Finite Group Databasebeta

← C2×#19137359 #25255463

Subgroups — C2×#19137359 #25255463

Order 11008.

3414 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063300C211yesmaximal, characteristic
2#19137359C2116yesmaximal, direct product factor
3C2×#14582801C211yesmaximal, characteristic, complemented
4C2×#14582800C211yesmaximal, characteristic, complemented
5C2×#14582791C211yesmaximal, characteristic, complemented
6C2×#14582789C211yesmaximal, characteristic, complemented
7C2×#14582785C211yesmaximal, characteristic, complemented
8C2×#14582777C211yesmaximal, characteristic, complemented
9C2×#14582777C211yesmaximal, characteristic, complemented
10C2×#14582777C211yesmaximal, characteristic, complemented
11C2×#14582777C211yesmaximal, characteristic, complemented
12C2×#14582761C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
14C2×#14582746C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C2×#13063300C4116yescomplemented
24C2×#13063300C2218yes—
25C22×C4⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41#14582801C2218yescomplemented
42#14582800C2218yescomplemented
43#14582791C2218yescomplemented
44#14582789C2218yescomplemented
45#14582785C2218yescomplemented
46#14582777C2218yescomplemented
47#14582777C2218yescomplemented
48#14582777C2218yescomplemented
49#14582777C2218yescomplemented
50#14582761C2218yescomplemented
51C4×(C2×D43)⋊C4C2218yescomplemented
52#14582746C2218yescomplemented
53#14582746C2218yescomplemented
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C42×C43C2211yescharacteristic
63C43×#387C2218yescomplemented
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C24×D43C2311yescharacteristic
70C24×D43C2311yescharacteristic
71C22×D172—42no—
72C22×D172—42no—
73C22×D172—42no—
74C22×D172—42no—
75C22×D172—42no—
76C22×D172—42no—
77C22×D172C2×C418yes—
78C22×D172C2×C418yescomplemented
79C22×D172C2×C418yescomplemented
80C22×D172C2314yes—
81C22×D172C2314yes—
82C22×D172C2314yes—
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43—42no—
93C22×C4×D43—42no—
94C22×C4×D43—42no—
95C22×C4×D43—42no—
96C22×C4×D43C2×C418yescomplemented
97C22×C4×D43C2314yes—
98C22×C4×D43C2314yes—
99C22×C4×D43C2314yes—
100#13063300C2×C4164yescomplemented
101C2×C4⋊Dic43—42no—
102C2×C4⋊Dic43C2314yes—
103C2×(C2×D43)⋊C4—24no—
104C2×(C2×D43)⋊C4—24no—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—42no—
108C2×(C2×D43)⋊C4—42no—
109C2×(C2×D43)⋊C4—42no—
110C2×(C2×D43)⋊C4—42no—
111C2×(C2×D43)⋊C4—42no—
112C2×(C2×D43)⋊C4—42no—
113C2×(C2×D43)⋊C4C2×C418yescomplemented
114C2×(C2×D43)⋊C4C2×C418yescomplemented
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×C4×Dic43—42no—
128C2×C4×Dic43—42no—
129C2×C4×Dic43—42no—
130C2×C4×Dic43C2314yes—
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—42no—
147C2×C4⋊C4×C43C2×C418yescomplemented
148C2×C4⋊C4×C43C2314yes—
149C2×C4⋊C4×C43C2314yes—
150C2×C42×C43—42no—
151C2×C42×C43C2314yes—
152#95×C43C2314yes—
153#95×C43C2314yes—
154#95×C43C2314yes—
155#95×C43C2314yes—
156C24×C43C2411yescharacteristic
157C23×D43—22no—
158C23×D43—22no—
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43C22×C414yes—
176C23×D43C22×C414yes—
177C23×D43C22×C414yes—
178C23×D43C2412yes—
179C23×D43C2412yes—
180C23×D43C2412yes—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43C22×C414yes—
199C22×C4×C43C22×C414yes—
200C22×C4×C43C22×C414yes—
201C22×C4×C43#4114yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2412yes—
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—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43C22×C414yes—
223C22×Dic43#4114yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C2×D172—416no—
230C2×D172—416no—
231C2×D172—416no—
232C2×D172—44no—
233C2×D172—44no—
234C2×D172—44no—
235C2×D172—44no—
236C2×D172—44no—
237C2×D172—44no—
238C2×D172C22×C4116yes—
239C2×D172C22×C4116yescomplemented
240C2×D172C22×C4116yescomplemented
241C2×C4×D43—28no—
242C2×C4×D43—28no—
243C2×C4×D43—416no—
244C2×C4×D43—44no—
245C2×C4×D43—44no—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43—44no—
249C2×C4×D43—44no—
250C2×C4×D43—416no—
251C2×C4×D43—416no—
252C2×C4×D43C22×C4116yescomplemented
253C4⋊C4×C43—44no—
254C4⋊C4×C43C22×C4116yescomplemented
255C42×C43—44no—
256(C2×D43)⋊C4—28no—
257(C2×D43)⋊C4—28no—
258(C2×D43)⋊C4—28no—
259(C2×D43)⋊C4—28no—
260(C2×D43)⋊C4—44no—
261(C2×D43)⋊C4—44no—
262(C2×D43)⋊C4—44no—
263(C2×D43)⋊C4—44no—
264(C2×D43)⋊C4—44no—
265(C2×D43)⋊C4—44no—
266(C2×D43)⋊C4C22×C4116yescomplemented
267(C2×D43)⋊C4C22×C4116yescomplemented
268C4⋊Dic43—44no—
269C4×Dic43—44no—
270C4×Dic43—44no—
271C4×Dic43—44no—
272C23×C43C23×C412yes—
273C23×C43C2×#4112yes—
274C23×C43C2×#4112yes—
275C23×C43H(5,𝔽2)12yes—
276C23×C43H(5,𝔽2)12yes—
277C23×C43H(5,𝔽2)12yes—
278C23×C43H(5,𝔽2)12yes—
279C23×C43C2511yescharacteristic
280C22×D43—28no—
281C22×D43—28no—
282C22×D43—28no—
283C22×D43—28no—
284C22×D43—28no—
285C22×D43—28no—
286C22×D43—28no—
287C22×D43—28no—
288C22×D43—28no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—44no—
308C22×D43—44no—
309C22×D43—44no—
310C22×D43—44no—
311C22×D43—44no—
312C22×D43—44no—
313C22×D43—44no—
314C22×D43—44no—
315C22×D43—44no—
316C22×D43—44no—
317C22×D43—44no—
318C22×D43—44no—
319C22×D43C23×C414yes—
320C22×D43C23×C414yes—
321C22×D43C23×C414yes—
322C2×C4×C43—28no—
323C2×C4×C43—28no—
324C2×C4×C43—28no—
325C2×C4×C43—28no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—44no—
344C2×C4×C43—44no—
345C2×C4×C43—44no—
346C2×C4×C43C23×C414yes—
347C2×C4×C43C23×C414yes—
348C2×C4×C43C23×C414yes—
349C2×C4×C43C2×#4114yes—
350C2×Dic43—28no—
351C2×Dic43—28no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—44no—
366C2×Dic43—44no—
367C2×Dic43—44no—
368C2×Dic43C23×C414yes—
369C2×Dic43C2×#4114yes—
370D172—416no—
371D172—416no—
372D172—416no—
373C4×D43—416no—
374C4×D43—416no—
375C4×D43—416no—
376C2×#2333—431nomaximal, Sylow
377C22×C43C4×#4114yes—
378C22×C43#51814yes—
379C22×C43#51814yes—
380C22×C43#53814yes—
381C22×C43#53814yes—
382C22×C43#54014yes—
383C22×C43#54014yes—
384C22×C43C24×C411yescharacteristic
385C22×C43C22×#4111yescharacteristic
386C22×C43C22×#4111yescharacteristic
387C22×C43C2×H(5,𝔽2)11yescharacteristic
388C22×C43C2×H(5,𝔽2)11yescharacteristic
389C22×C43C2×H(5,𝔽2)11yescharacteristic
390C22×C43C2×H(5,𝔽2)11yescharacteristic
391C2×D43—24no—
392C2×D43—24no—
393C2×D43—24no—
394C2×D43—24no—
395C2×D43—24no—
396C2×D43—24no—
397C2×D43—24no—
398C2×D43—24no—
399C2×D43—24no—
400C2×D43—416no—
401C2×D43—416no—
402C2×D43—416no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C4×C43—24no—
416C4×C43—24no—
417C4×C43—24no—
418C4×C43—24no—
419C4×C43—42no—
420C4×C43—42no—
421C4×C43—42no—
422Dic43—24no—
423Dic43—24no—
424Dic43—42no—
425Dic43—42no—
426Dic43—42no—
427C22×#121—431no—
428#2333—4316no—
429C2×#390—431no—
430C2×#390—431no—
431C2×#388—431no—
432C2×#388—431no—
433C2×#387—431no—
434C2×#387D4311yescharacteristic, complemented
435C2×#386—431no—
436C2×#386—431no—
437C2×#386—431no—
438C2×#386—431no—
439C2×#381—431no—
440C2×C4×C22⋊C4—431no—
441C2×C4×C22⋊C4—431no—
442C2×C4×C22⋊C4—431no—
443C2×C43#233318yescomplemented
444C2×C43C2×C4×#4111yescharacteristic
445C2×C43C2×#51811yescharacteristic
446C2×C43C2×#51811yescharacteristic
447C2×C43C2×#53811yescharacteristic
448C2×C43C2×#53811yescharacteristic
449C2×C43C2×#54011yescharacteristic
450C2×C43C2×#54011yescharacteristic
451D43—44no—
452D43—44no—
453D43—44no—
454C23×D4—431no—
455C23×D4—431no—
456C23×D4—431no—
457C24×C4—431no—
458C24×C4—431no—
459C24×C4—431no—
460C2×#121—438no—
461C2×#121—4316no—
462C22×C4⋊C4—431no—
463C22×C4⋊C4C2×D4311yescharacteristic
464C22×C4⋊C4C2×D4311yescharacteristic
465C22×C22⋊C4—431no—
466C22×C22⋊C4—431no—
467C22×C22⋊C4—431no—
468C22×C22⋊C4—431no—
469C22×C22⋊C4—431no—
470C22×C22⋊C4—431no—
471C22×C22⋊C4—431no—
472C22×C22⋊C4—431no—
473C22×C22⋊C4—431no—
474C22×C22⋊C4—431no—
475C22×C22⋊C4—431no—
476C22×C22⋊C4—431no—
477C22×C42—431no—
478C22×C42—431no—
479C22×C42—431no—
480C22×C42C2×D4311yescharacteristic
481#390—438no—
482#390—438no—
483#388—438no—
484#388—438no—
485#387—438no—
486#387C2×D4318yescomplemented
487#386—438no—
488#386—438no—
489#386—438no—
490#386—438no—
491#381—438no—
492C4×C22⋊C4—438no—
493C4×C22⋊C4—438no—
494C4×C22⋊C4—438no—
495C2×#95—431no—
496C2×#95—431no—
497C2×#95—431no—
498C2×#95—431no—
499C2×#95—431no—
500C2×#95—431no—
501C2×#95C2×D4311yescharacteristic
502C2×#95C2×D4311yescharacteristic
503C2×#95C2×D4311yescharacteristic
504C2×#95C2×D4311yescharacteristic
505C43C2×#233311yescharacteristic, complemented, Sylow
506C25—431no—
507C25—431no—
508C25—431no—
509C22×D4—438no—
510C22×D4—438no—
511C22×D4—438no—
512C22×D4—434no—
513C22×D4—434no—
514C22×D4—434no—
515C22×D4—1722no—
516C22×D4—1722no—
517C22×D4—1722no—
518C22×D4—1722no—
519C22×D4—1722no—
520C22×D4—1722no—
521C23×C4—431no—
522C23×C4—431no—
523C23×C4—438no—
524C23×C4—434no—
525C23×C4—431no—
526C23×C4—431no—
527C23×C4—431no—
528C23×C4—434no—
529C23×C4—434no—
530C23×C4—864no—
531C23×C4—864no—
532C23×C4—1722no—
533C23×C4—1722no—
534C23×C4—1722no—
535C23×C4—1722no—
536C23×C4—1722no—
537C23×C4—1722no—
538C23×C4C22×D4311yescharacteristic
539C23×C4C22×D4311yescharacteristic
540C23×C4C22×D4311yescharacteristic
541C23×C4C22×D4311yescharacteristic
542C23×C4C22×D4311yescharacteristic
543C23×C4C22×D4311yescharacteristic
544C23×C4C22×D4311yescharacteristic
545#121—4364no—
546C2×C4⋊C4—42no—
547C2×C4⋊C4—434no—
548C2×C4⋊C4—1722no—
549C2×C4⋊C4C4×D4318yescomplemented
550C2×C4⋊C4C22×D4314yes—
551C2×C4⋊C4C22×D4314yes—
552C2×C22⋊C4—438no—
553C2×C22⋊C4—438no—
554C2×C22⋊C4—434no—
555C2×C22⋊C4—434no—
556C2×C22⋊C4—434no—
557C2×C22⋊C4—434no—
558C2×C22⋊C4—434no—
559C2×C22⋊C4—434no—
560C2×C22⋊C4—434no—
561C2×C22⋊C4—434no—
562C2×C22⋊C4—434no—
563C2×C22⋊C4—434no—
564C2×C22⋊C4—434no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4—864no—
567C2×C22⋊C4—864no—
568C2×C22⋊C4—864no—
569C2×C22⋊C4—864no—
570C2×C22⋊C4—1722no—
571C2×C22⋊C4—1722no—
572C2×C22⋊C4—1722no—
573C2×C22⋊C4—1722no—
574C2×C22⋊C4—1722no—
575C2×C22⋊C4—1722no—
576C2×C42—42no—
577C2×C42—434no—
578C2×C42—434no—
579C2×C42—434no—
580C2×C42—1722no—
581C2×C42—1722no—
582C2×C42—1722no—
583C2×C42C22×D4314yes—
584#95—434no—
585#95—434no—
586#95—434no—
587#95—434no—
588#95—434no—
589#95—434no—
590#95C22×D4314yes—
591#95C22×D4314yes—
592#95C22×D4314yes—
593#95C22×D4314yes—
594C24—434no—
595C24—434no—
596C24—434no—
597C24—432no—
598C24—432no—
599C24—432no—
600C24—862no—
601C24—862no—
602C24—862no—
603C24—862no—
604C24—862no—
605C24—862no—
606C24—862no—
607C24—862no—
608C24—862no—
609C24—862no—
610C24—862no—
611C24—862no—
612C24—862no—
613C24—862no—
614C24—862no—
615C24—862no—
616C24—862no—
617C24—862no—
618C24C23×D4311yescharacteristic
619C2×D4—4316no—
620C2×D4—4316no—
621C2×D4—4316no—
622C2×D4—17216no—
623C2×D4—17216no—
624C2×D4—17216no—
625C2×D4—1724no—
626C2×D4—1724no—
627C2×D4—1724no—
628C2×D4—1724no—
629C2×D4—1724no—
630C2×D4—1724no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—434no—
649C22×C4—434no—
650C22×C4—432no—
651C22×C4—432no—
652C22×C4—4316no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—868no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—862no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—862no—
667C22×C4—862no—
668C22×C4—862no—
669C22×C4—862no—
670C22×C4—868no—
671C22×C4—17216no—
672C22×C4—1724no—
673C22×C4—1724no—
674C22×C4—1724no—
675C22×C4—1724no—
676C22×C4—1724no—
677C22×C4—1724no—
678C22×C4—17216no—
679C22×C4—17216no—
680C22×C4C2×C4×D4314yes—
681C22×C4C2×C4×D4314yes—
682C22×C4C2×C4×D4314yes—
683C22×C4#1062190214yes—
684C22×C4C23×D4312yes—
685C22×C4C23×D4312yes—
686C22×C4C23×D4312yes—
687C22×C4C23×D4312yes—
688C22×C4C23×D4312yes—
689C22×C4C23×D4312yes—
690C22×C4C23×D4312yes—
691C4⋊C4—44no—
692C4⋊C4—1724no—
693C4⋊C4C2×C4×D43116yescomplemented
694C22⋊C4—4316no—
695C22⋊C4—4316no—
696C22⋊C4—868no—
697C22⋊C4—868no—
698C22⋊C4—868no—
699C22⋊C4—868no—
700C22⋊C4—1724no—
701C22⋊C4—1724no—
702C22⋊C4—1724no—
703C22⋊C4—1724no—
704C22⋊C4—1724no—
705C22⋊C4—1724no—
706C42—44no—
707C42—1724no—
708C42—1724no—
709C42—1724no—
710C23—434no—
711C23—434no—
712C23—434no—
713C23—868no—
714C23—868no—
715C23—868no—
716C23—868no—
717C23—868no—
718C23—868no—
719C23—868no—
720C23—868no—
721C23—868no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—862no—
731C23—862no—
732C23—862no—
733C23—862no—
734C23—862no—
735C23—862no—
736C23—862no—
737C23—862no—
738C23—862no—
739C23—862no—
740C23—1724no—
741C23—1724no—
742C23—1724no—
743C23—1724no—
744C23—1724no—
745C23—1724no—
746C23—1724no—
747C23—1724no—
748C23—1724no—
749C23—1724no—
750C23—1724no—
751C23—1724no—
752C23C22×C4×D4312yes—
753C23#41×D4312yes—
754C23C2×#1062190212yes—
755C23#1306337012yes—
756C23#1306337112yes—
757C23#1306337112yes—
758C23#1306337112yes—
759C23C24×D4311yescharacteristic
760D4—17216no—
761D4—17216no—
762D4—17216no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—434no—
788C2×C4—434no—
789C2×C4—868no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—868no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—17216no—
805C2×C4—17216no—
806C2×C4—17216no—
807C2×C4—1724no—
808C2×C4—1724no—
809C2×C4—1724no—
810C2×C4C22×C4×D4314yes—
811C2×C4C22×C4×D4314yes—
812C2×C4C22×C4×D4314yes—
813C2×C4C2×#1062190214yes—
814C22—864no—
815C22—864no—
816C22—864no—
817C22—864no—
818C22—864no—
819C22—864no—
820C22—864no—
821C22—864no—
822C22—864no—
823C22—17216no—
824C22—17216no—
825C22—17216no—
826C22—1722no—
827C22—1722no—
828C22—1722no—
829C22—1722no—
830C22—1722no—
831C22—1722no—
832C22—1722no—
833C22—1722no—
834C22—1722no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22C4×#1062190214yes—
839C22#1458337114yes—
840C22#1458337314yes—
841C22#1458348814yes—
842C22#1458348914yes—
843C22#1458350114yes—
844C22#1458350514yes—
845C22C23×C4×D4311yescharacteristic
846C22C2×#41×D4311yescharacteristic
847C22C22×#1062190211yescharacteristic
848C22C2×#1306337011yescharacteristic
849C22C2×#1306337111yescharacteristic
850C22C2×#1306337111yescharacteristic
851C22C2×#1306337111yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—864no—
860C4—864no—
861C4—1722no—
862C4—1722no—
863C4—1722no—
864C2—1724no—
865C2—1724no—
866C2—1724no—
867C2#1913735918yesdirect product factor
868C2C2×C4×#1062190211yescharacteristic
869C2C2×#1458337111yescharacteristic
870C2C2×#1458337311yescharacteristic
871C2C2×#1458348811yescharacteristic
872C2C2×#1458348911yescharacteristic
873C2C2×#1458350111yescharacteristic
874C2C2×#1458350511yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC22×#13063300C2
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2333
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #19137359C2direct (N × H)
3. C2×#14582801C2semidirect
4. C2×#14582800C2semidirect
5. C2×#14582791C2semidirect
6. C2×#14582789C2semidirect
7. C2×#14582785C2semidirect
8. C2×#14582777C2semidirect
9. C2×#14582777C2semidirect
10. C2×#14582777C2semidirect
11. C2×#14582777C2semidirect
12. C2×#14582761C2semidirect
13. C2×C4×(C2×D43)⋊C4C2semidirect
14. C2×#14582746C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#387C2semidirect
23. C2×#13063300C4semidirect
41. #14582801C22semidirect
42. #14582800C22semidirect
43. #14582791C22semidirect
44. #14582789C22semidirect
45. #14582785C22semidirect
46. #14582777C22semidirect
47. #14582777C22semidirect
48. #14582777C22semidirect
49. #14582777C22semidirect
50. #14582761C22semidirect
51. C4×(C2×D43)⋊C4C22semidirect
52. #14582746C22semidirect
53. #14582746C22semidirect
63. C43×#387C22semidirect
78. C22×D172C2×C4semidirect
79. C22×D172C2×C4semidirect
96. C22×C4×D43C2×C4semidirect
100. #13063300C2×C4semidirect
113. C2×(C2×D43)⋊C4C2×C4semidirect
114. C2×(C2×D43)⋊C4C2×C4semidirect
147. C2×C4⋊C4×C43C2×C4semidirect
239. C2×D172C22×C4semidirect
240. C2×D172C22×C4semidirect
252. C2×C4×D43C22×C4semidirect
254. C4⋊C4×C43C22×C4semidirect
266. (C2×D43)⋊C4C22×C4semidirect
267. (C2×D43)⋊C4C22×C4semidirect
434. C2×#387D43semidirect
443. C2×C43#2333semidirect
486. #387C2×D43semidirect
505. C43C2×#2333semidirect
549. C2×C4⋊C4C4×D43semidirect
693. C4⋊C4C2×C4×D43semidirect
867. C2#19137359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633002
#191373592
C2×#145828012
C2×#145828002
C2×#145827912
C2×#145827892
C2×#145827852
C2×#145827772
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×C43×#3872
C2×#233343