Finite Group Databasebeta

← C2×#19137442 #25255809

Subgroups — C2×#19137442 #25255809

Order 11008.

4990 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic, complemented
2C23×(C2×D43)⋊C4C211yesmaximal, characteristic
3C22×C22⋊C4×D43C211yesmaximal, characteristic
4#19137442C2116yesmaximal, direct product factor
5C2×#14582791C211yesmaximal, characteristic, complemented
6C2×#14582791C211yesmaximal, characteristic, complemented
7C2×#14582789C211yesmaximal, characteristic, complemented
8C2×#14582789C211yesmaximal, characteristic, complemented
9C2×#14582774C211yesmaximal, characteristic, complemented
10C2×#14582761C211yesmaximal, characteristic, complemented
11C2×#14582756C211yesmaximal, characteristic, complemented
12C2×#14582754C211yesmaximal, characteristic
13C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C25×D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063283—28no—
22C2×#13063283C2218yescomplemented
23C22×C4⋊Dic43C2211yescharacteristic, complemented
24C22×C4⋊Dic43C2211yescharacteristic, complemented
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4—28no—
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2218yes—
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C2×C22⋊C4×D43C4116yescomplemented
40C2×C22⋊C4×D43C2218yes—
41C22×C4×Dic43C2211yescharacteristic, complemented
42C22×C4×Dic43C2211yescharacteristic, complemented
43C22×C4×Dic43C2211yescharacteristic, complemented
44C22×C4×Dic43C2211yescharacteristic, complemented
45#14582791C2218yescomplemented
46#14582791C2218yescomplemented
47#14582789C2218yescomplemented
48#14582789C2218yescomplemented
49#14582774C2218yescomplemented
50#14582761C2218yescomplemented
51#14582756C2218yescomplemented
52#14582754C2218yes—
53C22⋊C4×Dic43C2218yescomplemented
54C4×C22⋊Dic43C2218yescomplemented
55#14582746C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic, complemented
57C2×C43⋊#95C2211yescharacteristic, complemented
58C2×C43⋊#95C2211yescharacteristic, complemented
59C2×C43⋊#95C2211yescharacteristic, complemented
60C2×C43⋊#95C2211yescharacteristic, complemented
61C2×C43⋊#95C2211yescharacteristic, complemented
62C24×C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic, complemented
64C22×C4⋊C4×C43C2211yescharacteristic, complemented
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C43×#385C2218yescomplemented
68C2×#95×C43C2211yescharacteristic, complemented
69C2×#95×C43C2211yescharacteristic, complemented
70C24×D43—24no—
71C24×D43—24no—
72C24×D43—24no—
73C24×D43—24no—
74C24×D43—42no—
75C24×D43—42no—
76C24×D43C2×C418yes—
77C24×D43C2311yescharacteristic
78C24×D43C2314yes—
79C24×D43C2311yescharacteristic
80C23×Dic43—24no—
81C23×Dic43—24no—
82C23×Dic43—42no—
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2314yes—
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—42no—
93C22×C4×D43—42no—
94C22×C4×D43C2×C418yescomplemented
95C22×C4×D43C2×C418yescomplemented
96C22×C4×D43C2314yes—
97C22×C4×D43C2314yes—
98#13063283—232no—
99C2×C4⋊Dic43—24no—
100C2×C4⋊Dic43—42no—
101C2×C4⋊Dic43C2314yescomplemented
102C2×C4⋊Dic43C2314yescomplemented
103C2×C22⋊Dic43—24no—
104C2×C22⋊Dic43C2×C418yes—
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—24no—
112C2×(C2×D43)⋊C4—232no—
113C2×(C2×D43)⋊C4—42no—
114C2×(C2×D43)⋊C4—42no—
115C2×(C2×D43)⋊C4C2×C418yescomplemented
116C2×(C2×D43)⋊C4C2×C418yescomplemented
117C2×(C2×D43)⋊C4D418yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×(C2×D43)⋊C4C2314yes—
128C22⋊C4×D43C2×C4164yescomplemented
129C2×C4×Dic43—24no—
130C2×C4×Dic43—24no—
131C2×C4×Dic43—42no—
132C2×C4×Dic43—42no—
133C2×C4×Dic43C2314yescomplemented
134C2×C4×Dic43C2314yescomplemented
135C2×C4×Dic43C2314yescomplemented
136C2×C4×Dic43C2314yescomplemented
137C43⋊#95C2314yescomplemented
138C43⋊#95C2314yescomplemented
139C43⋊#95C2314yescomplemented
140C43⋊#95C2314yescomplemented
141C43⋊#95C2314yescomplemented
142C43⋊#95C2314yescomplemented
143C25×C43C2311yescharacteristic
144C23×C4×C43—24no—
145C23×C4×C43—24no—
146C23×C4×C43—42no—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2314yes—
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—24no—
155C2×C4⋊C4×C43—42no—
156C2×C4⋊C4×C43C2314yescomplemented
157C2×C4⋊C4×C43C2314yescomplemented
158C2×C22⋊C4×C43—24no—
159C2×C22⋊C4×C43C2×C418yes—
160C2×C22⋊C4×C43C2314yes—
161C2×C22⋊C4×C43C2314yes—
162#95×C43C2314yescomplemented
163#95×C43C2314yescomplemented
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—22no—
167C24×C43—22no—
168C24×C43C22×C414yes—
169C24×C43#4114yes—
170C24×C43#4114yes—
171C24×C43C2412yes—
172C24×C43C2411yescharacteristic
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—22no—
176C23×D43—22no—
177C23×D43—232no—
178C23×D43—22no—
179C23×D43—28no—
180C23×D43—28no—
181C23×D43—22no—
182C23×D43—22no—
183C23×D43—22no—
184C23×D43—22no—
185C23×D43—22no—
186C23×D43—232no—
187C23×D43—28no—
188C23×D43—28no—
189C23×D43—416no—
190C23×D43—44no—
191C23×D43—44no—
192C23×D43—416no—
193C23×D43—416no—
194C23×D43—416no—
195C23×D43—416no—
196C23×D43C22×C414yes—
197C23×D43C22×C4116yes—
198C23×D43C22×C414yes—
199C23×D43C2×D414yes—
200C23×D43#4114yes—
201C23×D43C2412yes—
202C23×D43C2412yes—
203C22×C4×C43—28no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—28no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—44no—
221C22×C4×C43—416no—
222C22×C4×C43C22×C414yes—
223C22×C4×C43C22×C414yes—
224C22×C4×C43C2×D414yes—
225C22×C4×C43C2412yes—
226C22×C4×C43C2412yes—
227C22×C4×C43C2412yes—
228C22×C4×C43C2412yes—
229C22×C4×C43C2412yes—
230C22×C4×C43C2412yes—
231C22×Dic43—28no—
232C22×Dic43—22no—
233C22×Dic43—22no—
234C22×Dic43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—22no—
239C22×Dic43—22no—
240C22×Dic43—28no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—22no—
244C22×Dic43—22no—
245C22×Dic43—22no—
246C22×Dic43—22no—
247C22×Dic43—22no—
248C22×Dic43—44no—
249C22×Dic43—416no—
250C22×Dic43C22×C414yes—
251C22×Dic43C22×C414yes—
252C22×Dic43C2×D414yes—
253C22×Dic43C2412yes—
254C22×Dic43C2412yes—
255C22×Dic43C2412yes—
256C22×Dic43C2412yes—
257C22×Dic43C2412yes—
258C22×Dic43C2412yes—
259C2×C4×D43—232no—
260C2×C4×D43—28no—
261C2×C4×D43—28no—
262C2×C4×D43—416no—
263C2×C4×D43—44no—
264C2×C4×D43—44no—
265C2×C4×D43C22×C4116yescomplemented
266C2×C4×D43C22×C4116yescomplemented
267C4⋊C4×C43—28no—
268C4⋊C4×C43—44no—
269C22⋊C4×C43—28no—
270C22⋊C4×C43C22×C4116yes—
271C22⋊Dic43—28no—
272C22⋊Dic43C22×C4116yes—
273(C2×D43)⋊C4—28no—
274(C2×D43)⋊C4—28no—
275(C2×D43)⋊C4—28no—
276(C2×D43)⋊C4—28no—
277(C2×D43)⋊C4—28no—
278(C2×D43)⋊C4—44no—
279(C2×D43)⋊C4—44no—
280(C2×D43)⋊C4C22×C4116yescomplemented
281(C2×D43)⋊C4C22×C4116yescomplemented
282(C2×D43)⋊C4C2×D4116yes—
283C4⋊Dic43—28no—
284C4⋊Dic43—44no—
285C4×Dic43—28no—
286C4×Dic43—28no—
287C4×Dic43—44no—
288C4×Dic43—44no—
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×C43#117116yescomplemented
300C23×C43C23×C414yes—
301C23×C43C23×C412yes—
302C23×C43C22×D412yes—
303C23×C43C2×#4112yes—
304C23×C43C2×#4114yes—
305C23×C43C2×#4112yes—
306C23×C43C2×#4114yes—
307C23×C43C2×#4112yes—
308C23×C43H(5,𝔽2)12yes—
309C23×C43H(5,𝔽2)12yes—
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×D43—28no—
322C22×D43—232no—
323C22×D43—28no—
324C22×D43—28no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—232no—
332C22×D43—416no—
333C22×D43—4128no—
334C22×D43—416no—
335C22×D43—416no—
336C22×D43—416no—
337C22×D43—416no—
338C22×D43—44no—
339C22×D43—44no—
340C22×D43—44no—
341C22×D43—44no—
342C22×D43C4×D4116yes—
343C22×D43C23×C414yes—
344C22×D43C23×C414yes—
345C22×D43C22×D414yes—
346C22×D43C2×#4114yes—
347C2×C4×C43—28no—
348C2×C4×C43—28no—
349C2×C4×C43—28no—
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—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—416no—
366C2×C4×C43—44no—
367C2×C4×C43—44no—
368C2×C4×C43—44no—
369C2×C4×C43C23×C414yes—
370C2×C4×C43C23×C414yes—
371C2×C4×C43C22×D414yes—
372C2×Dic43—28no—
373C2×Dic43—28no—
374C2×Dic43—28no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—416no—
391C2×Dic43—44no—
392C2×Dic43—44no—
393C2×Dic43—44no—
394C2×Dic43C23×C414yes—
395C2×Dic43C23×C414yes—
396C2×Dic43C22×D414yes—
397C4×D43—232no—
398C4×D43—416no—
399C2×#2342—431nomaximal, Sylow
400C22×C43—232no—
401C22×C43—24no—
402C22×C43—24no—
403C22×C43—24no—
404C22×C43—24no—
405C22×C43—24no—
406C22×C43—24no—
407C22×C43C2×#11714yes—
408C22×C43C2×#11718yescomplemented
409C22×C43C2×C4×D414yes—
410C22×C43#51814yes—
411C22×C43#54614yes—
412C22×C43#54614yes—
413C22×C43#55114yes—
414C22×C43#55114yes—
415C22×C43C24×C411yescharacteristic
416C22×C43C23×D411yescharacteristic
417C22×C43C22×#4111yescharacteristic
418C22×C43C22×#4111yescharacteristic
419C22×C43C22×#4111yescharacteristic
420C22×C43C2×H(5,𝔽2)11yescharacteristic
421C22×C43C2×H(5,𝔽2)11yescharacteristic
422C2×D43—232no—
423C2×D43—24no—
424C2×D43—24no—
425C2×D43—24no—
426C2×D43—24no—
427C2×D43—24no—
428C2×D43—24no—
429C2×D43—24no—
430C2×D43—24no—
431C2×D43—24no—
432C2×D43—464no—
433C2×D43—416no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43C2×C4×D418yes—
439C4×C43—24no—
440C4×C43—24no—
441C4×C43—24no—
442C4×C43—42no—
443C4×C43—42no—
444C4×C43—42no—
445Dic43—24no—
446Dic43—24no—
447Dic43—24no—
448Dic43—42no—
449Dic43—42no—
450Dic43—42no—
451C22×#117—431no—
452C23×C22⋊C4—431no—
453C23×C22⋊C4—431no—
454#2342—4316no—
455C2×#388—431no—
456C2×#388—431no—
457C2×#388—431no—
458C2×#388—431no—
459C2×#385—431no—
460C2×#385D4311yescharacteristic, complemented
461C2×#381—431no—
462C2×#380—431no—
463C2×#379—431no—
464C2×C4×C22⋊C4—431no—
465C2×C4×C22⋊C4—431no—
466C2×C4×C22⋊C4—431no—
467C2×C43—28no—
468C2×C43#234218yescomplemented
469C2×C43C22×#11711yescharacteristic
470C2×C43C22×C4×D411yescharacteristic
471C2×C43C2×#51811yescharacteristic
472C2×C43C2×#54611yescharacteristic
473C2×C43C2×#54611yescharacteristic
474C2×C43C2×#55111yescharacteristic
475C2×C43C2×#55111yescharacteristic
476D43—28no—
477D43—44no—
478C26—431no—
479C24×C4—431no—
480C24×C4—431no—
481C24×C4—431no—
482C24×C4C2×D4311yescharacteristic
483C2×#117—438no—
484C2×#117—868no—
485C22×C4⋊C4—431no—
486C22×C4⋊C4—431no—
487C22×C4⋊C4C2×D4311yescharacteristic, complemented
488C22×C4⋊C4C2×D4311yescharacteristic, complemented
489C22×C22⋊C4—431no—
490C22×C22⋊C4—431no—
491C22×C22⋊C4—431no—
492C22×C22⋊C4—431no—
493C22×C22⋊C4—438no—
494C22×C22⋊C4—4316no—
495C22×C22⋊C4—431no—
496C22×C22⋊C4—438no—
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×C22⋊C4—431no—
504C22×C22⋊C4—868no—
505C22×C22⋊C4C2×D4311yescharacteristic
506C22×C22⋊C4C2×D4311yescharacteristic
507C22×C42—431no—
508C22×C42—431no—
509C22×C42—431no—
510C22×C42—431no—
511#388—438no—
512#388—438no—
513#388—438no—
514#388—438no—
515#385—438no—
516#385C2×D4318yescomplemented
517#381—438no—
518#380—438no—
519#379—438no—
520C4×C22⋊C4—438no—
521C4×C22⋊C4—438no—
522C4×C22⋊C4—438no—
523C2×#95—431no—
524C2×#95—431no—
525C2×#95—431no—
526C2×#95—431no—
527C2×#95—431no—
528C2×#95—431no—
529C2×#95C2×D4311yescharacteristic, complemented
530C2×#95C2×D4311yescharacteristic, complemented
531C43C2×#234211yescharacteristic, complemented, Sylow
532C25—431no—
533C25—431no—
534C25—438no—
535C25—434no—
536C25—864no—
537C25—864no—
538C25—864no—
539C25—864no—
540C25—1722no—
541C25—1722no—
542C25C22×D4311yescharacteristic
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—42no—
546C23×C4—431no—
547C23×C4—431no—
548C23×C4—431no—
549C23×C4—438no—
550C23×C4—434no—
551C23×C4—438no—
552C23×C4—434no—
553C23×C4—431no—
554C23×C4—431no—
555C23×C4—431no—
556C23×C4—434no—
557C23×C4—864no—
558C23×C4—864no—
559C23×C4—864no—
560C23×C4—864no—
561C23×C4—1722no—
562C23×C4—1722no—
563C23×C4—1722no—
564C23×C4C22×D4311yescharacteristic
565C23×C4C22×D4311yescharacteristic
566C23×C4C22×D4311yescharacteristic
567C23×C4C22×D4314yes—
568C23×C4C22×D4311yescharacteristic
569C23×C4C22×D4311yescharacteristic
570C23×C4C22×D4311yescharacteristic
571#117—8632no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—42no—
574C2×C4⋊C4—434no—
575C2×C4⋊C4—434no—
576C2×C4⋊C4—864no—
577C2×C4⋊C4—1722no—
578C2×C4⋊C4C22×D4314yescomplemented
579C2×C4⋊C4C22×D4314yescomplemented
580C2×C22⋊C4—24no—
581C2×C22⋊C4—438no—
582C2×C22⋊C4—434no—
583C2×C22⋊C4—438no—
584C2×C22⋊C4—438no—
585C2×C22⋊C4—438no—
586C2×C22⋊C4—434no—
587C2×C22⋊C4—434no—
588C2×C22⋊C4—434no—
589C2×C22⋊C4—4364no—
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—8632no—
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—1722no—
606C2×C22⋊C4—1722no—
607C2×C22⋊C4C4×D4318yes—
608C2×C22⋊C4C22×D4314yes—
609C2×C22⋊C4C22×D4314yes—
610C2×C42—434no—
611C2×C42—434no—
612C2×C42—434no—
613C2×C42—434no—
614C2×C42—864no—
615C2×C42—864no—
616C2×C42—1722no—
617C2×C42—1722no—
618#95—434no—
619#95—434no—
620#95—434no—
621#95—434no—
622#95—434no—
623#95—434no—
624#95C22×D4314yescomplemented
625#95C22×D4314yescomplemented
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—434no—
631C24—434no—
632C24—434no—
633C24—432no—
634C24—434no—
635C24—432no—
636C24—4316no—
637C24—868no—
638C24—8632no—
639C24—868no—
640C24—862no—
641C24—862no—
642C24—862no—
643C24—862no—
644C24—8632no—
645C24—862no—
646C24—862no—
647C24—868no—
648C24—862no—
649C24—868no—
650C24—862no—
651C24—862no—
652C24—862no—
653C24—17216no—
654C24—1724no—
655C24—1724no—
656C24—17216no—
657C24—17216no—
658C24—17216no—
659C24—17216no—
660C24C2×C4×D4314yes—
661C24#1062190014yes—
662C24#1062190214yes—
663C24C23×D4312yes—
664C24C23×D4311yescharacteristic
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—28no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—28no—
682C22×C4—44no—
683C22×C4—416no—
684C22×C4—434no—
685C22×C4—434no—
686C22×C4—434no—
687C22×C4—432no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—4316no—
691C22×C4—4316no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—432no—
695C22×C4—868no—
696C22×C4—8632no—
697C22×C4—868no—
698C22×C4—868no—
699C22×C4—862no—
700C22×C4—862no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—862no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—868no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—862no—
715C22×C4—17216no—
716C22×C4—1724no—
717C22×C4—1724no—
718C22×C4—1724no—
719C22×C4—17216no—
720C22×C4C2×C4×D4314yes—
721C22×C4C2×C4×D4314yes—
722C22×C4D4×D4314yes—
723C22×C4C23×D4312yes—
724C22×C4C23×D4312yes—
725C22×C4C23×D4312yes—
726C22×C4C23×D4312yes—
727C22×C4C23×D4312yes—
728C22×C4C23×D4312yes—
729C4⋊C4—28no—
730C4⋊C4—44no—
731C4⋊C4—868no—
732C4⋊C4—1724no—
733C22⋊C4—28no—
734C22⋊C4—4316no—
735C22⋊C4—4316no—
736C22⋊C4—4316no—
737C22⋊C4—4316no—
738C22⋊C4—868no—
739C22⋊C4—868no—
740C22⋊C4—868no—
741C22⋊C4—868no—
742C22⋊C4—868no—
743C22⋊C4—868no—
744C22⋊C4—1724no—
745C22⋊C4—1724no—
746C22⋊C4C2×C4×D43116yes—
747C42—868no—
748C42—868no—
749C42—1724no—
750C42—1724no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—28no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—28no—
760C23—28no—
761C23—4316no—
762C23—434no—
763C23—434no—
764C23—434no—
765C23—434no—
766C23—8632no—
767C23—868no—
768C23—868no—
769C23—868no—
770C23—868no—
771C23—862no—
772C23—862no—
773C23—862no—
774C23—862no—
775C23—868no—
776C23—868no—
777C23—868no—
778C23—8632no—
779C23—868no—
780C23—868no—
781C23—862no—
782C23—862no—
783C23—862no—
784C23—862no—
785C23—862no—
786C23—862no—
787C23—17216no—
788C23—17216no—
789C23—17216no—
790C23—17216no—
791C23—17216no—
792C23—172128no—
793C23—1724no—
794C23—1724no—
795C23—1724no—
796C23—1724no—
797C23#13063283116yescomplemented
798C23C22×C4×D4314yes—
799C23C22×C4×D4312yes—
800C23C2×D4×D4312yes—
801C23#41×D4312yes—
802C23C2×#1062190014yes—
803C23C2×#1062190012yes—
804C23C2×#1062190214yes—
805C23C2×#1062190212yes—
806C23#1306337012yes—
807C23#1306337112yes—
808C23C24×D4311yescharacteristic
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—416no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—434no—
832C2×C4—434no—
833C2×C4—434no—
834C2×C4—8632no—
835C2×C4—868no—
836C2×C4—868no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—862no—
843C2×C4—868no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—17216no—
854C2×C4—17216no—
855C2×C4—1724no—
856C2×C4—1724no—
857C2×C4—1724no—
858C2×C4C22×C4×D4314yes—
859C2×C4C22×C4×D4314yes—
860C2×C4C2×D4×D4314yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—232no—
867C22—24no—
868C22—438no—
869C22—864no—
870C22—864no—
871C22—864no—
872C22—864no—
873C22—864no—
874C22—8632no—
875C22—864no—
876C22—864no—
877C22—864no—
878C22—864no—
879C22—17264no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—17216no—
885C22C2×#1306328314yes—
886C22C2×#1306328318yescomplemented
887C22C4×D4×D4314yes—
888C22#1458337114yes—
889C22#1458353614yes—
890C22#1458354014yes—
891C22#1458357214yes—
892C22#1458357614yes—
893C22C23×C4×D4311yescharacteristic
894C22C22×D4×D4311yescharacteristic
895C22C2×#41×D4311yescharacteristic
896C22C22×#1062190011yescharacteristic
897C22C22×#1062190211yescharacteristic
898C22C2×#1306337011yescharacteristic
899C22C2×#1306337111yescharacteristic
900C4—24no—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—864no—
907C4—864no—
908C4—864no—
909C4—1722no—
910C4—1722no—
911C4—1722no—
912C2—28no—
913C2—868no—
914C2—1724no—
915C2#1913744218yesdirect product factor
916C2C22×#1306328311yescharacteristic
917C2C2×C4×D4×D4311yescharacteristic
918C2C2×#1458337111yescharacteristic
919C2C2×#1458353611yescharacteristic
920C2C2×#1458354011yescharacteristic
921C2C2×#1458357211yescharacteristic
922C2C2×#1458357611yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC25×D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2342
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13063283C2semidirect
4. #19137442C2direct (N × H)
5. C2×#14582791C2semidirect
6. C2×#14582791C2semidirect
7. C2×#14582789C2semidirect
8. C2×#14582789C2semidirect
9. C2×#14582774C2semidirect
10. C2×#14582761C2semidirect
11. C2×#14582756C2semidirect
13. C2×C22⋊C4×Dic43C2semidirect
14. C2×C4×C22⋊Dic43C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#385C2semidirect
22. C2×#13063283C22semidirect
23. C22×C4⋊Dic43C22semidirect
24. C22×C4⋊Dic43C22semidirect
39. C2×C22⋊C4×D43C4semidirect
41. C22×C4×Dic43C22semidirect
42. C22×C4×Dic43C22semidirect
43. C22×C4×Dic43C22semidirect
44. C22×C4×Dic43C22semidirect
45. #14582791C22semidirect
46. #14582791C22semidirect
47. #14582789C22semidirect
48. #14582789C22semidirect
49. #14582774C22semidirect
50. #14582761C22semidirect
51. #14582756C22semidirect
53. C22⋊C4×Dic43C22semidirect
54. C4×C22⋊Dic43C22semidirect
55. #14582746C22semidirect
56. C2×C43⋊#95C22semidirect
57. C2×C43⋊#95C22semidirect
58. C2×C43⋊#95C22semidirect
59. C2×C43⋊#95C22semidirect
60. C2×C43⋊#95C22semidirect
61. C2×C43⋊#95C22semidirect
63. C22×C4⋊C4×C43C22semidirect
64. C22×C4⋊C4×C43C22semidirect
67. C43×#385C22semidirect
68. C2×#95×C43C22semidirect
69. C2×#95×C43C22semidirect
94. C22×C4×D43C2×C4semidirect
95. C22×C4×D43C2×C4semidirect
101. C2×C4⋊Dic43C23semidirect
102. C2×C4⋊Dic43C23semidirect
115. C2×(C2×D43)⋊C4C2×C4semidirect
116. C2×(C2×D43)⋊C4C2×C4semidirect
128. C22⋊C4×D43C2×C4semidirect
133. C2×C4×Dic43C23semidirect
134. C2×C4×Dic43C23semidirect
135. C2×C4×Dic43C23semidirect
136. C2×C4×Dic43C23semidirect
137. C43⋊#95C23semidirect
138. C43⋊#95C23semidirect
139. C43⋊#95C23semidirect
140. C43⋊#95C23semidirect
141. C43⋊#95C23semidirect
142. C43⋊#95C23semidirect
156. C2×C4⋊C4×C43C23semidirect
157. C2×C4⋊C4×C43C23semidirect
162. #95×C43C23semidirect
163. #95×C43C23semidirect
265. C2×C4×D43C22×C4semidirect
266. C2×C4×D43C22×C4semidirect
280. (C2×D43)⋊C4C22×C4semidirect
281. (C2×D43)⋊C4C22×C4semidirect
299. C23×C43#117semidirect
408. C22×C43C2×#117semidirect
460. C2×#385D43semidirect
468. C2×C43#2342semidirect
487. C22×C4⋊C4C2×D43semidirect
488. C22×C4⋊C4C2×D43semidirect
516. #385C2×D43semidirect
529. C2×#95C2×D43semidirect
530. C2×#95C2×D43semidirect
531. C43C2×#2342semidirect
578. C2×C4⋊C4C22×D43semidirect
579. C2×C4⋊C4C22×D43semidirect
624. #95C22×D43semidirect
625. #95C22×D43semidirect
797. C23#13063283semidirect
886. C22C2×#13063283semidirect
915. C2#19137442direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632832
C23×(C2×D43)⋊C42
C22×C22⋊C4×D432
#191374422
C2×#145827912
C2×#145827892
C2×#145827742
C2×#145827612
C2×#145827562
C2×#145827542
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
C2×#145827462
C2×C43×#3852
C2×#234243