Finite Group Databasebeta

← C2×#19138079 #25264309

Subgroups — C2×#19138079 #25264309

Order 11008.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic
2C22×C4×D172C211yesmaximal, characteristic
3#19138079C2116yesmaximal, direct product factor
4C2×#14582838C211yesmaximal, characteristic, complemented
5C2×#14582831C211yesmaximal, characteristic, complemented
6C2×#14582826C211yesmaximal, characteristic, complemented
7C2×#14582825C211yesmaximal, characteristic, complemented
8C2×#14582783C211yesmaximal, characteristic, complemented
9C2×#14582777C211yesmaximal, characteristic
10C2×#14582773C211yesmaximal, characteristic, complemented
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582761C211yesmaximal, characteristic, complemented
13C2×#14582761C211yesmaximal, characteristic, complemented
14C2×#14582756C211yesmaximal, 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×#13063310—28no—
23C2×#13063310C2218yes—
24C2×C4×D172—28no—
25C2×C4×D172C2218yes—
26C22×C4⋊Dic43C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊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×(C2×D43)⋊C4C2211yescharacteristic
39#14582838C2218yescomplemented
40#14582831C2218yescomplemented
41#14582826C2218yescomplemented
42#14582825C2218yescomplemented
43#14582783C2218yescomplemented
44#14582777C2218yes—
45#14582773C2218yescomplemented
46#14582773C2218yescomplemented
47#14582761C2218yescomplemented
48#14582761C2218yescomplemented
49#14582756C2218yescomplemented
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
59C2×C43⋊#95C2211yescharacteristic
60#95×D43C2218yescomplemented
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C42×C43C2211yescharacteristic
64C43×#387C2218yescomplemented
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C24×D43C2311yescharacteristic
71C22×D172—24no—
72C22×D172—24no—
73C22×D172D418yes—
74C22×D172C2314yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C22×C4×D43—24no—
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43—42no—
93C22×C4×D43C2314yes—
94C22×C4×D43C2314yes—
95C22×C4×D43C2314yes—
96C22×C4×D43C2314yes—
97#13063310—232no—
98C4×D172—232no—
99C2×C4⋊Dic43—24no—
100C2×C4⋊Dic43—42no—
101C2×C4⋊Dic43—42no—
102C2×C4⋊Dic43C2314yes—
103C2×C4⋊Dic43C2314yes—
104C2×C4⋊Dic43C2314yes—
105C2×Dic43⋊C4—24no—
106C2×Dic43⋊C4—24no—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×(C2×D43)⋊C4—24no—
110C2×(C2×D43)⋊C4—24no—
111C2×(C2×D43)⋊C4—24no—
112C2×(C2×D43)⋊C4—24no—
113C2×(C2×D43)⋊C4—24no—
114C2×(C2×D43)⋊C4—24no—
115C2×(C2×D43)⋊C4—24no—
116C2×(C2×D43)⋊C4—42no—
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—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43—24no—
143C2×C4⋊C4×C43—24no—
144C2×C4⋊C4×C43C2314yes—
145C2×C4⋊C4×C43C2314yes—
146C2×C42×C43—24no—
147C2×C42×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150#95×C43C2314yes—
151#95×C43C2314yes—
152C24×C43C2411yescharacteristic
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×D43—22no—
162C23×D43—22no—
163C23×D43C2×D414yes—
164C23×D43C2×D414yes—
165C23×D43#4114yes—
166C23×D43#4114yes—
167C23×D43C2412yes—
168C23×D43C2412yes—
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×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43C2×D414yes—
188C22×C4×C43#4114yes—
189C22×C4×C43#4114yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
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×Dic43C2412yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C2×D172—232no—
222C2×D172—28no—
223C2×D172—28no—
224C2×D172C2×D4116yes—
225C2×C4×D43—28no—
226C2×C4×D43—28no—
227C2×C4×D43—28no—
228C2×C4×D43—28no—
229C2×C4×D43—28no—
230C2×C4×D43—28no—
231C2×C4×D43—28no—
232C2×C4×D43—28no—
233C2×C4×D43—28no—
234C2×C4×D43—44no—
235C2×C4×D43—44no—
236C2×C4×D43—44no—
237C2×C4×D43—416no—
238C2×C4×D43—416no—
239C2×C4×D43—416no—
240C2×C4×D43—416no—
241C4⋊C4×C43—28no—
242C4⋊C4×C43—28no—
243C42×C43—28no—
244(C2×D43)⋊C4—28no—
245(C2×D43)⋊C4—28no—
246(C2×D43)⋊C4—28no—
247(C2×D43)⋊C4—28no—
248(C2×D43)⋊C4—28no—
249(C2×D43)⋊C4—28no—
250(C2×D43)⋊C4—28no—
251(C2×D43)⋊C4—44no—
252C4⋊Dic43—28no—
253C4⋊Dic43—44no—
254C4⋊Dic43—44no—
255Dic43⋊C4—28no—
256Dic43⋊C4—28no—
257C23×C43C22×D412yes—
258C23×C43C2×#4112yes—
259C23×C43C2×#4112yes—
260C23×C43C2×#4112yes—
261C23×C43C2×#4112yes—
262C23×C43H(5,𝔽2)12yes—
263C23×C432−1+412yes—
264C23×C43C2511yescharacteristic
265C22×D43—28no—
266C22×D43—28no—
267C22×D43—28no—
268C22×D43—28no—
269C22×D43—28no—
270C22×D43—28no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
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×D43#123116yes—
289C22×D43C22×D414yes—
290C22×D43C22×D414yes—
291C22×D43C2×#4114yes—
292C22×D43C2×#4114yes—
293C2×C4×C43—28no—
294C2×C4×C43—28no—
295C2×C4×C43—28no—
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—22no—
313C2×C4×C43—22no—
314C2×C4×C43—44no—
315C2×C4×C43—44no—
316C2×C4×C43—44no—
317C2×C4×C43—44no—
318C2×C4×C43C22×D414yes—
319C2×C4×C43C2×#4114yes—
320C2×C4×C43C2×#4114yes—
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—22no—
338C2×Dic43—22no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43—44no—
342C2×Dic43—44no—
343C2×Dic43—44no—
344C2×Dic43—44no—
345D172—232no—
346C4×D43—416no—
347C4×D43—416no—
348C4×D43—416no—
349C4×D43—416no—
350C2×#2419—431nomaximal, Sylow
351C22×C43C2×#12314yes—
352C22×C43#52914yes—
353C22×C43#53914yes—
354C22×C43#54614yes—
355C22×C43#54714yes—
356C22×C43#55114yes—
357C22×C43#55214yes—
358C22×C43C23×D411yescharacteristic
359C22×C43C22×#4111yescharacteristic
360C22×C43C22×#4111yescharacteristic
361C22×C43C22×#4111yescharacteristic
362C22×C43C22×#4111yescharacteristic
363C22×C43C2×H(5,𝔽2)11yescharacteristic
364C22×C43C2×2−1+411yescharacteristic
365C2×D43—24no—
366C2×D43—232no—
367C2×D43—24no—
368C2×D43—24no—
369C2×D43—24no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—24no—
373C2×D43—24no—
374C2×D43—24no—
375C2×D43—42no—
376C2×D43—416no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43C2×#12318yes—
381C4×C43—24no—
382C4×C43—24no—
383C4×C43—24no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43—42no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392Dic43—42no—
393Dic43—42no—
394C22×#123—431no—
395C22×C4×D4—431no—
396#2419—4316no—
397C2×#400—431no—
398C2×#398—431no—
399C2×#397—431no—
400C2×#397—431no—
401C2×#387—431no—
402C2×#387D4311yescharacteristic, complemented
403C2×#386—431no—
404C2×#385—431no—
405C2×#385—431no—
406C2×#381—431no—
407C2×#381—431no—
408C2×#380—431no—
409C22×#95—431no—
410C2×C43#241918yescomplemented
411C2×C43C22×#12311yescharacteristic
412C2×C43C2×#52911yescharacteristic
413C2×C43C2×#53911yescharacteristic
414C2×C43C2×#54611yescharacteristic
415C2×C43C2×#54711yescharacteristic
416C2×C43C2×#55111yescharacteristic
417C2×C43C2×#55211yescharacteristic
418D43—28no—
419D43—44no—
420C23×D4—431no—
421C24×C4—431no—
422C24×C4—431no—
423C24×C4—431no—
424C24×C4—431no—
425C2×#123—438no—
426C2×#123—868no—
427C2×C4×D4—438no—
428C2×C4×D4—868no—
429C22×C4⋊C4—431no—
430C22×C4⋊C4—431no—
431C22×C4⋊C4—431no—
432C22×C4⋊C4—431no—
433C22×C4⋊C4—431no—
434C22×C4⋊C4C2×D4311yescharacteristic
435C22×C4⋊C4C2×D4311yescharacteristic
436C22×C22⋊C4—431no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4—431no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4—431no—
441C22×C22⋊C4—431no—
442C22×C22⋊C4—431no—
443C22×C22⋊C4—431no—
444C22×C42C2×D4311yescharacteristic
445#400—438no—
446#398—438no—
447#397—438no—
448#397—438no—
449#387—438no—
450#387C2×D4318yescomplemented
451#386—438no—
452#385—438no—
453#385—438no—
454#381—438no—
455#381—438no—
456#380—438no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C2×#95—431no—
466C2×#95—431no—
467C2×#95—438no—
468C2×#95C2×D4311yescharacteristic
469C2×#95C2×D4311yescharacteristic
470C2×#95C2×D4311yescharacteristic
471C2×#95C2×D4311yescharacteristic
472C43C2×#241911yescharacteristic, complemented, Sylow
473C25—431no—
474C25—431no—
475C22×D4—438no—
476C22×D4—434no—
477C22×D4—864no—
478C22×D4—864no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—434no—
486C23×C4—434no—
487C23×C4—434no—
488C23×C4—434no—
489C23×C4—864no—
490C23×C4—864no—
491C23×C4—864no—
492C23×C4—864no—
493C23×C4—864no—
494C23×C4—864no—
495C23×C4—864no—
496C23×C4—864no—
497C23×C4—864no—
498C23×C4—1722no—
499C23×C4—1722no—
500C23×C4—1722no—
501C23×C4C22×D4311yescharacteristic
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C23×C4C22×D4311yescharacteristic
508#123—8632no—
509C4×D4—8632no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—434no—
513C2×C4⋊C4—434no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—864no—
518C2×C4⋊C4—864no—
519C2×C4⋊C4—864no—
520C2×C4⋊C4—1722no—
521C2×C4⋊C4—1722no—
522C2×C4⋊C4C22×D4314yes—
523C2×C4⋊C4C22×D4314yes—
524C2×C22⋊C4—434no—
525C2×C22⋊C4—434no—
526C2×C22⋊C4—434no—
527C2×C22⋊C4—434no—
528C2×C22⋊C4—434no—
529C2×C22⋊C4—434no—
530C2×C22⋊C4—434no—
531C2×C22⋊C4—434no—
532C2×C22⋊C4—864no—
533C2×C22⋊C4—864no—
534C2×C22⋊C4—864no—
535C2×C22⋊C4—864no—
536C2×C22⋊C4—864no—
537C2×C22⋊C4—864no—
538C2×C22⋊C4—864no—
539C2×C22⋊C4—1722no—
540C2×C42—24no—
541C2×C42C22×D4314yes—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548#95—434no—
549#95—434no—
550#95—434no—
551#95—434no—
552#95C22×D4314yes—
553#95C22×D4314yes—
554#95C22×D4314yes—
555#95C22×D4314yes—
556C24—434no—
557C24—434no—
558C24—434no—
559C24—432no—
560C24—434no—
561C24—432no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24—862no—
567C24—862no—
568C24—862no—
569C24—862no—
570C24—862no—
571C24—862no—
572C24C23×D4311yescharacteristic
573C2×D4—4316no—
574C2×D4—8632no—
575C2×D4—868no—
576C2×D4—868no—
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—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
602C22×C4—868no—
603C22×C4—868no—
604C22×C4—868no—
605C22×C4—868no—
606C22×C4—868no—
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—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—868no—
626C22×C4—868no—
627C22×C4—868no—
628C22×C4—1724no—
629C22×C4—1724no—
630C22×C4—1724no—
631C22×C4—17216no—
632C22×C4—17216no—
633C22×C4—17216no—
634C22×C4—17216no—
635C22×C4#1062189814yes—
636C22×C4D4×D4314yes—
637C22×C4#1062190214yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C22×C4C23×D4312yes—
642C22×C4C23×D4312yes—
643C22×C4C23×D4312yes—
644C22×C4C23×D4312yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—868no—
648C4⋊C4—868no—
649C4⋊C4—868no—
650C4⋊C4—1724no—
651C4⋊C4—1724no—
652C22⋊C4—868no—
653C22⋊C4—868no—
654C22⋊C4—868no—
655C22⋊C4—868no—
656C22⋊C4—868no—
657C22⋊C4—868no—
658C22⋊C4—868no—
659C22⋊C4—1724no—
660C42—28no—
661C23—4316no—
662C23—434no—
663C23—434no—
664C23—434no—
665C23—434no—
666C23—868no—
667C23—868no—
668C23—868no—
669C23—868no—
670C23—862no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—868no—
675C23—868no—
676C23—868no—
677C23—868no—
678C23—862no—
679C23—862no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—868no—
685C23—1724no—
686C23—1724no—
687C23—1724no—
688C23—1724no—
689C23C2×D4×D4312yes—
690C23#41×D4312yes—
691C23#41×D4312yes—
692C23C2×#1062189812yes—
693C23C2×#1062190212yes—
694C23#1306337112yes—
695C23#1306337212yes—
696C23C24×D4311yescharacteristic
697D4—8632no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—28no—
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—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
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—862no—
740C2×C4—862no—
741C2×C4—17216no—
742C2×C4—17216no—
743C2×C4—17216no—
744C2×C4—17216no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4—1724no—
748C2×C4—1724no—
749C2×C4—1724no—
750C2×C4—1724no—
751C2×C4C2×D4×D4314yes—
752C2×C4C2×#1062189814yes—
753C2×C4C2×#1062190214yes—
754C22—438no—
755C22—864no—
756C22—864no—
757C22—8632no—
758C22—864no—
759C22—864no—
760C22—864no—
761C22—864no—
762C22—864no—
763C22—864no—
764C22—864no—
765C22—17216no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22—1722no—
770C22#123×D4314yes—
771C22#1458343614yes—
772C22#1458349014yes—
773C22#1458354014yes—
774C22#1458355414yes—
775C22#1458357314yes—
776C22#1458358714yes—
777C22C22×D4×D4311yescharacteristic
778C22C2×#41×D4311yescharacteristic
779C22C2×#41×D4311yescharacteristic
780C22C22×#1062189811yescharacteristic
781C22C22×#1062190211yescharacteristic
782C22C2×#1306337111yescharacteristic
783C22C2×#1306337211yescharacteristic
784C4—24no—
785C4—24no—
786C4—24no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—1722no—
792C4—1722no—
793C4—1722no—
794C4—1722no—
795C4—1722no—
796C4—1722no—
797C2—868no—
798C2—1724no—
799C2#1913807918yesdirect product factor
800C2C2×#123×D4311yescharacteristic
801C2C2×#1458343611yescharacteristic
802C2C2×#1458349011yescharacteristic
803C2C2×#1458354011yescharacteristic
804C2C2×#1458355411yescharacteristic
805C2C2×#1458357311yescharacteristic
806C2C2×#1458358711yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×#387D43
hypocenterC43C2×#2419
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #19138079C2direct (N × H)
4. C2×#14582838C2semidirect
5. C2×#14582831C2semidirect
6. C2×#14582826C2semidirect
7. C2×#14582825C2semidirect
8. C2×#14582783C2semidirect
10. C2×#14582773C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582761C2semidirect
13. C2×#14582761C2semidirect
14. C2×#14582756C2semidirect
15. C2×#95×D43C2semidirect
16. C2×C43×#387C2semidirect
39. #14582838C22semidirect
40. #14582831C22semidirect
41. #14582826C22semidirect
42. #14582825C22semidirect
43. #14582783C22semidirect
45. #14582773C22semidirect
46. #14582773C22semidirect
47. #14582761C22semidirect
48. #14582761C22semidirect
49. #14582756C22semidirect
60. #95×D43C22semidirect
64. C43×#387C22semidirect
402. C2×#387D43semidirect
410. C2×C43#2419semidirect
450. #387C2×D43semidirect
472. C43C2×#2419semidirect
799. C2#19138079direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633102
C22×C4×D1722
#191380792
C2×#145828382
C2×#145828312
C2×#145828262
C2×#145828252
C2×#145827832
C2×#145827772
C2×#145827732
C2×#145827612
C2×#145827562
C2×#95×D432
C2×C43×#3872
C2×#241943