Finite Group Databasebeta

← C2×#19137390 #25255496

Subgroups — C2×#19137390 #25255496

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
1C22×#13063309C211yesmaximal, characteristic
2#19137390C2116yesmaximal, direct product factor
3C2×#14582799C211yesmaximal, characteristic
4C2×#14582795C211yesmaximal, characteristic, complemented
5C2×#14582792C211yesmaximal, characteristic, complemented
6C2×#14582790C211yesmaximal, characteristic, complemented
7C2×#14582789C211yesmaximal, characteristic, complemented
8C2×#14582784C211yesmaximal, characteristic, complemented
9C2×#14582782C211yesmaximal, characteristic, complemented
10C2×#14582775C211yesmaximal, characteristic
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582757C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063309C4116yescomplemented
21C2×#13063309C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582799C2218yes—
40#14582795C2218yescomplemented
41#14582792C2218yescomplemented
42#14582790C2218yescomplemented
43#14582789C2218yescomplemented
44#14582784C2218yescomplemented
45#14582782C2218yescomplemented
46#14582775C2218yes—
47#14582773C2218yescomplemented
48#14582757C2218yescomplemented
49C4×C4⋊Dic43C2218yescomplemented
50C22⋊C4×Dic43C2218yescomplemented
51#14582746C2218yescomplemented
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#388C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×C22⋊D43—42no—
70C22×C22⋊D43—42no—
71C22×C22⋊D43C2×C418yes—
72C22×C22⋊D43C2314yes—
73C23×Dic43—42no—
74C23×Dic43—42no—
75C23×Dic43C2×C418yescomplemented
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2314yes—
84C22×C4×D43—24no—
85C22×C4×D43—42no—
86C22×C4×D43—42no—
87C22×C4×D43C2314yes—
88#13063309C2×C4164yescomplemented
89C2×C4⋊Dic43—24no—
90C2×C4⋊Dic43C2×C418yescomplemented
91C2×C4⋊Dic43C2×C418yescomplemented
92C2×C4⋊Dic43C2314yes—
93C2×C4⋊Dic43C2314yes—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4—42no—
96C2×Dic43⋊C4—42no—
97C2×Dic43⋊C4—42no—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×C22⋊Dic43—24no—
102C2×C22⋊Dic43—42no—
103C2×C22⋊Dic43C2314yes—
104C2×C22⋊Dic43C2314yes—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—42no—
107C2×(C2×D43)⋊C4—42no—
108C2×(C2×D43)⋊C4C2×C418yes—
109C2×(C2×D43)⋊C4C2×C418yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×C4×Dic43—42no—
116C2×C4×Dic43—42no—
117C2×C4×Dic43—42no—
118C2×C4×Dic43—42no—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C25×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—42no—
139C2×C4⋊C4×C43C2314yes—
140C2×C22⋊C4×C43—24no—
141C2×C22⋊C4×C43—42no—
142C2×C22⋊C4×C43C2×C418yescomplemented
143C2×C22⋊C4×C43C2314yes—
144C2×C22⋊C4×C43C2314yes—
145C2×C22⋊C4×C43C2314yes—
146C2×C42×C43—24no—
147C2×C42×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C22×C414yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43C22×C414yes—
166C23×D43C2412yes—
167C22×C4×C43—22no—
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×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43C22×C414yes—
183C22×C4×C43C22×C414yes—
184C22×C4×C43#4114yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C2×C22⋊D43—416no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—44no—
194C2×C22⋊D43C22×C4116yes—
195C22×Dic43—22no—
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—416no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43C22×C414yes—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C4116yescomplemented
219C22×Dic43#4114yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—28no—
228C2×C4×D43—44no—
229C2×C4×D43—44no—
230C2×C4×D43—416no—
231C4⋊C4×C43—44no—
232C22⋊C4×C43—28no—
233C22⋊C4×C43—44no—
234C22⋊C4×C43C22×C4116yescomplemented
235C42×C43—28no—
236C22⋊Dic43—28no—
237C22⋊Dic43—44no—
238(C2×D43)⋊C4—28no—
239(C2×D43)⋊C4—44no—
240(C2×D43)⋊C4—44no—
241(C2×D43)⋊C4C22×C4116yes—
242(C2×D43)⋊C4C22×C4116yes—
243C4⋊Dic43—28no—
244C4⋊Dic43C22×C4116yescomplemented
245C4⋊Dic43C22×C4116yescomplemented
246Dic43⋊C4—44no—
247Dic43⋊C4—44no—
248Dic43⋊C4—44no—
249C4×Dic43—44no—
250C4×Dic43—44no—
251C4×Dic43—44no—
252C4×Dic43—44no—
253C23×C43—28no—
254C23×C43—28no—
255C23×C43—28no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43C23×C414yes—
267C23×C43C23×C412yes—
268C23×C43C2×#4112yes—
269C23×C43C2×#4112yes—
270C23×C43H(5,𝔽2)12yes—
271C23×C43H(5,𝔽2)12yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C432−1+412yes—
274C23×C43C2511yescharacteristic
275C22×D43—28no—
276C22×D43—28no—
277C22×D43—28no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—44no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43C23×C414yes—
289C2×C4×C43—28no—
290C2×C4×C43—28no—
291C2×C4×C43—28no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
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—22no—
306C2×C4×C43—22no—
307C2×C4×C43—44no—
308C2×C4×C43—44no—
309C2×C4×C43—44no—
310C2×C4×C43C23×C414yes—
311C2×C4×C43C23×C414yes—
312C2×C4×C43C2×#4114yes—
313C22⋊D43—416no—
314C2×Dic43—28no—
315C2×Dic43—28no—
316C2×Dic43—28no—
317C2×Dic43—28no—
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×Dic43C23×C414yes—
340C2×Dic43C23×C414yes—
341C2×Dic43C23×C414yes—
342C2×Dic43C2×#4114yes—
343C4×D43—416no—
344C2×#2335—431nomaximal, Sylow
345C22×C43—24no—
346C22×C43—24no—
347C22×C43—24no—
348C22×C43—416no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43C4×#4114yes—
354C22×C43#51814yes—
355C22×C43#52014yes—
356C22×C43#53814yes—
357C22×C43#53914yes—
358C22×C43#54014yes—
359C22×C43#54214yes—
360C22×C43C24×C411yescharacteristic
361C22×C43C22×#4111yescharacteristic
362C22×C43C22×#4111yescharacteristic
363C22×C43C2×H(5,𝔽2)11yescharacteristic
364C22×C43C2×H(5,𝔽2)11yescharacteristic
365C22×C43C2×H(5,𝔽2)11yescharacteristic
366C22×C43C2×2−1+411yescharacteristic
367C2×D43—24no—
368C2×D43—24no—
369C2×D43—24no—
370C2×D43—416no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C4×C43—24no—
376C4×C43—24no—
377C4×C43—24no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—42no—
381Dic43—24no—
382Dic43—24no—
383Dic43—24no—
384Dic43—24no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388C22×#123—431no—
389#2335—4316no—
390C2×#390—431no—
391C2×#389—431no—
392C2×#388—431no—
393C2×#388—431no—
394C2×#388—431no—
395C2×#388D4311yescharacteristic, complemented
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#233518yescomplemented
406C2×C43C2×C4×#4111yescharacteristic
407C2×C43C2×#51811yescharacteristic
408C2×C43C2×#52011yescharacteristic
409C2×C43C2×#53811yescharacteristic
410C2×C43C2×#53911yescharacteristic
411C2×C43C2×#54011yescharacteristic
412C2×C43C2×#54211yescharacteristic
413D43—44no—
414C23×D4—431no—
415C24×C4—431no—
416C24×C4—431no—
417C2×#123—438no—
418C2×#123—4316no—
419C22×C4⋊C4—431no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
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×C42C2×D4311yescharacteristic
441#390—438no—
442#389—438no—
443#388—438no—
444#388—438no—
445#388—438no—
446#388C2×D4318yescomplemented
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×#95C2×D4311yescharacteristic
464C2×#95C2×D4311yescharacteristic
465C43C2×#233511yescharacteristic, complemented, Sylow
466C25—431no—
467C25C22×D4311yescharacteristic
468C22×D4—438no—
469C22×D4—434no—
470C22×D4—1722no—
471C22×D4—1722no—
472C23×C4—431no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—438no—
477C23×C4—434no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—434no—
482C23×C4—864no—
483C23×C4—1722no—
484C23×C4—1722no—
485C23×C4—1722no—
486C23×C4—1722no—
487C23×C4C22×D4311yescharacteristic
488C23×C4C22×D4311yescharacteristic
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C23×C4C22×D4311yescharacteristic
493#123—4364no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—438no—
496C2×C4⋊C4—438no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—434no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—434no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—864no—
504C2×C4⋊C4—1722no—
505C2×C4⋊C4—1722no—
506C2×C4⋊C4—1722no—
507C2×C4⋊C4C22×D4314yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—438no—
511C2×C22⋊C4—438no—
512C2×C22⋊C4—434no—
513C2×C22⋊C4—434no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—864no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—1722no—
522C2×C22⋊C4—1722no—
523C2×C22⋊C4—1722no—
524C2×C22⋊C4C4×D4318yescomplemented
525C2×C22⋊C4C22×D4314yes—
526C2×C22⋊C4C22×D4314yes—
527C2×C22⋊C4C22×D4314yes—
528C2×C42—24no—
529C2×C42—434no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—434no—
533C2×C42—1722no—
534C2×C42—1722no—
535C2×C42—1722no—
536C2×C42—1722no—
537C2×C42C22×D4314yes—
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#95C22×D4314yes—
547#95C22×D4314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—434no—
555C24—432no—
556C24—862no—
557C24—862no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24C2×C4×D4314yes—
563C24C23×D4312yes—
564C24C23×D4311yescharacteristic
565C2×D4—4316no—
566C2×D4—17216no—
567C2×D4—1724no—
568C2×D4—1724no—
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—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—434no—
585C22×C4—434no—
586C22×C4—434no—
587C22×C4—434no—
588C22×C4—432no—
589C22×C4—432no—
590C22×C4—432no—
591C22×C4—432no—
592C22×C4—4316no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—868no—
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—1724no—
615C22×C4—1724no—
616C22×C4—17216no—
617C22×C4—17216no—
618C22×C4—1724no—
619C22×C4—1724no—
620C22×C4C2×C4×D4314yes—
621C22×C4C2×C4×D4314yes—
622C22×C4#1062190014yes—
623C22×C4C23×D4312yes—
624C22×C4C23×D4312yes—
625C22×C4C23×D4312yes—
626C22×C4C23×D4312yes—
627C22×C4C23×D4312yes—
628C22×C4C23×D4312yes—
629C4⋊C4—44no—
630C4⋊C4—4316no—
631C4⋊C4—4316no—
632C4⋊C4—868no—
633C4⋊C4—1724no—
634C4⋊C4—1724no—
635C4⋊C4—1724no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—4316no—
639C22⋊C4—4316no—
640C22⋊C4—868no—
641C22⋊C4—868no—
642C22⋊C4—1724no—
643C22⋊C4—1724no—
644C22⋊C4—1724no—
645C22⋊C4C2×C4×D43116yescomplemented
646C42—28no—
647C42—1724no—
648C42—1724no—
649C42—1724no—
650C42—1724no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—434no—
665C23—868no—
666C23—868no—
667C23—868no—
668C23—862no—
669C23—862no—
670C23—862no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—1724no—
675C23—1724no—
676C23—1724no—
677C23—1724no—
678C23C22×C4×D4314yes—
679C23C22×C4×D4312yes—
680C23#41×D4312yes—
681C23C2×#1062190012yes—
682C23#1306337012yes—
683C23#1306337112yes—
684C23#1306337112yes—
685C23#1306337212yes—
686C23C24×D4311yescharacteristic
687D4—17216no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—434no—
710C2×C4—434no—
711C2×C4—434no—
712C2×C4—434no—
713C2×C4—868no—
714C2×C4—868no—
715C2×C4—868no—
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—868no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—17216no—
735C2×C4—17216no—
736C2×C4—1724no—
737C2×C4—1724no—
738C2×C4—1724no—
739C2×C4C22×C4×D4314yes—
740C2×C4C22×C4×D4314yes—
741C2×C4C2×#1062190014yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—864no—
751C22—864no—
752C22—864no—
753C22—17216no—
754C22—1722no—
755C22—1722no—
756C22—1722no—
757C22—1722no—
758C22C4×#1062190014yes—
759C22#1458337314yes—
760C22#1458337814yes—
761C22#1458348314yes—
762C22#1458349314yes—
763C22#1458350214yes—
764C22#1458351514yes—
765C22C23×C4×D4311yescharacteristic
766C22C2×#41×D4311yescharacteristic
767C22C22×#1062190011yescharacteristic
768C22C2×#1306337011yescharacteristic
769C22C2×#1306337111yescharacteristic
770C22C2×#1306337111yescharacteristic
771C22C2×#1306337211yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—864no—
779C4—864no—
780C4—864no—
781C4—864no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C2—44no—
786C2—1724no—
787C2#1913739018yesdirect product factor
788C2C2×C4×#1062190011yescharacteristic
789C2C2×#1458337311yescharacteristic
790C2C2×#1458337811yescharacteristic
791C2C2×#1458348311yescharacteristic
792C2C2×#1458349311yescharacteristic
793C2C2×#1458350211yescharacteristic
794C2C2×#1458351511yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2335
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #19137390C2direct (N × H)
4. C2×#14582795C2semidirect
5. C2×#14582792C2semidirect
6. C2×#14582790C2semidirect
7. C2×#14582789C2semidirect
8. C2×#14582784C2semidirect
9. C2×#14582782C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582757C2semidirect
13. C2×C4×C4⋊Dic43C2semidirect
14. C2×C22⋊C4×Dic43C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#388C2semidirect
20. C2×#13063309C4semidirect
40. #14582795C22semidirect
41. #14582792C22semidirect
42. #14582790C22semidirect
43. #14582789C22semidirect
44. #14582784C22semidirect
45. #14582782C22semidirect
47. #14582773C22semidirect
48. #14582757C22semidirect
49. C4×C4⋊Dic43C22semidirect
50. C22⋊C4×Dic43C22semidirect
51. #14582746C22semidirect
65. C43×#388C22semidirect
75. C23×Dic43C2×C4semidirect
88. #13063309C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
91. C2×C4⋊Dic43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
218. C22×Dic43C22×C4semidirect
234. C22⋊C4×C43C22×C4semidirect
244. C4⋊Dic43C22×C4semidirect
245. C4⋊Dic43C22×C4semidirect
395. C2×#388D43semidirect
405. C2×C43#2335semidirect
446. #388C2×D43semidirect
465. C43C2×#2335semidirect
524. C2×C22⋊C4C4×D43semidirect
645. C22⋊C4C2×C4×D43semidirect
787. C2#19137390direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633092
#191373902
C2×#145827992
C2×#145827952
C2×#145827922
C2×#145827902
C2×#145827892
C2×#145827842
C2×#145827822
C2×#145827752
C2×#145827732
C2×#145827572
C2×C4×C4⋊Dic432
C2×C22⋊C4×Dic432
C2×#145827462
C2×C43×#3882
C2×#233543