Finite Group Databasebeta

← C2×#19137227 #25255234

Subgroups — C2×#19137227 #25255234

Order 11008.

3262 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2#19137227C2116yesmaximal, direct product factor
3C2×#14582790C211yesmaximal, characteristic, complemented
4C2×#14582788C211yesmaximal, characteristic, complemented
5C2×#14582785C211yesmaximal, characteristic, complemented
6C2×#14582777C211yesmaximal, characteristic
7C2×#14582777C211yesmaximal, characteristic
8C2×#14582773C211yesmaximal, characteristic, complemented
9C2×#14582770C211yesmaximal, characteristic, complemented
10C2×#14582766C211yesmaximal, characteristic, complemented
11C2×#14582763C211yesmaximal, characteristic, complemented
12C2×#14582761C211yesmaximal, characteristic, complemented
13C2×#14582756C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D43C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063287C4116yescomplemented
23C2×#13063287C2218yes—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊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×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582790C2218yescomplemented
38#14582788C2218yescomplemented
39#14582785C2218yescomplemented
40#14582777C2218yes—
41#14582777C2218yes—
42#14582773C2218yescomplemented
43#14582770C2218yescomplemented
44#14582766C2218yescomplemented
45#14582763C2218yescomplemented
46#14582761C2218yescomplemented
47#14582756C2218yescomplemented
48C4×(C2×D43)⋊C4C2218yescomplemented
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
59#95×D43C2218yescomplemented
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
70C22×D172—24no—
71C22×D172—24no—
72C22×D172C2×C418yes—
73C22×D172C2314yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—24no—
81C22×C4×D43—24no—
82C22×C4×D43—42no—
83C22×C4×D43—42no—
84C22×C4×D43—42no—
85C22×C4×D43—42no—
86C22×C4×D43—42no—
87C22×C4×D43—42no—
88C22×C4×D43—42no—
89C22×C4×D43—42no—
90C22×C4×D43C2×C418yes—
91C22×C4×D43C2×C418yescomplemented
92C22×C4×D43C2314yes—
93C22×C4×D43C2314yes—
94C22×C4×D43C2314yes—
95C22×C4×D43C2314yes—
96#13063287C2×C4164yescomplemented
97C2×C4⋊Dic43—42no—
98C2×C4⋊Dic43C2314yes—
99C2×Dic43⋊C4—42no—
100C2×Dic43⋊C4—42no—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×(C2×D43)⋊C4—24no—
104C2×(C2×D43)⋊C4—24no—
105C2×(C2×D43)⋊C4—42no—
106C2×(C2×D43)⋊C4—42no—
107C2×(C2×D43)⋊C4—42no—
108C2×(C2×D43)⋊C4—42no—
109C2×(C2×D43)⋊C4C2×C418yes—
110C2×(C2×D43)⋊C4C2×C418yescomplemented
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×C4×Dic43—42no—
120C2×C4×Dic43C2×C418yescomplemented
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43—42no—
141C2×C4⋊C4×C43C2×C418yescomplemented
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C42×C43—42no—
145C2×C42×C43C2314yes—
146#95×C43C2314yes—
147#95×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43C2411yescharacteristic
151C23×D43—22no—
152C23×D43—22no—
153C23×D43—22no—
154C23×D43—22no—
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—22no—
159C23×D43—22no—
160C23×D43—22no—
161C23×D43C22×C414yes—
162C23×D43C22×C414yes—
163C23×D43#4114yes—
164C23×D43#4114yes—
165C23×D43C2412yes—
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×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43C22×C414yes—
186C22×C4×C43C22×C414yes—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
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×Dic43C22×C414yes—
212C22×Dic43C22×C414yes—
213C22×Dic43C2412yes—
214C22×Dic43C2412yes—
215C22×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C2×D172—232no—
220C2×D172—28no—
221C2×D172—28no—
222C2×D172C22×C4116yes—
223C2×C4×D43—28no—
224C2×C4×D43—28no—
225C2×C4×D43—416no—
226C2×C4×D43—416no—
227C2×C4×D43—44no—
228C2×C4×D43—44no—
229C2×C4×D43—44no—
230C2×C4×D43—44no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—44no—
235C2×C4×D43—416no—
236C2×C4×D43—416no—
237C2×C4×D43C22×C4116yes—
238C2×C4×D43C22×C4116yescomplemented
239C4⋊C4×C43—44no—
240C4⋊C4×C43C22×C4116yescomplemented
241C42×C43—44no—
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—28no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4—44no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4C22×C4116yes—
249(C2×D43)⋊C4C22×C4116yescomplemented
250C4⋊Dic43—44no—
251Dic43⋊C4—44no—
252Dic43⋊C4—44no—
253C4×Dic43—44no—
254C4×Dic43C22×C4116yescomplemented
255C23×C43C23×C412yes—
256C23×C43C2×#4112yes—
257C23×C43C2×#4112yes—
258C23×C43H(5,𝔽2)12yes—
259C23×C43H(5,𝔽2)12yes—
260C23×C43H(5,𝔽2)12yes—
261C23×C432−1+412yes—
262C23×C43C2511yescharacteristic
263C22×D43—28no—
264C22×D43—28no—
265C22×D43—28no—
266C22×D43—28no—
267C22×D43—28no—
268C22×D43—28no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—28no—
274C22×D43—28no—
275C22×D43—28no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—44no—
283C22×D43—44no—
284C22×D43—44no—
285C22×D43—44no—
286C22×D43#117116yes—
287C22×D43C23×C414yes—
288C22×D43C23×C414yes—
289C22×D43C2×#4114yes—
290C22×D43C2×#4114yes—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
293C2×C4×C43—28no—
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—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—44no—
313C2×C4×C43—44no—
314C2×C4×C43—44no—
315C2×C4×C43—44no—
316C2×C4×C43C23×C414yes—
317C2×C4×C43C23×C414yes—
318C2×C4×C43C23×C414yes—
319C2×Dic43—28no—
320C2×Dic43—28no—
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—22no—
336C2×Dic43—22no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43C23×C414yes—
342C2×Dic43C23×C414yes—
343D172—232no—
344C4×D43—416no—
345C4×D43—416no—
346C4×D43—416no—
347C4×D43—416no—
348C2×#2318—431nomaximal, Sylow
349C22×C43C2×#11714yes—
350C22×C43#51814yes—
351C22×C43#52014yes—
352C22×C43#53814yes—
353C22×C43#53814yes—
354C22×C43#53914yes—
355C22×C43#53914yes—
356C22×C43C24×C411yescharacteristic
357C22×C43C22×#4111yescharacteristic
358C22×C43C22×#4111yescharacteristic
359C22×C43C2×H(5,𝔽2)11yescharacteristic
360C22×C43C2×H(5,𝔽2)11yescharacteristic
361C22×C43C2×H(5,𝔽2)11yescharacteristic
362C22×C43C2×2−1+411yescharacteristic
363C2×D43—232no—
364C2×D43—24no—
365C2×D43—24no—
366C2×D43—24no—
367C2×D43—24no—
368C2×D43—24no—
369C2×D43—24no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—24no—
373C2×D43—416no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43C2×#11718yes—
379C4×C43—24no—
380C4×C43—24no—
381C4×C43—24no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385C4×C43—42no—
386Dic43—24no—
387Dic43—24no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392C22×C4×D4—431no—
393#2318—4316no—
394C2×#388—431no—
395C2×#388—431no—
396C2×#387—431no—
397C2×#387D4311yescharacteristic, complemented
398C2×#386—431no—
399C2×#386—431no—
400C2×#385—431no—
401C2×#385—431no—
402C2×#383—431no—
403C2×#382—431no—
404C2×#381—431no—
405C2×#380—431no—
406C2×C4×C22⋊C4—431no—
407C22×#95—431no—
408C2×C43#231818yescomplemented
409C2×C43C22×#11711yescharacteristic
410C2×C43C2×#51811yescharacteristic
411C2×C43C2×#52011yescharacteristic
412C2×C43C2×#53811yescharacteristic
413C2×C43C2×#53811yescharacteristic
414C2×C43C2×#53911yescharacteristic
415C2×C43C2×#53911yescharacteristic
416D43—28no—
417D43—44no—
418C23×D4—431no—
419C24×C4—431no—
420C24×C4—431no—
421C24×C4—431no—
422C24×C4—431no—
423C2×C4×D4—438no—
424C2×C4×D4—4316no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4C2×D4311yescharacteristic
429C22×C4⋊C4C2×D4311yescharacteristic
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4—431no—
434C22×C22⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—431no—
437C22×C22⋊C4—431no—
438C22×C42—431no—
439C22×C42—431no—
440C22×C42C2×D4311yescharacteristic
441#388—438no—
442#388—438no—
443#387—438no—
444#387C2×D4318yescomplemented
445#386—438no—
446#386—438no—
447#385—438no—
448#385—438no—
449#383—438no—
450#382—438no—
451#381—438no—
452#380—438no—
453C4×C22⋊C4—438no—
454C2×#95—431no—
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—438no—
465C2×#95C2×D4311yescharacteristic
466C2×#95C2×D4311yescharacteristic
467C2×#95C2×D4311yescharacteristic
468C2×#95C2×D4311yescharacteristic
469C43C2×#231811yescharacteristic, complemented, Sylow
470C25—431no—
471C25—431no—
472C22×D4—438no—
473C22×D4—434no—
474C22×D4—864no—
475C22×D4—864no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—438no—
479C23×C4—438no—
480C23×C4—434no—
481C23×C4—434no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—434no—
487C23×C4—434no—
488C23×C4—864no—
489C23×C4—864no—
490C23×C4—1722no—
491C23×C4—1722no—
492C23×C4—1722no—
493C23×C4—1722no—
494C23×C4—1722no—
495C23×C4—1722no—
496C23×C4—1722no—
497C23×C4—1722no—
498C23×C4C22×D4311yescharacteristic
499C23×C4C22×D4311yescharacteristic
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C4×D4—4364no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4—434no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—1722no—
511C2×C4⋊C4—1722no—
512C2×C4⋊C4—1722no—
513C2×C4⋊C4C4×D4318yescomplemented
514C2×C4⋊C4C22×D4314yes—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—438no—
517C2×C22⋊C4—438no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—434no—
523C2×C22⋊C4—434no—
524C2×C22⋊C4—434no—
525C2×C22⋊C4—434no—
526C2×C22⋊C4—864no—
527C2×C22⋊C4—864no—
528C2×C22⋊C4—1722no—
529C2×C22⋊C4—1722no—
530C2×C22⋊C4—1722no—
531C2×C22⋊C4—1722no—
532C2×C42—42no—
533C2×C42—438no—
534C2×C42—434no—
535C2×C42—434no—
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#95—434no—
547#95—434no—
548#95C22×D4314yes—
549#95C22×D4314yes—
550#95C22×D4314yes—
551#95C22×D4314yes—
552C24—434no—
553C24—434no—
554C24—434no—
555C24—432no—
556C24—434no—
557C24—432no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24—862no—
567C24—862no—
568C24C23×D4311yescharacteristic
569C2×D4—4316no—
570C2×D4—8632no—
571C2×D4—868no—
572C2×D4—868no—
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—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—434no—
592C22×C4—434no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—4316no—
596C22×C4—4316no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
602C22×C4—868no—
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—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—17216no—
620C22×C4—17216no—
621C22×C4—1724no—
622C22×C4—1724no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4—1724no—
629C22×C4—17216no—
630C22×C4—17216no—
631C22×C4C2×C4×D4314yes—
632C22×C4C2×C4×D4314yes—
633C22×C4C2×C4×D4314yes—
634C22×C4C23×D4312yes—
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4312yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C4⋊C4—44no—
642C4⋊C4—1724no—
643C4⋊C4—1724no—
644C4⋊C4—1724no—
645C4⋊C4C2×C4×D43116yescomplemented
646C22⋊C4—4316no—
647C22⋊C4—4316no—
648C22⋊C4—868no—
649C22⋊C4—868no—
650C22⋊C4—1724no—
651C22⋊C4—1724no—
652C22⋊C4—1724no—
653C22⋊C4—1724no—
654C42—44no—
655C42—4316no—
656C42—1724no—
657C23—4316no—
658C23—434no—
659C23—434no—
660C23—434no—
661C23—434no—
662C23—868no—
663C23—868no—
664C23—862no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23—868no—
669C23—868no—
670C23—868no—
671C23—868no—
672C23—868no—
673C23—868no—
674C23—868no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23—1724no—
682C23—1724no—
683C23—1724no—
684C23—1724no—
685C23C22×C4×D4312yes—
686C23#41×D4312yes—
687C23#41×D4312yes—
688C23#1306337012yes—
689C23#1306337112yes—
690C23#1306337112yes—
691C23#1306337312yes—
692C23C24×D4311yescharacteristic
693D4—8632no—
694C2×C4—28no—
695C2×C4—28no—
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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—434no—
720C2×C4—434no—
721C2×C4—868no—
722C2×C4—868no—
723C2×C4—862no—
724C2×C4—862no—
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—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—17216no—
740C2×C4—17216no—
741C2×C4—17216no—
742C2×C4—17216no—
743C2×C4—1724no—
744C2×C4—1724no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4C22×C4×D4314yes—
748C2×C4C22×C4×D4314yes—
749C2×C4C22×C4×D4314yes—
750C22—438no—
751C22—864no—
752C22—864no—
753C22—864no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—8632no—
758C22—864no—
759C22—864no—
760C22—864no—
761C22—1722no—
762C22—1722no—
763C22—1722no—
764C22—1722no—
765C22—17216no—
766C22#117×D4314yes—
767C22#1458337114yes—
768C22#1458338114yes—
769C22#1458348514yes—
770C22#1458348814yes—
771C22#1458349514yes—
772C22#1458349714yes—
773C22C23×C4×D4311yescharacteristic
774C22C2×#41×D4311yescharacteristic
775C22C2×#41×D4311yescharacteristic
776C22C2×#1306337011yescharacteristic
777C22C2×#1306337111yescharacteristic
778C22C2×#1306337111yescharacteristic
779C22C2×#1306337311yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—864no—
788C4—864no—
789C4—1722no—
790C4—1722no—
791C4—1722no—
792C4—1722no—
793C2—868no—
794C2—1724no—
795C2#1913722718yesdirect product factor
796C2C2×#117×D4311yescharacteristic
797C2C2×#1458337111yescharacteristic
798C2C2×#1458338111yescharacteristic
799C2C2×#1458348511yescharacteristic
800C2C2×#1458348811yescharacteristic
801C2C2×#1458349511yescharacteristic
802C2C2×#1458349711yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC23×D172C22
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2318
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #19137227C2direct (N × H)
3. C2×#14582790C2semidirect
4. C2×#14582788C2semidirect
5. C2×#14582785C2semidirect
8. C2×#14582773C2semidirect
9. C2×#14582770C2semidirect
10. C2×#14582766C2semidirect
11. C2×#14582763C2semidirect
12. C2×#14582761C2semidirect
13. C2×#14582756C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#95×D43C2semidirect
16. C2×C43×#387C2semidirect
22. C2×#13063287C4semidirect
37. #14582790C22semidirect
38. #14582788C22semidirect
39. #14582785C22semidirect
42. #14582773C22semidirect
43. #14582770C22semidirect
44. #14582766C22semidirect
45. #14582763C22semidirect
46. #14582761C22semidirect
47. #14582756C22semidirect
48. C4×(C2×D43)⋊C4C22semidirect
59. #95×D43C22semidirect
63. C43×#387C22semidirect
91. C22×C4×D43C2×C4semidirect
96. #13063287C2×C4semidirect
110. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×C4×Dic43C2×C4semidirect
141. C2×C4⋊C4×C43C2×C4semidirect
238. C2×C4×D43C22×C4semidirect
240. C4⋊C4×C43C22×C4semidirect
249. (C2×D43)⋊C4C22×C4semidirect
254. C4×Dic43C22×C4semidirect
397. C2×#387D43semidirect
408. C2×C43#2318semidirect
444. #387C2×D43semidirect
469. C43C2×#2318semidirect
513. C2×C4⋊C4C4×D43semidirect
645. C4⋊C4C2×C4×D43semidirect
795. C2#19137227direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632872
#191372272
C2×#145827902
C2×#145827882
C2×#145827852
C2×#145827772
C2×#145827732
C2×#145827702
C2×#145827662
C2×#145827632
C2×#145827612
C2×#145827562
C2×C4×(C2×D43)⋊C42
C2×#95×D432
C2×C43×#3872
C2×#231843