Finite Group Databasebeta

← C2×#19137389 #25255495

Subgroups — C2×#19137389 #25255495

Order 11008.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137389C2116yesmaximal, direct product factor
2C2×#14582802C211yesmaximal, characteristic
3C2×#14582798C211yesmaximal, characteristic, complemented
4C2×#14582792C211yesmaximal, characteristic, complemented
5C2×#14582792C211yesmaximal, characteristic, complemented
6C2×#14582792C211yesmaximal, characteristic, complemented
7C2×#14582792C211yesmaximal, characteristic, complemented
8C2×#14582785C211yesmaximal, characteristic, complemented
9C2×#14582785C211yesmaximal, characteristic, complemented
10C2×#14582779C211yesmaximal, characteristic
11C2×#14582774C211yesmaximal, characteristic, complemented
12C2×#14582759C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
16C22×#123×C43C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582802C2218yes—
36#14582798C2218yescomplemented
37#14582792C2218yescomplemented
38#14582792C2218yescomplemented
39#14582792C2218yescomplemented
40#14582792C2218yescomplemented
41#14582785C2218yescomplemented
42#14582785C2218yescomplemented
43#14582779C2218yes—
44#14582774C2218yescomplemented
45#14582759C2218yescomplemented
46C4⋊C4×Dic43C2218yescomplemented
47C22⋊C4×Dic43C2218yescomplemented
48C4×C22⋊Dic43C2218yescomplemented
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C23×D4×C43C2211yescharacteristic
60C24×C4×C43C2211yescharacteristic
61C2×#123×C43C4116yescomplemented
62C2×#123×C43C2218yes—
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C23×Dic43—24no—
69C23×Dic43—42no—
70C23×Dic43—42no—
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2314yes—
80C2×C4⋊Dic43—24no—
81C2×C4⋊Dic43—42no—
82C2×C4⋊Dic43—42no—
83C2×C4⋊Dic43—42no—
84C2×C4⋊Dic43—42no—
85C2×C4⋊Dic43C2314yes—
86C2×C4⋊Dic43C2314yes—
87C2×C4⋊Dic43C2314yes—
88C2×C4⋊Dic43C2314yes—
89C2×C4⋊Dic43C2314yes—
90C2×C22⋊Dic43—24no—
91C2×C22⋊Dic43—24no—
92C2×C22⋊Dic43—24no—
93C2×C22⋊Dic43—42no—
94C2×C22⋊Dic43—42no—
95C2×C22⋊Dic43—42no—
96C2×C22⋊Dic43—42no—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×C22⋊Dic43C2314yes—
100C2×C22⋊Dic43C2314yes—
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×C22⋊Dic43C2314yes—
104C2×C4×Dic43—24no—
105C2×C4×Dic43—42no—
106C2×C4×Dic43—42no—
107C2×C4×Dic43—42no—
108C2×C4×Dic43—42no—
109C2×C4×Dic43C2314yes—
110C2×C4×Dic43C2314yes—
111C2×C4×Dic43C2314yes—
112C2×C4×Dic43C2314yes—
113C2×C4×Dic43C2314yes—
114C43⋊#95C2314yes—
115C43⋊#95C2314yes—
116C43⋊#95C2314yes—
117C43⋊#95C2314yes—
118C43⋊#95C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C25×C43C2311yescharacteristic
125C25×C43C2311yescharacteristic
126C22×D4×C43—42no—
127C22×D4×C43—42no—
128C22×D4×C43C2×C418yes—
129C22×D4×C43C2314yes—
130C23×C4×C43—42no—
131C23×C4×C43—42no—
132C23×C4×C43C2×C418yescomplemented
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2314yes—
139#123×C43C2×C4164yescomplemented
140C2×C4⋊C4×C43C2×C418yescomplemented
141C2×C4⋊C4×C43C2×C418yescomplemented
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C22⋊C4×C43C2×C418yes—
145C2×C22⋊C4×C43C2×C418yes—
146C2×C22⋊C4×C43C2×C418yescomplemented
147C2×C22⋊C4×C43C2314yes—
148C2×C22⋊C4×C43C2314yes—
149C2×C22⋊C4×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43C22×C414yes—
163C24×C43C22×C414yes—
164C24×C43C2412yes—
165C24×C43C2412yes—
166C24×C43C2411yescharacteristic
167C2×D4×C43—416no—
168C2×D4×C43—44no—
169C2×D4×C43—44no—
170C2×D4×C43C22×C4116yes—
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×C43—22no—
181C22×C4×C43—416no—
182C22×C4×C43—44no—
183C22×C4×C43—44no—
184C22×C4×C43C22×C414yes—
185C22×C4×C43C22×C414yes—
186C22×C4×C43C22×C414yes—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C22×C414yes—
189C22×C4×C43C22×C4116yescomplemented
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×Dic43—28no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
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—22no—
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×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—44no—
219C22×Dic43—44no—
220C22×Dic43—416no—
221C22×Dic43#4114yes—
222C22×Dic43#4114yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C4⋊C4×C43C22×C4116yescomplemented
232C4⋊C4×C43C22×C4116yescomplemented
233C22⋊C4×C43C22×C4116yes—
234C22⋊C4×C43C22×C4116yes—
235C22⋊C4×C43C22×C4116yescomplemented
236C22⋊Dic43—28no—
237C22⋊Dic43—28no—
238C22⋊Dic43—28no—
239C22⋊Dic43—44no—
240C22⋊Dic43—44no—
241C22⋊Dic43—44no—
242C22⋊Dic43—44no—
243C4⋊Dic43—28no—
244C4⋊Dic43—44no—
245C4⋊Dic43—44no—
246C4⋊Dic43—44no—
247C4⋊Dic43—44no—
248C4×Dic43—28no—
249C4×Dic43—44no—
250C4×Dic43—44no—
251C4×Dic43—44no—
252C4×Dic43—44no—
253C23×C43—28no—
254C23×C43—28no—
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—28no—
258C23×C43—28no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—44no—
272C23×C43—44no—
273C23×C43—44no—
274C23×C43—44no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43C23×C414yes—
280C23×C43C23×C414yes—
281C23×C43C23×C412yes—
282C23×C43C2×#4112yes—
283C23×C43C2×#4112yes—
284C23×C43H(5,𝔽2)12yes—
285C23×C43H(5,𝔽2)12yes—
286C23×C43H(5,𝔽2)12yes—
287C23×C432−1+412yes—
288C23×C43C2511yescharacteristic
289D4×C43—416no—
290C2×C4×C43—28no—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
293C2×C4×C43—28no—
294C2×C4×C43—28no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—416no—
306C2×C4×C43C23×C414yes—
307C2×C4×C43C23×C414yes—
308C2×C4×C43C23×C414yes—
309C2×C4×C43C23×C414yes—
310C2×C4×C43C23×C414yes—
311C2×Dic43—28no—
312C2×Dic43—28no—
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—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—416no—
336C2×Dic43—44no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43—44no—
342C2×Dic43C2×#4114yes—
343C2×Dic43C2×#4114yes—
344C2×#2335—431nomaximal, Sylow
345C22×C43—24no—
346C22×C43—24no—
347C22×C43—24no—
348C22×C43—24no—
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—416no—
352C22×C43—416no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43C4×#4114yes—
362C22×C43#51814yes—
363C22×C43#52014yes—
364C22×C43#53814yes—
365C22×C43#53914yes—
366C22×C43#54014yes—
367C22×C43#54214yes—
368C22×C43C24×C411yescharacteristic
369C22×C43C22×#4111yescharacteristic
370C22×C43C22×#4111yescharacteristic
371C22×C43C2×H(5,𝔽2)11yescharacteristic
372C22×C43C2×H(5,𝔽2)11yescharacteristic
373C22×C43C2×H(5,𝔽2)11yescharacteristic
374C22×C43C2×2−1+411yescharacteristic
375C4×C43—24no—
376C4×C43—24no—
377C4×C43—24no—
378C4×C43—24no—
379C4×C43—24no—
380Dic43—24no—
381Dic43—24no—
382Dic43—42no—
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C22×#123D4311yescharacteristic
389#2335—4316no—
390C2×#390—431no—
391C2×#389—431no—
392C2×#388—431no—
393C2×#388—431no—
394C2×#388—431no—
395C2×#388—431no—
396C2×#387—431no—
397C2×#387—431no—
398C2×#386—431no—
399C2×#385—431no—
400C2×#380—431no—
401C2×C4×C4⋊C4—431no—
402C2×C4×C22⋊C4—431no—
403C2×C4×C22⋊C4—431no—
404C2×C43—44no—
405C2×C43—44no—
406C2×C43#233518yescomplemented
407C2×C43C2×C4×#4111yescharacteristic
408C2×C43C2×#51811yescharacteristic
409C2×C43C2×#52011yescharacteristic
410C2×C43C2×#53811yescharacteristic
411C2×C43C2×#53911yescharacteristic
412C2×C43C2×#54011yescharacteristic
413C2×C43C2×#54211yescharacteristic
414C23×D4C2×D4311yescharacteristic
415C24×C4—431no—
416C24×C4C2×D4311yescharacteristic
417C2×#123Dic43116yescomplemented
418C2×#123C2×D4318yes—
419C22×C4⋊C4—431no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4C2×D4311yescharacteristic
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4—431no—
427C22×C22⋊C4—431no—
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4C2×D4311yescharacteristic
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C22×C42—431no—
437C22×C42—431no—
438C22×C42—431no—
439C22×C42—431no—
440C22×C42—431no—
441#390—438no—
442#389—438no—
443#388—438no—
444#388—438no—
445#388—438no—
446#388—438no—
447#387—438no—
448#387—438no—
449#386—438no—
450#385—438no—
451#380—438no—
452C4×C4⋊C4—438no—
453C4×C22⋊C4—438no—
454C4×C22⋊C4—438no—
455C2×#95—431no—
456C2×#95—431no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C43C2×#233511yescharacteristic, complemented, Sylow
466C25C22×D4311yescharacteristic
467C25C22×D4311yescharacteristic
468C22×D4—42no—
469C22×D4—42no—
470C22×D4C2×Dic4318yes—
471C22×D4C22×D4314yes—
472C23×C4—42no—
473C23×C4—42no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—434no—
483C23×C4—864no—
484C23×C4—1722no—
485C23×C4—1722no—
486C23×C4C2×Dic4318yescomplemented
487C23×C4C22×D4311yescharacteristic
488C23×C4C22×D4311yescharacteristic
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C23×C4C22×D4314yes—
493#123C2×Dic43164yescomplemented
494C2×C4⋊C4—434no—
495C2×C4⋊C4—434no—
496C2×C4⋊C4—434no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—864no—
500C2×C4⋊C4—1722no—
501C2×C4⋊C4—1722no—
502C2×C4⋊C4—1722no—
503C2×C4⋊C4—1722no—
504C2×C4⋊C4C2×Dic4318yescomplemented
505C2×C4⋊C4C2×Dic4318yescomplemented
506C2×C4⋊C4C22×D4314yes—
507C2×C4⋊C4C22×D4314yes—
508C2×C22⋊C4—434no—
509C2×C22⋊C4—434no—
510C2×C22⋊C4—434no—
511C2×C22⋊C4—434no—
512C2×C22⋊C4—434no—
513C2×C22⋊C4—434no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—864no—
516C2×C22⋊C4—864no—
517C2×C22⋊C4—864no—
518C2×C22⋊C4—1722no—
519C2×C22⋊C4—1722no—
520C2×C22⋊C4—1722no—
521C2×C22⋊C4—1722no—
522C2×C22⋊C4C2×Dic4318yes—
523C2×C22⋊C4C2×Dic4318yes—
524C2×C22⋊C4C2×Dic4318yescomplemented
525C2×C22⋊C4C22×D4314yes—
526C2×C22⋊C4C22×D4314yes—
527C2×C22⋊C4C22×D4314yes—
528C2×C42—434no—
529C2×C42—434no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—434no—
533C2×C42—864no—
534C2×C42—1722no—
535C2×C42—1722no—
536C2×C42—1722no—
537C2×C42—1722no—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C22×Dic4314yes—
561C24C22×Dic4314yes—
562C24C23×D4312yes—
563C24C23×D4312yes—
564C24C23×D4311yescharacteristic
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—416no—
568C2×D4C22×Dic43116yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—416no—
582C22×C4—434no—
583C22×C4—434no—
584C22×C4—432no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—868no—
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—862no—
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×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—1724no—
616C22×C4—1724no—
617C22×C4—17216no—
618C22×C4C22×Dic4314yes—
619C22×C4C22×Dic4314yes—
620C22×C4C22×Dic4314yes—
621C22×C4C22×Dic4314yes—
622C22×C4C22×Dic4314yes—
623C22×C4C22×Dic43116yescomplemented
624C22×C4C23×D4312yes—
625C22×C4C23×D4312yes—
626C22×C4C23×D4312yes—
627C22×C4C23×D4312yes—
628C22×C4C23×D4312yes—
629C4⋊C4—868no—
630C4⋊C4—1724no—
631C4⋊C4—1724no—
632C4⋊C4—1724no—
633C4⋊C4—1724no—
634C4⋊C4C22×Dic43116yescomplemented
635C4⋊C4C22×Dic43116yescomplemented
636C22⋊C4—868no—
637C22⋊C4—868no—
638C22⋊C4—868no—
639C22⋊C4—1724no—
640C22⋊C4—1724no—
641C22⋊C4—1724no—
642C22⋊C4—1724no—
643C22⋊C4C22×Dic43116yes—
644C22⋊C4C22×Dic43116yes—
645C22⋊C4C22×Dic43116yescomplemented
646C42—868no—
647C42—1724no—
648C42—1724no—
649C42—1724no—
650C42—1724no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23C23×Dic4314yes—
678C23C23×Dic4314yes—
679C23C23×Dic4312yes—
680C23#41×D4312yes—
681C23#41×D4312yes—
682C23#1306337012yes—
683C23#1306337012yes—
684C23#1306337112yes—
685C23#1306337212yes—
686C23C24×D4311yescharacteristic
687D4—416no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—416no—
704C2×C4—434no—
705C2×C4—434no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—868no—
711C2×C4—868no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—17216no—
731C2×C4—1724no—
732C2×C4—1724no—
733C2×C4—1724no—
734C2×C4—1724no—
735C2×C4—1724no—
736C2×C4—1724no—
737C2×C4C23×Dic4314yes—
738C2×C4C23×Dic4314yes—
739C2×C4C23×Dic4314yes—
740C2×C4C23×Dic4314yes—
741C2×C4C23×Dic4314yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—416no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22#41×Dic4314yes—
759C22#1458337414yes—
760C22#1458338214yes—
761C22#1458348514yes—
762C22#1458349214yes—
763C22#1458350114yes—
764C22#1458351714yes—
765C22C24×Dic4311yescharacteristic
766C22C2×#41×D4311yescharacteristic
767C22C2×#41×D4311yescharacteristic
768C22C2×#1306337011yescharacteristic
769C22C2×#1306337011yescharacteristic
770C22C2×#1306337111yescharacteristic
771C22C2×#1306337211yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—864no—
778C4—864no—
779C4—1722no—
780C4—1722no—
781C4—1722no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C2—44no—
786C2—44no—
787C2#1913738918yesdirect product factor
788C2C2×#41×Dic4311yescharacteristic
789C2C2×#1458337411yescharacteristic
790C2C2×#1458338211yescharacteristic
791C2C2×#1458348511yescharacteristic
792C2C2×#1458349211yescharacteristic
793C2C2×#1458350111yescharacteristic
794C2C2×#1458351711yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×#123×C43C2
socleC24×C43C24
prime radicalC23×D4×C43C22
cosocleC23×C43C25
hypercenterC22×#123D43
hypocenterC43C2×#2335
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. #19137389C2direct (N × H)
3. C2×#14582798C2semidirect
4. C2×#14582792C2semidirect
5. C2×#14582792C2semidirect
6. C2×#14582792C2semidirect
7. C2×#14582792C2semidirect
8. C2×#14582785C2semidirect
9. C2×#14582785C2semidirect
11. C2×#14582774C2semidirect
12. C2×#14582759C2semidirect
13. C2×C4⋊C4×Dic43C2semidirect
14. C2×C22⋊C4×Dic43C2semidirect
15. C2×C4×C22⋊Dic43C2semidirect
36. #14582798C22semidirect
37. #14582792C22semidirect
38. #14582792C22semidirect
39. #14582792C22semidirect
40. #14582792C22semidirect
41. #14582785C22semidirect
42. #14582785C22semidirect
44. #14582774C22semidirect
45. #14582759C22semidirect
46. C4⋊C4×Dic43C22semidirect
47. C22⋊C4×Dic43C22semidirect
48. C4×C22⋊Dic43C22semidirect
61. C2×#123×C43C4semidirect
132. C23×C4×C43C2×C4semidirect
139. #123×C43C2×C4semidirect
140. C2×C4⋊C4×C43C2×C4semidirect
141. C2×C4⋊C4×C43C2×C4semidirect
146. C2×C22⋊C4×C43C2×C4semidirect
189. C22×C4×C43C22×C4semidirect
231. C4⋊C4×C43C22×C4semidirect
232. C4⋊C4×C43C22×C4semidirect
235. C22⋊C4×C43C22×C4semidirect
406. C2×C43#2335semidirect
417. C2×#123Dic43semidirect
465. C43C2×#2335semidirect
486. C23×C4C2×Dic43semidirect
493. #123C2×Dic43semidirect
504. C2×C4⋊C4C2×Dic43semidirect
505. C2×C4⋊C4C2×Dic43semidirect
524. C2×C22⋊C4C2×Dic43semidirect
623. C22×C4C22×Dic43semidirect
634. C4⋊C4C22×Dic43semidirect
635. C4⋊C4C22×Dic43semidirect
645. C22⋊C4C22×Dic43semidirect
787. C2#19137389direct (N × H)

Maximal subgroups

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

subgroupindex
#191373892
C2×#145828022
C2×#145827982
C2×#145827922
C2×#145827852
C2×#145827792
C2×#145827742
C2×#145827592
C2×C4⋊C4×Dic432
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
C22×#123×C432
C2×#233543