Finite Group Databasebeta

← C2×#19138479 #25264100

Subgroups — C2×#19138479 #25264100

Order 11008.

3894 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic, complemented
2C22×#13063310C211yesmaximal, characteristic, complemented
3C22×C4×D172C211yesmaximal, characteristic, complemented
4C22×#13063287C211yesmaximal, characteristic, complemented
5#19138479C2116yesmaximal, direct product factor
6C2×#14582834C211yesmaximal, characteristic, complemented
7C2×#14582817C211yesmaximal, characteristic, complemented
8C2×#14582816C211yesmaximal, characteristic, complemented
9C2×#14582809C211yesmaximal, characteristic
10C2×#14582796C211yesmaximal, characteristic, complemented
11C2×#14582790C211yesmaximal, characteristic, complemented
12C2×#14582789C211yesmaximal, characteristic, complemented
13C2×#14582773C211yesmaximal, characteristic, complemented
14C2×#14582770C211yesmaximal, characteristic, complemented
15C2×#14582770C211yesmaximal, characteristic, complemented
16C2×C43×#389C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C2×#13063310—28no—
24C2×#13063310—28no—
25C2×#13063310C2218yescomplemented
26C2×#13063310C2218yescomplemented
27C2×C4×D172—28no—
28C2×C4×D172C2218yescomplemented
29C2×#13063287—28no—
30C2×#13063287C2218yescomplemented
31C22×C4⋊Dic43C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44C22×(C2×D43)⋊C4C2211yescharacteristic
45C22×(C2×D43)⋊C4C2211yescharacteristic
46C22×(C2×D43)⋊C4C2211yescharacteristic
47C22×(C2×D43)⋊C4C2211yescharacteristic
48C22×C4×Dic43C2211yescharacteristic
49#14582834C2218yescomplemented
50#14582817C2218yescomplemented
51#14582816C2218yescomplemented
52#14582809C2218yes—
53#14582796C2218yescomplemented
54#14582790C2218yescomplemented
55#14582789C2218yescomplemented
56#14582773C2218yescomplemented
57#14582770C2218yescomplemented
58#14582770C2218yescomplemented
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C2×C43⋊#95C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C4⋊C4×C43C2211yescharacteristic
66C22×C4⋊C4×C43C2211yescharacteristic
67C22×C42×C43C2211yescharacteristic
68C43×#389C2218yescomplemented
69C2×#95×C43C2211yescharacteristic
70C2×#95×C43C2211yescharacteristic
71C24×D43C2311yescharacteristic
72C24×D43C2311yescharacteristic
73C24×D43C2311yescharacteristic
74C22×D172—24no—
75C22×D172—24no—
76C22×D172—24no—
77C22×D172—24no—
78C22×D172—24no—
79C22×D172—24no—
80C22×D172—24no—
81C22×D172—24no—
82C22×D172—42no—
83C22×D172C2314yes—
84C22×D172C2314yes—
85C22×D172C2314yes—
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C22×C4×D43—24no—
92C22×C4×D43—24no—
93C22×C4×D43—24no—
94C22×C4×D43—24no—
95C22×C4×D43—24no—
96C22×C4×D43—24no—
97C22×C4×D43—42no—
98C22×C4×D43—42no—
99C22×C4×D43—42no—
100C22×C4×D43C2314yes—
101C22×C4×D43C2314yes—
102C22×C4×D43C2314yes—
103#13063310—232no—
104#13063310—232no—
105C4×D172—232no—
106#13063287—232no—
107C2×C4⋊Dic43—24no—
108C2×C4⋊Dic43C2314yes—
109C2×Dic43⋊C4—24no—
110C2×Dic43⋊C4—24no—
111C2×Dic43⋊C4—24no—
112C2×Dic43⋊C4—42no—
113C2×Dic43⋊C4C2314yes—
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2314yes—
116C2×Dic43⋊C4C2314yes—
117C2×(C2×D43)⋊C4—24no—
118C2×(C2×D43)⋊C4—24no—
119C2×(C2×D43)⋊C4—24no—
120C2×(C2×D43)⋊C4—24no—
121C2×(C2×D43)⋊C4—24no—
122C2×(C2×D43)⋊C4—24no—
123C2×(C2×D43)⋊C4—24no—
124C2×(C2×D43)⋊C4—24no—
125C2×(C2×D43)⋊C4—24no—
126C2×(C2×D43)⋊C4—42no—
127C2×(C2×D43)⋊C4D418yescomplemented
128C2×(C2×D43)⋊C4D418yescomplemented
129C2×(C2×D43)⋊C4C2314yes—
130C2×(C2×D43)⋊C4C2314yes—
131C2×(C2×D43)⋊C4C2314yes—
132C2×(C2×D43)⋊C4C2314yes—
133C2×(C2×D43)⋊C4C2314yes—
134C2×(C2×D43)⋊C4C2314yes—
135C2×(C2×D43)⋊C4C2314yes—
136C2×(C2×D43)⋊C4C2314yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×(C2×D43)⋊C4C2314yes—
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×C4×Dic43—24no—
142C2×C4×Dic43C2314yes—
143C43⋊#95C2314yes—
144C43⋊#95C2314yes—
145C43⋊#95C2314yes—
146C43⋊#95C2314yes—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—24no—
155C2×C4⋊C4×C43—24no—
156C2×C4⋊C4×C43—24no—
157C2×C4⋊C4×C43—24no—
158C2×C4⋊C4×C43C2314yes—
159C2×C4⋊C4×C43C2314yes—
160C2×C4⋊C4×C43C2314yes—
161C2×C4⋊C4×C43C2314yes—
162C2×C42×C43—24no—
163C2×C42×C43C2314yes—
164#95×C43C2314yes—
165#95×C43C2314yes—
166C24×C43C2411yescharacteristic
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×D43—22no—
176C23×D43—22no—
177C23×D43—22no—
178C23×D43—22no—
179C23×D43—22no—
180C23×D43—22no—
181C23×D43—22no—
182C23×D43—22no—
183C23×D43—22no—
184C23×D43—22no—
185C23×D43C2×D414yes—
186C23×D43C2×D414yes—
187C23×D43#4114yes—
188C23×D43C2412yes—
189C23×D43C2412yes—
190C23×D43C2412yes—
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×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43C2×D414yes—
209C22×C4×C43C2×D414yes—
210C22×C4×C43#4114yes—
211C22×C4×C43#4114yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2412yes—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—22no—
231C22×Dic43—22no—
232C22×Dic43C2×D414yes—
233C22×Dic43C2×D414yes—
234C22×Dic43C2412yes—
235C22×Dic43C2412yes—
236C22×Dic43C2412yes—
237C22×Dic43C2412yes—
238C22×Dic43C2412yes—
239C2×D172—232no—
240C2×D172—232no—
241C2×D172—28no—
242C2×D172—28no—
243C2×D172—28no—
244C2×D172—28no—
245C2×D172—28no—
246C2×D172—28no—
247C2×D172—28no—
248C2×D172—28no—
249C2×D172—44no—
250C2×D172—416no—
251C2×C4×D43—28no—
252C2×C4×D43—28no—
253C2×C4×D43—28no—
254C2×C4×D43—28no—
255C2×C4×D43—28no—
256C2×C4×D43—28no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×C4×D43—44no—
260C2×C4×D43—416no—
261C2×C4×D43—416no—
262C2×C4×D43—416no—
263C4⋊C4×C43—28no—
264C4⋊C4×C43—28no—
265C4⋊C4×C43—28no—
266C4⋊C4×C43—28no—
267C42×C43—28no—
268(C2×D43)⋊C4—28no—
269(C2×D43)⋊C4—28no—
270(C2×D43)⋊C4—28no—
271(C2×D43)⋊C4—28no—
272(C2×D43)⋊C4—28no—
273(C2×D43)⋊C4—28no—
274(C2×D43)⋊C4—28no—
275(C2×D43)⋊C4—28no—
276(C2×D43)⋊C4—28no—
277(C2×D43)⋊C4—44no—
278(C2×D43)⋊C4C2×D4116yescomplemented
279(C2×D43)⋊C4C2×D4116yescomplemented
280C4⋊Dic43—28no—
281Dic43⋊C4—28no—
282Dic43⋊C4—28no—
283Dic43⋊C4—28no—
284Dic43⋊C4—44no—
285C4×Dic43—28no—
286C23×C43C22×D412yes—
287C23×C43C22×D412yes—
288C23×C43C2×#4112yes—
289C23×C43C2×#4112yes—
290C23×C43C2×#4112yes—
291C23×C43H(5,𝔽2)12yes—
292C23×C432−1+412yes—
293C23×C43C2511yescharacteristic
294C22×D43—28no—
295C22×D43—28no—
296C22×D43—28no—
297C22×D43—28no—
298C22×D43—28no—
299C22×D43—28no—
300C22×D43—28no—
301C22×D43—28no—
302C22×D43—28no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—44no—
322C22×D43—44no—
323C22×D43—44no—
324C22×D43—44no—
325C22×D43—44no—
326C22×D43—44no—
327C22×D43—44no—
328C22×D43—44no—
329C22×D43—44no—
330C22×D43—44no—
331C22×D43—44no—
332C22×D43—44no—
333C22×D43C22×D414yes—
334C22×D43C22×D414yes—
335C22×D43C2×#4114yes—
336C2×C4×C43—28no—
337C2×C4×C43—28no—
338C2×C4×C43—28no—
339C2×C4×C43—28no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—44no—
358C2×C4×C43—44no—
359C2×C4×C43—44no—
360C2×C4×C43C22×D414yes—
361C2×C4×C43C22×D414yes—
362C2×C4×C43C2×#4114yes—
363C2×C4×C43C2×#4114yes—
364C2×Dic43—28no—
365C2×Dic43—28no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—22no—
372C2×Dic43—22no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—44no—
380C2×Dic43—44no—
381C2×Dic43—44no—
382C2×Dic43C22×D414yes—
383C2×Dic43C22×D414yes—
384D172—232no—
385D172—232no—
386D172—416no—
387C4×D43—416no—
388C4×D43—416no—
389C4×D43—416no—
390C2×#2455—431nomaximal, Sylow
391C22×C43#52514yes—
392C22×C43#52514yes—
393C22×C43#53914yes—
394C22×C43D4214yes—
395C22×C43#54714yes—
396C22×C43#54714yes—
397C22×C43#55914yes—
398C22×C43C23×D411yescharacteristic
399C22×C43C23×D411yescharacteristic
400C22×C43C22×#4111yescharacteristic
401C22×C43C22×#4111yescharacteristic
402C22×C43C22×#4111yescharacteristic
403C22×C43C2×H(5,𝔽2)11yescharacteristic
404C22×C43C2×2−1+411yescharacteristic
405C2×D43—24no—
406C2×D43—24no—
407C2×D43—24no—
408C2×D43—24no—
409C2×D43—24no—
410C2×D43—24no—
411C2×D43—24no—
412C2×D43—24no—
413C2×D43—24no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—416no—
424C2×D43—416no—
425C2×D43—416no—
426C2×D43—42no—
427C2×D43—42no—
428C2×D43—42no—
429C4×C43—24no—
430C4×C43—24no—
431C4×C43—24no—
432C4×C43—24no—
433C4×C43—42no—
434C4×C43—42no—
435C4×C43—42no—
436Dic43—24no—
437Dic43—24no—
438Dic43—42no—
439Dic43—42no—
440Dic43—42no—
441C22×#123—431no—
442C22×#123—431no—
443C22×C4×D4—431no—
444C22×C4×D4—431no—
445#2455—4316no—
446C2×#399—431no—
447C2×#394—431no—
448C2×#394—431no—
449C2×#392—431no—
450C2×#389—431no—
451C2×#389D4311yescharacteristic, complemented
452C2×#388—431no—
453C2×#388—431no—
454C2×#385—431no—
455C2×#385—431no—
456C2×#385—431no—
457C2×C43#245518yescomplemented
458C2×C43C2×#52511yescharacteristic
459C2×C43C2×#52511yescharacteristic
460C2×C43C2×#53911yescharacteristic
461C2×C43C2×D4211yescharacteristic
462C2×C43C2×#54711yescharacteristic
463C2×C43C2×#54711yescharacteristic
464C2×C43C2×#55911yescharacteristic
465D43—44no—
466D43—44no—
467D43—44no—
468C23×D4—431no—
469C23×D4—431no—
470C23×D4—431no—
471C24×C4—431no—
472C24×C4—431no—
473C24×C4—431no—
474C2×#123—438no—
475C2×#123—438no—
476C2×#123—868no—
477C2×#123—868no—
478C2×C4×D4—438no—
479C2×C4×D4—438no—
480C2×C4×D4—868no—
481C2×C4×D4—868no—
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C4⋊C4—431no—
485C22×C4⋊C4—431no—
486C22×C4⋊C4—431no—
487C22×C4⋊C4C2×D4311yescharacteristic
488C22×C4⋊C4C2×D4311yescharacteristic
489C22×C4⋊C4C2×D4311yescharacteristic
490C22×C4⋊C4C2×D4311yescharacteristic
491C22×C22⋊C4—431no—
492C22×C22⋊C4—431no—
493C22×C22⋊C4—431no—
494C22×C22⋊C4—431no—
495C22×C22⋊C4—431no—
496C22×C22⋊C4—431no—
497C22×C22⋊C4—431no—
498C22×C22⋊C4—431no—
499C22×C22⋊C4—431no—
500C22×C22⋊C4—431no—
501C22×C22⋊C4—431no—
502C22×C22⋊C4—431no—
503C22×C42—431no—
504C22×C42C2×D4311yescharacteristic
505#399—438no—
506#394—438no—
507#394—438no—
508#392—438no—
509#389—438no—
510#389C2×D4318yescomplemented
511#388—438no—
512#388—438no—
513#385—438no—
514#385—438no—
515#385—438no—
516C2×#95—431no—
517C2×#95—431no—
518C2×#95—431no—
519C2×#95—431no—
520C2×#95C2×D4311yescharacteristic
521C2×#95C2×D4311yescharacteristic
522C43C2×#245511yescharacteristic, complemented, Sylow
523C25—431no—
524C25—431no—
525C25—431no—
526C22×D4—434no—
527C22×D4—434no—
528C22×D4—434no—
529C22×D4—864no—
530C22×D4—864no—
531C22×D4—864no—
532C22×D4—864no—
533C22×D4—864no—
534C22×D4—864no—
535C22×D4—864no—
536C22×D4—864no—
537C22×D4—1722no—
538C23×C4—431no—
539C23×C4—431no—
540C23×C4—431no—
541C23×C4—431no—
542C23×C4—431no—
543C23×C4—434no—
544C23×C4—434no—
545C23×C4—434no—
546C23×C4—864no—
547C23×C4—864no—
548C23×C4—864no—
549C23×C4—864no—
550C23×C4—864no—
551C23×C4—864no—
552C23×C4—1722no—
553C23×C4—1722no—
554C23×C4—1722no—
555C23×C4C22×D4311yescharacteristic
556C23×C4C22×D4311yescharacteristic
557C23×C4C22×D4311yescharacteristic
558C23×C4C22×D4311yescharacteristic
559C23×C4C22×D4311yescharacteristic
560C23×C4C22×D4311yescharacteristic
561C23×C4C22×D4311yescharacteristic
562#123—8632no—
563#123—8632no—
564C4×D4—8632no—
565C4×D4—8632no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—24no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4—434no—
571C2×C4⋊C4—434no—
572C2×C4⋊C4—434no—
573C2×C4⋊C4—434no—
574C2×C4⋊C4—434no—
575C2×C4⋊C4—864no—
576C2×C4⋊C4—864no—
577C2×C4⋊C4—864no—
578C2×C4⋊C4—864no—
579C2×C4⋊C4—1722no—
580C2×C4⋊C4C22×D4314yes—
581C2×C4⋊C4C22×D4314yes—
582C2×C4⋊C4C22×D4314yes—
583C2×C4⋊C4C22×D4314yes—
584C2×C22⋊C4—438no—
585C2×C22⋊C4—438no—
586C2×C22⋊C4—434no—
587C2×C22⋊C4—434no—
588C2×C22⋊C4—434no—
589C2×C22⋊C4—434no—
590C2×C22⋊C4—434no—
591C2×C22⋊C4—434no—
592C2×C22⋊C4—434no—
593C2×C22⋊C4—434no—
594C2×C22⋊C4—434no—
595C2×C22⋊C4—434no—
596C2×C22⋊C4—434no—
597C2×C22⋊C4—434no—
598C2×C22⋊C4—864no—
599C2×C22⋊C4—864no—
600C2×C22⋊C4—864no—
601C2×C22⋊C4—864no—
602C2×C22⋊C4—864no—
603C2×C22⋊C4—864no—
604C2×C22⋊C4—864no—
605C2×C22⋊C4—864no—
606C2×C22⋊C4—864no—
607C2×C22⋊C4—1722no—
608C2×C42—24no—
609C2×C42—434no—
610C2×C42—864no—
611C2×C42C22×D4314yes—
612#95—434no—
613#95—434no—
614#95—434no—
615#95—434no—
616#95C22×D4314yes—
617#95C22×D4314yes—
618C24—434no—
619C24—434no—
620C24—434no—
621C24—432no—
622C24—432no—
623C24—432no—
624C24—862no—
625C24—862no—
626C24—862no—
627C24—862no—
628C24—862no—
629C24—862no—
630C24—862no—
631C24—862no—
632C24—862no—
633C24—862no—
634C24—862no—
635C24—862no—
636C24—862no—
637C24—862no—
638C24—862no—
639C24—862no—
640C24—862no—
641C24—862no—
642C24C23×D4311yescharacteristic
643C2×D4—868no—
644C2×D4—868no—
645C2×D4—868no—
646C2×D4—868no—
647C2×D4—8632no—
648C2×D4—8632no—
649C2×D4—868no—
650C2×D4—868no—
651C2×D4—868no—
652C2×D4—868no—
653C2×D4—1724no—
654C2×D4—17216no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—434no—
673C22×C4—434no—
674C22×C4—432no—
675C22×C4—432no—
676C22×C4—432no—
677C22×C4—432no—
678C22×C4—432no—
679C22×C4—868no—
680C22×C4—868no—
681C22×C4—868no—
682C22×C4—868no—
683C22×C4—862no—
684C22×C4—862no—
685C22×C4—862no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—862no—
693C22×C4—862no—
694C22×C4—862no—
695C22×C4—862no—
696C22×C4—868no—
697C22×C4—868no—
698C22×C4—1724no—
699C22×C4—1724no—
700C22×C4—1724no—
701C22×C4—17216no—
702C22×C4—17216no—
703C22×C4—17216no—
704C22×C4#1062189814yes—
705C22×C4D4×D4314yes—
706C22×C4D4×D4314yes—
707C22×C4#1062190214yes—
708C22×C4C23×D4312yes—
709C22×C4C23×D4312yes—
710C22×C4C23×D4312yes—
711C22×C4C23×D4312yes—
712C22×C4C23×D4312yes—
713C22×C4C23×D4312yes—
714C22×C4C23×D4312yes—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—868no—
720C4⋊C4—868no—
721C4⋊C4—868no—
722C4⋊C4—868no—
723C4⋊C4—1724no—
724C22⋊C4—4316no—
725C22⋊C4—4316no—
726C22⋊C4—868no—
727C22⋊C4—868no—
728C22⋊C4—868no—
729C22⋊C4—868no—
730C22⋊C4—868no—
731C22⋊C4—868no—
732C22⋊C4—868no—
733C22⋊C4—868no—
734C22⋊C4—868no—
735C22⋊C4—1724no—
736C42—28no—
737C42—868no—
738C23—434no—
739C23—434no—
740C23—434no—
741C23—868no—
742C23—868no—
743C23—868no—
744C23—868no—
745C23—868no—
746C23—862no—
747C23—862no—
748C23—862no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—862no—
755C23—862no—
756C23—862no—
757C23—862no—
758C23—862no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—862no—
763C23—862no—
764C23—868no—
765C23—868no—
766C23—868no—
767C23—868no—
768C23—1724no—
769C23—1724no—
770C23—1724no—
771C23—1724no—
772C23—1724no—
773C23—1724no—
774C23—1724no—
775C23—1724no—
776C23—1724no—
777C23—1724no—
778C23—1724no—
779C23—1724no—
780C23C2×D4×D4312yes—
781C23C2×D4×D4312yes—
782C23#41×D4312yes—
783C23C2×#1062189812yes—
784C23C2×#1062190212yes—
785C23#1306337112yes—
786C23#1306337312yes—
787C23C24×D4311yescharacteristic
788D4—8632no—
789D4—8632no—
790D4—17216no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—28no—
802C2×C4—28no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—434no—
816C2×C4—434no—
817C2×C4—868no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—868no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—862no—
832C2×C4—17216no—
833C2×C4—17216no—
834C2×C4—17216no—
835C2×C4—1724no—
836C2×C4—1724no—
837C2×C4—1724no—
838C2×C4C2×D4×D4314yes—
839C2×C4C2×D4×D4314yes—
840C2×C4C2×#1062189814yes—
841C2×C4C2×#1062190214yes—
842C22—864no—
843C22—864no—
844C22—864no—
845C22—864no—
846C22—864no—
847C22—864no—
848C22—864no—
849C22—864no—
850C22—864no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1722no—
862C22—1722no—
863C22—17216no—
864C22—17216no—
865C22—17216no—
866C22#1458340814yes—
867C22#1458341214yes—
868C22#1458349714yes—
869C22#1458353314yes—
870C22#1458355014yes—
871C22#1458355214yes—
872C22#1458363414yes—
873C22C22×D4×D4311yescharacteristic
874C22C22×D4×D4311yescharacteristic
875C22C2×#41×D4311yescharacteristic
876C22C22×#1062189811yescharacteristic
877C22C22×#1062190211yescharacteristic
878C22C2×#1306337111yescharacteristic
879C22C2×#1306337311yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—864no—
888C4—864no—
889C4—1722no—
890C4—1722no—
891C4—1722no—
892C2—1724no—
893C2—1724no—
894C2—1724no—
895C2#1913847918yesdirect product factor
896C2C2×#1458340811yescharacteristic
897C2C2×#1458341211yescharacteristic
898C2C2×#1458349711yescharacteristic
899C2C2×#1458353311yescharacteristic
900C2C2×#1458355011yescharacteristic
901C2C2×#1458355211yescharacteristic
902C2C2×#1458363411yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#389C2
socleC24×C43C24
prime radicalC2×#14582809C2
hypercenterC2×#389D43
hypocenterC43C2×#2455
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#13063310C2semidirect
2. C22×#13063310C2semidirect
3. C22×C4×D172C2semidirect
4. C22×#13063287C2semidirect
5. #19138479C2direct (N × H)
6. C2×#14582834C2semidirect
7. C2×#14582817C2semidirect
8. C2×#14582816C2semidirect
10. C2×#14582796C2semidirect
11. C2×#14582790C2semidirect
12. C2×#14582789C2semidirect
13. C2×#14582773C2semidirect
14. C2×#14582770C2semidirect
15. C2×#14582770C2semidirect
16. C2×C43×#389C2semidirect
25. C2×#13063310C22semidirect
26. C2×#13063310C22semidirect
28. C2×C4×D172C22semidirect
30. C2×#13063287C22semidirect
49. #14582834C22semidirect
50. #14582817C22semidirect
51. #14582816C22semidirect
53. #14582796C22semidirect
54. #14582790C22semidirect
55. #14582789C22semidirect
56. #14582773C22semidirect
57. #14582770C22semidirect
58. #14582770C22semidirect
68. C43×#389C22semidirect
127. C2×(C2×D43)⋊C4D4semidirect
128. C2×(C2×D43)⋊C4D4semidirect
278. (C2×D43)⋊C4C2×D4semidirect
279. (C2×D43)⋊C4C2×D4semidirect
451. C2×#389D43semidirect
457. C2×C43#2455semidirect
510. #389C2×D43semidirect
522. C43C2×#2455semidirect
895. C2#19138479direct (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
C22×#130632872
#191384792
C2×#145828342
C2×#145828172
C2×#145828162
C2×#145828092
C2×#145827962
C2×#145827902
C2×#145827892
C2×#145827732
C2×#145827702
C2×C43×#3892
C2×#245543