Finite Group Databasebeta

← C2×#19138554 #25264253

Subgroups — C2×#19138554 #25264253

Order 11008.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063316C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3#19138554C2116yesmaximal, direct product factor
4C2×#14582826C211yesmaximal, characteristic, complemented
5C2×#14582821C211yesmaximal, characteristic, complemented
6C2×#14582815C211yesmaximal, characteristic
7C2×#14582815C211yesmaximal, characteristic
8C2×#14582793C211yesmaximal, characteristic, complemented
9C2×#14582787C211yesmaximal, characteristic, complemented
10C2×#14582786C211yesmaximal, characteristic, complemented
11C2×#14582786C211yesmaximal, characteristic, complemented
12C2×#14582785C211yesmaximal, characteristic, complemented
13C2×#14582770C211yesmaximal, characteristic, complemented
14C2×#14582759C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C2×#13063316—28no—
20C2×#13063316C2218yescomplemented
21C2×C4×C22⋊D43—28no—
22C2×C4×C22⋊D43C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
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#14582826C2218yescomplemented
42#14582821C2218yescomplemented
43#14582815C2218yes—
44#14582815C2218yes—
45#14582793C2218yescomplemented
46#14582787C2218yescomplemented
47#14582786C2218yescomplemented
48#14582786C2218yescomplemented
49#14582785C2218yescomplemented
50#14582770C2218yescomplemented
51#14582759C2218yescomplemented
52#14582746C2218yescomplemented
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C24×C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C43×#385C2218yescomplemented
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×C22⋊D43—24no—
71C22×C22⋊D43—24no—
72C22×C22⋊D43—24no—
73C22×C22⋊D43C2314yes—
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C22×C4×D43—24no—
82C22×C4×D43—24no—
83C22×C4×D43—42no—
84C22×C4×D43C2314yes—
85#13063316—232no—
86C4×C22⋊D43—232no—
87C2×C4⋊Dic43—24no—
88C2×C4⋊Dic43—24no—
89C2×C4⋊Dic43—24no—
90C2×C4⋊Dic43—42no—
91C2×C4⋊Dic43C2314yes—
92C2×C4⋊Dic43C2314yes—
93C2×C4⋊Dic43C2314yes—
94C2×C4⋊Dic43C2314yes—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4D418yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×Dic43⋊C4C2314yes—
101C2×C22⋊Dic43—24no—
102C2×C22⋊Dic43—24no—
103C2×C22⋊Dic43—24no—
104C2×C22⋊Dic43C2314yes—
105C2×C22⋊Dic43C2314yes—
106C2×C22⋊Dic43C2314yes—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4—24no—
110C2×(C2×D43)⋊C4—24no—
111C2×(C2×D43)⋊C4—42no—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×C4×Dic43—24no—
118C2×C4×Dic43—24no—
119C2×C4×Dic43—42no—
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×C43—24no—
133C23×C4×C43—24no—
134C23×C4×C43—42no—
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2314yes—
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×C22⋊C4×C43—24no—
147C2×C22⋊C4×C43—42no—
148C2×C22⋊C4×C43C2314yes—
149C2×C22⋊C4×C43C2314yes—
150#95×C43C2314yes—
151#95×C43C2314yes—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43#4114yes—
159C24×C43C2412yes—
160C24×C43C2411yescharacteristic
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43#4114yes—
168C23×D43C2412yes—
169C22×C4×C43—28no—
170C22×C4×C43—28no—
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—44no—
187C22×C4×C43—416no—
188C22×C4×C43C2×D414yes—
189C22×C4×C43#4114yes—
190C22×C4×C43#4114yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C2×C22⋊D43—232no—
198C2×C22⋊D43—28no—
199C2×C22⋊D43—28no—
200C2×C22⋊D43—28no—
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×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43C2×D414yes—
221C22×Dic43C2×D414yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C2×C4×D43—28no—
230C2×C4×D43—28no—
231C2×C4×D43—44no—
232C2×C4×D43—416no—
233C4⋊C4×C43—28no—
234C4⋊C4×C43—28no—
235C22⋊C4×C43—28no—
236C22⋊C4×C43—44no—
237C22⋊Dic43—28no—
238C22⋊Dic43—28no—
239C22⋊Dic43—28no—
240(C2×D43)⋊C4—28no—
241(C2×D43)⋊C4—28no—
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—28no—
244(C2×D43)⋊C4—44no—
245C4⋊Dic43—28no—
246C4⋊Dic43—28no—
247C4⋊Dic43—28no—
248C4⋊Dic43—44no—
249Dic43⋊C4—28no—
250Dic43⋊C4—28no—
251Dic43⋊C4C2×D4116yes—
252C4×Dic43—28no—
253C4×Dic43—28no—
254C4×Dic43—44no—
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—28no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—44no—
268C23×C43C22×D412yes—
269C23×C43C2×#4112yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43C2×#4114yes—
273C23×C43C2×#4112yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C432−1+412yes—
276C23×C43C2511yescharacteristic
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
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—416no—
310C2×C4×C43—44no—
311C2×C4×C43—44no—
312C2×C4×C43—44no—
313C2×C4×C43C22×D414yes—
314C2×C4×C43C2×#4114yes—
315C2×C4×C43C2×#4114yes—
316C22⋊D43—232no—
317C2×Dic43—28no—
318C2×Dic43—28no—
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—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43—44no—
342C2×Dic43—44no—
343C2×Dic43C22×D414yes—
344C2×Dic43C22×D414yes—
345C4×D43—416no—
346C2×#2460—431nomaximal, Sylow
347C22×C43—24no—
348C22×C43—24no—
349C22×C43—24no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—416no—
355C22×C43#52514yes—
356C22×C43#52914yes—
357C22×C43#53914yes—
358C22×C43#54614yes—
359C22×C43#54814yes—
360C22×C43#55214yes—
361C22×C43#55314yes—
362C22×C43C23×D411yescharacteristic
363C22×C43C22×#4111yescharacteristic
364C22×C43C22×#4111yescharacteristic
365C22×C43C22×#4111yescharacteristic
366C22×C43C22×#4111yescharacteristic
367C22×C43C2×H(5,𝔽2)11yescharacteristic
368C22×C43C2×2−1+411yescharacteristic
369C2×D43—24no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—416no—
377C4×C43—24no—
378C4×C43—24no—
379C4×C43—24no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383Dic43—24no—
384Dic43—24no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C22×#125—431no—
391C22×C4×D4—431no—
392#2460—4316no—
393C2×#397—431no—
394C2×#396—431no—
395C2×#394—431no—
396C2×#394—431no—
397C2×#388—431no—
398C2×#388—431no—
399C2×#387—431no—
400C2×#387—431no—
401C2×#387—431no—
402C2×#385—431no—
403C2×#385D4311yescharacteristic, complemented
404C2×#380—431no—
405C2×C4×C22⋊C4—431no—
406C2×C43—44no—
407C2×C43#246018yescomplemented
408C2×C43C2×#52511yescharacteristic
409C2×C43C2×#52911yescharacteristic
410C2×C43C2×#53911yescharacteristic
411C2×C43C2×#54611yescharacteristic
412C2×C43C2×#54811yescharacteristic
413C2×C43C2×#55211yescharacteristic
414C2×C43C2×#55311yescharacteristic
415D43—44no—
416C23×D4—431no—
417C24×C4—431no—
418C24×C4C2×D4311yescharacteristic
419C2×#125—438no—
420C2×#125—868no—
421C2×C4×D4—438no—
422C2×C4×D4—868no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
429C22×C4⋊C4—431no—
430C22×C4⋊C4C2×D4311yescharacteristic
431C22×C4⋊C4C2×D4311yescharacteristic
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×C22⋊C4—431no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4C2×D4311yescharacteristic
441C22×C22⋊C4C2×D4311yescharacteristic
442C22×C42—431no—
443C22×C42—431no—
444C22×C42—431no—
445#397—438no—
446#396—438no—
447#394—438no—
448#394—438no—
449#388—438no—
450#388—438no—
451#387—438no—
452#387—438no—
453#387—438no—
454#385—438no—
455#385C2×D4318yescomplemented
456#380—438no—
457C4×C22⋊C4—438no—
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×#95C2×D4311yescharacteristic
467C2×#95C2×D4311yescharacteristic
468C43C2×#246011yescharacteristic, complemented, Sylow
469C25—431no—
470C25C22×D4311yescharacteristic
471C22×D4—434no—
472C22×D4—864no—
473C22×D4—864no—
474C22×D4—864no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—42no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—434no—
486C23×C4—864no—
487C23×C4—864no—
488C23×C4—1722no—
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C23×C4C22×D4314yes—
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496#125—8632no—
497C4×D4—8632no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—438no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—434no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—434no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4—864no—
509C2×C4⋊C4—864no—
510C2×C4⋊C4—864no—
511C2×C4⋊C4—864no—
512C2×C4⋊C4—864no—
513C2×C4⋊C4—1722no—
514C2×C4⋊C4C22×D4314yes—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
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—864no—
529C2×C22⋊C4—864no—
530C2×C22⋊C4—864no—
531C2×C22⋊C4—864no—
532C2×C22⋊C4—864no—
533C2×C22⋊C4—1722no—
534C2×C22⋊C4C22×D4314yes—
535C2×C22⋊C4C22×D4314yes—
536C2×C42—434no—
537C2×C42—434no—
538C2×C42—434no—
539C2×C42—864no—
540C2×C42—864no—
541C2×C42—1722no—
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#95C22×D4314yes—
551#95C22×D4314yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—434no—
559C24—432no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24#1062190214yes—
567C24C23×D4312yes—
568C24C23×D4311yescharacteristic
569C2×D4—868no—
570C2×D4—868no—
571C2×D4—8632no—
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—28no—
589C22×C4—28no—
590C22×C4—44no—
591C22×C4—416no—
592C22×C4—434no—
593C22×C4—434no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
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—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—868no—
622C22×C4—1724no—
623C22×C4—17216no—
624C22×C4#1062189814yes—
625C22×C4D4×D4314yes—
626C22×C4#1062190014yes—
627C22×C4C23×D4312yes—
628C22×C4C23×D4312yes—
629C22×C4C23×D4312yes—
630C22×C4C23×D4312yes—
631C22×C4C23×D4312yes—
632C22×C4C23×D4312yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—4316no—
636C4⋊C4—868no—
637C4⋊C4—868no—
638C4⋊C4—868no—
639C4⋊C4—868no—
640C4⋊C4—868no—
641C4⋊C4—1724no—
642C22⋊C4—28no—
643C22⋊C4—44no—
644C22⋊C4—868no—
645C22⋊C4—868no—
646C22⋊C4—868no—
647C22⋊C4—868no—
648C22⋊C4—868no—
649C22⋊C4—868no—
650C22⋊C4—868no—
651C22⋊C4—1724no—
652C42—868no—
653C42—868no—
654C42—1724no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—434no—
669C23—868no—
670C23—868no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—868no—
678C23—1724no—
679C23—1724no—
680C23—1724no—
681C23—1724no—
682C23C2×D4×D4312yes—
683C23#41×D4312yes—
684C23C2×#1062190012yes—
685C23C2×#1062189812yes—
686C23C2×#1062190214yes—
687C23C2×#1062190212yes—
688C23#1306337012yes—
689C23#1306337212yes—
690C23C24×D4311yescharacteristic
691D4—8632no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—28no—
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—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—434no—
715C2×C4—434no—
716C2×C4—868no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—868no—
722C2×C4—862no—
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—17216no—
738C2×C4—1724no—
739C2×C4—1724no—
740C2×C4—1724no—
741C2×C4—1724no—
742C2×C4—1724no—
743C2×C4C2×D4×D4314yes—
744C2×C4C2×#1062190014yes—
745C2×C4C2×#1062189814yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—17216no—
762C22#1458341214yes—
763C22#1458343114yes—
764C22#1458349214yes—
765C22#1458353614yes—
766C22#1458355814yes—
767C22#1458359114yes—
768C22#1458359714yes—
769C22C22×D4×D4311yescharacteristic
770C22C2×#41×D4311yescharacteristic
771C22C22×#1062190011yescharacteristic
772C22C22×#1062189811yescharacteristic
773C22C22×#1062190211yescharacteristic
774C22C2×#1306337011yescharacteristic
775C22C2×#1306337211yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—864no—
784C4—1722no—
785C4—1722no—
786C4—1722no—
787C4—1722no—
788C4—1722no—
789C2—44no—
790C2—1724no—
791C2#1913855418yesdirect product factor
792C2C2×#1458341211yescharacteristic
793C2C2×#1458343111yescharacteristic
794C2C2×#1458349211yescharacteristic
795C2C2×#1458353611yescharacteristic
796C2C2×#1458355811yescharacteristic
797C2C2×#1458359111yescharacteristic
798C2C2×#1458359711yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#385D43
hypocenterC43C2×#2460
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13063316C2semidirect
3. #19138554C2direct (N × H)
4. C2×#14582826C2semidirect
5. C2×#14582821C2semidirect
8. C2×#14582793C2semidirect
9. C2×#14582787C2semidirect
10. C2×#14582786C2semidirect
11. C2×#14582786C2semidirect
12. C2×#14582785C2semidirect
13. C2×#14582770C2semidirect
14. C2×#14582759C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#385C2semidirect
20. C2×#13063316C22semidirect
41. #14582826C22semidirect
42. #14582821C22semidirect
45. #14582793C22semidirect
46. #14582787C22semidirect
47. #14582786C22semidirect
48. #14582786C22semidirect
49. #14582785C22semidirect
50. #14582770C22semidirect
51. #14582759C22semidirect
52. #14582746C22semidirect
66. C43×#385C22semidirect
403. C2×#385D43semidirect
407. C2×C43#2460semidirect
455. #385C2×D43semidirect
468. C43C2×#2460semidirect
791. C2#19138554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633162
C22×C4×C22⋊D432
#191385542
C2×#145828262
C2×#145828212
C2×#145828152
C2×#145827932
C2×#145827872
C2×#145827862
C2×#145827852
C2×#145827702
C2×#145827592
C2×#145827462
C2×C43×#3852
C2×#246043