented
165#944—38no—
166#944—38no—
167#944—68no—
168#939—316no—
169#935—316no—
170D4×Dic3—38no—
171#929—316no—
172C4×#67—38no—
173C4×#67—38no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4C2×D312yes—
179C2×C4⋊Dic3—32no—
180C2×C4⋊Dic3C2×D311yescharacteristic
181#924—38no—
182C2×Dic3⋊C4—32no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4—32no—
185C2×Dic3⋊C4—32no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—32no—
189C2×Dic3⋊C4—316no—
190C2×Dic3⋊C4—62no—
191C2×Dic3⋊C4—62no—
192C2×Dic3⋊C4C2×D312yes—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—61no—
196#897—38no—
197#894—316no—
198#893—38no—
199D3×C4⋊C4—316no—
200#884—316no—
201#883—316no—
202C23×C32C2411yescharacteristic
203C22×C3×D3—24no—
204C22×C3×D3—24no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3C2×D418yes—
212C22×C3×D3C2412yes—
213C22×C3×D3C2412yes—
214C22×C3×D3C2414yes—
215C32×Q8—28no—
216C2×C32×C4—24no—
217C2×C32×C4C2×D414yes—
218C2×C32×C4C2414yes—
219C2×C32×C4C2412yes—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—24no—
222C2×C3⋊Dic3#4114yescomplemented
223C2×C3⋊Dic3C2412yes—
224C2×C3⋊Dic3C2414yes—
225C2×C3⋊Dic3C2412yes—
226#634—28no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2412yes—
233C3×D12—216no—
234C3×D12C2×D4116yescomplemented
235C3×C4×D3—216no—
236C3×C4×D3—28no—
237C3×C4×D3—28no—
238#625—216no—
239#625—28no—
240D3×Dic3—216no—
241D3×Dic3—216no—
242C22×#41—31no—
243C22×#41—91no—
244#547—916no—
245C2×C4⋊Q8—91no—
246C2×#123—92no—
247C2×#123—92no—
248C2×C22⋊Q8—31no—
249C2×C22⋊Q8—91no—
250C2×#121—92no—
251C2×C4×D4—91no—
252C2×C4×D4—91no—
253C22×C4⋊C4—92no—
254C24×C3—32no—
255C24×C3—31no—
256C24×C3—31no—
257C23×D3C22×D311yescharacteristic
258C23×D3C22×D311yescharacteristic
259C23×D3C22×D312yes—
260C3×#41—632no—
261C2×C3×Q8—24no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—44no—
265C2×C3×Q8C22×D314yes—
266C2×C3×Q8C22×D314yes—
267C2×C3×D4—38no—
268C2×C3×D4—34no—
269C2×C3×D4—38no—
270C2×C3×D4—68no—
271C22×C3×C4—21no—
272C22×C3×C4—22no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—38no—
277C22×C3×C4—34no—
278C22×C3×C4—34no—
279C22×C3×C4—68no—
280C22×C3×C4—64no—
281C22×C3×C4—64no—
282C22×C3×C4C22×D312yes—
283C22×C3×C4C22×D312yes—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C2×#67—38no—
287C2×#67—34no—
288C2×#67—34no—
289C2×#67—38no—
290C2×#67—64no—
291C2×#67—64no—
292C2×#67—68no—
293C2×#67—68no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—32no—
299C22×Dic3—32no—
300C22×Dic3—38no—
301C22×Dic3—38no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—62no—
305C22×Dic3—68no—
306C22×Dic3—68no—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D312yes—
309C22×Dic3C22×D311yescharacteristic
310#239—232no—
311#237—632no—
312#235—632no—
313C2×D12—28no—
314C2×D12#6718yescomplemented
315C2×D12C22×D318yes—
316C2×D12C22×D314yes—
317C2×C4×D3—28no—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—38no—
321C2×C4×D3—38no—
322C2×C4×D3—68no—
323C2×C4×D3—68no—
324C2×C4×D3C22×D318yes—
325C2×C4×D3C22×D314yes—
326C2×C4×D3C22×D314yes—
327C2×Dic6—34no—
328C2×Dic6—34no—
329C2×Dic6—64no—
330C2×Dic6—64no—
331C2×Dic6—64no—
332C2×Dic6—124no—
333C3×C4⋊C4—38no—
334C3×C4⋊C4—34no—
335C3×C22⋊C4—38no—
336#217—34no—
337#217—38no—
338#217—34no—
339#217—38no—
340(C2×D3)⋊C4—38no—
341(C2×D3)⋊C4—38no—
342(C2×D3)⋊C4—34no—
343(C2×D3)⋊C4—34no—
344(C2×D3)⋊C4C22×D318yes—
345C4⋊Dic3—38no—
346C4⋊Dic3C22×D314yes—
347Dic3⋊C4—38no—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—34no—
352Dic3⋊C4—38no—
353Dic3⋊C4—34no—
354Dic3⋊C4—68no—
355Dic3⋊C4—68no—
356Dic3⋊C4C22×D318yes—
357C4×Dic3—34no—
358C4×Dic3—34no—
359C4×Dic3—64no—
360C22×C32C22×D412yes—
361C22×C32C2×#4112yes—
362C22×C322−1+412yes—
363C22×C32C2511yescharacteristic
364C2×C3×D3—216no—
365C2×C3×D3—24no—
366C2×C3×D3—24no—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—44no—
374C2×C3×D3—44no—
375C2×C3×D3C22×D418yes—
376C32×C4—24no—
377C32×C4C22×D414yes—
378C3⋊Dic3—22no—
379C3⋊Dic3—24no—
380C3⋊Dic3C2×#4114yescomplemented
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—24no—
384C2×#41—38no—
385C2×#41—68no—
386C2×#41—98no—
387C2×#41—188no—
388C22×Q8—91no—
389C22×Q8D3211yescharacteristic
390C22×D4—31no—
391C22×D4—32no—
392C22×D4—91no—
393C22×D4—92no—
394C23×C4—32no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—92no—
398C23×C4—92no—
399C4⋊Q8—98no—
400#123—916no—
401#123—916no—
402C22⋊Q8—38no—
403C22⋊Q8—98no—
404#121—916no—
405C4×D4—98no—
406C4×D4—98no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—916no—
410C2×C4⋊C4—91no—
411C2×C4⋊C4—92no—
412C2×C4⋊C4—92no—
413C2×C4⋊C4—92no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—92no—
416C2×C22⋊C4—91no—
417C2×C22⋊C4—91no—
418C2×C22⋊C4—92no—
419C2×C42—91no—
420C23×C3—21no—
421C23×C3—38no—
422C23×C3—34no—
423C23×C3—32no—
424C23×C3—32no—
425C23×C3—64no—
426C23×C3—64no—
427C23×C3—62no—
428C23×C3—62no—
429C23×C3—62no—
430C23×C3—62no—
431C23×C3—62no—
432C23×C3—62no—
433C23×C3C23×D311yescharacteristic
434C23×C3C23×D311yescharacteristic
435C22×D3—24no—
436C22×D3—24no—
437C22×D3—22no—
438C22×D3—22no—
439C22×D3—22no—
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—22no—
443C22×D3C2×#6718yes—
444C22×D3C23×D312yes—
445C22×D3C23×D312yes—
446C22×D3C23×D314yes—
447C3×Q8—28no—
448C3×Q8—28no—
449C3×Q8—48no—
450C3×D4—316no—
451C3×D4—616no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—34no—
460C2×C3×C4—44no—
461C2×C3×C4—616no—
462C2×C3×C4—62no—
463C2×C3×C4—64no—
464C2×C3×C4—62no—
465C2×C3×C4—68no—
466C2×C3×C4—68no—
467C2×C3×C4D3×D414yes—
468C2×C3×C4C2×#6714yes—
469C2×C3×C4C23×D314yes—
470C2×C3×C4C23×D314yes—
471C2×C3×C4C23×D312yes—
472C2×C3×C4C23×D312yes—
473#67—68no—
474#67—68no—
475#67—616no—
476#67—616no—
477C2×Dic3—22no—
478C2×Dic3—24no—
479C2×Dic3—22no—
480C2×Dic3—34no—
481C2×Dic3—34no—
482C2×Dic3—32no—
483C2×Dic3—32no—
484C2×Dic3—32no—
485C2×Dic3—32no—
486C2×Dic3—34no—
487C2×Dic3—34no—
488C2×Dic3—64no—
489C2×Dic3—62no—
490C2×Dic3—62no—
491C2×Dic3—64no—
492C2×Dic3—616no—
493C2×Dic3—616no—
494C2×Dic3—64no—
495C2×Dic3—64no—
496C2×Dic3—62no—
497C2×Dic3—62no—
498C2×Dic3—64no—
499C2×Dic3—124no—
500C2×Dic3C23×D312yes—
501C2×Dic3C23×D314yes—
502C2×Dic3C23×D312yes—
503D12—216no—
504D12C2×#67116yescomplemented
505C4×D3—216no—
506C4×D3—28no—
507C4×D3—28no—
508C4×D3—616no—
509C4×D3—616no—
510Dic6—68no—
511Dic6—68no—
512Dic6—128no—
513C2×C32#54714yescomplemented
514C2×C32C23×D411yescharacteristic
515C2×C32C22×#4111yescharacteristic
516C2×C32C2×2−1+411yescharacteristic
517C3×D3—28no—
518C3×D3—42no—
519C3×D3—42no—
520C24—32no—
521C24—31no—
522C24—31no—
523#41—632no—
524#41—1832no—
525C2×Q8—24no—
526C2×Q8—94no—
527C2×Q8—184no—
528C2×Q8C2×D3214yes—
529C2×D4—34no—
530C2×D4—38no—
531C2×D4—38no—
532C2×D4—68no—
533C2×D4—94no—
534C2×D4—98no—
535C2×D4—184no—
536C2×D4—188no—
537C22×C4—32no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—38no—
541C22×C4—34no—
542C22×C4—34no—
543C22×C4—68no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—98no—
547C22×C4—98no—
548C22×C4—91no—
549C22×C4—91no—
550C22×C4—92no—
551C22×C4—188no—
552C22×C4—188no—
553C22×C4C2×D3212yes—
554C22×C4C2×D3211yescharacteristic
555C4⋊C4—38no—
556C4⋊C4—34no—
557C4⋊C4—94no—
558C4⋊C4—98no—
559C4⋊C4—98no—
560C4⋊C4—98no—
561C22⋊C4—38no—
562C22⋊C4—98no—
563C22⋊C4—94no—
564C22⋊C4—94no—
565C22⋊C4—98no—
566C42—94no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—21no—
571C22×C3—38no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—616no—
575C22×C3—62no—
576C22×C3—62no—
577C22×C3—62no—
578C22×C3—62no—
579C22×C3—62no—
580C22×C3—62no—
581C22×C3—124no—
582C22×C3—124no—
583C22×C3C2×D3×D412yes—
584C22×C3#100712yes—
585C22×C3D3×#4112yes—
586C22×C3D3×#4112yes—
587C22×C3#101012yes—
588C22×C3C22×#6712yes—
589C22×C3C24×D311yescharacteristic
590C22×C3C24×D311yescharacteristic
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—216no—
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—44no—
601C2×D3—44no—
602C2×D3C22×#6718yes—
603C3×C4—24no—
604C3×C4—24no—
605C3×C4—24no—
606C3×C4—44no—
607C3×C4—62no—
608C3×C4—64no—
609C3×C4—62no—
610C3×C4C2×D3×D414yes—
611C3×C4C22×#6714yes—
612Dic3—22no—
613Dic3—24no—
614Dic3—22no—
615Dic3—34no—
616Dic3—34no—
617Dic3—64no—
618Dic3—64no—
619Dic3—64no—
620Dic3—62no—
621Dic3—62no—
622Dic3—64no—
623Dic3—124no—
624C32C2×#54711yescharacteristic, complemented, Sylow
625C23—38no—
626C23—34no—
627C23—32no—
628C23—32no—
629C23—64no—
630C23—64no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23C22×D3211yescharacteristic
638Q8—28no—
639Q8—188no—
640D4—316no—
641D4—616no—
642D4—188no—
643D4—1816no—
644C2×C4—24no—
645C2×C4—34no—
646C2×C4—32no—
647C2×C4—32no—
648C2×C4—616no—
649C2×C4—64no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—68no—
653C2×C4—68no—
654C2×C4—94no—
655C2×C4—92no—
656C2×C4—92no—
657C2×C4—94no—
658C2×C4—1816no—
659C2×C4—1816no—
660C2×C4—182no—
661C2×C4—184no—
662C2×C4D3×#6714yes—
663C2×C4C22×D3214yes—
664C2×C4C22×D3212yes—
665C2×C3—24no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—68no—
670C2×C3—122no—
671C2×C3—122no—
672C2×C3#563114yescomplemented
673C2×C3#582414yescomplemented
674C2×C3C22×D3×D411yescharacteristic
675C2×C3C2×#100711yescharacteristic
676C2×C3C2×D3×#4111yescharacteristic
677C2×C3C2×D3×#4111yescharacteristic
678C2×C3C2×#101011yescharacteristic
679C2×C3C23×#6711yescharacteristic
680D3—28no—
681D3—42no—
682D3—42no—
683C22—38no—
684C22—616no—
685C22—64no—
686C22—64no—
687C22—62no—
688C22—62no—
689C22—62no—
690C22—62no—
691C22—62no—
692C22—62no—
693C22—124no—
694C22—124no—
695C22#6431512yes—
696C22#6431912yes—
697C22C2×D3×#6712yes—
698C22C23×D3211yescharacteristic
699C4—24no—
700C4—64no—
701C4—62no—
702C4—62no—
703C4—94no—
704C4—182no—
705C4—184no—
706C4C2×D3×#6714yes—
707C3—21no—
708C3C2×#563111yescharacteristic, complemented
709C3C2×#582411yescharacteristic, complemented
710C2—68no—
711C2—122no—
712C2—122no—
713C2#1059535714yesdirect product factor
714C2C2×#6431511yescharacteristic
715C2C2×#6431911yescharacteristic
716C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#547
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×#3795C2semidirect
3. C2×#64153C2semidirect
4. C2×C3×#946C2semidirect
5. #10595357C2direct (N × H)
6. C2×#63905C2semidirect
7. C2×C4×#625C2semidirect
8. C2×#63898C2semidirect
9. C2×#63885C2semidirect
10. C2×#63884C2semidirect
11. C2×D3×Dic3⋊C4C2semidirect
12. C2×#63857C2semidirect
18. C2×C3×#239C22semidirect
29. C2×#3795C22semidirect
30. #64153C22semidirect
34. C3×#946C22semidirect
44. #63905C22semidirect
45. C4×#625C22semidirect
46. #63898C22semidirect
47. #63885C22semidirect
48. #63884C22semidirect
49. D3×Dic3⋊C4C22semidirect
50. #63857C22semidirect
52. C22×#239D3semidirect
57. C2×#946D3semidirect
93. C2×C3×D12D4semidirect
141. C2×#239C2×D3semidirect
164. #946C2×D3semidirect
222. C2×C3⋊Dic3#41semidirect
234. C3×D12C2×D4semidirect
314. C2×D12#67semidirect
380. C3⋊Dic3C2×#41semidirect
504. D12C2×#67semidirect
513. C2×C32#547semidirect
624. C32C2×#547semidirect
672. C2×C3#5631semidirect
673. C2×C3#5824semidirect
708. C3C2×#5631semidirect
709. C3C2×#5824semidirect
713. C2#10595357direct (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×#37952
C2×#641532
C2×C3×#9462
#105953572
C2×#639052
C2×C4×#6252
C2×#638982
C2×#638852
C2×#638842
C2×D3×Dic3⋊C42
C2×#638572
C2×#58243
C2×#56313