Finite Group Databasebeta

← C2×#10594517 #11902553

Subgroups — C2×#10594517 #11902553

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C212yesmaximal, complemented
2C2×#64104C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#888C211yesmaximal, characteristic, complemented
5C2×#63909C211yesmaximal, characteristic, complemented
6C2×C4×#626C211yesmaximal, characteristic, complemented
7C2×#63900C211yesmaximal, characteristic, complemented
8C2×#63897C212yesmaximal, complemented
9C2×#63894C211yesmaximal, characteristic, complemented
10C2×#63888C212yesmaximal, complemented
11C2×#63850C212yesmaximal, complemented
12#10594517C2116yesmaximal, direct product factor
13C2×#5726—31nomaximal
14C2×#5507—31nomaximal
15C22×C4⋊(C3⋊D3)C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C3×C4×D3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2212yes—
21C22×#626C2212yes—
22C22×#626C2211yescharacteristic
23C22×#624C2212yes—
24C22×#624C2212yes—
25C2×#3799—216no—
26C2×#3799C22116yescomplemented
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×#3752C2212yes—
29#64104C2218yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×D3×C4⋊C4C2218yescomplemented
36C3×#888C2218yescomplemented
37C2×#3724C2212yes—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×#3722C2212yes—
40C2×#3722C2212yes—
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43#63909C2218yescomplemented
44C4×#626C2218yescomplemented
45#63900C2218yescomplemented
46#63897C22116yescomplemented
47#63894C2218yescomplemented
48#63888C22116yescomplemented
49#63850C22116yescomplemented
50C22×#239—32no—
51C22×#235—32no—
52C2×C3×C4⋊Q8—31no—
53C22×C3×C4⋊C4—31no—
54C2×#946—32no—
55C2×#930—31no—
56C2×#929—32no—
57C2×C4×#67—31no—
58#5726—316no—
59C2×#896—32no—
60#5507—316no—
61C2×#895—31no—
62C2×#895—31no—
63C2×#895—31no—
64C2×#895—61no—
65C2×#894—32no—
66C2×#894—32no—
67C2×#894—32no—
68C2×#893—31no—
69C2×D3×C4⋊C4—31no—
70C2×D3×C4⋊C4—31no—
71C2×D3×C4⋊C4D311yescharacteristic, complemented
72C2×#888D311yescharacteristic, complemented
73C2×C4×D12—31no—
74C2×C4×D12—31no—
75C23×C3⋊D3C2312yes—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C2×C4⋊(C3⋊D3)—28no—
82C2×C4⋊(C3⋊D3)—24no—
83C2×C4⋊(C3⋊D3)C2318yes—
84C2×C4⋊(C3⋊D3)C2314yes—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3C2314yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2311yescharacteristic
92C2×C3×C4×D3—28no—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3C2318yes—
95C2×C3×C4×D3C2314yes—
96C2×C3×Dic6—28no—
97C2×C3×Dic6C2318yes—
98C2×#626—28no—
99C2×#626D418yescomplemented
100C2×#626C2318yes—
101C2×#626C2314yes—
102C2×#624—28no—
103C2×#624—28no—
104C2×#624C2318yes—
105C2×#624C2318yes—
106#3799—264no—
107C32×C4⋊C4C2314yes—
108#3752C2318yes—
109C3×C4⋊Dic3C2314yes—
110C3×C4⋊Dic3C2314yes—
111C3×Dic3⋊C4C2318yes—
112C3×Dic3⋊C4C2318yes—
113C3×C4×Dic3C2314yes—
114#3724C2318yes—
115Dic3⋊Dic3C2314yes—
116#3722C2318yes—
117#3722C2318yes—
118#3722C2314yes—
119(C2×D3)⋊Dic3C2314yes—
120C2×#547—91noSylow
121C22×C3×Q8—32no—
122C23×C3×C4—32no—
123C23×C3×C4—31no—
124C22×#67—31no—
125C22×#67—32no—
126C2×#239—316no—
127C2×#239—616no—
128C2×#235—316no—
129C2×#235—616no—
130C22×D12—31no—
131C22×D12—32no—
132C22×D12—32no—
133C22×D12—32no—
134C22×D12—31no—
135C22×D12—31no—
136C22×D12—61no—
137C22×D12—62no—
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—32no—
141C22×C4×D3—32no—
142C22×C4×D3—32no—
143C22×C4×D3—32no—
144C22×C4×D3—61no—
145C22×C4×D3C2×D312yes—
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6C2×D312yes—
148C3×C4⋊Q8—38no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—32no—
151C2×C3×C4⋊C4—32no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—38no—
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C4⋊C4C2×D311yescharacteristic
157C2×C3×C42—31no—
158C2×#217—31no—
159#946—316no—
160#930—38no—
161#929—316no—
162C4×#67—38no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—32no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—32no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—32no—
171C2×(C2×D3)⋊C4—32no—
172C2×(C2×D3)⋊C4—62no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175C2×C4⋊Dic3C2×D311yescharacteristic
176C2×Dic3⋊C4—32no—
177C2×Dic3⋊C4—32no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4C2×D312yes—
180C2×Dic3⋊C4C2×D312yes—
181C2×C4×Dic3C2×D311yescharacteristic
182#896—316no—
183#895—38no—
184#895—38no—
185#895—38no—
186#895—68no—
187#894—316no—
188#894—316no—
189#894—316no—
190#893—38no—
191D3×C4⋊C4—38no—
192D3×C4⋊C4—38no—
193D3×C4⋊C4C2×D318yescomplemented
194#888C2×D318yescomplemented
195C4×D12—38no—
196C4×D12—38no—
197C23×C32C2411yescharacteristic
198C22×C3⋊D3—22no—
199C22×C3⋊D3—22no—
200C22×C3⋊D3—24no—
201C22×C3⋊D3—24no—
202C22×C3⋊D3—24no—
203C22×C3⋊D3C2×D414yes—
204C22×C3⋊D3C2414yes—
205C22×C3⋊D3C2412yes—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×D414yes—
209C22×C3×D3C2412yes—
210C2×C32×C4—24no—
211C2×C32×C4#4114yescomplemented
212C2×C32×C4C2414yes—
213C2×C32×C4C2412yes—
214C2×C3⋊Dic3—22no—
215C2×C3⋊Dic3C2412yes—
216C4⋊(C3⋊D3)—216no—
217C4⋊(C3⋊D3)—28no—
218C4×C3⋊D3—28no—
219C2×C3×Dic3—24no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C2×D414yes—
224C2×C3×Dic3C2412yes—
225C2×C3×Dic3C2412yes—
226C2×C3×Dic3C2414yes—
227C2×C3×Dic3C2414yes—
228C2×C3×Dic3C2412yes—
229C3×C4×D3—216no—
230C3×C4×D3—28no—
231C3×Dic6—216no—
232#626—216no—
233#626C2×D4116yescomplemented
234#624—216no—
235#624—216no—
236C22×#41—92no—
237#547—916no—
238C2×C4⋊Q8—31no—
239C2×#123—92no—
240C2×#123—92no—
241C2×C22⋊Q8—92no—
242C2×#121—91no—
243C2×#121—91no—
244C2×C4×D4—91no—
245C2×C4×D4—91no—
246C22×C4⋊C4—31no—
247C22×C4⋊C4—91no—
248C24×C3—31no—
249C23×D3—31no—
250C23×D3—31no—
251C23×D3—32no—
252C23×D3—32no—
253C23×D3—61no—
254C23×D3—62no—
255C23×D3C22×D311yescharacteristic
256C2×C3×Q8—38no—
257C2×C3×Q8—68no—
258C22×C3×C4—21no—
259C22×C3×C4—22no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—32no—
264C22×C3×C4—31no—
265C22×C3×C4—34no—
266C22×C3×C4—38no—
267C22×C3×C4—68no—
268C22×C3×C4—64no—
269C22×C3×C4C22×D312yes—
270C22×C3×C4C22×D312yes—
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C2×#67—38no—
274C2×#67—34no—
275C2×#67—38no—
276C2×#67—68no—
277C22×Dic3—31no—
278C22×Dic3—31no—
279C22×Dic3—61no—
280C22×Dic3C22×D311yescharacteristic
281C22×Dic3C22×D312yes—
282C22×Dic3C22×D312yes—
283C22×Dic3C22×D311yescharacteristic
284C22×Dic3C22×D311yescharacteristic
285#239—664no—
286#235—664no—
287C2×D12—38no—
288C2×D12—34no—
289C2×D12—38no—
290C2×D12—34no—
291C2×D12—34no—
292C2×D12—38no—
293C2×D12—38no—
294C2×D12—64no—
295C2×D12—68no—
296C2×D12—68no—
297C2×D12—68no—
298C2×D12—68no—
299C2×D12—64no—
300C2×D12—64no—
301C2×D12—124no—
302C2×D12—128no—
303C2×C4×D3—28no—
304C2×C4×D3—24no—
305C2×C4×D3—34no—
306C2×C4×D3—34no—
307C2×C4×D3—38no—
308C2×C4×D3—38no—
309C2×C4×D3—38no—
310C2×C4×D3—38no—
311C2×C4×D3—64no—
312C2×C4×D3—68no—
313C2×C4×D3—68no—
314C2×C4×D3—68no—
315C2×C4×D3—64no—
316C2×C4×D3—64no—
317C2×C4×D3—68no—
318C2×C4×D3—124no—
319C2×C4×D3C22×D314yes—
320C2×C4×D3C22×D318yes—
321C2×Dic6—28no—
322C2×Dic6C22×D318yes—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—38no—
327C3×C4⋊C4—38no—
328C3×C4⋊C4C22×D314yes—
329C3×C4⋊C4C22×D314yes—
330C3×C42—34no—
331#217—34no—
332(C2×D3)⋊C4—34no—
333(C2×D3)⋊C4—38no—
334(C2×D3)⋊C4—38no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—34no—
337(C2×D3)⋊C4—38no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—38no—
340(C2×D3)⋊C4—38no—
341(C2×D3)⋊C4—68no—
342C4⋊Dic3—34no—
343C4⋊Dic3C22×D314yes—
344C4⋊Dic3C22×D314yes—
345Dic3⋊C4—38no—
346Dic3⋊C4—38no—
347Dic3⋊C4—34no—
348Dic3⋊C4C22×D318yes—
349Dic3⋊C4C22×D318yes—
350C4×Dic3C22×D314yes—
351C22×C32C22×D412yes—
352C22×C32C2×#4112yes—
353C22×C322−1+412yes—
354C22×C32C2511yescharacteristic
355C2×C3⋊D3—28no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—24no—
359C2×C3⋊D3—24no—
360C2×C3⋊D3—24no—
361C2×C3⋊D3—48no—
362C2×C3⋊D3C22×D414yes—
363C2×C3×D3—28no—
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3C22×D414yes—
367C32×C4—24no—
368C32×C4C2×#4114yescomplemented
369C3⋊Dic3—22no—
370C3×Dic3—24no—
371C3×Dic3—24no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3C22×D414yes—
375C2×#41—916no—
376C2×#41—1816no—
377C22×Q8—32no—
378C22×D4—91no—
379C22×D4—92no—
380C22×D4—91no—
381C22×D4—92no—
382C23×C4—31no—
383C23×C4—32no—
384C23×C4—92no—
385C23×C4—92no—
386C23×C4—91no—
387C4⋊Q8—38no—
388#123—916no—
389#123—916no—
390C22⋊Q8—916no—
391#121—98no—
392#121—98no—
393C4×D4—98no—
394C4×D4—98no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—38no—
400C2×C4⋊C4—98no—
401C2×C4⋊C4—92no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4D3211yescharacteristic
404C2×C22⋊C4—91no—
405C2×C22⋊C4—92no—
406C2×C22⋊C4—92no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—92no—
409C2×C42—31no—
410C23×C3—21no—
411C23×C3—34no—
412C23×C3—32no—
413C23×C3—62no—
414C23×C3—62no—
415C23×C3C23×D311yescharacteristic
416C23×C3C23×D311yescharacteristic
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—34no—
420C22×D3—34no—
421C22×D3—32no—
422C22×D3—32no—
423C22×D3—34no—
424C22×D3—34no—
425C22×D3—64no—
426C22×D3—62no—
427C22×D3—64no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—62no—
431C22×D3—62no—
432C22×D3—64no—
433C22×D3—64no—
434C22×D3—64no—
435C22×D3—64no—
436C22×D3—64no—
437C22×D3—64no—
438C22×D3—122no—
439C22×D3—122no—
440C22×D3—124no—
441C22×D3—124no—
442C22×D3—124no—
443C22×D3D3×D414yes—
444C22×D3C23×D312yes—
445C3×Q8—616no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—34no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—34no—
455C2×C3×C4—34no—
456C2×C3×C4—32no—
457C2×C3×C4—44no—
458C2×C3×C4—616no—
459C2×C3×C4—64no—
460C2×C3×C4—64no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—68no—
464C2×C3×C4#23514yescomplemented
465C2×C3×C4#23914yescomplemented
466C2×C3×C4C23×D314yes—
467C2×C3×C4C23×D314yes—
468C2×C3×C4C23×D312yes—
469C2×C3×C4C23×D312yes—
470#67—316no—
471#67—616no—
472C2×Dic3—22no—
473C2×Dic3—24no—
474C2×Dic3—24no—
475C2×Dic3—22no—
476C2×Dic3—32no—
477C2×Dic3—32no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—122no—
482C2×Dic3D3×D414yes—
483C2×Dic3C23×D312yes—
484C2×Dic3C23×D314yes—
485C2×Dic3C23×D314yes—
486C2×Dic3C23×D312yes—
487C2×Dic3C23×D312yes—
488D12—316no—
489D12—616no—
490D12—616no—
491D12—616no—
492D12—68no—
493D12—68no—
494D12—128no—
495D12—1216no—
496C4×D3—216no—
497C4×D3—28no—
498C4×D3—616no—
499C4×D3—616no—
500C4×D3—616no—
501C4×D3—68no—
502C4×D3—68no—
503C4×D3—616no—
504C4×D3—128no—
505Dic6—216no—
506C2×C32#54714yescomplemented
507C2×C32C23×D411yescharacteristic
508C2×C32C22×#4111yescharacteristic
509C2×C32C2×2−1+411yescharacteristic
510C3⋊D3—24no—
511C3⋊D3—44no—
512C3×D3—24no—
513C24—31no—
514C24—91no—
515C24—92no—
516#41—1864no—
517C2×Q8—38no—
518C2×Q8—68no—
519C2×D4—94no—
520C2×D4—98no—
521C2×D4—98no—
522C2×D4—94no—
523C2×D4—98no—
524C2×D4—188no—
525C2×D4—188no—
526C2×D4—184no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—32no—
531C22×C4—32no—
532C22×C4—34no—
533C22×C4—38no—
534C22×C4—68no—
535C22×C4—64no—
536C22×C4—98no—
537C22×C4—98no—
538C22×C4—91no—
539C22×C4—94no—
540C22×C4—188no—
541C22×C4—188no—
542C22×C4—184no—
543C22×C4C2×D3212yes—
544C22×C4C2×D3211yescharacteristic
545C4⋊C4—34no—
546C4⋊C4—38no—
547C4⋊C4—34no—
548C4⋊C4—38no—
549C4⋊C4—98no—
550C4⋊C4—94no—
551C4⋊C4C2×D3214yes—
552C22⋊C4—94no—
553C22⋊C4—98no—
554C22⋊C4—98no—
555C22⋊C4—94no—
556C22⋊C4—98no—
557C42—34no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—21no—
562C22×C3—34no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—68no—
566C22×C3C2×#23512yes—
567C22×C3C2×D3×D412yes—
568C22×C3C2×D3×D412yes—
569C22×C3C2×#23912yes—
570C22×C3#100712yes—
571C22×C3#100712yes—
572C22×C3C24×D311yescharacteristic
573C22×C3C24×D311yescharacteristic
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—28no—
577C2×D3—34no—
578C2×D3—34no—
579C2×D3—64no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—68no—
585C2×D3—68no—
586C2×D3—64no—
587C2×D3—64no—
588C2×D3—64no—
589C2×D3—64no—
590C2×D3—64no—
591C2×D3—64no—
592C2×D3—122no—
593C2×D3—122no—
594C2×D3—128no—
595C2×D3—124no—
596C2×D3—124no—
597C2×D3—124no—
598C2×D3—128no—
599C2×D3—128no—
600C2×D3—248no—
601C2×D3C2×D3×D414yes—
602C3×C4—24no—
603C3×C4—24no—
604C3×C4—24no—
605C3×C4—34no—
606C3×C4—44no—
607C3×C4—64no—
608C3×C4—64no—
609C3×C4—62no—
610C3×C4—62no—
611C3×C4C2×#23514yescomplemented
612C3×C4C2×#23914yescomplemented
613Dic3—22no—
614Dic3—24no—
615Dic3—24no—
616Dic3—22no—
617Dic3—62no—
618Dic3—62no—
619Dic3—122no—
620Dic3C2×D3×D414yes—
621C32C2×#54711yescharacteristic, complemented, Sylow
622C23—34no—
623C23—32no—
624C23—62no—
625C23—62no—
626C23—94no—
627C23—92no—
628C23—94no—
629C23—182no—
630C23—182no—
631C23—184no—
632C23—184no—
633C23—184no—
634C23C22×D3211yescharacteristic
635Q8—616no—
636D4—916no—
637D4—1816no—
638D4—1816no—
639D4—188no—
640C2×C4—24no—
641C2×C4—34no—
642C2×C4—32no—
643C2×C4—32no—
644C2×C4—32no—
645C2×C4—34no—
646C2×C4—34no—
647C2×C4—616no—
648C2×C4—62no—
649C2×C4—64no—
650C2×C4—64no—
651C2×C4—62no—
652C2×C4—68no—
653C2×C4—92no—
654C2×C4—1816no—
655C2×C4—1816no—
656C2×C4—182no—
657C2×C4—188no—
658C2×C4#379914yescomplemented
659C2×C4C22×D3214yes—
660C2×C4C22×D3212yes—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—24no—
665C2×C3—64no—
666C2×C3#550714yescomplemented
667C2×C3#572614yescomplemented
668C2×C3C22×#23511yescharacteristic
669C2×C3C22×D3×D411yescharacteristic
670C2×C3C22×D3×D411yescharacteristic
671C2×C3C22×#23911yescharacteristic
672C2×C3C2×#100711yescharacteristic
673C2×C3C2×#100711yescharacteristic
674D3—24no—
675D3—64no—
676D3—64no—
677D3—124no—
678D3—124no—
679D3—124no—
680D3—244no—
681C22—34no—
682C22—62no—
683C22—62no—
684C22—68no—
685C22—94no—
686C22—182no—
687C22—182no—
688C22—188no—
689C22—184no—
690C22—184no—
691C22—184no—
692C22—368no—
693C22C2×#379912yes—
694C22D32×D412yes—
695C22#6431612yes—
696C22C23×D3211yescharacteristic
697C4—24no—
698C4—34no—
699C4—62no—
700C4—64no—
701C4—64no—
702C4—62no—
703C4—182no—
704C4C2×#379914yescomplemented
705C3—21no—
706C3C2×#550711yescharacteristic, complemented
707C3C2×#572611yescharacteristic, complemented
708C2—64no—
709C2—184no—
710C2—364no—
711C2#1059451714yesdirect product factor
712C2C22×#379911yescharacteristic
713C2C2×D32×D411yescharacteristic
714C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#547
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×#3799C2semidirect
2. C2×#64104C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
4. C2×C3×#888C2semidirect
5. C2×#63909C2semidirect
6. C2×C4×#626C2semidirect
7. C2×#63900C2semidirect
8. C2×#63897C2semidirect
9. C2×#63894C2semidirect
10. C2×#63888C2semidirect
11. C2×#63850C2semidirect
12. #10594517C2direct (N × H)
26. C2×#3799C22semidirect
29. #64104C22semidirect
35. C3×D3×C4⋊C4C22semidirect
36. C3×#888C22semidirect
43. #63909C22semidirect
44. C4×#626C22semidirect
45. #63900C22semidirect
46. #63897C22semidirect
47. #63894C22semidirect
48. #63888C22semidirect
49. #63850C22semidirect
71. C2×D3×C4⋊C4D3semidirect
72. C2×#888D3semidirect
99. C2×#626D4semidirect
193. D3×C4⋊C4C2×D3semidirect
194. #888C2×D3semidirect
211. C2×C32×C4#41semidirect
233. #626C2×D4semidirect
368. C32×C4C2×#41semidirect
464. C2×C3×C4#235semidirect
465. C2×C3×C4#239semidirect
506. C2×C32#547semidirect
611. C3×C4C2×#235semidirect
612. C3×C4C2×#239semidirect
621. C32C2×#547semidirect
658. C2×C4#3799semidirect
666. C2×C3#5507semidirect
667. C2×C3#5726semidirect
704. C4C2×#3799semidirect
706. C3C2×#5507semidirect
707. C3C2×#5726semidirect
711. C2#10594517direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C2×#641042
C2×C3×D3×C4⋊C42
C2×C3×#8882
C2×#639092
C2×C4×#6262
C2×#639002
C2×#638972
C2×#638942
C2×#638882
C2×#638502
#105945172
C2×#57263
C2×#55073