Finite Group Databasebeta

← C2×#19137519 #25255919

Subgroups — C2×#19137519 #25255919

Order 11008.

3894 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063287C211yesmaximal, characteristic
2C22×#13063282C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19137519C2116yesmaximal, direct product factor
5C2×#14582791C211yesmaximal, characteristic, complemented
6C2×#14582789C211yesmaximal, characteristic, complemented
7C2×#14582785C211yesmaximal, characteristic, complemented
8C2×#14582777C211yesmaximal, characteristic
9C2×#14582777C211yesmaximal, characteristic
10C2×#14582763C211yesmaximal, characteristic, complemented
11C2×#14582758C211yesmaximal, characteristic, complemented
12C2×#14582758C211yesmaximal, characteristic, complemented
13C2×#14582750C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063287C4116yescomplemented
23C2×#13063287C2218yes—
24C2×#13063282—28no—
25C2×#13063282C2218yescomplemented
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C2×C4⋊C4×D43—28no—
32C2×C4⋊C4×D43C2218yescomplemented
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43C22×C4×Dic43C2211yescharacteristic
44C22×C4×Dic43C2211yescharacteristic
45#14582791C2218yescomplemented
46#14582789C2218yescomplemented
47#14582785C2218yescomplemented
48#14582777C2218yes—
49#14582777C2218yes—
50#14582763C2218yescomplemented
51#14582758C2218yescomplemented
52#14582758C2218yescomplemented
53#14582750C2218yescomplemented
54C4×(C2×D43)⋊C4C2218yescomplemented
55#14582746C2218yescomplemented
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#387C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C24×D43C2311yescharacteristic
72C22×D172—24no—
73C22×D172—24no—
74C22×D172C2×C418yes—
75C22×D172C2314yes—
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C22×C4×D43—24no—
83C22×C4×D43—24no—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43C2×C418yes—
93C22×C4×D43C2×C418yescomplemented
94C22×C4×D43C2314yes—
95C22×C4×D43C2314yes—
96C22×C4×D43C2314yes—
97C22×C4×D43C2314yes—
98#13063287C2×C4164yescomplemented
99#13063282—232no—
100C2×C4⋊Dic43—24no—
101C2×C4⋊Dic43C2314yes—
102C2×Dic43⋊C4—24no—
103C2×Dic43⋊C4—24no—
104C2×Dic43⋊C4—24no—
105C2×Dic43⋊C4D418yescomplemented
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2314yes—
109C2×Dic43⋊C4C2314yes—
110C4⋊C4×D43—232no—
111C2×(C2×D43)⋊C4—24no—
112C2×(C2×D43)⋊C4—24no—
113C2×(C2×D43)⋊C4—24no—
114C2×(C2×D43)⋊C4—24no—
115C2×(C2×D43)⋊C4—42no—
116C2×(C2×D43)⋊C4—42no—
117C2×(C2×D43)⋊C4C2×C418yes—
118C2×(C2×D43)⋊C4C2×C418yescomplemented
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×C4×Dic43—24no—
128C2×C4×Dic43—42no—
129C2×C4×Dic43—42no—
130C2×C4×Dic43C2×C418yescomplemented
131C2×C4×Dic43C2314yes—
132C2×C4×Dic43C2314yes—
133C2×C4×Dic43C2314yes—
134C2×C4×Dic43C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C43⋊#95C2314yes—
140C43⋊#95C2314yes—
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43—24no—
149C2×C4⋊C4×C43C2×C418yescomplemented
150C2×C4⋊C4×C43C2314yes—
151C2×C4⋊C4×C43C2314yes—
152C2×C42×C43—24no—
153C2×C42×C43C2314yes—
154#95×C43C2314yes—
155#95×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43C22×C414yes—
170C23×D43C22×C414yes—
171C23×D43#4114yes—
172C23×D43#4114yes—
173C23×D43C2412yes—
174C23×D43C2412yes—
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×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43C22×C414yes—
193C22×C4×C43C22×C414yes—
194C22×C4×C43C22×C414yes—
195C22×C4×C43C2×D414yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
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×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C2×D414yes—
219C22×Dic43C2×D414yes—
220C22×Dic43#4114yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×D172—232no—
228C2×D172—28no—
229C2×D172—28no—
230C2×D172C22×C4116yes—
231C2×C4×D43—232no—
232C2×C4×D43—232no—
233C2×C4×D43—28no—
234C2×C4×D43—28no—
235C2×C4×D43—28no—
236C2×C4×D43—28no—
237C2×C4×D43—28no—
238C2×C4×D43—28no—
239C2×C4×D43—28no—
240C2×C4×D43—28no—
241C2×C4×D43—44no—
242C2×C4×D43—44no—
243C2×C4×D43—416no—
244C2×C4×D43—416no—
245C2×C4×D43C22×C4116yes—
246C2×C4×D43C22×C4116yescomplemented
247C4⋊C4×C43—28no—
248C4⋊C4×C43C22×C4116yescomplemented
249C42×C43—28no—
250(C2×D43)⋊C4—28no—
251(C2×D43)⋊C4—28no—
252(C2×D43)⋊C4—28no—
253(C2×D43)⋊C4—28no—
254(C2×D43)⋊C4—44no—
255(C2×D43)⋊C4—44no—
256(C2×D43)⋊C4C22×C4116yes—
257(C2×D43)⋊C4C22×C4116yescomplemented
258C4⋊Dic43—28no—
259Dic43⋊C4—28no—
260Dic43⋊C4—28no—
261Dic43⋊C4—28no—
262Dic43⋊C4C2×D4116yescomplemented
263C4×Dic43—28no—
264C4×Dic43—44no—
265C4×Dic43—44no—
266C4×Dic43C22×C4116yescomplemented
267C23×C43C23×C412yes—
268C23×C43C22×D412yes—
269C23×C43C2×#4112yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C432−1+412yes—
274C23×C43C2511yescharacteristic
275C22×D43—28no—
276C22×D43—28no—
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—28no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—28no—
286C22×D43—28no—
287C22×D43—28no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—44no—
295C22×D43—44no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43#117116yescomplemented
299C22×D43C23×C414yes—
300C22×D43C23×C414yes—
301C22×D43C2×#4114yes—
302C22×D43C2×#4114yes—
303C2×C4×C43—28no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—28no—
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—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—44no—
325C2×C4×C43—44no—
326C2×C4×C43—44no—
327C2×C4×C43C23×C414yes—
328C2×C4×C43C23×C414yes—
329C2×C4×C43C23×C414yes—
330C2×C4×C43C22×D414yes—
331C2×Dic43—28no—
332C2×Dic43—28no—
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—44no—
347C2×Dic43—44no—
348C2×Dic43—44no—
349C2×Dic43C4×D4116yes—
350C2×Dic43C23×C414yes—
351C2×Dic43C23×C414yes—
352C2×Dic43C22×D414yes—
353C2×Dic43C22×D414yes—
354C2×Dic43C2×#4114yes—
355D172—232no—
356C4×D43—232no—
357C4×D43—232no—
358C4×D43—416no—
359C4×D43—416no—
360C2×#2352—431nomaximal, Sylow
361C22×C43C2×#11714yes—
362C22×C43C2×C4×D414yes—
363C22×C43#52014yes—
364C22×C43#54614yes—
365C22×C43#54814yes—
366C22×C43#55214yes—
367C22×C43#55314yes—
368C22×C43C24×C411yescharacteristic
369C22×C43C23×D411yescharacteristic
370C22×C43C22×#4111yescharacteristic
371C22×C43C22×#4111yescharacteristic
372C22×C43C22×#4111yescharacteristic
373C22×C43C2×H(5,𝔽2)11yescharacteristic
374C22×C43C2×2−1+411yescharacteristic
375C2×D43—232no—
376C2×D43—24no—
377C2×D43—24no—
378C2×D43—24no—
379C2×D43—24no—
380C2×D43—24no—
381C2×D43—24no—
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—24no—
385C2×D43—416no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43C2×#11718yescomplemented
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—24no—
395C4×C43—42no—
396C4×C43—42no—
397C4×C43—42no—
398Dic43—24no—
399Dic43—24no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43C2×C4×D418yes—
404C22×C4×D4—431no—
405C22×#117—431no—
406C23×C4⋊C4—431no—
407#2352—4316no—
408C2×#388—431no—
409C2×#388—431no—
410C2×#387—431no—
411C2×#387D4311yescharacteristic, complemented
412C2×#386—431no—
413C2×#386—431no—
414C2×#382—431no—
415C2×#380—431no—
416C2×#380—431no—
417C2×C4×C4⋊C4—431no—
418C2×C4×C22⋊C4—431no—
419C2×C4×C22⋊C4—431no—
420C2×C43#235218yescomplemented
421C2×C43C22×#11711yescharacteristic
422C2×C43C22×C4×D411yescharacteristic
423C2×C43C2×#52011yescharacteristic
424C2×C43C2×#54611yescharacteristic
425C2×C43C2×#54811yescharacteristic
426C2×C43C2×#55211yescharacteristic
427C2×C43C2×#55311yescharacteristic
428D43—28no—
429D43—44no—
430C23×D4—431no—
431C24×C4—431no—
432C24×C4—431no—
433C24×C4—431no—
434C24×C4—431no—
435C2×C4×D4—438no—
436C2×C4×D4—4316no—
437C2×#117—438no—
438C2×#117—868no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—438no—
445C22×C4⋊C4—868no—
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⋊C4—431no—
454C22×C22⋊C4—431no—
455C22×C22⋊C4—431no—
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#388—438no—
462#388—438no—
463#387—438no—
464#387C2×D4318yescomplemented
465#386—438no—
466#386—438no—
467#382—438no—
468#380—438no—
469#380—438no—
470C4×C4⋊C4—438no—
471C4×C22⋊C4—438no—
472C4×C22⋊C4—438no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95C2×D4311yescharacteristic
480C2×#95C2×D4311yescharacteristic
481C2×#95C2×D4311yescharacteristic
482C2×#95C2×D4311yescharacteristic
483C43C2×#235211yescharacteristic, complemented, Sylow
484C25—431no—
485C25—431no—
486C22×D4—438no—
487C22×D4—434no—
488C22×D4—864no—
489C22×D4—864no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—431no—
493C23×C4—438no—
494C23×C4—438no—
495C23×C4—434no—
496C23×C4—434no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—434no—
501C23×C4—434no—
502C23×C4—864no—
503C23×C4—864no—
504C23×C4—864no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—1722no—
511C23×C4—1722no—
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519C4×D4—4364no—
520#117—8632no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—438no—
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⋊C4C4×D4318yescomplemented
534C2×C4⋊C4C22×D4314yes—
535C2×C4⋊C4C22×D4314yes—
536C2×C22⋊C4—438no—
537C2×C22⋊C4—438no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—864no—
548C2×C22⋊C4—864no—
549C2×C22⋊C4—864no—
550C2×C22⋊C4—1722no—
551C2×C22⋊C4—1722no—
552C2×C42—24no—
553C2×C42—438no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—434no—
557C2×C42—434no—
558C2×C42—864no—
559C2×C42—1722no—
560C2×C42—1722no—
561C2×C42C22×D4314yes—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95C22×D4314yes—
569#95C22×D4314yes—
570#95C22×D4314yes—
571#95C22×D4314yes—
572C24—434no—
573C24—434no—
574C24—434no—
575C24—432no—
576C24—434no—
577C24—432no—
578C24—862no—
579C24—862no—
580C24—862no—
581C24—862no—
582C24—862no—
583C24—862no—
584C24—862no—
585C24—862no—
586C24—862no—
587C24—862no—
588C24C23×D4311yescharacteristic
589C2×D4—4316no—
590C2×D4—8632no—
591C2×D4—868no—
592C2×D4—868no—
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—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—434no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—432no—
614C22×C4—434no—
615C22×C4—434no—
616C22×C4—432no—
617C22×C4—432no—
618C22×C4—4316no—
619C22×C4—4316no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—868no—
624C22×C4—868no—
625C22×C4—8632no—
626C22×C4—8632no—
627C22×C4—868no—
628C22×C4—868no—
629C22×C4—868no—
630C22×C4—868no—
631C22×C4—868no—
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—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—868no—
646C22×C4—1724no—
647C22×C4—1724no—
648C22×C4—17216no—
649C22×C4—17216no—
650C22×C4C2×C4×D4314yes—
651C22×C4C2×C4×D4314yes—
652C22×C4C2×C4×D4314yes—
653C22×C4D4×D4314yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—28no—
662C4⋊C4—4316no—
663C4⋊C4—868no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C4⋊C4—868no—
667C4⋊C4C2×C4×D43116yescomplemented
668C22⋊C4—4316no—
669C22⋊C4—4316no—
670C22⋊C4—868no—
671C22⋊C4—868no—
672C22⋊C4—868no—
673C22⋊C4—868no—
674C22⋊C4—1724no—
675C22⋊C4—1724no—
676C42—28no—
677C42—4316no—
678C42—868no—
679C42—1724no—
680C42—1724no—
681C23—4316no—
682C23—434no—
683C23—434no—
684C23—434no—
685C23—434no—
686C23—868no—
687C23—868no—
688C23—868no—
689C23—868no—
690C23—868no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—868no—
696C23—868no—
697C23—868no—
698C23—868no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—862no—
703C23—862no—
704C23—862no—
705C23—1724no—
706C23—1724no—
707C23—1724no—
708C23—1724no—
709C23C22×C4×D4312yes—
710C23C2×D4×D4312yes—
711C23#41×D4312yes—
712C23#41×D4312yes—
713C23#41×D4312yes—
714C23#1306337112yes—
715C23#1306337312yes—
716C23C24×D4311yescharacteristic
717D4—8632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
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—28no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—4316no—
743C2×C4—434no—
744C2×C4—434no—
745C2×C4—434no—
746C2×C4—434no—
747C2×C4—434no—
748C2×C4—8632no—
749C2×C4—8632no—
750C2×C4—868no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—868no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—17216no—
766C2×C4—17216no—
767C2×C4—1724no—
768C2×C4—1724no—
769C2×C4—1724no—
770C2×C4C22×C4×D4314yes—
771C2×C4C22×C4×D4314yes—
772C2×C4C22×C4×D4314yes—
773C2×C4C2×D4×D4314yes—
774C22—438no—
775C22—864no—
776C22—864no—
777C22—864no—
778C22—864no—
779C22—864no—
780C22—8632no—
781C22—864no—
782C22—864no—
783C22—864no—
784C22—864no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—17216no—
790C22#117×D4314yes—
791C22C4×D4×D4314yes—
792C22#1458338114yes—
793C22#1458354114yes—
794C22#1458355914yes—
795C22#1458358114yes—
796C22#1458360014yes—
797C22C23×C4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C2×#41×D4311yescharacteristic
801C22C2×#41×D4311yescharacteristic
802C22C2×#1306337111yescharacteristic
803C22C2×#1306337311yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—438no—
812C4—864no—
813C4—864no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C2—868no—
818C2—1724no—
819C2#1913751918yesdirect product factor
820C2C2×#117×D4311yescharacteristic
821C2C2×C4×D4×D4311yescharacteristic
822C2C2×#1458338111yescharacteristic
823C2C2×#1458354111yescharacteristic
824C2C2×#1458355911yescharacteristic
825C2C2×#1458358111yescharacteristic
826C2C2×#1458360011yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC23×D172C22
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2352
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×#13063282C2semidirect
3. C22×C4⋊C4×D43C2semidirect
4. #19137519C2direct (N × H)
5. C2×#14582791C2semidirect
6. C2×#14582789C2semidirect
7. C2×#14582785C2semidirect
10. C2×#14582763C2semidirect
11. C2×#14582758C2semidirect
12. C2×#14582758C2semidirect
13. C2×#14582750C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#387C2semidirect
22. C2×#13063287C4semidirect
25. C2×#13063282C22semidirect
32. C2×C4⋊C4×D43C22semidirect
45. #14582791C22semidirect
46. #14582789C22semidirect
47. #14582785C22semidirect
50. #14582763C22semidirect
51. #14582758C22semidirect
52. #14582758C22semidirect
53. #14582750C22semidirect
54. C4×(C2×D43)⋊C4C22semidirect
55. #14582746C22semidirect
65. C43×#387C22semidirect
93. C22×C4×D43C2×C4semidirect
98. #13063287C2×C4semidirect
105. C2×Dic43⋊C4D4semidirect
118. C2×(C2×D43)⋊C4C2×C4semidirect
130. C2×C4×Dic43C2×C4semidirect
149. C2×C4⋊C4×C43C2×C4semidirect
246. C2×C4×D43C22×C4semidirect
248. C4⋊C4×C43C22×C4semidirect
257. (C2×D43)⋊C4C22×C4semidirect
262. Dic43⋊C4C2×D4semidirect
266. C4×Dic43C22×C4semidirect
298. C22×D43#117semidirect
390. C2×D43C2×#117semidirect
411. C2×#387D43semidirect
420. C2×C43#2352semidirect
464. #387C2×D43semidirect
483. C43C2×#2352semidirect
533. C2×C4⋊C4C4×D43semidirect
667. C4⋊C4C2×C4×D43semidirect
819. C2#19137519direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632872
C22×#130632822
C22×C4⋊C4×D432
#191375192
C2×#145827912
C2×#145827892
C2×#145827852
C2×#145827772
C2×#145827632
C2×#145827582
C2×#145827502
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×C43×#3872
C2×#235243