Finite Group Databasebeta

← C2×C4×#13063302 #25255043

Subgroups — C2×C4×#13063302 #25255043

Order 11008.

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×#13063302C211yesmaximal, characteristic
2C22×C4×Dic86C211yesmaximal, characteristic, complemented
3C23×C4×Dic43C211yesmaximal, characteristic
4C4×#13063302C2116yesmaximal, direct product factor
5C2×#14582803C211yesmaximal, characteristic, complemented
6C2×#14582796C211yesmaximal, characteristic, complemented
7C2×#14582786C211yesmaximal, characteristic, complemented
8C2×#14582782C211yesmaximal, characteristic, complemented
9C2×#14582774C211yesmaximal, characteristic
10C2×#14582771C211yesmaximal, characteristic
11C2×#14582757C211yesmaximal, characteristic
12C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic43C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
17C23×Dic86C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C2×#13063302C4116yesdirect product factor
21C2×#13063302C2218yes—
22C2×C4×Dic86—28no—
23C2×C4×Dic86C2218yescomplemented
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C4×Dic43—28no—
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2218yes—
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582803C2218yescomplemented
44#14582796C2218yescomplemented
45#14582786C2218yescomplemented
46#14582782C2218yescomplemented
47#14582774C2218yes—
48#14582771C2218yes—
49#14582757C2218yes—
50C4×Dic43⋊C4C2218yescomplemented
51C4×Dic43⋊C4C2218yescomplemented
52C4×C4⋊Dic43C2218yescomplemented
53C4×C22⋊Dic43C2218yes—
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C24×C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C4×C22⋊C4×C43C2218yes—
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86C2×C418yescomplemented
73C22×Dic86C2314yes—
74C23×Dic43—24no—
75C23×Dic43—24no—
76C23×Dic43—24no—
77C23×Dic43—24no—
78C23×Dic43—24no—
79C23×Dic43C2×C418yes—
80C23×Dic43C2314yes—
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2314yes—
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90#13063302C2×C4164yesdirect product factor
91C4×Dic86—232no—
92C2×C4⋊Dic43—24no—
93C2×C4⋊Dic43—24no—
94C2×C4⋊Dic43C2×C418yescomplemented
95C2×C4⋊Dic43C2314yes—
96C2×C4⋊Dic43C2314yes—
97C2×C4⋊Dic43C2314yes—
98C2×Dic43⋊C4—24no—
99C2×Dic43⋊C4—24no—
100C2×Dic43⋊C4—24no—
101C2×Dic43⋊C4—24no—
102C2×Dic43⋊C4C2×C418yescomplemented
103C2×Dic43⋊C4C2×C418yescomplemented
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C2×C22⋊Dic43—24no—
111C2×C22⋊Dic43C2×C418yes—
112C2×C22⋊Dic43C2314yes—
113C2×C22⋊Dic43C2314yes—
114C2×C4×Dic43—24no—
115C2×C4×Dic43—24no—
116C2×C4×Dic43—24no—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43—232no—
120C2×C4×Dic43D418yes—
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C2×C4×Dic43C2314yes—
124C2×C4×Dic43C2314yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C25×C43C2311yescharacteristic
136C23×C4×C43—24no—
137C23×C4×C43—24no—
138C23×C4×C43Q818yescomplemented
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2314yes—
145C23×C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—24no—
147C2×C22⋊C4×C43C2×C418yes—
148C2×C22⋊C4×C43C2314yes—
149C2×C22⋊C4×C43C2314yes—
150C2×C42×C43—24no—
151C2×C42×C43—24no—
152C2×C42×C43C2314yes—
153C2×C42×C43C2314yes—
154#95×C43C2314yes—
155#95×C43C2314yes—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43C22×C414yes—
161C24×C43C2×Q814yes—
162C24×C43#4114yes—
163C24×C43C2412yes—
164C24×C43C2411yescharacteristic
165C22×C4×C43—232no—
166C22×C4×C43—28no—
167C22×C4×C43—28no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43C22×C414yes—
181C22×C4×C43C22×C414yes—
182C22×C4×C43C2×D414yes—
183C22×C4×C43C2×Q814yes—
184C22×C4×C43C2×Q814yes—
185C22×C4×C43C2×Q8116yescomplemented
186C22×C4×C43#4114yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×Dic43—232no—
194C22×Dic43—232no—
195C22×Dic43—28no—
196C22×Dic43—28no—
197C22×Dic43—28no—
198C22×Dic43—28no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—28no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C414yes—
219C22×Dic43C22×C4116yes—
220C22×Dic43C22×C414yes—
221C22×Dic43C2×D414yes—
222C22×Dic43C2×D414yes—
223C22×Dic43#4114yes—
224C22×Dic43#4114yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C2×Dic86—232no—
234C2×Dic86—28no—
235C2×Dic86—28no—
236C2×Dic86C22×C4116yescomplemented
237C22⋊C4×C43—28no—
238C22⋊C4×C43C22×C4116yes—
239C42×C43—28no—
240C42×C43—28no—
241C22⋊Dic43—28no—
242C22⋊Dic43C22×C4116yes—
243C4⋊Dic43—28no—
244C4⋊Dic43—28no—
245C4⋊Dic43C22×C4116yescomplemented
246Dic43⋊C4—28no—
247Dic43⋊C4—28no—
248Dic43⋊C4—28no—
249Dic43⋊C4—28no—
250Dic43⋊C4C22×C4116yescomplemented
251Dic43⋊C4C22×C4116yescomplemented
252C4×Dic43—28no—
253C4×Dic43—28no—
254C4×Dic43—28no—
255C4×Dic43—28no—
256C4×Dic43—28no—
257C4×Dic43C2×D4116yes—
258C23×C43—28no—
259C23×C43—28no—
260C23×C43—28no—
261C23×C43—28no—
262C23×C43—28no—
263C23×C43—28no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43C4×Q8116yescomplemented
269C23×C43C23×C414yes—
270C23×C43C23×C412yes—
271C23×C43C22×D412yes—
272C23×C43C22×Q814yes—
273C23×C43C22×Q812yes—
274C23×C43C2×#4112yes—
275C23×C43C2×#4112yes—
276C23×C43C2×#4112yes—
277C23×C43C2×#4114yes—
278C23×C43C2×#4112yes—
279C23×C43C2511yescharacteristic
280C2×C4×C43—28no—
281C2×C4×C43—28no—
282C2×C4×C43—28no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—232no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—44no—
297C2×C4×C43—44no—
298C2×C4×C43C22⋊Q8116yescomplemented
299C2×C4×C43C23×C414yes—
300C2×C4×C43C23×C414yes—
301C2×C4×C43C22×D414yes—
302C2×C4×C43C22×Q814yes—
303C2×C4×C43C22×Q814yes—
304C2×C4×C43C2×#4114yes—
305C2×Dic43—232no—
306C2×Dic43—28no—
307C2×Dic43—28no—
308C2×Dic43—28no—
309C2×Dic43—28no—
310C2×Dic43—28no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—232no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—44no—
329C2×Dic43—44no—
330C2×Dic43C4×D4116yes—
331C2×Dic43C23×C414yes—
332C2×Dic43C23×C414yes—
333C2×Dic43C23×C414yes—
334C2×Dic43C23×C414yes—
335C2×Dic43C22×D414yes—
336C2×Dic43C22×D414yes—
337C2×Dic43C2×#4114yes—
338C2×Dic43C2×#4114yes—
339Dic86—232no—
340C2×C4×C22⋊Q8—431nomaximal, Sylow
341C22×C43—24no—
342C22×C43—24no—
343C22×C43—24no—
344C22×C43—24no—
345C22×C43—24no—
346C22×C43—24no—
347C22×C43—232no—
348C22×C43C2×C4×D414yes—
349C22×C43C2×C4×Q814yes—
350C22×C43C2×C4×Q818yescomplemented
351C22×C43C4×#4114yes—
352C22×C43C2×C22⋊Q814yes—
353C22×C43#52514yes—
354C22×C43#52914yes—
355C22×C43#53314yes—
356C22×C43C24×C411yescharacteristic
357C22×C43C23×D411yescharacteristic
358C22×C43C23×Q811yescharacteristic
359C22×C43C22×#4111yescharacteristic
360C22×C43C22×#4111yescharacteristic
361C22×C43C22×#4111yescharacteristic
362C22×C43C22×#4111yescharacteristic
363C4×C43—24no—
364C4×C43—24no—
365C4×C43—24no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43C2×C22⋊Q818yescomplemented
369Dic43—24no—
370Dic43—24no—
371Dic43—24no—
372Dic43—24no—
373Dic43—24no—
374Dic43—42no—
375Dic43—42no—
376Dic43C2×C4×D418yes—
377C22×C22⋊Q8—431no—
378C22×C4×Q8—431no—
379C23×C42—431no—
380C4×C22⋊Q8—4316no—
381C2×#391—431no—
382C2×#389—431no—
383C2×#387—431no—
384C2×#387—431no—
385C2×#385—431no—
386C2×#385—431no—
387C2×#380—431no—
388C2×C4×C4⋊C4—431no—
389C2×C4×C4⋊C4—431no—
390C2×C4×C4⋊C4—431no—
391C2×C4×C22⋊C4—431no—
392C2×C4×C22⋊C4D4311yescharacteristic
393C2×C43—28no—
394C2×C43C4×C22⋊Q818yescomplemented
395C2×C43C22×C4×D411yescharacteristic
396C2×C43C22×C4×Q811yescharacteristic
397C2×C43C2×C4×#4111yescharacteristic
398C2×C43C22×C22⋊Q811yescharacteristic
399C2×C43C2×#52511yescharacteristic
400C2×C43C2×#52911yescharacteristic
401C2×C43C2×#53311yescharacteristic
402C23×Q8—431no—
403C24×C4—431no—
404C24×C4—431no—
405C24×C4C2×D4311yescharacteristic
406C2×C22⋊Q8—438no—
407C2×C22⋊Q8—4316no—
408C2×C4×Q8—438no—
409C2×C4×Q8—868no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—431no—
412C22×C4⋊C4—431no—
413C22×C4⋊C4—431no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—431no—
418C22×C4⋊C4—431no—
419C22×C22⋊C4—431no—
420C22×C22⋊C4—431no—
421C22×C22⋊C4C2×D4311yescharacteristic
422C22×C22⋊C4C2×D4311yescharacteristic
423C22×C42—431no—
424C22×C42—431no—
425C22×C42—431no—
426C22×C42—438no—
427C22×C42—431no—
428C22×C42—431no—
429C22×C42—431no—
430C22×C42—868no—
431C22×C42C2×D4311yescharacteristic
432C22×C42C2×D4311yescharacteristic
433#391—438no—
434#389—438no—
435#387—438no—
436#387—438no—
437#385—438no—
438#385—438no—
439#380—438no—
440C4×C4⋊C4—438no—
441C4×C4⋊C4—438no—
442C4×C4⋊C4—438no—
443C4×C22⋊C4—438no—
444C4×C22⋊C4C2×D4318yes—
445C2×#95—431no—
446C2×#95—431no—
447C2×#95—431no—
448C2×#95—431no—
449C2×#95—431no—
450C2×#95—431no—
451C2×#95—431no—
452C2×#95—431no—
453C2×#95C2×D4311yescharacteristic
454C2×#95C2×D4311yescharacteristic
455C43C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
456C25C22×D4311yescharacteristic
457C22×Q8—438no—
458C22×Q8—434no—
459C22×Q8—864no—
460C22×Q8—864no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—431no—
464C23×C4—438no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—431no—
469C23×C4—431no—
470C23×C4—434no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—434no—
474C23×C4—864no—
475C23×C4—864no—
476C23×C4—864no—
477C23×C4—864no—
478C23×C4—864no—
479C23×C4Dic8618yescomplemented
480C23×C4C22×D4311yescharacteristic
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C23×C4C22×D4314yes—
484C23×C4C22×D4311yescharacteristic
485C23×C4C22×D4311yescharacteristic
486C23×C4C22×D4311yescharacteristic
487C22⋊Q8—4364no—
488C4×Q8—8632no—
489C2×C4⋊C4—438no—
490C2×C4⋊C4—438no—
491C2×C4⋊C4—438no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—434no—
496C2×C4⋊C4—434no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—434no—
501C2×C4⋊C4—864no—
502C2×C4⋊C4—864no—
503C2×C4⋊C4—864no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—864no—
506C2×C4⋊C4—864no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—438no—
509C2×C22⋊C4—434no—
510C2×C22⋊C4—434no—
511C2×C22⋊C4—864no—
512C2×C22⋊C4C4×D4318yes—
513C2×C22⋊C4C22×D4314yes—
514C2×C22⋊C4C22×D4314yes—
515C2×C42—24no—
516C2×C42—24no—
517C2×C42—438no—
518C2×C42—434no—
519C2×C42—434no—
520C2×C42—434no—
521C2×C42—434no—
522C2×C42—434no—
523C2×C42—434no—
524C2×C42—8632no—
525C2×C42—864no—
526C2×C42—864no—
527C2×C42—864no—
528C2×C42—864no—
529C2×C42—864no—
530C2×C42C22×D4314yes—
531C2×C42C22×D4314yes—
532#95—434no—
533#95—434no—
534#95—434no—
535#95—434no—
536#95—434no—
537#95—434no—
538#95—434no—
539#95—434no—
540#95C22×D4314yes—
541#95C22×D4314yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×Dic8614yes—
547C24C2×C4×D4314yes—
548C24#1062189814yes—
549C24C23×D4312yes—
550C24C23×D4311yescharacteristic
551C2×Q8—4316no—
552C2×Q8—868no—
553C2×Q8—8632no—
554C2×Q8—868no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—232no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—434no—
571C22×C4—434no—
572C22×C4—434no—
573C22×C4—432no—
574C22×C4—434no—
575C22×C4—434no—
576C22×C4—434no—
577C22×C4—4316no—
578C22×C4—434no—
579C22×C4—434no—
580C22×C4—432no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—868no—
588C22×C4—868no—
589C22×C4—8632no—
590C22×C4—868no—
591C22×C4—868no—
592C22×C4—8632no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—868no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4C2×Dic8614yes—
611C22×C4C2×Dic8614yes—
612C22×C4C2×Dic86116yescomplemented
613C22×C4C2×C4×D4314yes—
614C22×C4C2×C4×D4314yes—
615C22×C4D4×D4314yes—
616C22×C4#1062190014yes—
617C22×C4C23×D4312yes—
618C22×C4C23×D4312yes—
619C22×C4C23×D4312yes—
620C22×C4C23×D4312yes—
621C22×C4C23×D4312yes—
622C22×C4C23×D4312yes—
623C4⋊C4—4316no—
624C4⋊C4—4316no—
625C4⋊C4—4316no—
626C4⋊C4—868no—
627C4⋊C4—868no—
628C4⋊C4—868no—
629C4⋊C4—868no—
630C4⋊C4—868no—
631C4⋊C4—868no—
632C22⋊C4—28no—
633C22⋊C4—4316no—
634C22⋊C4—868no—
635C22⋊C4C2×C4×D43116yes—
636C42—28no—
637C42—28no—
638C42—4316no—
639C42—868no—
640C42—868no—
641C42—868no—
642C42—868no—
643C42—868no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23C4×Dic86116yescomplemented
655C23C22×C4×D4314yes—
656C23C22×C4×D4312yes—
657C23C2×D4×D4312yes—
658C23C22×Dic8614yes—
659C23C22×Dic8612yes—
660C23#41×D4312yes—
661C23#41×D4312yes—
662C23C2×#1062190012yes—
663C23C2×#1062189814yes—
664C23C2×#1062189812yes—
665C23C24×D4311yescharacteristic
666Q8—8632no—
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—4316no—
686C2×C4—434no—
687C2×C4—434no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—434no—
691C2×C4—434no—
692C2×C4—434no—
693C2×C4—434no—
694C2×C4—8632no—
695C2×C4—8632no—
696C2×C4—868no—
697C2×C4—868no—
698C2×C4—868no—
699C2×C4—868no—
700C2×C4—868no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—1724no—
718C2×C4—1724no—
719C2×C4#13063302116yesdirect product factor
720C2×C4C22×C4×D4314yes—
721C2×C4C22×C4×D4314yes—
722C2×C4C2×D4×D4314yes—
723C2×C4C22×Dic8614yes—
724C2×C4C22×Dic8614yes—
725C2×C4C2×#1062190014yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—232no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22C4×D4×D4314yes—
734C22C2×C4×Dic8614yes—
735C22C2×C4×Dic8618yescomplemented
736C22C4×#1062190014yes—
737C22C2×#1306330214yes—
738C22#1458340814yes—
739C22#1458342914yes—
740C22#1458345214yes—
741C22C23×C4×D4311yescharacteristic
742C22C22×D4×D4311yescharacteristic
743C22C23×Dic8611yescharacteristic
744C22C2×#41×D4311yescharacteristic
745C22C2×#41×D4311yescharacteristic
746C22C22×#1062190011yescharacteristic
747C22C22×#1062189811yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—438no—
754C4—864no—
755C4—864no—
756C4—864no—
757C4—864no—
758C4—864no—
759C4—1722no—
760C4—1722no—
761C4C2×#1306330218yesdirect product factor
762C2—28no—
763C2C4×#1306330218yesdirect product factor
764C2C2×C4×D4×D4311yescharacteristic
765C2C22×C4×Dic8611yescharacteristic
766C2C2×C4×#1062190011yescharacteristic
767C2C22×#1306330211yescharacteristic
768C2C2×#1458340811yescharacteristic
769C2C2×#1458342911yescharacteristic
770C2C2×#1458345211yescharacteristic
subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×C22⋊Q8
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic86C2semidirect
4. C4×#13063302C2direct (N × H)
5. C2×#14582803C2semidirect
6. C2×#14582796C2semidirect
7. C2×#14582786C2semidirect
8. C2×#14582782C2semidirect
12. C2×C4×Dic43⋊C4C2semidirect
13. C2×C4×Dic43⋊C4C2semidirect
14. C2×C4×C4⋊Dic43C2semidirect
20. C2×#13063302C4direct (N × H)
23. C2×C4×Dic86C22semidirect
43. #14582803C22semidirect
44. #14582796C22semidirect
45. #14582786C22semidirect
46. #14582782C22semidirect
50. C4×Dic43⋊C4C22semidirect
51. C4×Dic43⋊C4C22semidirect
52. C4×C4⋊Dic43C22semidirect
72. C22×Dic86C2×C4semidirect
90. #13063302C2×C4direct (N × H)
94. C2×C4⋊Dic43C2×C4semidirect
102. C2×Dic43⋊C4C2×C4semidirect
103. C2×Dic43⋊C4C2×C4semidirect
138. C23×C4×C43Q8semidirect
185. C22×C4×C43C2×Q8semidirect
236. C2×Dic86C22×C4semidirect
245. C4⋊Dic43C22×C4semidirect
250. Dic43⋊C4C22×C4semidirect
251. Dic43⋊C4C22×C4semidirect
268. C23×C43C4×Q8semidirect
298. C2×C4×C43C22⋊Q8semidirect
350. C22×C43C2×C4×Q8semidirect
368. C4×C43C2×C22⋊Q8semidirect
394. C2×C43C4×C22⋊Q8semidirect
455. C43C2×C4×C22⋊Q8semidirect
479. C23×C4Dic86semidirect
612. C22×C4C2×Dic86semidirect
654. C23C4×Dic86semidirect
719. C2×C4#13063302direct (N × H)
735. C22C2×C4×Dic86semidirect
761. C4C2×#13063302direct (N × H)
763. C2C4×#13063302direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633022
C22×C4×Dic862
C23×C4×Dic432
C4×#130633022
C2×#145828032
C2×#145827962
C2×#145827862
C2×#145827822
C2×#145827742
C2×#145827712
C2×#145827572
C2×C4×Dic43⋊C42
C2×C4×C4⋊Dic432
C2×C4×C22⋊Dic432
C2×C4×C22⋊C4×C432
C2×C4×C22⋊Q843