Finite Group Databasebeta

← C2×#19137493 #25255880

Subgroups — C2×#19137493 #25255880

Order 11008.

4718 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
3C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
4C23×Dic43⋊C4C211yesmaximal, characteristic, complemented
5C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
6#19137493C2116yesmaximal, direct product factor
7C2×#14582796C211yesmaximal, characteristic, complemented
8C2×#14582794C211yesmaximal, characteristic, complemented
9C2×#14582774C211yesmaximal, characteristic, complemented
10C2×#14582773C211yesmaximal, characteristic, complemented
11C2×#14582770C211yesmaximal, characteristic, complemented
12C2×#14582768C211yesmaximal, characteristic, complemented
13C2×#14582758C211yesmaximal, characteristic, complemented
14C2×#14582757C211yesmaximal, characteristic, complemented
15C2×#14582750C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C2×C4×C22⋊D43—28no—
24C2×C4×C22⋊D43C2218yes—
25C2×(C22⋊D43)⋊C4—28no—
26C2×(C22⋊D43)⋊C4C4116yescomplemented
27C2×(C22⋊D43)⋊C4C2218yes—
28C2×(C22⋊D43)⋊C4C2218yes—
29C22×C4⋊Dic43C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×Dic43⋊C4—28no—
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C22×Dic43⋊C4C2211yescharacteristic
38C22×Dic43⋊C4C2211yescharacteristic
39C22×Dic43⋊C4C2211yescharacteristic
40C22×Dic43⋊C4C2211yescharacteristic
41C22×Dic43⋊C4C2218yescomplemented
42C2×C4⋊C4×D43—28no—
43C2×C4⋊C4×D43C2218yescomplemented
44C22×C22⋊Dic43C2211yescharacteristic
45C22×(C2×D43)⋊C4C2211yescharacteristic
46C22×(C2×D43)⋊C4C2211yescharacteristic
47C22×(C2×D43)⋊C4C2211yescharacteristic
48C22×C4×Dic43C2211yescharacteristic
49C22×C4×Dic43C2211yescharacteristic
50C22×C4×Dic43C2211yescharacteristic
51#14582796C2218yescomplemented
52#14582794C2218yescomplemented
53#14582774C2218yescomplemented
54#14582773C2218yescomplemented
55#14582770C2218yescomplemented
56#14582768C2218yescomplemented
57#14582758C2218yescomplemented
58#14582757C2218yescomplemented
59#14582750C2218yescomplemented
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C2×C43⋊#95C2211yescharacteristic
63C2×C43⋊#95C2211yescharacteristic
64C24×C4×C43C2211yescharacteristic
65C22×C4⋊C4×C43C2211yescharacteristic
66C22×C4⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C22×C22⋊C4×C43C2211yescharacteristic
69C43×#385C2218yescomplemented
70C2×#95×C43C2211yescharacteristic
71C2×#95×C43C2211yescharacteristic
72C24×D43C2311yescharacteristic
73C22×C22⋊D43C2×C418yes—
74C22×C22⋊D43D418yes—
75C22×C22⋊D43Q818yes—
76C22×C22⋊D43C2314yes—
77C23×Dic43—24no—
78C23×Dic43—24no—
79C23×Dic43—24no—
80C23×Dic43—24no—
81C23×Dic43—42no—
82C23×Dic43C2×C418yescomplemented
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2314yes—
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2314yes—
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C23×Dic43C2311yescharacteristic
92C22×C4×D43—24no—
93C22×C4×D43—24no—
94C22×C4×D43—24no—
95C22×C4×D43—24no—
96C22×C4×D43—24no—
97C22×C4×D43—24no—
98C22×C4×D43—42no—
99C22×C4×D43—42no—
100C22×C4×D43C2×C418yescomplemented
101C22×C4×D43C2314yes—
102C22×C4×D43C2314yes—
103C22×C4×D43C2314yes—
104C4×C22⋊D43—232no—
105(C22⋊D43)⋊C4—232no—
106(C22⋊D43)⋊C4C2×C4164yescomplemented
107C2×C4⋊Dic43—24no—
108C2×C4⋊Dic43—42no—
109C2×C4⋊Dic43C2314yes—
110C2×C4⋊Dic43C2314yes—
111C2×Dic43⋊C4—24no—
112C2×Dic43⋊C4—24no—
113C2×Dic43⋊C4—24no—
114C2×Dic43⋊C4—24no—
115C2×Dic43⋊C4—24no—
116C2×Dic43⋊C4—24no—
117C2×Dic43⋊C4—24no—
118C2×Dic43⋊C4—232no—
119C2×Dic43⋊C4C2×C418yescomplemented
120C2×Dic43⋊C4D418yescomplemented
121C2×Dic43⋊C4C2314yes—
122C2×Dic43⋊C4C2314yes—
123C2×Dic43⋊C4C2314yes—
124C2×Dic43⋊C4C2314yes—
125C2×Dic43⋊C4C2314yes—
126C2×Dic43⋊C4C2314yes—
127C2×Dic43⋊C4C2314yes—
128C2×Dic43⋊C4C2314yes—
129C2×Dic43⋊C4C2314yes—
130C4⋊C4×D43—232no—
131C2×C22⋊Dic43—24no—
132C2×C22⋊Dic43C2314yes—
133C2×(C2×D43)⋊C4—24no—
134C2×(C2×D43)⋊C4—24no—
135C2×(C2×D43)⋊C4C2×C418yescomplemented
136C2×(C2×D43)⋊C4C2314yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×(C2×D43)⋊C4C2314yes—
139C2×C4×Dic43—24no—
140C2×C4×Dic43—24no—
141C2×C4×Dic43C2×C418yescomplemented
142C2×C4×Dic43C2314yes—
143C2×C4×Dic43C2314yes—
144C2×C4×Dic43C2314yes—
145C43⋊#95C2314yes—
146C43⋊#95C2314yes—
147C43⋊#95C2314yes—
148C43⋊#95C2314yes—
149C25×C43C2311yescharacteristic
150C23×C4×C43—24no—
151C23×C4×C43—24no—
152C23×C4×C43—42no—
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2314yes—
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43—24no—
161C2×C4⋊C4×C43—42no—
162C2×C4⋊C4×C43C2314yes—
163C2×C4⋊C4×C43C2314yes—
164C2×C22⋊C4×C43—24no—
165C2×C22⋊C4×C43C2×C418yescomplemented
166C2×C22⋊C4×C43C2314yes—
167C2×C22⋊C4×C43C2314yes—
168#95×C43C2314yes—
169#95×C43C2314yes—
170C24×C43—22no—
171C24×C43—22no—
172C24×C43—22no—
173C24×C43—22no—
174C24×C43C22×C414yes—
175C24×C43C2×D414yes—
176C24×C43C2×Q814yes—
177C24×C43C2412yes—
178C24×C43C2411yescharacteristic
179C23×D43—22no—
180C23×D43—22no—
181C23×D43—22no—
182C23×D43—22no—
183C23×D43C22×C414yes—
184C23×D43C2×D414yes—
185C23×D43C2×Q814yes—
186C23×D43C2412yes—
187C22×C4×C43—28no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—28no—
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—44no—
205C22×C4×C43—416no—
206C22×C4×C43C22×C414yes—
207C22×C4×C43C22×C414yes—
208C22×C4×C43C2×D414yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2412yes—
214C22×C4×C43C2412yes—
215C2×C22⋊D43C4⋊C4164yescomplemented
216C2×C22⋊D43C22×C4116yes—
217C2×C22⋊D43C2×D4116yes—
218C2×C22⋊D43C2×Q8116yes—
219C22×Dic43—232no—
220C22×Dic43—28no—
221C22×Dic43—28no—
222C22×Dic43—28no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—28no—
231C22×Dic43—22no—
232C22×Dic43—22no—
233C22×Dic43—22no—
234C22×Dic43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—44no—
238C22×Dic43—416no—
239C22×Dic43C22×C414yes—
240C22×Dic43C22×C414yes—
241C22×Dic43C22×C414yes—
242C22×Dic43C22×C4116yescomplemented
243C22×Dic43C2×D414yes—
244C22×Dic43C2×D414yes—
245C22×Dic43C2×D414yes—
246C22×Dic43C2×Q814yes—
247C22×Dic43#4114yes—
248C22×Dic43C2412yes—
249C22×Dic43C2412yes—
250C22×Dic43C2412yes—
251C22×Dic43C2412yes—
252C22×Dic43C2412yes—
253C22×Dic43C2412yes—
254C22×Dic43C2412yes—
255C2×C4×D43—232no—
256C2×C4×D43—28no—
257C2×C4×D43—28no—
258C2×C4×D43—28no—
259C2×C4×D43—28no—
260C2×C4×D43—28no—
261C2×C4×D43—28no—
262C2×C4×D43—44no—
263C2×C4×D43—44no—
264C2×C4×D43—416no—
265C2×C4×D43—416no—
266C2×C4×D43C22×C4116yescomplemented
267C4⋊C4×C43—28no—
268C4⋊C4×C43—44no—
269C22⋊C4×C43—28no—
270C22⋊C4×C43C22×C4116yescomplemented
271C22⋊Dic43—28no—
272(C2×D43)⋊C4—28no—
273(C2×D43)⋊C4—28no—
274(C2×D43)⋊C4C22×C4116yescomplemented
275C4⋊Dic43—28no—
276C4⋊Dic43—44no—
277Dic43⋊C4—28no—
278Dic43⋊C4—28no—
279Dic43⋊C4—28no—
280Dic43⋊C4—28no—
281Dic43⋊C4—28no—
282Dic43⋊C4—28no—
283Dic43⋊C4—28no—
284Dic43⋊C4C22×C4116yescomplemented
285Dic43⋊C4C2×D4116yescomplemented
286C4×Dic43—28no—
287C4×Dic43—28no—
288C4×Dic43C22×C4116yescomplemented
289C23×C43—28no—
290C23×C43—28no—
291C23×C43—28no—
292C23×C43—28no—
293C23×C43—28no—
294C23×C43—28no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43C2×C4⋊C4116yescomplemented
300C23×C43C23×C414yes—
301C23×C43C23×C412yes—
302C23×C43C22×D414yes—
303C23×C43C22×D412yes—
304C23×C43C22×D412yes—
305C23×C43C22×Q814yes—
306C23×C43C22×Q812yes—
307C23×C43C2×#4112yes—
308C23×C43H(5,𝔽2)12yes—
309C23×C432−1+412yes—
310C23×C43C2511yescharacteristic
311C22×D43—28no—
312C22×D43—28no—
313C22×D43—28no—
314C22×D43—28no—
315C22×D43—28no—
316C22×D43—28no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43C2×C4⋊C4116yescomplemented
322C22×D43C23×C414yes—
323C22×D43C22×D414yes—
324C22×D43C22×Q814yes—
325C2×C4×C43—28no—
326C2×C4×C43—28no—
327C2×C4×C43—28no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—416no—
344C2×C4×C43—44no—
345C2×C4×C43—44no—
346C2×C4×C43—44no—
347C2×C4×C43C23×C414yes—
348C2×C4×C43C23×C414yes—
349C2×C4×C43C22×D414yes—
350C22⋊D43C2×C4⋊C4164yescomplemented
351C2×Dic43—28no—
352C2×Dic43—28no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—232no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—416no—
368C2×Dic43—44no—
369C2×Dic43—44no—
370C2×Dic43—44no—
371C2×Dic43C2×C4⋊C4116yescomplemented
372C2×Dic43C4×D4116yescomplemented
373C2×Dic43C23×C414yes—
374C2×Dic43C23×C414yes—
375C2×Dic43C23×C414yes—
376C2×Dic43C22×D414yes—
377C2×Dic43C22×D414yes—
378C2×Dic43C22×D414yes—
379C2×Dic43C22×Q814yes—
380C2×Dic43C2×#4114yes—
381C4×D43—232no—
382C4×D43—416no—
383C4×D43—416no—
384C2×D4×C4⋊C4—431nomaximal, Sylow
385C22×C43—232no—
386C22×C43—24no—
387C22×C43—24no—
388C22×C43—24no—
389C22×C43—24no—
390C22×C43—24no—
391C22×C43—24no—
392C22×C43C22×C4⋊C414yes—
393C22×C43C22×C4⋊C418yescomplemented
394C22×C43C2×C4×D414yes—
395C22×C43#52014yes—
396C22×C43D4214yes—
397C22×C43#54714yes—
398C22×C43D4×Q814yes—
399C22×C43#55414yes—
400C22×C43C24×C411yescharacteristic
401C22×C43C23×D411yescharacteristic
402C22×C43C23×D411yescharacteristic
403C22×C43C23×Q811yescharacteristic
404C22×C43C22×#4111yescharacteristic
405C22×C43C2×H(5,𝔽2)11yescharacteristic
406C22×C43C2×2−1+411yescharacteristic
407C2×D43—232no—
408C2×D43—24no—
409C2×D43—24no—
410C2×D43—24no—
411C2×D43—24no—
412C2×D43—24no—
413C2×D43—24no—
414C2×D43C22×C4⋊C418yescomplemented
415C4×C43—24no—
416C4×C43—24no—
417C4×C43—24no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43—42no—
421Dic43—24no—
422Dic43—24no—
423Dic43—42no—
424Dic43—42no—
425Dic43—42no—
426Dic43C22×C4⋊C418yescomplemented
427Dic43C2×C4×D418yescomplemented
428C22×C4×D4—431no—
429C22×C4×D4—431no—
430C22×C4×D4—431no—
431C23×C4⋊C4—431no—
432C23×C4⋊C4—431no—
433D4×C4⋊C4—4316no—
434C2×#389—431no—
435C2×#389—431no—
436C2×#385—431no—
437C2×#385—431no—
438C2×#385—431no—
439C2×#385D4311yescharacteristic, complemented
440C2×#384—431no—
441C2×#380—431no—
442C2×#380—431no—
443C2×C4×C4⋊C4—431no—
444C2×C43—28no—
445C2×C43D4×C4⋊C418yescomplemented
446C2×C43C23×C4⋊C411yescharacteristic
447C2×C43C22×C4×D411yescharacteristic
448C2×C43C2×#52011yescharacteristic
449C2×C43C2×D4211yescharacteristic
450C2×C43C2×#54711yescharacteristic
451C2×C43C2×D4×Q811yescharacteristic
452C2×C43C2×#55411yescharacteristic
453D43—28no—
454C23×D4—431no—
455C24×C4—431no—
456C24×C4—431no—
457C24×C4—431no—
458C24×C4—431no—
459C24×C4—431no—
460C24×C4C2×D4311yescharacteristic
461C2×C4×D4—438no—
462C2×C4×D4—438no—
463C2×C4×D4—438no—
464C2×C4×D4—4316no—
465C2×C4×D4—868no—
466C2×C4×D4—868no—
467C22×C4⋊C4—431no—
468C22×C4⋊C4—431no—
469C22×C4⋊C4—438no—
470C22×C4⋊C4—431no—
471C22×C4⋊C4—431no—
472C22×C4⋊C4—431no—
473C22×C4⋊C4—431no—
474C22×C4⋊C4—431no—
475C22×C4⋊C4—431no—
476C22×C4⋊C4—431no—
477C22×C4⋊C4—431no—
478C22×C4⋊C4—431no—
479C22×C4⋊C4—438no—
480C22×C4⋊C4—868no—
481C22×C4⋊C4—868no—
482C22×C4⋊C4C2×D4311yescharacteristic
483C22×C4⋊C4C2×D4311yescharacteristic
484C22×C22⋊C4—431no—
485C22×C22⋊C4—431no—
486C22×C22⋊C4—431no—
487C22×C22⋊C4—431no—
488C22×C22⋊C4C2×D4311yescharacteristic
489C22×C22⋊C4C2×D4311yescharacteristic
490C22×C42—431no—
491C22×C42—431no—
492C22×C42—431no—
493#389—438no—
494#389—438no—
495#385—438no—
496#385—438no—
497#385—438no—
498#385C2×D4318yescomplemented
499#384—438no—
500#380—438no—
501#380—438no—
502C4×C4⋊C4—438no—
503C2×#95—431no—
504C2×#95—431no—
505C2×#95—431no—
506C2×#95—431no—
507C2×#95C2×D4311yescharacteristic
508C2×#95C2×D4311yescharacteristic
509C43C2×D4×C4⋊C411yescharacteristic, complemented, Sylow
510C25—431no—
511C25C22×D4311yescharacteristic
512C22×D4—438no—
513C22×D4—438no—
514C22×D4—438no—
515C22×D4—434no—
516C23×C4—24no—
517C23×C4—24no—
518C23×C4—42no—
519C23×C4—431no—
520C23×C4—431no—
521C23×C4—438no—
522C23×C4—434no—
523C23×C4—431no—
524C23×C4—431no—
525C23×C4—438no—
526C23×C4—434no—
527C23×C4—431no—
528C23×C4—431no—
529C23×C4—431no—
530C23×C4—434no—
531C23×C4—434no—
532C23×C4—434no—
533C23×C4—864no—
534C23×C4—864no—
535C23×C4—864no—
536C23×C4—864no—
537C23×C4—864no—
538C23×C4—864no—
539C23×C4—864no—
540C23×C4—864no—
541C23×C4—864no—
542C23×C4—864no—
543C23×C4—1722no—
544C23×C4—1722no—
545C23×C4—1722no—
546C23×C4C22×D4311yescharacteristic
547C23×C4C22×D4311yescharacteristic
548C23×C4C22×D4311yescharacteristic
549C23×C4C22×D4314yes—
550C23×C4C22×D4311yescharacteristic
551C23×C4C22×D4311yescharacteristic
552C23×C4C22×D4311yescharacteristic
553C4×D4—4364no—
554C4×D4—8632no—
555C4×D4—8632no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—42no—
558C2×C4⋊C4—438no—
559C2×C4⋊C4—438no—
560C2×C4⋊C4—434no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—434no—
563C2×C4⋊C4—434no—
564C2×C4⋊C4—434no—
565C2×C4⋊C4—434no—
566C2×C4⋊C4—434no—
567C2×C4⋊C4—434no—
568C2×C4⋊C4—434no—
569C2×C4⋊C4—434no—
570C2×C4⋊C4—434no—
571C2×C4⋊C4—8632no—
572C2×C4⋊C4—8632no—
573C2×C4⋊C4—864no—
574C2×C4⋊C4—864no—
575C2×C4⋊C4—864no—
576C2×C4⋊C4—864no—
577C2×C4⋊C4—864no—
578C2×C4⋊C4—864no—
579C2×C4⋊C4—864no—
580C2×C4⋊C4—864no—
581C2×C4⋊C4—1722no—
582C2×C4⋊C4C22×D4314yes—
583C2×C4⋊C4C22×D4314yes—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—438no—
586C2×C22⋊C4—434no—
587C2×C22⋊C4—434no—
588C2×C22⋊C4—434no—
589C2×C22⋊C4—434no—
590C2×C22⋊C4—864no—
591C2×C22⋊C4—864no—
592C2×C22⋊C4—864no—
593C2×C22⋊C4C4×D4318yescomplemented
594C2×C22⋊C4C22×D4314yes—
595C2×C22⋊C4C22×D4314yes—
596C2×C42—438no—
597C2×C42—434no—
598C2×C42—434no—
599C2×C42—434no—
600C2×C42—864no—
601C2×C42—864no—
602#95—434no—
603#95—434no—
604#95—434no—
605#95—434no—
606#95C22×D4314yes—
607#95C22×D4314yes—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—434no—
613C24—434no—
614C24—434no—
615C24—432no—
616C24—862no—
617C24—862no—
618C24—862no—
619C24—862no—
620C24C2×C4×D4314yes—
621C24D4×D4314yes—
622C24Q8×D4314yes—
623C24C23×D4312yes—
624C24C23×D4311yescharacteristic
625C2×D4—4364no—
626C2×D4—4316no—
627C2×D4—4316no—
628C2×D4—4316no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—44no—
647C22×C4—416no—
648C22×C4—434no—
649C22×C4—434no—
650C22×C4—434no—
651C22×C4—434no—
652C22×C4—434no—
653C22×C4—434no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—434no—
657C22×C4—4316no—
658C22×C4—434no—
659C22×C4—432no—
660C22×C4—432no—
661C22×C4—4316no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—868no—
666C22×C4—8632no—
667C22×C4—868no—
668C22×C4—868no—
669C22×C4—868no—
670C22×C4—868no—
671C22×C4—868no—
672C22×C4—8632no—
673C22×C4—868no—
674C22×C4—868no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4—862no—
680C22×C4—862no—
681C22×C4—862no—
682C22×C4—862no—
683C22×C4—862no—
684C22×C4—868no—
685C22×C4—862no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—862no—
689C22×C4—868no—
690C22×C4—1724no—
691C22×C4—1724no—
692C22×C4—17216no—
693C22×C4—17216no—
694C22×C4—1724no—
695C22×C4—17216no—
696C22×C4C2×C4×D4314yes—
697C22×C4C2×C4×D4314yes—
698C22×C4D4×D4314yes—
699C22×C4C23×D4312yes—
700C22×C4C23×D4312yes—
701C22×C4C23×D4312yes—
702C22×C4C23×D4312yes—
703C22×C4C23×D4312yes—
704C22×C4C23×D4312yes—
705C4⋊C4—28no—
706C4⋊C4—44no—
707C4⋊C4—4316no—
708C4⋊C4—4316no—
709C4⋊C4—868no—
710C4⋊C4—868no—
711C4⋊C4—868no—
712C4⋊C4—868no—
713C4⋊C4—868no—
714C4⋊C4—868no—
715C4⋊C4—868no—
716C4⋊C4—868no—
717C4⋊C4—1724no—
718C22⋊C4—28no—
719C22⋊C4—4316no—
720C22⋊C4—868no—
721C22⋊C4—868no—
722C22⋊C4—868no—
723C22⋊C4C2×C4×D43116yescomplemented
724C42—4316no—
725C42—868no—
726C42—868no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—28no—
736C23—28no—
737C23—4316no—
738C23—434no—
739C23—434no—
740C23—434no—
741C23—868no—
742C23—868no—
743C23—868no—
744C23—868no—
745C23—862no—
746C23—862no—
747C23—862no—
748C23—862no—
749C23—868no—
750C23—868no—
751C23C4⋊C4×D43116yescomplemented
752C23C22×C4×D4314yes—
753C23C22×C4×D4312yes—
754C23C2×D4×D4314yes—
755C23C2×D4×D4312yes—
756C23C2×D4×D4312yes—
757C23C2×Q8×D4314yes—
758C23C2×Q8×D4312yes—
759C23#41×D4312yes—
760C23#1306337012yes—
761C23#1306337212yes—
762C23C24×D4311yescharacteristic
763D4—4364no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—28no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—4316no—
787C2×C4—4316no—
788C2×C4—434no—
789C2×C4—434no—
790C2×C4—434no—
791C2×C4—434no—
792C2×C4—434no—
793C2×C4—434no—
794C2×C4—434no—
795C2×C4—434no—
796C2×C4—8632no—
797C2×C4—8632no—
798C2×C4—868no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—868no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—17216no—
814C2×C4—17216no—
815C2×C4—17216no—
816C2×C4—1724no—
817C2×C4—1724no—
818C2×C4—1724no—
819C2×C4C22×C4×D4314yes—
820C2×C4C22×C4×D4314yes—
821C2×C4C2×D4×D4314yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—232no—
827C22—24no—
828C22—24no—
829C22—438no—
830C22—864no—
831C22—864no—
832C22—864no—
833C22—864no—
834C22—8632no—
835C22—864no—
836C22—864no—
837C22C2×C4⋊C4×D4314yes—
838C22C2×C4⋊C4×D4318yescomplemented
839C22C4×D4×D4314yes—
840C22#1458337814yes—
841C22#1458353114yes—
842C22#1458354714yes—
843C22#1458356214yes—
844C22#1458360314yes—
845C22C23×C4×D4311yescharacteristic
846C22C22×D4×D4311yescharacteristic
847C22C22×D4×D4311yescharacteristic
848C22C22×Q8×D4311yescharacteristic
849C22C2×#41×D4311yescharacteristic
850C22C2×#1306337011yescharacteristic
851C22C2×#1306337211yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—438no—
859C4—438no—
860C4—864no—
861C4—864no—
862C4—1722no—
863C4—1722no—
864C4—1722no—
865C2—28no—
866C2—868no—
867C2#1913749318yesdirect product factor
868C2C22×C4⋊C4×D4311yescharacteristic
869C2C2×C4×D4×D4311yescharacteristic
870C2C2×#1458337811yescharacteristic
871C2C2×#1458353111yescharacteristic
872C2C2×#1458354711yescharacteristic
873C2C2×#1458356211yescharacteristic
874C2C2×#1458360311yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×D4×C4⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C23×Dic43⋊C4C2semidirect
5. C22×C4⋊C4×D43C2semidirect
6. #19137493C2direct (N × H)
7. C2×#14582796C2semidirect
8. C2×#14582794C2semidirect
9. C2×#14582774C2semidirect
10. C2×#14582773C2semidirect
11. C2×#14582770C2semidirect
12. C2×#14582768C2semidirect
13. C2×#14582758C2semidirect
14. C2×#14582757C2semidirect
15. C2×#14582750C2semidirect
16. C2×C43×#385C2semidirect
26. C2×(C22⋊D43)⋊C4C4semidirect
41. C22×Dic43⋊C4C22semidirect
43. C2×C4⋊C4×D43C22semidirect
51. #14582796C22semidirect
52. #14582794C22semidirect
53. #14582774C22semidirect
54. #14582773C22semidirect
55. #14582770C22semidirect
56. #14582768C22semidirect
57. #14582758C22semidirect
58. #14582757C22semidirect
59. #14582750C22semidirect
69. C43×#385C22semidirect
82. C23×Dic43C2×C4semidirect
100. C22×C4×D43C2×C4semidirect
106. (C22⋊D43)⋊C4C2×C4semidirect
119. C2×Dic43⋊C4C2×C4semidirect
120. C2×Dic43⋊C4D4semidirect
135. C2×(C2×D43)⋊C4C2×C4semidirect
141. C2×C4×Dic43C2×C4semidirect
165. C2×C22⋊C4×C43C2×C4semidirect
215. C2×C22⋊D43C4⋊C4semidirect
242. C22×Dic43C22×C4semidirect
266. C2×C4×D43C22×C4semidirect
270. C22⋊C4×C43C22×C4semidirect
274. (C2×D43)⋊C4C22×C4semidirect
284. Dic43⋊C4C22×C4semidirect
285. Dic43⋊C4C2×D4semidirect
288. C4×Dic43C22×C4semidirect
299. C23×C43C2×C4⋊C4semidirect
321. C22×D43C2×C4⋊C4semidirect
350. C22⋊D43C2×C4⋊C4semidirect
371. C2×Dic43C2×C4⋊C4semidirect
372. C2×Dic43C4×D4semidirect
393. C22×C43C22×C4⋊C4semidirect
414. C2×D43C22×C4⋊C4semidirect
426. Dic43C22×C4⋊C4semidirect
427. Dic43C2×C4×D4semidirect
439. C2×#385D43semidirect
445. C2×C43D4×C4⋊C4semidirect
498. #385C2×D43semidirect
509. C43C2×D4×C4⋊C4semidirect
593. C2×C22⋊C4C4×D43semidirect
723. C22⋊C4C2×C4×D43semidirect
751. C23C4⋊C4×D43semidirect
838. C22C2×C4⋊C4×D43semidirect
867. C2#19137493direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×(C22⋊D43)⋊C42
C23×Dic43⋊C42
C22×C4⋊C4×D432
#191374932
C2×#145827962
C2×#145827942
C2×#145827742
C2×#145827732
C2×#145827702
C2×#145827682
C2×#145827582
C2×#145827572
C2×#145827502
C2×C43×#3852
C2×D4×C4⋊C443