Finite Group Databasebeta

← C2×#19137530 #25255931

Subgroups — C2×#19137530 #25255931

Order 11008.

3374 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×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2#19137530C2116yesmaximal, direct product factor
3C2×#14582792C211yesmaximal, characteristic, complemented
4C2×#14582786C211yesmaximal, characteristic, complemented
5C2×#14582780C211yesmaximal, characteristic, complemented
6C2×#14582775C211yesmaximal, characteristic
7C2×#14582775C211yesmaximal, characteristic
8C2×#14582766C211yesmaximal, characteristic, complemented
9C2×#14582760C211yesmaximal, characteristic, complemented
10C2×#14582756C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
13C2×#14582746C211yesmaximal, characteristic, complemented
14C2×#14582745C211yesmaximal, characteristic, complemented
15C2×#95×D43C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×(C22⋊D43)⋊C4C4116yescomplemented
23C2×(C22⋊D43)⋊C4C2218yes—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582792C2218yescomplemented
36#14582786C2218yescomplemented
37#14582780C2218yescomplemented
38#14582775C2218yes—
39#14582775C2218yes—
40#14582766C2218yescomplemented
41#14582760C2218yescomplemented
42#14582756C2218yescomplemented
43C22⋊C4×Dic43C2218yescomplemented
44C4×(C2×D43)⋊C4C2218yescomplemented
45#14582746C2218yescomplemented
46#14582745C2218yescomplemented
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
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×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#388C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×C22⋊D43—24no—
70C22×C22⋊D43—24no—
71C22×C22⋊D43C2×C418yes—
72C22×C22⋊D43C2314yes—
73C23×Dic43—42no—
74C23×Dic43—42no—
75C23×Dic43C2×C418yescomplemented
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2314yes—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—42no—
89C22×C4×D43—42no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43C2×C418yes—
93C22×C4×D43C2314yes—
94C22×C4×D43C2314yes—
95C22×C4×D43C2314yes—
96(C22⋊D43)⋊C4C2×C4164yescomplemented
97C2×C4⋊Dic43—42no—
98C2×C4⋊Dic43C2314yes—
99C2×Dic43⋊C4C2×C418yescomplemented
100C2×Dic43⋊C4C2314yes—
101C2×C22⋊Dic43—24no—
102C2×C22⋊Dic43—42no—
103C2×C22⋊Dic43C2314yes—
104C2×C22⋊Dic43C2314yes—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4C2×C418yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×C4×Dic43—24no—
112C2×C4×Dic43—42no—
113C2×C4×Dic43—42no—
114C2×C4×Dic43C2×C418yescomplemented
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C2×C4×Dic43C2314yes—
118C2×C4×Dic43C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C25×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—42no—
139C2×C4⋊C4×C43C2314yes—
140C2×C22⋊C4×C43—24no—
141C2×C22⋊C4×C43—42no—
142C2×C22⋊C4×C43C2×C418yescomplemented
143C2×C22⋊C4×C43C2314yes—
144C2×C22⋊C4×C43C2314yes—
145C2×C22⋊C4×C43C2314yes—
146C2×C42×C43—24no—
147C2×C42×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C22×C414yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43C22×C414yes—
164C23×D43#4114yes—
165C23×D43#4114yes—
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×C43C22×C414yes—
183C22×C4×C43C22×C414yes—
184C22×C4×C43#4114yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C2×C22⋊D43—232no—
192C2×C22⋊D43—28no—
193C2×C22⋊D43—28no—
194C2×C22⋊D43C22×C4116yes—
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×Dic43—22no—
212C22×Dic43—416no—
213C22×Dic43—44no—
214C22×Dic43—44no—
215C22×Dic43C22×C414yes—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C4116yescomplemented
219C22×Dic43#4114yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—28no—
228C2×C4×D43—28no—
229C2×C4×D43—28no—
230C2×C4×D43—28no—
231C2×C4×D43—416no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—44no—
235C2×C4×D43—44no—
236C2×C4×D43—416no—
237C2×C4×D43—416no—
238C2×C4×D43C22×C4116yes—
239C4⋊C4×C43—44no—
240C22⋊C4×C43—28no—
241C22⋊C4×C43—44no—
242C22⋊C4×C43C22×C4116yescomplemented
243C42×C43—28no—
244C22⋊Dic43—28no—
245C22⋊Dic43—44no—
246(C2×D43)⋊C4—28no—
247(C2×D43)⋊C4—28no—
248(C2×D43)⋊C4C22×C4116yes—
249C4⋊Dic43—44no—
250Dic43⋊C4C22×C4116yescomplemented
251C4×Dic43—28no—
252C4×Dic43—44no—
253C4×Dic43—44no—
254C4×Dic43C22×C4116yescomplemented
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×C43C23×C414yes—
269C23×C43C23×C412yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43C2×#4112yes—
273C23×C43C2×#4112yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C43H(5,𝔽2)12yes—
276C23×C43C2511yescharacteristic
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—28no—
281C22×D43—28no—
282C22×D43—28no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43#117116yes—
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—44no—
310C2×C4×C43—44no—
311C2×C4×C43—44no—
312C2×C4×C43C23×C414yes—
313C2×C4×C43C23×C414yes—
314C2×C4×C43C2×#4114yes—
315C22⋊D43—232no—
316C2×Dic43—28no—
317C2×Dic43—28no—
318C2×Dic43—28no—
319C2×Dic43—28no—
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—416no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43C23×C414yes—
342C2×Dic43C23×C414yes—
343C2×Dic43C23×C414yes—
344C2×Dic43C2×#4114yes—
345C4×D43—416no—
346C4×D43—416no—
347C4×D43—416no—
348C2×#2353—431nomaximal, Sylow
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—24no—
352C22×C43—416no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43C2×#11714yes—
358C22×C43C4×#4114yes—
359C22×C43#51814yes—
360C22×C43#55114yes—
361C22×C43#55114yes—
362C22×C43#55314yes—
363C22×C43#55314yes—
364C22×C43C24×C411yescharacteristic
365C22×C43C22×#4111yescharacteristic
366C22×C43C22×#4111yescharacteristic
367C22×C43C22×#4111yescharacteristic
368C22×C43C22×#4111yescharacteristic
369C22×C43C2×H(5,𝔽2)11yescharacteristic
370C22×C43C2×H(5,𝔽2)11yescharacteristic
371C2×D43—232no—
372C2×D43—24no—
373C2×D43—24no—
374C2×D43—24no—
375C2×D43—24no—
376C2×D43—24no—
377C2×D43—24no—
378C2×D43C2×#11718yes—
379C4×C43—24no—
380C4×C43—24no—
381C4×C43—24no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385Dic43—24no—
386Dic43—24no—
387Dic43—24no—
388Dic43—24no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392C22×C4×D4—431no—
393#2353—4316no—
394C2×#388—431no—
395C2×#388D4311yescharacteristic, complemented
396C2×#387—431no—
397C2×#387—431no—
398C2×#386—431no—
399C2×#386—431no—
400C2×#383—431no—
401C2×#381—431no—
402C2×#380—431no—
403C2×C4×C22⋊C4—431no—
404C2×C4×C22⋊C4—431no—
405C2×C4×C22⋊C4—431no—
406C2×#376—431no—
407C22×#95—431no—
408C2×C43—44no—
409C2×C43#235318yescomplemented
410C2×C43C22×#11711yescharacteristic
411C2×C43C2×C4×#4111yescharacteristic
412C2×C43C2×#51811yescharacteristic
413C2×C43C2×#55111yescharacteristic
414C2×C43C2×#55111yescharacteristic
415C2×C43C2×#55311yescharacteristic
416C2×C43C2×#55311yescharacteristic
417D43—28no—
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⋊C4C2×D4311yescharacteristic
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4C2×D4311yescharacteristic
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C22×C42—431no—
437C22×C42—431no—
438C22×C42—431no—
439C22×C42—431no—
440C22×C42C2×D4311yescharacteristic
441#388—438no—
442#388C2×D4318yescomplemented
443#387—438no—
444#387—438no—
445#386—438no—
446#386—438no—
447#383—438no—
448#381—438no—
449#380—438no—
450C4×C22⋊C4—438no—
451C4×C22⋊C4—438no—
452C4×C22⋊C4—438no—
453#376—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—431no—
465C2×#95—431no—
466C2×#95—438no—
467C2×#95C2×D4311yescharacteristic
468C2×#95C2×D4311yescharacteristic
469C43C2×#235311yescharacteristic, complemented, Sylow
470C25—431no—
471C25C22×D4311yescharacteristic
472C22×D4—438no—
473C22×D4—434no—
474C22×D4—864no—
475C22×D4—864no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—438no—
481C23×C4—434no—
482C23×C4—438no—
483C23×C4—434no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—434no—
488C23×C4—434no—
489C23×C4—864no—
490C23×C4—864no—
491C23×C4—864no—
492C23×C4—864no—
493C23×C4—1722no—
494C23×C4—1722no—
495C23×C4—1722no—
496C23×C4—1722no—
497C23×C4—1722no—
498C23×C4—1722no—
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—438no—
508C2×C4⋊C4—434no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—1722no—
511C2×C4⋊C4C22×D4314yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—438no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—864no—
523C2×C22⋊C4—1722no—
524C2×C22⋊C4C4×D4318yescomplemented
525C2×C22⋊C4C22×D4314yes—
526C2×C22⋊C4C22×D4314yes—
527C2×C22⋊C4C22×D4314yes—
528C2×C42—24no—
529C2×C42—438no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—864no—
535C2×C42—1722no—
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#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—434no—
560C24—434no—
561C24—432no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24C2×C4×D4314yes—
567C24C23×D4312yes—
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—434no—
589C22×C4—434no—
590C22×C4—434no—
591C22×C4—434no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—4316no—
597C22×C4—4316no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
602C22×C4—868no—
603C22×C4—868no—
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—17216no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—17216no—
628C22×C4—17216no—
629C22×C4—17216no—
630C22×C4—1724no—
631C22×C4—1724no—
632C22×C4C2×C4×D4314yes—
633C22×C4C2×C4×D4314yes—
634C22×C4#1062190014yes—
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4312yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C4⋊C4—44no—
642C4⋊C4—4316no—
643C4⋊C4—1724no—
644C22⋊C4—28no—
645C22⋊C4—44no—
646C22⋊C4—4316no—
647C22⋊C4—868no—
648C22⋊C4—868no—
649C22⋊C4—868no—
650C22⋊C4—1724no—
651C22⋊C4C2×C4×D43116yescomplemented
652C42—28no—
653C42—4316no—
654C42—868no—
655C42—1724no—
656C42—1724no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—4316no—
671C23—434no—
672C23—434no—
673C23—434no—
674C23—868no—
675C23—868no—
676C23—868no—
677C23—868no—
678C23—868no—
679C23—868no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23C22×C4×D4314yes—
685C23C22×C4×D4312yes—
686C23#41×D4312yes—
687C23#41×D4312yes—
688C23#41×D4312yes—
689C23C2×#1062190012yes—
690C23#1306337012yes—
691C23#1306337112yes—
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—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—434no—
716C2×C4—434no—
717C2×C4—434no—
718C2×C4—434no—
719C2×C4—868no—
720C2×C4—868no—
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—862no—
740C2×C4—17216no—
741C2×C4—17216no—
742C2×C4—17216no—
743C2×C4—17216no—
744C2×C4—1724no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4C22×C4×D4314yes—
748C2×C4C22×C4×D4314yes—
749C2×C4C2×#1062190014yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—416no—
758C22—438no—
759C22—864no—
760C22—864no—
761C22—864no—
762C22—864no—
763C22—864no—
764C22—8632no—
765C22—864no—
766C22#117×D4314yes—
767C22C4×#1062190014yes—
768C22#1458337114yes—
769C22#1458357214yes—
770C22#1458357914yes—
771C22#1458359614yes—
772C22#1458360014yes—
773C22C23×C4×D4311yescharacteristic
774C22C2×#41×D4311yescharacteristic
775C22C2×#41×D4311yescharacteristic
776C22C2×#41×D4311yescharacteristic
777C22C22×#1062190011yescharacteristic
778C22C2×#1306337011yescharacteristic
779C22C2×#1306337111yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—864no—
787C4—864no—
788C4—864no—
789C4—864no—
790C4—1722no—
791C4—1722no—
792C4—1722no—
793C2—44no—
794C2—868no—
795C2#1913753018yesdirect product factor
796C2C2×#117×D4311yescharacteristic
797C2C2×C4×#1062190011yescharacteristic
798C2C2×#1458337111yescharacteristic
799C2C2×#1458357211yescharacteristic
800C2C2×#1458357911yescharacteristic
801C2C2×#1458359611yescharacteristic
802C2C2×#1458360011yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2353
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #19137530C2direct (N × H)
3. C2×#14582792C2semidirect
4. C2×#14582786C2semidirect
5. C2×#14582780C2semidirect
8. C2×#14582766C2semidirect
9. C2×#14582760C2semidirect
10. C2×#14582756C2semidirect
11. C2×C22⋊C4×Dic43C2semidirect
12. C2×C4×(C2×D43)⋊C4C2semidirect
13. C2×#14582746C2semidirect
14. C2×#14582745C2semidirect
15. C2×#95×D43C2semidirect
16. C2×C43×#388C2semidirect
22. C2×(C22⋊D43)⋊C4C4semidirect
35. #14582792C22semidirect
36. #14582786C22semidirect
37. #14582780C22semidirect
40. #14582766C22semidirect
41. #14582760C22semidirect
42. #14582756C22semidirect
43. C22⋊C4×Dic43C22semidirect
44. C4×(C2×D43)⋊C4C22semidirect
45. #14582746C22semidirect
46. #14582745C22semidirect
59. #95×D43C22semidirect
65. C43×#388C22semidirect
75. C23×Dic43C2×C4semidirect
96. (C22⋊D43)⋊C4C2×C4semidirect
99. C2×Dic43⋊C4C2×C4semidirect
114. C2×C4×Dic43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
218. C22×Dic43C22×C4semidirect
242. C22⋊C4×C43C22×C4semidirect
250. Dic43⋊C4C22×C4semidirect
254. C4×Dic43C22×C4semidirect
395. C2×#388D43semidirect
409. C2×C43#2353semidirect
442. #388C2×D43semidirect
469. C43C2×#2353semidirect
524. C2×C22⋊C4C4×D43semidirect
651. C22⋊C4C2×C4×D43semidirect
795. C2#19137530direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
#191375302
C2×#145827922
C2×#145827862
C2×#145827802
C2×#145827752
C2×#145827662
C2×#145827602
C2×#145827562
C2×C22⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×#145827452
C2×#95×D432
C2×C43×#3882
C2×#235343