Finite Group Databasebeta

← C2×#10594383 #11902669

Subgroups — C2×#10594383 #11902669

Order 1152.

3297 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64106C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×#887C211yesmaximal, characteristic, complemented
6C2×#63918C212yesmaximal, complemented
7C2×C4×#626C211yesmaximal, characteristic
8C2×#63895C212yesmaximal, complemented
9C2×#63893C212yesmaximal, complemented
10C2×#63880C212yesmaximal
11C2×#63866C211yesmaximal, characteristic, complemented
12#10594383C2116yesmaximal, direct product factor
13C2×#5632—31nomaximal
14C2×Q8×D12—31nomaximal
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2212yes—
21C22×#627C2212yes—
22C22×#626C2211yescharacteristic
23C22×#624C2212yes—
24C22×D3×Dic3C2212yes—
25C2×#3797—28no—
26C2×#3797C2218yescomplemented
27C2×D3×Dic6—28no—
28C2×D3×Dic6C2218yescomplemented
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×#3752C2212yes—
31C2×C4⋊(C3⋊Dic3)C2212yes—
32#64106C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2212yes—
38C3×#897C2218yescomplemented
39C3×#887C2218yescomplemented
40C2×Dic3⋊Dic3C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45#63918C22116yescomplemented
46C4×#626C2218yes—
47#63895C22116yescomplemented
48#63893C22116yescomplemented
49#63880C22116yes—
50#63866C2218yescomplemented
51C22×D3×Q8—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C23×Dic6—31no—
55C2×C3×C22⋊Q8—31no—
56C2×C3×C4×Q8—31no—
57C2×#944—31no—
58C2×C4×#67—31no—
59#5632—316no—
60Q8×D12—316no—
61C2×#897—31no—
62C2×#897—31no—
63C2×#897—32no—
64C2×#897—32no—
65C2×#897—61no—
66C2×#897D311yescharacteristic, complemented
67C2×#896—32no—
68C2×#888—32no—
69C2×#887D311yescharacteristic, complemented
70C2×#67⋊C4—32no—
71C2×#878—32no—
72C2×C4×D12—31no—
73C2×C4×D12—32no—
74C2×#869—31no—
75C2×#869—32no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C3⋊Dic3C2312yes—
81C22×C3⋊Dic3C2311yescharacteristic
82C2×C4×C3⋊D3—24no—
83C2×C4×C3⋊D3C2314yes—
84C2×#634—24no—
85C2×#634C2314yes—
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2311yescharacteristic
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6—24no—
94C2×C3×Dic6D418yescomplemented
95C2×C3×Dic6C2314yes—
96C2×C3×Dic6C2314yes—
97C2×#627—28no—
98C2×#627—28no—
99C2×#627C2318yes—
100C2×#627C2318yes—
101C2×#626Q818yescomplemented
102C2×#626C2314yes—
103C2×#624—28no—
104C2×#624C2318yes—
105C2×D3×Dic3—28no—
106C2×D3×Dic3C2318yes—
107#3797—232no—
108D3×Dic6—232no—
109C32×C4⋊C4C2314yes—
110#3752C2318yes—
111C4⋊(C3⋊Dic3)C2318yes—
112C3×(C2×D3)⋊C4C2318yes—
113C3×C4⋊Dic3C2318yes—
114C3×Dic3⋊C4C2318yes—
115C3×C4×Dic3C2314yes—
116C3×C4×Dic3C2318yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2318yes—
119Dic3⋊Dic3C2314yes—
120#3722C2314yes—
121(C2×D3)⋊Dic3C2314yes—
122C2×D4×Q8—91noSylow
123C22×C3×Q8—31no—
124C22×C3×Q8—31no—
125C23×C3×C4—31no—
126C22×#67—31no—
127C23×Dic3—32no—
128C2×D3×Q8—38no—
129C2×D3×Q8—38no—
130C2×D3×Q8—38no—
131C2×D3×Q8—68no—
132C2×D3×Q8—68no—
133C2×D3×Q8—68no—
134C22×D12—31no—
135C22×C4×D3—32no—
136C22×C4×D3—31no—
137C22×C4×D3—31no—
138C22×C4×D3—32no—
139C22×C4×D3—32no—
140C22×C4×D3—61no—
141C22×C4×D3C2×D311yescharacteristic
142C22×Dic6—31no—
143C22×Dic6—31no—
144C22×Dic6—32no—
145C22×Dic6—32no—
146C22×Dic6—32no—
147C22×Dic6—32no—
148C22×Dic6—38no—
149C22×Dic6—61no—
150C22×Dic6—68no—
151C22×Dic6C2×D311yescharacteristic
152C22×Dic6C2×D311yescharacteristic
153C3×C22⋊Q8—38no—
154C3×C4×Q8—38no—
155C2×C3×C4⋊C4—21no—
156C2×C3×C4⋊C4—32no—
157C2×C3×C4⋊C4—32no—
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4—32no—
161C2×C3×C42—32no—
162C2×C3×C42—31no—
163C2×#217—31no—
164#944—38no—
165C4×#67—38no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—32no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—62no—
172C2×(C2×D3)⋊C4C2×D312yes—
173C2×C4⋊Dic3—32no—
174C2×C4⋊Dic3—32no—
175C2×C4⋊Dic3—32no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—32no—
178C2×C4⋊Dic3—62no—
179C2×C4⋊Dic3C2×D312yes—
180C2×Dic3⋊C4—32no—
181C2×Dic3⋊C4—32no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4C2×D312yes—
184C2×C4×Dic3C2×D312yes—
185C2×C4×Dic3C2×D311yescharacteristic
186#897—38no—
187#897—38no—
188#897—316no—
189#897—316no—
190#897—68no—
191#897C2×D318yescomplemented
192#896—316no—
193#888—316no—
194#887C2×D318yescomplemented
195#67⋊C4—316no—
196#878—316no—
197C4×D12—38no—
198C4×D12—316no—
199#869—38no—
200#869—316no—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—22no—
203C22×C3⋊D3—22no—
204C22×C3⋊D3C2×Q814yescomplemented
205C22×C3⋊D3C2412yes—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×Q814yescomplemented
209C22×C3×D3C2412yes—
210C2×C32×C4—24no—
211C2×C32×C4C2×D414yes—
212C2×C32×C4C2414yes—
213C2×C32×C4C2412yes—
214C2×C3⋊Dic3—24no—
215C2×C3⋊Dic3—22no—
216C2×C3⋊Dic3C2412yes—
217C2×C3⋊Dic3C2414yes—
218C4×C3⋊D3—28no—
219#634—28no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C2×D418yes—
224C2×C3×Dic3C2×Q814yescomplemented
225C2×C3×Dic3C2412yes—
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2414yes—
228C2×C3×Dic3C2414yes—
229C2×C3×Dic3C2412yes—
230C3×C4×D3—28no—
231C3×Dic6—28no—
232C3×Dic6C2×D4116yescomplemented
233#627—216no—
234#627—216no—
235#626C2×Q8116yescomplemented
236#624—216no—
237D3×Dic3—216no—
238C23×Q8—91no—
239C23×Q8—91no—
240D4×Q8—916no—
241C2×C4⋊Q8—92no—
242C2×C4⋊Q8—91no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—92no—
245C2×C22⋊Q8—92no—
246C2×C22⋊Q8—91no—
247C2×C4×Q8—31no—
248C2×C4×D4—92no—
249C2×C4×D4—91no—
250C24×C3—31no—
251C23×D3—31no—
252C23×D3—31no—
253C23×D3—61no—
254C23×D3C22×D311yescharacteristic
255C2×C3×Q8—38no—
256C2×C3×Q8—34no—
257C2×C3×Q8—34no—
258C2×C3×Q8—64no—
259C22×C3×C4—21no—
260C22×C3×C4—22no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—32no—
264C22×C3×C4—31no—
265C22×C3×C4—31no—
266C22×C3×C4—34no—
267C22×C3×C4—64no—
268C22×C3×C4C22×D312yes—
269C22×C3×C4C22×D312yes—
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C2×#67—38no—
273C2×#67—34no—
274C22×Dic3—32no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—32no—
278C22×Dic3—38no—
279C22×Dic3—61no—
280C22×Dic3—62no—
281C22×Dic3—68no—
282C22×Dic3C22×D311yescharacteristic
283C22×Dic3C22×D312yes—
284C22×Dic3C22×D311yescharacteristic
285C22×Dic3C22×D312yes—
286C22×Dic3C22×D311yescharacteristic
287D3×Q8—632no—
288D3×Q8—632no—
289D3×Q8—632no—
290C2×D12—38no—
291C2×D12—34no—
292C2×C4×D3—24no—
293C2×C4×D3—38no—
294C2×C4×D3—34no—
295C2×C4×D3—34no—
296C2×C4×D3—38no—
297C2×C4×D3—38no—
298C2×C4×D3—64no—
299C2×C4×D3—68no—
300C2×C4×D3—68no—
301C2×C4×D3—64no—
302C2×C4×D3—64no—
303C2×C4×D3—68no—
304C2×C4×D3—124no—
305C2×C4×D3C22×D314yes—
306C2×Dic6—24no—
307C2×Dic6—34no—
308C2×Dic6—34no—
309C2×Dic6—38no—
310C2×Dic6—38no—
311C2×Dic6—38no—
312C2×Dic6—38no—
313C2×Dic6—64no—
314C2×Dic6—68no—
315C2×Dic6—68no—
316C2×Dic6—64no—
317C2×Dic6—64no—
318C2×Dic6—68no—
319C2×Dic6—68no—
320C2×Dic6—632no—
321C2×Dic6—124no—
322C2×Dic6D1218yescomplemented
323C2×Dic6C22×D314yes—
324C2×Dic6C22×D314yes—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—38no—
327C3×C4⋊C4—38no—
328C3×C4⋊C4C22×D314yes—
329C3×C4⋊C4C22×D314yes—
330C3×C22⋊C4—38no—
331C3×C42—38no—
332C3×C42—34no—
333#217—34no—
334(C2×D3)⋊C4—34no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—38no—
337(C2×D3)⋊C4—34no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—68no—
340(C2×D3)⋊C4C22×D318yes—
341C4⋊Dic3—38no—
342C4⋊Dic3—38no—
343C4⋊Dic3—38no—
344C4⋊Dic3—34no—
345C4⋊Dic3—38no—
346C4⋊Dic3—68no—
347C4⋊Dic3C22×D318yes—
348Dic3⋊C4—38no—
349Dic3⋊C4—38no—
350Dic3⋊C4—34no—
351Dic3⋊C4C22×D318yes—
352C4×Dic3C22×D318yes—
353C4×Dic3C22×D314yes—
354C22×C32C22×D412yes—
355C22×C32C22×Q812yes—
356C22×C322−1+412yes—
357C22×C32C2511yescharacteristic
358C2×C3⋊D3—28no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3C22×Q814yescomplemented
362C2×C3×D3—28no—
363C2×C3×D3—22no—
364C2×C3×D3—22no—
365C2×C3×D3C22×Q814yescomplemented
366C32×C4—24no—
367C32×C4C22×D414yes—
368C3⋊Dic3—24no—
369C3⋊Dic3—22no—
370C3×Dic3—24no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3C22×D418yes—
374C3×Dic3C22×Q814yescomplemented
375C22×Q8—31no—
376C22×Q8—31no—
377C22×Q8—92no—
378C22×Q8—92no—
379C22×Q8—98no—
380C22×Q8—98no—
381C22×Q8—91no—
382C22×Q8—188no—
383C22×Q8—188no—
384C22×D4—91no—
385C23×C4—31no—
386C23×C4—92no—
387C23×C4—92no—
388C23×C4—91no—
389C4⋊Q8—916no—
390C4⋊Q8—98no—
391C22⋊Q8—38no—
392C22⋊Q8—916no—
393C22⋊Q8—916no—
394C22⋊Q8—98no—
395C4×Q8—38no—
396C4×D4—916no—
397C4×D4—98no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—92no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—92no—
403C2×C4⋊C4—92no—
404C2×C4⋊C4D3211yescharacteristic
405C2×C22⋊C4—32no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—92no—
409C2×C42—32no—
410C2×C42—31no—
411C23×C3—21no—
412C23×C3—34no—
413C23×C3—32no—
414C23×C3—62no—
415C23×C3—62no—
416C23×C3C23×D311yescharacteristic
417C23×C3C23×D311yescharacteristic
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—34no—
421C22×D3—34no—
422C22×D3—32no—
423C22×D3—32no—
424C22×D3—64no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—122no—
431C22×D3—122no—
432C22×D3D3×Q814yescomplemented
433C22×D3C23×D312yes—
434C3×Q8—316no—
435C3×Q8—68no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—38no—
442C2×C3×C4—34no—
443C2×C3×C4—32no—
444C2×C3×C4—34no—
445C2×C3×C4—34no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—44no—
449C2×C3×C4—62no—
450C2×C3×C4—64no—
451C2×C3×C4—62no—
452C2×C3×C4—68no—
453C2×C3×C4C2×D1214yes—
454C2×C3×C4D3×D414yes—
455C2×C3×C4C23×D314yes—
456C2×C3×C4C23×D314yes—
457C2×C3×C4C23×D312yes—
458C2×C3×C4C23×D312yes—
459#67—316no—
460C2×Dic3—24no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—34no—
464C2×Dic3—32no—
465C2×Dic3—32no—
466C2×Dic3—34no—
467C2×Dic3—62no—
468C2×Dic3—64no—
469C2×Dic3—62no—
470C2×Dic3—64no—
471C2×Dic3—64no—
472C2×Dic3—62no—
473C2×Dic3—616no—
474C2×Dic3—124no—
475C2×Dic3—122no—
476C2×Dic3C2×D1218yes—
477C2×Dic3D3×Q814yescomplemented
478C2×Dic3C23×D312yes—
479C2×Dic3C23×D314yes—
480C2×Dic3C23×D312yes—
481C2×Dic3C23×D314yes—
482C2×Dic3C23×D312yes—
483D12—316no—
484C4×D3—28no—
485C4×D3—616no—
486C4×D3—616no—
487C4×D3—68no—
488C4×D3—68no—
489C4×D3—616no—
490C4×D3—128no—
491Dic6—28no—
492Dic6—616no—
493Dic6—616no—
494Dic6—68no—
495Dic6—68no—
496Dic6—616no—
497Dic6—616no—
498Dic6—128no—
499Dic6C2×D12116yescomplemented
500C2×C32D4×Q814yescomplemented
501C2×C32C23×D411yescharacteristic
502C2×C32C23×Q811yescharacteristic
503C2×C32C2×2−1+411yescharacteristic
504C3⋊D3—24no—
505C3×D3—24no—
506C24—31no—
507C24—91no—
508C2×Q8—34no—
509C2×Q8—34no—
510C2×Q8—38no—
511C2×Q8—64no—
512C2×Q8—98no—
513C2×Q8—98no—
514C2×Q8—94no—
515C2×Q8—188no—
516C2×Q8—188no—
517C2×Q8—1832no—
518C2×Q8—1832no—
519C2×Q8—184no—
520C2×D4—94no—
521C2×D4—98no—
522C22×C4—31no—
523C22×C4—32no—
524C22×C4—31no—
525C22×C4—32no—
526C22×C4—31no—
527C22×C4—34no—
528C22×C4—64no—
529C22×C4—98no—
530C22×C4—98no—
531C22×C4—91no—
532C22×C4—92no—
533C22×C4—94no—
534C22×C4—188no—
535C22×C4—188no—
536C22×C4—184no—
537C22×C4C2×D3212yes—
538C22×C4C2×D3211yescharacteristic
539C4⋊C4—38no—
540C4⋊C4—38no—
541C4⋊C4—98no—
542C4⋊C4—94no—
543C4⋊C4—98no—
544C4⋊C4—98no—
545C4⋊C4C2×D3214yes—
546C22⋊C4—38no—
547C22⋊C4—94no—
548C22⋊C4—94no—
549C22⋊C4—98no—
550C42—38no—
551C42—34no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—21no—
556C22×C3—34no—
557C22×C3—62no—
558C22×C3—62no—
559C22×C3—68no—
560C22×C3C22×D1212yes—
561C22×C3C2×D3×D412yes—
562C22×C3C2×D3×Q812yes—
563C22×C3C2×D3×Q812yes—
564C22×C3#101012yes—
565C22×C3#101012yes—
566C22×C3C24×D311yescharacteristic
567C22×C3C24×D311yescharacteristic
568C2×D3—28no—
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—34no—
572C2×D3—34no—
573C2×D3—64no—
574C2×D3—68no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—68no—
580C2×D3—122no—
581C2×D3—122no—
582C2×D3—128no—
583C2×D3C2×D3×Q814yescomplemented
584C3×C4—24no—
585C3×C4—24no—
586C3×C4—24no—
587C3×C4—38no—
588C3×C4—34no—
589C3×C4—44no—
590C3×C4—62no—
591C3×C4—64no—
592C3×C4—62no—
593C3×C4C22×D1214yes—
594C3×C4C2×D3×D414yes—
595Dic3—24no—
596Dic3—22no—
597Dic3—22no—
598Dic3—62no—
599Dic3—64no—
600Dic3—62no—
601Dic3—64no—
602Dic3—124no—
603Dic3—122no—
604Dic3C22×D1218yes—
605Dic3C2×D3×Q814yescomplemented
606C32C2×D4×Q811yescharacteristic, complemented, Sylow
607C23—34no—
608C23—32no—
609C23—62no—
610C23—62no—
611C23—94no—
612C23—92no—
613C23—182no—
614C23—182no—
615C23C22×D3211yescharacteristic
616Q8—316no—
617Q8—68no—
618Q8—1816no—
619Q8—1816no—
620Q8—188no—
621D4—916no—
622C2×C4—24no—
623C2×C4—38no—
624C2×C4—34no—
625C2×C4—32no—
626C2×C4—34no—
627C2×C4—32no—
628C2×C4—34no—
629C2×C4—32no—
630C2×C4—62no—
631C2×C4—64no—
632C2×C4—62no—
633C2×C4—68no—
634C2×C4—92no—
635C2×C4—94no—
636C2×C4—1816no—
637C2×C4—1816no—
638C2×C4—184no—
639C2×C4—182no—
640C2×C4—188no—
641C2×C4D3×D1214yes—
642C2×C4C22×D3214yes—
643C2×C4C22×D3212yes—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—24no—
648C2×C3—64no—
649C2×C3Q8×D1214yescomplemented
650C2×C3#563214yescomplemented
651C2×C3C23×D1211yescharacteristic
652C2×C3C22×D3×D411yescharacteristic
653C2×C3C22×D3×Q811yescharacteristic
654C2×C3C22×D3×Q811yescharacteristic
655C2×C3C2×#101011yescharacteristic
656C2×C3C2×#101011yescharacteristic
657D3—24no—
658D3—64no—
659D3—64no—
660D3—124no—
661C22—34no—
662C22—62no—
663C22—62no—
664C22—68no—
665C22—94no—
666C22—182no—
667C22—182no—
668C22—188no—
669C22C2×D3×D1212yes—
670C22#6430912yes—
671C22D32×Q812yes—
672C22C23×D3211yescharacteristic
673C4—24no—
674C4—38no—
675C4—34no—
676C4—62no—
677C4—64no—
678C4—62no—
679C4—184no—
680C4—182no—
681C4C2×D3×D1214yes—
682C3—21no—
683C3C2×Q8×D1211yescharacteristic, complemented
684C3C2×#563211yescharacteristic, complemented
685C2—64no—
686C2—184no—
687C2#1059438314yesdirect product factor
688C2C22×D3×D1211yescharacteristic
689C2C2×#6430911yescharacteristic
690C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×D4×Q8
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×#3797C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×#64106C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×#887C2semidirect
6. C2×#63918C2semidirect
8. C2×#63895C2semidirect
9. C2×#63893C2semidirect
11. C2×#63866C2semidirect
12. #10594383C2direct (N × H)
26. C2×#3797C22semidirect
28. C2×D3×Dic6C22semidirect
32. #64106C22semidirect
38. C3×#897C22semidirect
39. C3×#887C22semidirect
45. #63918C22semidirect
47. #63895C22semidirect
48. #63893C22semidirect
50. #63866C22semidirect
66. C2×#897D3semidirect
69. C2×#887D3semidirect
94. C2×C3×Dic6D4semidirect
101. C2×#626Q8semidirect
191. #897C2×D3semidirect
194. #887C2×D3semidirect
204. C22×C3⋊D3C2×Q8semidirect
208. C22×C3×D3C2×Q8semidirect
224. C2×C3×Dic3C2×Q8semidirect
232. C3×Dic6C2×D4semidirect
235. #626C2×Q8semidirect
322. C2×Dic6D12semidirect
361. C2×C3⋊D3C22×Q8semidirect
365. C2×C3×D3C22×Q8semidirect
374. C3×Dic3C22×Q8semidirect
432. C22×D3D3×Q8semidirect
477. C2×Dic3D3×Q8semidirect
499. Dic6C2×D12semidirect
500. C2×C32D4×Q8semidirect
583. C2×D3C2×D3×Q8semidirect
605. Dic3C2×D3×Q8semidirect
606. C32C2×D4×Q8semidirect
649. C2×C3Q8×D12semidirect
650. C2×C3#5632semidirect
683. C3C2×Q8×D12semidirect
684. C3C2×#5632semidirect
687. C2#10594383direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37972
C22×D3×Dic62
C2×#641062
C2×C3×#8972
C2×C3×#8872
C2×#639182
C2×C4×#6262
C2×#638952
C2×#638932
C2×#638802
C2×#638662
#105943832
C2×#56323
C2×Q8×D123