Finite Group Databasebeta

← C2×C4×#66931 #14912219

Subgroups — C2×C4×#66931 #14912219

Order 2816.

3854 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3C23×C4×Dic11C211yesmaximal, characteristic
4C4×#66931C2116yesmaximal, direct product factor
5C2×#10622259C211yesmaximal, characteristic, complemented
6C2×#10622260C211yesmaximal, characteristic, complemented
7C2×#10622268C211yesmaximal, characteristic, complemented
8C2×#10622267C211yesmaximal, characteristic, complemented
9C2×#10622563C211yesmaximal, characteristic
10C2×#10622559C211yesmaximal, characteristic
11C2×#10622555C211yesmaximal, characteristic
12C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic
16C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11—28no—
37C22×C4×Dic11C2218yes—
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66931C4116yesdirect product factor
45C2×#66931C2218yes—
46C2×C4×Dic22—28no—
47C2×C4×Dic22C2218yescomplemented
48C4×C11×C22⋊C4C2218yes—
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C4×C22⋊Dic11C2218yes—
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622563C2218yes—
61#10622559C2218yes—
62#10622555C2218yes—
63C4×C4⋊Dic11C2218yescomplemented
64C4×Dic11⋊C4C2218yescomplemented
65C4×Dic11⋊C4C2218yescomplemented
66#10622268C2218yescomplemented
67#10622267C2218yescomplemented
68#10622260C2218yescomplemented
69#10622259C2218yescomplemented
70C25×C11C2311yescharacteristic
71C23×C4×C11—24no—
72C23×C4×C11—24no—
73C23×C4×C11Q818yescomplemented
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2314yes—
80C23×C4×C11C2311yescharacteristic
81C23×Dic11—24no—
82C23×Dic11—24no—
83C23×Dic11—24no—
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11C2×C418yes—
87C23×Dic11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2314yes—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C22×Dic22—24no—
98C22×Dic22—24no—
99C22×Dic22C2×C418yescomplemented
100C22×Dic22C2314yes—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4C2×C418yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C42×C11—24no—
106C2×C42×C11—24no—
107C2×C42×C11C2314yes—
108C2×C42×C11C2314yes—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11C2×C418yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11C2×C418yescomplemented
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2314yes—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4C2×C418yescomplemented
124C2×Dic11⋊C4C2×C418yescomplemented
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×C4×Dic11—24no—
132C2×C4×Dic11—24no—
133C2×C4×Dic11—24no—
134C2×C4×Dic11—24no—
135C2×C4×Dic11—24no—
136C2×C4×Dic11—232no—
137C2×C4×Dic11D418yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144#66931C2×C4164yesdirect product factor
145C4×Dic22—232no—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×C4×C22⋊Q8—111nomaximal, Sylow
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11C22×C414yes—
162C24×C11C2×Q814yes—
163C24×C11#4114yes—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—232no—
173C22×C4×C11—28no—
174C22×C4×C11—28no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11C22×C414yes—
182C22×C4×C11C22×C414yes—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×Q814yes—
185C22×C4×C11C2×Q814yes—
186C22×C4×C11C2×Q8116yescomplemented
187C22×C4×C11#4114yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×Dic11—232no—
195C22×Dic11—232no—
196C22×Dic11—28no—
197C22×Dic11—28no—
198C22×Dic11—28no—
199C22×Dic11—28no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—28no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11C22×C4116yes—
218C22×Dic11C22×C414yes—
219C22×Dic11C22×C414yes—
220C22×Dic11C22×C414yes—
221C22×Dic11C22×C414yes—
222C22×Dic11C2×D414yes—
223C22×Dic11C2×D414yes—
224C22×Dic11#4114yes—
225C22×Dic11#4114yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C2×Dic22—232no—
235C2×Dic22—28no—
236C2×Dic22—28no—
237C2×Dic22C22×C4116yescomplemented
238C11×C22⋊C4—28no—
239C11×C22⋊C4C22×C4116yes—
240C42×C11—28no—
241C42×C11—28no—
242C22⋊Dic11—28no—
243C22⋊Dic11C22×C4116yes—
244C4⋊Dic11—28no—
245C4⋊Dic11—28no—
246C4⋊Dic11C22×C4116yescomplemented
247Dic11⋊C4—28no—
248Dic11⋊C4—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4C22×C4116yescomplemented
252Dic11⋊C4C22×C4116yescomplemented
253C4×Dic11—28no—
254C4×Dic11—28no—
255C4×Dic11—28no—
256C4×Dic11—28no—
257C4×Dic11—28no—
258C4×Dic11C2×D4116yes—
259C22×C22⋊Q8—111no—
260C22×C4×Q8—111no—
261C23×C42—111no—
262C4×C22⋊Q8—1116no—
263C2×#391—111no—
264C2×#389—111no—
265C2×#387—111no—
266C2×#387—111no—
267C2×#385—111no—
268C2×#385—111no—
269C2×#380—111no—
270C2×C4×C4⋊C4—111no—
271C2×C4×C4⋊C4—111no—
272C2×C4×C4⋊C4—111no—
273C2×C4×C22⋊C4—111no—
274C2×C4×C22⋊C4D1111yescharacteristic
275C23×C11—28no—
276C23×C11—28no—
277C23×C11—28no—
278C23×C11—28no—
279C23×C11—28no—
280C23×C11—28no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11C4×Q8116yescomplemented
286C23×C11C23×C414yes—
287C23×C11C23×C412yes—
288C23×C11C22×D412yes—
289C23×C11C22×Q814yes—
290C23×C11C22×Q812yes—
291C23×C11C2×#4114yes—
292C23×C11C2×#4112yes—
293C23×C11C2×#4112yes—
294C23×C11C2×#4112yes—
295C23×C11C2×#4112yes—
296C23×C11C2511yescharacteristic
297C2×C4×C11—28no—
298C2×C4×C11—28no—
299C2×C4×C11—28no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—232no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—44no—
314C2×C4×C11—44no—
315C2×C4×C11C22⋊Q8116yescomplemented
316C2×C4×C11C23×C414yes—
317C2×C4×C11C23×C414yes—
318C2×C4×C11C22×D414yes—
319C2×C4×C11C22×Q814yes—
320C2×C4×C11C22×Q814yes—
321C2×C4×C11C2×#4114yes—
322C2×Dic11—232no—
323C2×Dic11—28no—
324C2×Dic11—28no—
325C2×Dic11—28no—
326C2×Dic11—28no—
327C2×Dic11—28no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—232no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—44no—
346C2×Dic11—44no—
347C2×Dic11C4×D4116yes—
348C2×Dic11C23×C414yes—
349C2×Dic11C23×C414yes—
350C2×Dic11C23×C414yes—
351C2×Dic11C23×C414yes—
352C2×Dic11C22×D414yes—
353C2×Dic11C22×D414yes—
354C2×Dic11C2×#4114yes—
355C2×Dic11C2×#4114yes—
356Dic22—232no—
357C23×Q8—111no—
358C24×C4—111no—
359C24×C4—111no—
360C24×C4C2×D1111yescharacteristic
361C2×C22⋊Q8—118no—
362C2×C22⋊Q8—1116no—
363C2×C4×Q8—118no—
364C2×C4×Q8—228no—
365C22×C4⋊C4—111no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—111no—
376C22×C22⋊C4C2×D1111yescharacteristic
377C22×C22⋊C4C2×D1111yescharacteristic
378C22×C42—111no—
379C22×C42—111no—
380C22×C42—111no—
381C22×C42—118no—
382C22×C42—111no—
383C22×C42—111no—
384C22×C42—111no—
385C22×C42—228no—
386C22×C42C2×D1111yescharacteristic
387C22×C42C2×D1111yescharacteristic
388#391—118no—
389#389—118no—
390#387—118no—
391#387—118no—
392#385—118no—
393#385—118no—
394#380—118no—
395C4×C4⋊C4—118no—
396C4×C4⋊C4—118no—
397C4×C4⋊C4—118no—
398C4×C22⋊C4—118no—
399C4×C22⋊C4C2×D1118yes—
400C2×#95—111no—
401C2×#95—111no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95C2×D1111yescharacteristic
409C2×#95C2×D1111yescharacteristic
410C22×C11—24no—
411C22×C11—24no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—232no—
417C22×C11C2×C4×D414yes—
418C22×C11C2×C4×Q814yes—
419C22×C11C2×C4×Q818yescomplemented
420C22×C11C4×#4114yes—
421C22×C11C2×C22⋊Q814yes—
422C22×C11#52514yes—
423C22×C11#52914yes—
424C22×C11#53314yes—
425C22×C11C24×C411yescharacteristic
426C22×C11C23×D411yescharacteristic
427C22×C11C23×Q811yescharacteristic
428C22×C11C22×#4111yescharacteristic
429C22×C11C22×#4111yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C22×#4111yescharacteristic
432C4×C11—24no—
433C4×C11—24no—
434C4×C11—24no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11C2×C22⋊Q818yescomplemented
438Dic11—24no—
439Dic11—24no—
440Dic11—24no—
441Dic11—24no—
442Dic11—24no—
443Dic11—42no—
444Dic11—42no—
445Dic11C2×C4×D418yes—
446C25C22×D1111yescharacteristic
447C22×Q8—118no—
448C22×Q8—114no—
449C22×Q8—224no—
450C22×Q8—224no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—111no—
454C23×C4—118no—
455C23×C4—111no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—114no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—114no—
464C23×C4—224no—
465C23×C4—224no—
466C23×C4—224no—
467C23×C4—224no—
468C23×C4—224no—
469C23×C4Dic2218yescomplemented
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1114yes—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C22⋊Q8—1164no—
478C4×Q8—2232no—
479C2×C4⋊C4—118no—
480C2×C4⋊C4—118no—
481C2×C4⋊C4—118no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—224no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—224no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—118no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4C4×D1118yes—
503C2×C22⋊C4C22×D1114yes—
504C2×C22⋊C4C22×D1114yes—
505C2×C42—24no—
506C2×C42—24no—
507C2×C42—118no—
508C2×C42—114no—
509C2×C42—114no—
510C2×C42—114no—
511C2×C42—114no—
512C2×C42—114no—
513C2×C42—114no—
514C2×C42—2232no—
515C2×C42—224no—
516C2×C42—224no—
517C2×C42—224no—
518C2×C42—224no—
519C2×C42—224no—
520C2×C42C22×D1114yes—
521C2×C42C22×D1114yes—
522#95—114no—
523#95—114no—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95C22×D1114yes—
531#95C22×D1114yes—
532C2×C11—28no—
533C2×C11C4×C22⋊Q818yescomplemented
534C2×C11C22×C4×D411yescharacteristic
535C2×C11C22×C4×Q811yescharacteristic
536C2×C11C2×C4×#4111yescharacteristic
537C2×C11C22×C22⋊Q811yescharacteristic
538C2×C11C2×#52511yescharacteristic
539C2×C11C2×#52911yescharacteristic
540C2×C11C2×#53311yescharacteristic
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24C2×Dic2214yes—
546C24C2×C4×D1114yes—
547C24#433914yes—
548C24C23×D1112yes—
549C24C23×D1111yescharacteristic
550C2×Q8—1116no—
551C2×Q8—228no—
552C2×Q8—2232no—
553C2×Q8—228no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—232no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—114no—
570C22×C4—114no—
571C22×C4—114no—
572C22×C4—112no—
573C22×C4—114no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—1116no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—228no—
587C22×C4—228no—
588C22×C4—2232no—
589C22×C4—228no—
590C22×C4—228no—
591C22×C4—2232no—
592C22×C4—228no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4C2×Dic2214yes—
610C22×C4C2×Dic2214yes—
611C22×C4C2×Dic22116yescomplemented
612C22×C4C2×C4×D1114yes—
613C22×C4C2×C4×D1114yes—
614C22×C4D4×D1114yes—
615C22×C4#434114yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1112yes—
620C22×C4C23×D1112yes—
621C22×C4C23×D1112yes—
622C4⋊C4—1116no—
623C4⋊C4—1116no—
624C4⋊C4—1116no—
625C4⋊C4—228no—
626C4⋊C4—228no—
627C4⋊C4—228no—
628C4⋊C4—228no—
629C4⋊C4—228no—
630C4⋊C4—228no—
631C22⋊C4—28no—
632C22⋊C4—1116no—
633C22⋊C4—228no—
634C22⋊C4C2×C4×D11116yes—
635C42—28no—
636C42—28no—
637C42—1116no—
638C42—228no—
639C42—228no—
640C42—228no—
641C42—228no—
642C42—228no—
643C11C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23C4×Dic22116yescomplemented
655C23C22×Dic2214yes—
656C23C22×Dic2212yes—
657C23C22×C4×D1114yes—
658C23C22×C4×D1112yes—
659C23C2×#433914yes—
660C23C2×#433912yes—
661C23C2×D4×D1112yes—
662C23C2×#434112yes—
663C23#41×D1112yes—
664C23#41×D1112yes—
665C23C24×D1111yescharacteristic
666Q8—2232no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—232no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—1116no—
686C2×C4—114no—
687C2×C4—114no—
688C2×C4—114no—
689C2×C4—114no—
690C2×C4—114no—
691C2×C4—114no—
692C2×C4—114no—
693C2×C4—114no—
694C2×C4—2232no—
695C2×C4—2232no—
696C2×C4—228no—
697C2×C4—228no—
698C2×C4—228no—
699C2×C4—228no—
700C2×C4—228no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—444no—
718C2×C4—444no—
719C2×C4#66931116yesdirect product factor
720C2×C4C22×Dic2214yes—
721C2×C4C22×Dic2214yes—
722C2×C4C22×C4×D1114yes—
723C2×C4C22×C4×D1114yes—
724C2×C4C2×D4×D1114yes—
725C2×C4C2×#434114yes—
726C22—24no—
727C22—24no—
728C22—232no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22C2×C4×Dic2214yes—
734C22C2×C4×Dic2218yescomplemented
735C22C2×#6693114yes—
736C22#1062304814yes—
737C22C4×#434114yes—
738C22#1062306914yes—
739C22C4×D4×D1114yes—
740C22#1062307814yes—
741C22C23×Dic2211yescharacteristic
742C22C23×C4×D1111yescharacteristic
743C22C22×#433911yescharacteristic
744C22C22×D4×D1111yescharacteristic
745C22C22×#434111yescharacteristic
746C22C2×#41×D1111yescharacteristic
747C22C2×#41×D1111yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—118no—
754C4—224no—
755C4—224no—
756C4—224no—
757C4—224no—
758C4—224no—
759C4—442no—
760C4—442no—
761C4C2×#6693118yesdirect product factor
762C2—28no—
763C2C4×#6693118yesdirect product factor
764C2C2×C4×D4×D1111yescharacteristic
765C2C22×C4×Dic2211yescharacteristic
766C2C2×C4×#434111yescharacteristic
767C2C22×#6693111yescharacteristic
768C2C2×#1062307811yescharacteristic
769C2C2×#1062306911yescharacteristic
770C2C2×#1062304811yescharacteristic
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×C4×C22⋊Q8
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
4. C4×#66931C2direct (N × H)
5. C2×#10622259C2semidirect
6. C2×#10622260C2semidirect
7. C2×#10622268C2semidirect
8. C2×#10622267C2semidirect
12. C2×C4×Dic11⋊C4C2semidirect
13. C2×C4×Dic11⋊C4C2semidirect
14. C2×C4×C4⋊Dic11C2semidirect
44. C2×#66931C4direct (N × H)
47. C2×C4×Dic22C22semidirect
63. C4×C4⋊Dic11C22semidirect
64. C4×Dic11⋊C4C22semidirect
65. C4×Dic11⋊C4C22semidirect
66. #10622268C22semidirect
67. #10622267C22semidirect
68. #10622260C22semidirect
69. #10622259C22semidirect
73. C23×C4×C11Q8semidirect
99. C22×Dic22C2×C4semidirect
115. C2×C4⋊Dic11C2×C4semidirect
123. C2×Dic11⋊C4C2×C4semidirect
124. C2×Dic11⋊C4C2×C4semidirect
144. #66931C2×C4direct (N × H)
186. C22×C4×C11C2×Q8semidirect
237. C2×Dic22C22×C4semidirect
246. C4⋊Dic11C22×C4semidirect
251. Dic11⋊C4C22×C4semidirect
252. Dic11⋊C4C22×C4semidirect
285. C23×C11C4×Q8semidirect
315. C2×C4×C11C22⋊Q8semidirect
419. C22×C11C2×C4×Q8semidirect
437. C4×C11C2×C22⋊Q8semidirect
469. C23×C4Dic22semidirect
533. C2×C11C4×C22⋊Q8semidirect
611. C22×C4C2×Dic22semidirect
643. C11C2×C4×C22⋊Q8semidirect
654. C23C4×Dic22semidirect
719. C2×C4#66931direct (N × H)
734. C22C2×C4×Dic22semidirect
761. C4C2×#66931direct (N × H)
763. C2C4×#66931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×C4×Dic222
C23×C4×Dic112
C4×#669312
C2×#106222592
C2×#106222602
C2×#106222682
C2×#106222672
C2×#106225632
C2×#106225592
C2×#106225552
C2×C4×Dic11⋊C42
C2×C4×C4⋊Dic112
C2×C4×C22⋊Dic112
C2×C4×C11×C22⋊C42
C2×C4×C22⋊Q811