Finite Group Databasebeta

← C2×#10595361 #11902667

Subgroups — C2×#10595361 #11902667

Order 1152.

3561 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5#10595361C2116yesmaximal, direct product factor
6C2×C4×#626C211yesmaximal, characteristic
7C2×#63896C212yesmaximal, complemented
8C2×#63881C212yesmaximal
9C2×#63871C211yesmaximal, characteristic, complemented
10C2×#63865C212yesmaximal, complemented
11C2×#63844C211yesmaximal, characteristic, complemented
12C2×#63840C212yesmaximal, complemented
13C2×#5727—31nomaximal
14C2×#5632—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C2×Q8×C3⋊D3—28no—
17C2×Q8×C3⋊D3C2218yescomplemented
18C22×C4×C3⋊D3C2212yes—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2212yes—
21C22×#634C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#627C2212yes—
25C22×#626C2211yescharacteristic
26C22×D3×Dic3C2212yes—
27C2×D3×Dic6—28no—
28C2×D3×Dic6C2218yescomplemented
29C3×#946C2218yescomplemented
30C3×#944C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2212yes—
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×#3724C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2212yes—
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2212yes—
44C4×#626C2218yes—
45#63896C22116yescomplemented
46#63881C22116yes—
47#63871C2218yescomplemented
48#63865C22116yescomplemented
49#63844C2218yescomplemented
50#63840C22116yescomplemented
51C22×D3×Q8—31no—
52C22×D3×Q8—31no—
53C22×D3×Q8—31no—
54C22×D3×Q8—61no—
55C23×Dic6—31no—
56C2×C3×C4⋊Q8—31no—
57C2×C3×C22⋊Q8—31no—
58C2×#946—31no—
59C2×#946D311yescharacteristic, complemented
60C2×#944D311yescharacteristic, complemented
61C2×C4×#67—31no—
62#5727—316no—
63#5632—316no—
64C2×#897—31no—
65C2×#896—32no—
66C2×#896—32no—
67C2×#896—32no—
68C2×#893—32no—
69C2×#888—32no—
70C2×#888—32no—
71C2×#887—31no—
72C2×#67⋊C4—32no—
73C2×#878—32no—
74C2×C4×D12—31no—
75C2×C4×Dic6—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C2×C32×Q8—24no—
79C2×C32×Q8C2314yes—
80C22×C32×C4C2312yes—
81C22×C32×C4C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2312yes—
84Q8×C3⋊D3—232no—
85C2×C4×C3⋊D3—24no—
86C2×C4×C3⋊D3—28no—
87C2×C4×C3⋊D3C2318yes—
88C2×C4×C3⋊D3C2314yes—
89C2×#634—28no—
90C2×#634D418yescomplemented
91C2×#634C2318yes—
92C2×#634C2314yes—
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2311yescharacteristic
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3C2314yes—
100C2×C3×Dic6—24no—
101C2×C3×Dic6C2314yes—
102C2×#627—28no—
103C2×#627C2318yes—
104C2×#626Q818yescomplemented
105C2×#626C2314yes—
106C2×D3×Dic3—28no—
107C2×D3×Dic3C2318yes—
108D3×Dic6—232no—
109C3×(C2×D3)⋊C4C2318yes—
110C3×C4⋊Dic3C2314yes—
111C3×Dic3⋊C4C2318yes—
112C3×Dic3⋊C4C2318yes—
113C3×Dic3⋊C4C2318yes—
114C3×C4×Dic3C2314yes—
115#3724C2318yes—
116Dic3⋊Dic3C2314yes—
117Dic3⋊Dic3C2318yes—
118#3722C2314yes—
119#3722C2318yes—
120(C2×D3)⋊Dic3C2314yes—
121Dic32C2318yes—
122C2×D4×Q8—91noSylow
123C22×C3×Q8—21no—
124C22×C3×Q8—31no—
125C22×C3×Q8C2×D311yescharacteristic
126C22×C3×Q8C2×D311yescharacteristic
127C23×C3×C4—31no—
128C22×#67—31no—
129C23×Dic3—32no—
130C2×D3×Q8—38no—
131C2×D3×Q8—38no—
132C2×D3×Q8—38no—
133C2×D3×Q8—68no—
134C2×D3×Q8—68no—
135C2×D3×Q8—68no—
136C2×D3×Q8—68no—
137C2×D3×Q8—616no—
138C22×D12—31no—
139C22×C4×D3—32no—
140C22×C4×D3—31no—
141C22×C4×D3—32no—
142C22×C4×D3—32no—
143C22×C4×D3—31no—
144C22×C4×D3—62no—
145C22×C4×D3—61no—
146C22×C4×D3C2×D311yescharacteristic
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—32no—
150C22×Dic6—32no—
151C22×Dic6—32no—
152C22×Dic6—32no—
153C22×Dic6—38no—
154C22×Dic6—61no—
155C22×Dic6—62no—
156C22×Dic6—68no—
157C22×Dic6C2×D311yescharacteristic
158C3×C4⋊Q8—38no—
159C3×C22⋊Q8—38no—
160C2×C3×C4⋊C4—32no—
161C2×C3×C4⋊C4—32no—
162C2×C3×C4⋊C4—32no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—32no—
165C2×C3×C42—31no—
166C2×#217—31no—
167#946—38no—
168#946C2×D318yescomplemented
169#944C2×D318yescomplemented
170C4×#67—38no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4C2×D312yes—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—32no—
179C2×C4⋊Dic3C2×D311yescharacteristic
180C2×Dic3⋊C4—32no—
181C2×Dic3⋊C4—32no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—32no—
184C2×Dic3⋊C4C2×D312yes—
185C2×Dic3⋊C4C2×D312yes—
186C2×Dic3⋊C4C2×D312yes—
187C2×C4×Dic3—32no—
188C2×C4×Dic3—32no—
189C2×C4×Dic3C2×D311yescharacteristic
190#897—38no—
191#896—316no—
192#896—316no—
193#896—316no—
194#893—316no—
195#888—316no—
196#888—316no—
197#887—38no—
198#67⋊C4—316no—
199#878—316no—
200C4×D12—38no—
201C4×Dic6—38no—
202C23×C32C2411yescharacteristic
203C22×C3⋊D3—22no—
204C22×C3⋊D3—22no—
205C22×C3⋊D3C2×Q814yescomplemented
206C22×C3⋊D3C2412yes—
207C22×C3×D3—22no—
208C22×C3×D3—22no—
209C22×C3×D3C2×Q814yescomplemented
210C22×C3×D3C2412yes—
211C32×Q8—28no—
212C2×C32×C4—24no—
213C2×C32×C4C2×D414yes—
214C2×C32×C4C2414yes—
215C2×C32×C4C2412yes—
216C2×C3⋊Dic3—22no—
217C2×C3⋊Dic3C2×D418yes—
218C2×C3⋊Dic3C2412yes—
219C2×C3⋊Dic3C2414yes—
220C4×C3⋊D3—28no—
221C4×C3⋊D3—216no—
222#634—216no—
223#634C2×D4116yescomplemented
224C2×C3×Dic3—24no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—24no—
228C2×C3×Dic3C2×Q814yescomplemented
229C2×C3×Dic3C2414yes—
230C2×C3×Dic3C2412yes—
231C2×C3×Dic3C2414yes—
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2412yes—
234C3×C4×D3—28no—
235C3×Dic6—28no—
236#627—216no—
237#626C2×Q8116yescomplemented
238D3×Dic3—216no—
239C23×Q8—91no—
240C23×Q8—91no—
241D4×Q8—916no—
242C2×C4⋊Q8—31no—
243C2×C4⋊Q8—92no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—92no—
246C2×C22⋊Q8—92no—
247C2×C22⋊Q8—91no—
248C2×C4×Q8—91no—
249C2×C4×D4—91no—
250C2×C4×D4—92no—
251C24×C3—31no—
252C23×D3—31no—
253C23×D3—31no—
254C23×D3—61no—
255C23×D3C22×D311yescharacteristic
256C2×C3×Q8—28no—
257C2×C3×Q8—24no—
258C2×C3×Q8—24no—
259C2×C3×Q8—24no—
260C2×C3×Q8—34no—
261C2×C3×Q8—64no—
262C2×C3×Q8C22×D314yes—
263C2×C3×Q8C22×D314yes—
264C22×C3×C4—22no—
265C22×C3×C4—21no—
266C22×C3×C4—31no—
267C22×C3×C4—32no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—34no—
272C22×C3×C4—64no—
273C22×C3×C4C22×D312yes—
274C22×C3×C4C22×D312yes—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C2×#67—38no—
278C2×#67—34no—
279C22×Dic3—32no—
280C22×Dic3—32no—
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—38no—
284C22×Dic3—62no—
285C22×Dic3—61no—
286C22×Dic3—68no—
287C22×Dic3C22×D312yes—
288C22×Dic3C22×D311yescharacteristic
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D312yes—
291C22×Dic3C22×D311yescharacteristic
292D3×Q8—632no—
293D3×Q8—632no—
294D3×Q8—632no—
295D3×Q8—664no—
296C2×D12—38no—
297C2×D12—34no—
298C2×C4×D3—24no—
299C2×C4×D3—38no—
300C2×C4×D3—34no—
301C2×C4×D3—38no—
302C2×C4×D3—38no—
303C2×C4×D3—34no—
304C2×C4×D3—68no—
305C2×C4×D3—64no—
306C2×C4×D3—68no—
307C2×C4×D3—68no—
308C2×C4×D3—68no—
309C2×C4×D3—616no—
310C2×C4×D3—68no—
311C2×C4×D3—64no—
312C2×C4×D3—64no—
313C2×C4×D3C22×D314yes—
314C2×Dic6—24no—
315C2×Dic6—38no—
316C2×Dic6—38no—
317C2×Dic6—34no—
318C2×Dic6—34no—
319C2×Dic6—38no—
320C2×Dic6—38no—
321C2×Dic6—38no—
322C2×Dic6—38no—
323C2×Dic6—68no—
324C2×Dic6—64no—
325C2×Dic6—68no—
326C2×Dic6—632no—
327C2×Dic6—68no—
328C2×Dic6—68no—
329C2×Dic6—68no—
330C2×Dic6—68no—
331C2×Dic6—616no—
332C2×Dic6C22×D314yes—
333C3×C4⋊C4—34no—
334C3×C4⋊C4—38no—
335C3×C4⋊C4—38no—
336C3×C4⋊C4—38no—
337C3×C22⋊C4—38no—
338C3×C42—34no—
339#217—34no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—34no—
342(C2×D3)⋊C4—38no—
343(C2×D3)⋊C4—38no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4C22×D318yes—
346C4⋊Dic3—34no—
347C4⋊Dic3—38no—
348C4⋊Dic3C22×D314yes—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—34no—
352Dic3⋊C4—38no—
353Dic3⋊C4C22×D318yes—
354Dic3⋊C4C22×D318yes—
355Dic3⋊C4C22×D318yes—
356C4×Dic3—38no—
357C4×Dic3—38no—
358C4×Dic3C22×D314yes—
359C22×C32C22×D412yes—
360C22×C32C22×Q812yes—
361C22×C322−1+412yes—
362C22×C32C2511yescharacteristic
363C2×C3⋊D3—28no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3C22×Q814yescomplemented
367C2×C3×D3—28no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3C22×Q814yescomplemented
371C32×C4—24no—
372C32×C4C22×D414yes—
373C3⋊Dic3—22no—
374C3⋊Dic3C22×D418yes—
375C3×Dic3—24no—
376C3×Dic3—22no—
377C3×Dic3—22no—
378C3×Dic3—24no—
379C3×Dic3C22×Q814yescomplemented
380C22×Q8—31no—
381C22×Q8—92no—
382C22×Q8—98no—
383C22×Q8—98no—
384C22×Q8—91no—
385C22×Q8—92no—
386C22×Q8—188no—
387C22×Q8—188no—
388C22×Q8D3211yescharacteristic
389C22×D4—91no—
390C23×C4—31no—
391C23×C4—92no—
392C23×C4—92no—
393C23×C4—91no—
394C4⋊Q8—38no—
395C4⋊Q8—916no—
396C22⋊Q8—38no—
397C22⋊Q8—916no—
398C22⋊Q8—916no—
399C22⋊Q8—98no—
400C4×Q8—98no—
401C4×D4—98no—
402C4×D4—916no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—91no—
408C2×C4⋊C4—92no—
409C2×C4⋊C4—92no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—91no—
412C2×C22⋊C4—92no—
413C2×C22⋊C4—91no—
414C2×C42—31no—
415C2×C42—92no—
416C23×C3—21no—
417C23×C3—34no—
418C23×C3—32no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3C23×D311yescharacteristic
422C23×C3C23×D311yescharacteristic
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—34no—
426C22×D3—34no—
427C22×D3—32no—
428C22×D3—32no—
429C22×D3—64no—
430C22×D3—62no—
431C22×D3—64no—
432C22×D3—64no—
433C22×D3—62no—
434C22×D3—62no—
435C22×D3—62no—
436C22×D3—62no—
437C22×D3D3×Q814yescomplemented
438C22×D3C23×D312yes—
439C3×Q8—216no—
440C3×Q8—28no—
441C3×Q8—28no—
442C3×Q8—68no—
443C2×C3×C4—28no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—24no—
449C2×C3×C4—34no—
450C2×C3×C4—32no—
451C2×C3×C4—34no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—34no—
455C2×C3×C4—62no—
456C2×C3×C4—64no—
457C2×C3×C4—64no—
458C2×C3×C4—62no—
459C2×C3×C4—68no—
460C2×C3×C4D3×D414yes—
461C2×C3×C4D3×D414yes—
462C2×C3×C4C23×D314yes—
463C2×C3×C4C23×D314yes—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D312yes—
466#67—316no—
467C2×Dic3—24no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—24no—
471C2×Dic3—38no—
472C2×Dic3—38no—
473C2×Dic3—34no—
474C2×Dic3—34no—
475C2×Dic3—32no—
476C2×Dic3—32no—
477C2×Dic3—68no—
478C2×Dic3—64no—
479C2×Dic3—62no—
480C2×Dic3—616no—
481C2×Dic3—64no—
482C2×Dic3—62no—
483C2×Dic3—62no—
484C2×Dic3D3×Q814yescomplemented
485C2×Dic3C23×D314yes—
486C2×Dic3C23×D312yes—
487C2×Dic3C23×D312yes—
488C2×Dic3C23×D314yes—
489C2×Dic3C23×D312yes—
490D12—316no—
491C4×D3—28no—
492C4×D3—616no—
493C4×D3—616no—
494C4×D3—616no—
495C4×D3—632no—
496C4×D3—616no—
497C4×D3—68no—
498C4×D3—68no—
499Dic6—28no—
500Dic6—316no—
501Dic6—316no—
502Dic6—616no—
503Dic6—616no—
504Dic6—616no—
505Dic6—616no—
506Dic6—616no—
507Dic6—632no—
508C2×C32D4×Q814yescomplemented
509C2×C32C23×D411yescharacteristic
510C2×C32C23×Q811yescharacteristic
511C2×C32C2×2−1+411yescharacteristic
512C3⋊D3—24no—
513C3×D3—24no—
514C24—31no—
515C24—91no—
516C2×Q8—24no—
517C2×Q8—34no—
518C2×Q8—64no—
519C2×Q8—98no—
520C2×Q8—94no—
521C2×Q8—98no—
522C2×Q8—98no—
523C2×Q8—188no—
524C2×Q8—188no—
525C2×Q8—1832no—
526C2×Q8—1832no—
527C2×Q8C2×D3214yes—
528C2×D4—94no—
529C2×D4—98no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—32no—
533C22×C4—31no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—64no—
537C22×C4—98no—
538C22×C4—92no—
539C22×C4—91no—
540C22×C4—98no—
541C22×C4—94no—
542C22×C4—188no—
543C22×C4—188no—
544C22×C4—184no—
545C22×C4C2×D3212yes—
546C22×C4C2×D3211yescharacteristic
547C4⋊C4—38no—
548C4⋊C4—34no—
549C4⋊C4—38no—
550C4⋊C4—38no—
551C4⋊C4—94no—
552C4⋊C4—98no—
553C4⋊C4—98no—
554C22⋊C4—38no—
555C22⋊C4—94no—
556C22⋊C4—98no—
557C22⋊C4—94no—
558C42—34no—
559C42—98no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—21no—
564C22×C3—34no—
565C22×C3—62no—
566C22×C3—62no—
567C22×C3—68no—
568C22×C3C2×D3×D412yes—
569C22×C3C2×D3×D412yes—
570C22×C3C2×D3×Q812yes—
571C22×C3C2×D3×Q812yes—
572C22×C3#100712yes—
573C22×C3#101012yes—
574C22×C3C24×D311yescharacteristic
575C22×C3C24×D311yescharacteristic
576C2×D3—28no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3—34no—
580C2×D3—34no—
581C2×D3—64no—
582C2×D3—64no—
583C2×D3—616no—
584C2×D3—64no—
585C2×D3—68no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—68no—
591C2×D3C2×D3×Q814yescomplemented
592C3×C4—28no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—24no—
596C3×C4—34no—
597C3×C4—62no—
598C3×C4—64no—
599C3×C4—64no—
600C3×C4—62no—
601C3×C4C2×D3×D414yes—
602C3×C4C2×D3×D414yes—
603Dic3—24no—
604Dic3—22no—
605Dic3—22no—
606Dic3—24no—
607Dic3—38no—
608Dic3—38no—
609Dic3—68no—
610Dic3—64no—
611Dic3—62no—
612Dic3—62no—
613Dic3C2×D3×Q814yescomplemented
614C32C2×D4×Q811yescharacteristic, complemented, Sylow
615C23—34no—
616C23—32no—
617C23—62no—
618C23—62no—
619C23—94no—
620C23—92no—
621C23—182no—
622C23—182no—
623C23C22×D3211yescharacteristic
624Q8—28no—
625Q8—68no—
626Q8—916no—
627Q8—1816no—
628Q8—1816no—
629D4—916no—
630C2×C4—24no—
631C2×C4—34no—
632C2×C4—32no—
633C2×C4—32no—
634C2×C4—34no—
635C2×C4—32no—
636C2×C4—34no—
637C2×C4—62no—
638C2×C4—64no—
639C2×C4—62no—
640C2×C4—64no—
641C2×C4—68no—
642C2×C4—98no—
643C2×C4—94no—
644C2×C4—92no—
645C2×C4—1816no—
646C2×C4—1816no—
647C2×C4—182no—
648C2×C4—188no—
649C2×C4#381114yes—
650C2×C4C22×D3214yes—
651C2×C4C22×D3212yes—
652C2×C3—24no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—64no—
657C2×C3#563214yescomplemented
658C2×C3#572714yescomplemented
659C2×C3C22×D3×D411yescharacteristic
660C2×C3C22×D3×D411yescharacteristic
661C2×C3C22×D3×Q811yescharacteristic
662C2×C3C22×D3×Q811yescharacteristic
663C2×C3C2×#100711yescharacteristic
664C2×C3C2×#101011yescharacteristic
665D3—24no—
666D3—68no—
667D3—64no—
668D3—64no—
669C22—34no—
670C22—68no—
671C22—62no—
672C22—62no—
673C22—94no—
674C22—188no—
675C22—182no—
676C22—182no—
677C22#6431512yes—
678C22D32×Q812yes—
679C22C2×#381112yes—
680C22C23×D3211yescharacteristic
681C4—24no—
682C4—34no—
683C4—62no—
684C4—64no—
685C4—62no—
686C4—64no—
687C4—98no—
688C4—182no—
689C4C2×#381114yes—
690C3—21no—
691C3C2×#563211yescharacteristic, complemented
692C3C2×#572711yescharacteristic, complemented
693C2—64no—
694C2—184no—
695C2#1059536114yesdirect product factor
696C2C2×#6431511yescharacteristic
697C2C2×D32×Q811yescharacteristic
698C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC22×Q8D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
2. C22×D3×Dic6C2semidirect
3. C2×C3×#946C2semidirect
4. C2×C3×#944C2semidirect
5. #10595361C2direct (N × H)
7. C2×#63896C2semidirect
9. C2×#63871C2semidirect
10. C2×#63865C2semidirect
11. C2×#63844C2semidirect
12. C2×#63840C2semidirect
17. C2×Q8×C3⋊D3C22semidirect
28. C2×D3×Dic6C22semidirect
29. C3×#946C22semidirect
30. C3×#944C22semidirect
45. #63896C22semidirect
47. #63871C22semidirect
48. #63865C22semidirect
49. #63844C22semidirect
50. #63840C22semidirect
59. C2×#946D3semidirect
60. C2×#944D3semidirect
90. C2×#634D4semidirect
104. C2×#626Q8semidirect
168. #946C2×D3semidirect
169. #944C2×D3semidirect
205. C22×C3⋊D3C2×Q8semidirect
209. C22×C3×D3C2×Q8semidirect
223. #634C2×D4semidirect
228. C2×C3×Dic3C2×Q8semidirect
237. #626C2×Q8semidirect
366. C2×C3⋊D3C22×Q8semidirect
370. C2×C3×D3C22×Q8semidirect
379. C3×Dic3C22×Q8semidirect
437. C22×D3D3×Q8semidirect
484. C2×Dic3D3×Q8semidirect
508. C2×C32D4×Q8semidirect
591. C2×D3C2×D3×Q8semidirect
613. Dic3C2×D3×Q8semidirect
614. C32C2×D4×Q8semidirect
657. C2×C3#5632semidirect
658. C2×C3#5727semidirect
691. C3C2×#5632semidirect
692. C3C2×#5727semidirect
695. C2#10595361direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C22×D3×Dic62
C2×C3×#9462
C2×C3×#9442
#105953612
C2×C4×#6262
C2×#638962
C2×#638812
C2×#638712
C2×#638652
C2×#638442
C2×#638402
C2×#57273
C2×#56323