Finite Group Databasebeta

← C2×#19139937 #25266798

Subgroups — C2×#19139937 #25266798

Order 11008.

3374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#19139937C2116yesmaximal, direct product factor
4C2×#14582832C211yesmaximal, characteristic, complemented
5C2×#14582829C211yesmaximal, characteristic, complemented
6C2×#14582822C211yesmaximal, characteristic, complemented
7C2×#14582785C211yesmaximal, characteristic, complemented
8C2×#14582781C211yesmaximal, characteristic, complemented
9C2×#14582775C211yesmaximal, characteristic
10C2×#14582775C211yesmaximal, characteristic
11C2×#14582774C211yesmaximal, characteristic, complemented
12C2×#14582773C211yesmaximal, characteristic, complemented
13C2×#14582771C211yesmaximal, characteristic, complemented
14C2×#14582770C211yesmaximal, characteristic, complemented
15C2×#14582756C211yesmaximal, characteristic, complemented
16C2×C43×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—28no—
23C2×(C22⋊D43)⋊C4C2218yes—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C2×C4⋊C4×D43—28no—
33C2×C4⋊C4×D43C2218yescomplemented
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C22⋊Dic43C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14582832C2218yescomplemented
41#14582829C2218yescomplemented
42#14582822C2218yescomplemented
43#14582785C2218yescomplemented
44#14582781C2218yescomplemented
45#14582775C2218yes—
46#14582775C2218yes—
47#14582774C2218yescomplemented
48#14582773C2218yescomplemented
49#14582771C2218yescomplemented
50#14582770C2218yescomplemented
51#14582756C2218yescomplemented
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#396C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×C22⋊D43—24no—
71C22×C22⋊D43—24no—
72C22×C22⋊D43Q818yes—
73C22×C22⋊D43C2314yes—
74C23×Dic43—24no—
75C23×Dic43—42no—
76C23×Dic43—42no—
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2314yes—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—42no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43—42no—
93C22×C4×D43D418yes—
94C22×C4×D43C2314yes—
95C22×C4×D43C2314yes—
96C22×C4×D43C2314yes—
97(C22⋊D43)⋊C4—232no—
98C2×C4⋊Dic43—24no—
99C2×C4⋊Dic43—42no—
100C2×C4⋊Dic43—42no—
101C2×C4⋊Dic43C2314yes—
102C2×C4⋊Dic43C2314yes—
103C2×C4⋊Dic43C2314yes—
104C2×Dic43⋊C4—24no—
105C2×Dic43⋊C4—24no—
106C2×Dic43⋊C4—24no—
107C2×Dic43⋊C4—24no—
108C2×Dic43⋊C4—42no—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2314yes—
112C2×Dic43⋊C4C2314yes—
113C2×Dic43⋊C4C2314yes—
114C4⋊C4×D43—232no—
115C2×C22⋊Dic43—24no—
116C2×C22⋊Dic43—42no—
117C2×C22⋊Dic43C2314yes—
118C2×C22⋊Dic43C2314yes—
119C2×(C2×D43)⋊C4—24no—
120C2×(C2×D43)⋊C4—24no—
121C2×(C2×D43)⋊C4—24no—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×C4×Dic43—24no—
126C2×C4×Dic43C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C25×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43—24no—
144C2×C4⋊C4×C43—24no—
145C2×C4⋊C4×C43—42no—
146C2×C4⋊C4×C43C2314yes—
147C2×C4⋊C4×C43C2314yes—
148C2×C4⋊C4×C43C2314yes—
149C2×C22⋊C4×C43—24no—
150C2×C22⋊C4×C43—24no—
151C2×C22⋊C4×C43—42no—
152C2×C22⋊C4×C43C2314yes—
153C2×C22⋊C4×C43C2314yes—
154C2×C22⋊C4×C43C2314yes—
155#95×C43C2314yes—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43C2×Q814yes—
163C24×C43C2412yes—
164C24×C43C2411yescharacteristic
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43C2×D414yes—
170C23×D43C2×Q814yes—
171C23×D43#4114yes—
172C23×D43C2412yes—
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×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43C2×D414yes—
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⋊D43C2×Q8116yes—
201C22×Dic43—28no—
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×Dic43—44no—
221C22×Dic43—44no—
222C22×Dic43—416no—
223C22×Dic43C2×D414yes—
224C22×Dic43C2×Q814yes—
225C22×Dic43#4114yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C2×C4×D43—232no—
234C2×C4×D43—28no—
235C2×C4×D43—28no—
236C2×C4×D43—28no—
237C2×C4×D43—28no—
238C2×C4×D43—416no—
239C2×C4×D43—44no—
240C2×C4×D43—44no—
241C2×C4×D43—44no—
242C2×C4×D43—44no—
243C2×C4×D43—416no—
244C2×C4×D43C2×D4116yes—
245C4⋊C4×C43—28no—
246C4⋊C4×C43—28no—
247C4⋊C4×C43—44no—
248C22⋊C4×C43—28no—
249C22⋊C4×C43—28no—
250C22⋊C4×C43—44no—
251C22⋊Dic43—28no—
252C22⋊Dic43—44no—
253(C2×D43)⋊C4—28no—
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256C4⋊Dic43—28no—
257C4⋊Dic43—44no—
258C4⋊Dic43—44no—
259Dic43⋊C4—28no—
260Dic43⋊C4—28no—
261Dic43⋊C4—28no—
262Dic43⋊C4—28no—
263Dic43⋊C4—44no—
264C4×Dic43—28no—
265C23×C43—28no—
266C23×C43—28no—
267C23×C43—28no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—44no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43C22×D412yes—
279C23×C43C22×Q814yes—
280C23×C43C22×Q812yes—
281C23×C43C2×#4112yes—
282C23×C43C2×#4112yes—
283C23×C43C2×#4112yes—
284C23×C43H(5,𝔽2)12yes—
285C23×C43H(5,𝔽2)12yes—
286C23×C43C2511yescharacteristic
287C22×D43—28no—
288C22×D43—28no—
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—28no—
292C22×D43—28no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43C22⋊Q8116yes—
298C22×D43C22×D414yes—
299C22×D43C22×Q814yes—
300C22×D43C2×#4114yes—
301C2×C4×C43—28no—
302C2×C4×C43—28no—
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—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—44no—
320C2×C4×C43—44no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43C22×D414yes—
324C2×C4×C43C2×#4114yes—
325C22⋊D43—232no—
326C2×Dic43—28no—
327C2×Dic43—28no—
328C2×Dic43—28no—
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—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—416no—
348C2×Dic43—44no—
349C2×Dic43—44no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43C22×D414yes—
353C2×Dic43C22×Q814yes—
354C2×Dic43C2×#4114yes—
355C4×D43—232no—
356C4×D43—416no—
357C4×D43—416no—
358C2×#2579—431nomaximal, Sylow
359C22×C43—24no—
360C22×C43—24no—
361C22×C43—24no—
362C22×C43—416no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43C2×C22⋊Q814yes—
368C22×C43#52514yes—
369C22×C43#53414yes—
370C22×C43#55314yes—
371C22×C43#55314yes—
372C22×C43#55414yes—
373C22×C43#55414yes—
374C22×C43C23×D411yescharacteristic
375C22×C43C23×Q811yescharacteristic
376C22×C43C22×#4111yescharacteristic
377C22×C43C22×#4111yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C2×H(5,𝔽2)11yescharacteristic
380C22×C43C2×H(5,𝔽2)11yescharacteristic
381C2×D43—232no—
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—24no—
386C2×D43—24no—
387C2×D43—24no—
388C2×D43C2×C22⋊Q818yes—
389C4×C43—24no—
390C4×C43—24no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395Dic43—24no—
396Dic43—24no—
397Dic43—24no—
398Dic43—42no—
399Dic43—42no—
400Dic43—42no—
401Dic43—42no—
402C22×C4×D4—431no—
403C23×C4⋊C4—431no—
404#2579—4316no—
405C2×#398—431no—
406C2×#398—431no—
407C2×#396—431no—
408C2×#396D4311yescharacteristic, complemented
409C2×#387—431no—
410C2×#387—431no—
411C2×#386—431no—
412C2×#386—431no—
413C2×#385—431no—
414C2×#385—431no—
415C2×#385—431no—
416C2×#385—431no—
417C2×#380—431no—
418C2×C43—44no—
419C2×C43#257918yescomplemented
420C2×C43C22×C22⋊Q811yescharacteristic
421C2×C43C2×#52511yescharacteristic
422C2×C43C2×#53411yescharacteristic
423C2×C43C2×#55311yescharacteristic
424C2×C43C2×#55311yescharacteristic
425C2×C43C2×#55411yescharacteristic
426C2×C43C2×#55411yescharacteristic
427D43—28no—
428C23×D4—431no—
429C24×C4—431no—
430C24×C4—431no—
431C24×C4—431no—
432C24×C4—431no—
433C2×C4×D4—438no—
434C2×C4×D4—868no—
435C22×C4⋊C4—431no—
436C22×C4⋊C4—431no—
437C22×C4⋊C4—431no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—438no—
444C22×C4⋊C4—868no—
445C22×C4⋊C4C2×D4311yescharacteristic
446C22×C4⋊C4C2×D4311yescharacteristic
447C22×C4⋊C4C2×D4311yescharacteristic
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4C2×D4311yescharacteristic
454C22×C22⋊C4C2×D4311yescharacteristic
455C22×C22⋊C4C2×D4311yescharacteristic
456C22×C42—431no—
457#398—438no—
458#398—438no—
459#396—438no—
460#396C2×D4318yescomplemented
461#387—438no—
462#387—438no—
463#386—438no—
464#386—438no—
465#385—438no—
466#385—438no—
467#385—438no—
468#385—438no—
469#380—438no—
470C2×#95—431no—
471C2×#95—431no—
472C2×#95—431no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95C2×D4311yescharacteristic
480C43C2×#257911yescharacteristic, complemented, Sylow
481C25—431no—
482C25C22×D4311yescharacteristic
483C22×D4—438no—
484C22×D4—434no—
485C22×D4—864no—
486C22×D4—864no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4—438no—
491C23×C4—434no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—434no—
497C23×C4—434no—
498C23×C4—434no—
499C23×C4—864no—
500C23×C4—864no—
501C23×C4—864no—
502C23×C4—864no—
503C23×C4—864no—
504C23×C4—1722no—
505C23×C4—1722no—
506C23×C4—1722no—
507C23×C4—1722no—
508C23×C4—1722no—
509C23×C4—1722no—
510C23×C4C22×D4311yescharacteristic
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C4×D4—8632no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—434no—
528C2×C4⋊C4—8632no—
529C2×C4⋊C4—864no—
530C2×C4⋊C4—864no—
531C2×C4⋊C4—864no—
532C2×C4⋊C4—864no—
533C2×C4⋊C4—864no—
534C2×C4⋊C4—1722no—
535C2×C4⋊C4—1722no—
536C2×C4⋊C4—1722no—
537C2×C4⋊C4C22×D4314yes—
538C2×C4⋊C4C22×D4314yes—
539C2×C4⋊C4C22×D4314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—434no—
547C2×C22⋊C4—434no—
548C2×C22⋊C4—864no—
549C2×C22⋊C4—864no—
550C2×C22⋊C4—864no—
551C2×C22⋊C4—864no—
552C2×C22⋊C4—1722no—
553C2×C22⋊C4C22×D4314yes—
554C2×C22⋊C4C22×D4314yes—
555C2×C22⋊C4C22×D4314yes—
556C2×C42—434no—
557C2×C42—864no—
558#95—434no—
559#95—434no—
560#95—434no—
561#95—434no—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95C22×D4314yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—434no—
575C24—434no—
576C24—434no—
577C24—432no—
578C24—862no—
579C24—862no—
580C24—862no—
581C24—862no—
582C24Q8×D4314yes—
583C24C23×D4312yes—
584C24C23×D4311yescharacteristic
585C2×D4—4316no—
586C2×D4—868no—
587C2×D4—8632no—
588C2×D4—868no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—434no—
606C22×C4—434no—
607C22×C4—434no—
608C22×C4—432no—
609C22×C4—432no—
610C22×C4—432no—
611C22×C4—4316no—
612C22×C4—432no—
613C22×C4—432no—
614C22×C4—432no—
615C22×C4—432no—
616C22×C4—868no—
617C22×C4—868no—
618C22×C4—8632no—
619C22×C4—868no—
620C22×C4—868no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—868no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—17216no—
641C22×C4—1724no—
642C22×C4—1724no—
643C22×C4—1724no—
644C22×C4—1724no—
645C22×C4—17216no—
646C22×C4—1724no—
647C22×C4—1724no—
648C22×C4—17216no—
649C22×C4D4×D4314yes—
650C22×C4#1062190014yes—
651C22×C4C23×D4312yes—
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—44no—
660C4⋊C4—868no—
661C4⋊C4—868no—
662C4⋊C4—868no—
663C4⋊C4—868no—
664C4⋊C4—868no—
665C4⋊C4—1724no—
666C4⋊C4—1724no—
667C4⋊C4—1724no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—44no—
671C22⋊C4—868no—
672C22⋊C4—868no—
673C22⋊C4—868no—
674C22⋊C4—868no—
675C22⋊C4—1724no—
676C42—868no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—4316no—
691C23—434no—
692C23—434no—
693C23—434no—
694C23—868no—
695C23—868no—
696C23—868no—
697C23—868no—
698C23—868no—
699C23—868no—
700C23—862no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23C2×D4×D4312yes—
705C23C2×Q8×D4314yes—
706C23C2×Q8×D4312yes—
707C23#41×D4312yes—
708C23#41×D4312yes—
709C23C2×#1062190012yes—
710C23#1306337012yes—
711C23#1306337112yes—
712C23C24×D4311yescharacteristic
713D4—8632no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—434no—
737C2×C4—434no—
738C2×C4—434no—
739C2×C4—8632no—
740C2×C4—868no—
741C2×C4—868no—
742C2×C4—868no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—17216no—
762C2×C4—17216no—
763C2×C4—17216no—
764C2×C4—1724no—
765C2×C4—1724no—
766C2×C4—1724no—
767C2×C4—1724no—
768C2×C4C2×D4×D4314yes—
769C2×C4C2×#1062190014yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—438no—
779C22—864no—
780C22—864no—
781C22—864no—
782C22—864no—
783C22—864no—
784C22—8632no—
785C22—864no—
786C22C22⋊Q8×D4314yes—
787C22#1458340914yes—
788C22#1458345714yes—
789C22#1458359614yes—
790C22#1458360014yes—
791C22#1458360314yes—
792C22#1458360714yes—
793C22C22×D4×D4311yescharacteristic
794C22C22×Q8×D4311yescharacteristic
795C22C2×#41×D4311yescharacteristic
796C22C2×#41×D4311yescharacteristic
797C22C22×#1062190011yescharacteristic
798C22C2×#1306337011yescharacteristic
799C22C2×#1306337111yescharacteristic
800C4—24no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—864no—
807C4—864no—
808C4—864no—
809C4—1722no—
810C4—1722no—
811C4—1722no—
812C4—1722no—
813C2—44no—
814C2—868no—
815C2#1913993718yesdirect product factor
816C2C2×C22⋊Q8×D4311yescharacteristic
817C2C2×#1458340911yescharacteristic
818C2C2×#1458345711yescharacteristic
819C2C2×#1458359611yescharacteristic
820C2C2×#1458360011yescharacteristic
821C2C2×#1458360311yescharacteristic
822C2C2×#1458360711yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#396C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#396D43
hypocenterC43C2×#2579
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. #19139937C2direct (N × H)
4. C2×#14582832C2semidirect
5. C2×#14582829C2semidirect
6. C2×#14582822C2semidirect
7. C2×#14582785C2semidirect
8. C2×#14582781C2semidirect
11. C2×#14582774C2semidirect
12. C2×#14582773C2semidirect
13. C2×#14582771C2semidirect
14. C2×#14582770C2semidirect
15. C2×#14582756C2semidirect
16. C2×C43×#396C2semidirect
33. C2×C4⋊C4×D43C22semidirect
40. #14582832C22semidirect
41. #14582829C22semidirect
42. #14582822C22semidirect
43. #14582785C22semidirect
44. #14582781C22semidirect
47. #14582774C22semidirect
48. #14582773C22semidirect
49. #14582771C22semidirect
50. #14582770C22semidirect
51. #14582756C22semidirect
67. C43×#396C22semidirect
408. C2×#396D43semidirect
419. C2×C43#2579semidirect
460. #396C2×D43semidirect
480. C43C2×#2579semidirect
815. C2#19139937direct (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
C22×C4⋊C4×D432
#191399372
C2×#145828322
C2×#145828292
C2×#145828222
C2×#145827852
C2×#145827812
C2×#145827752
C2×#145827742
C2×#145827732
C2×#145827712
C2×#145827702
C2×#145827562
C2×C43×#3962
C2×#257943