Finite Group Databasebeta

← C2×#19143251 #25960349

Subgroups — C2×#19143251 #25960349

Order 11008.

2254 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2#19143251C2116yesmaximal, direct product factor
3C2×#14582960C211yesmaximal, characteristic, complemented
4C2×#14582957C211yesmaximal, characteristic, complemented
5C2×#14582957C211yesmaximal, characteristic, complemented
6C2×#14582955C211yesmaximal, characteristic, complemented
7C2×#14582954C211yesmaximal, characteristic, complemented
8C2×#14582951C211yesmaximal, characteristic, complemented
9C2×#14582950C211yesmaximal, characteristic, complemented
10C2×#14582924C211yesmaximal, characteristic, complemented
11C2×#14582924C211yesmaximal, characteristic, complemented
12C2×#14582861C211yesmaximal, characteristic
13C2×C22⋊C8×D43C211yesmaximal, characteristic
14C2×#14582856C211yesmaximal, characteristic, complemented
15C2×#14582853C211yesmaximal, characteristic, complemented
16C2×C43×#433C211yesmaximal, characteristic, complemented
17C23×C4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23C2×#13063283C411yescharacteristic
24C2×#13063283C411yescharacteristic
25C2×#13063282C2211yescharacteristic
26C2×#13063282C2211yescharacteristic
27C2×#13063281C411yescharacteristic
28C2×#13063281C411yescharacteristic
29#117×D43C418yes—
30#117×D43C2218yes—
31C2×C4⋊C4×D43C411yescharacteristic
32C2×C4⋊C4×D43C411yescharacteristic
33C2×C22⋊C4×D43C411yescharacteristic
34C2×C22⋊C4×D43C411yescharacteristic
35C2×C42×D43C2211yescharacteristic
36C2×C42×D43C2211yescharacteristic
37#14582960C2218yescomplemented
38#14582957C2218yescomplemented
39#14582957C2218yescomplemented
40#14582955C2218yescomplemented
41#14582954C2218yescomplemented
42#14582951C2218yescomplemented
43#14582950C2218yescomplemented
44#14582924C2218yescomplemented
45#14582924C2218yescomplemented
46C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
47C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
48C2×Dic43⋊C8C2211yescharacteristic, complemented
49C2×Dic43⋊C8C2211yescharacteristic, complemented
50C2×Dic43⋊C8C2211yescharacteristic, complemented
51C2×Dic43⋊C8C2211yescharacteristic, complemented
52#14582861C2218yes—
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C2×C22⋊(C43⋊C8)C2211yescharacteristic
55C2×(C2×D43)⋊C8C2211yescharacteristic
56C2×(C2×D43)⋊C8C2211yescharacteristic
57C2×(C2×D43)⋊C8C2211yescharacteristic
58C2×(C2×D43)⋊C8C2211yescharacteristic
59C22⋊C8×D43C2218yes—
60#14582856C2218yescomplemented
61#14582853C2218yescomplemented
62C2×#13063236C2211yescharacteristic, complemented
63C2×#13063235C2211yescharacteristic, complemented
64C2×#13063235C2211yescharacteristic, complemented
65C2×C4×C43⋊C8C2211yescharacteristic, complemented
66C2×C8×Dic43C2211yescharacteristic, complemented
67C2×C8×Dic43C2211yescharacteristic, complemented
68C2×#117×C43C2211yescharacteristic
69C43×#433C2218yescomplemented
70C2×C4⋊C8×C43C2211yescharacteristic, complemented
71C2×C4⋊C8×C43C2211yescharacteristic, complemented
72C2×C22⋊C8×C43C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic, complemented
75C2×C4×C8×C43C2211yescharacteristic, complemented
76C24×D43C2×C411yescharacteristic
77C23×Dic43C2×C411yescharacteristic
78C22×C4×D43—24no—
79C22×C4×D43—24no—
80C22×C4×D43C2×C411yescharacteristic
81C22×C4×D43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2×C414yes—
84C22×C4×D43C2×C411yescharacteristic
85C22×C4×D43C2×C411yescharacteristic
86C22×C4×D43C2×C411yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C22×C4×D43C2314yes—
89C22×C4×D43C2311yescharacteristic
90C2×#10621872—24no—
91C2×#10621872—24no—
92C2×#10621872C2314yes—
93C2×#10621872C2314yes—
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C2×C8×D43—24no—
99C2×C8×D43—24no—
100C2×C8×D43C2314yes—
101C2×C8×D43C2314yes—
102#13063284C2×C414yes—
103#13063284C2314yes—
104#13063283C2×C418yes—
105#13063283C2×C418yes—
106#13063282C2×C414yes—
107#13063282C2×C414yes—
108#13063282C2314yes—
109#13063282C2314yes—
110#13063281C2×C418yes—
111#13063281C2×C418yes—
112C2×C4⋊Dic43C2×C411yescharacteristic
113C2×C4⋊Dic43C2×C411yescharacteristic
114C2×Dic43⋊C4C2×C411yescharacteristic
115C2×Dic43⋊C4C2×C411yescharacteristic
116C2×Dic43⋊C4C2×C411yescharacteristic
117C2×Dic43⋊C4C2×C411yescharacteristic
118C4⋊C4×D43C2×C418yes—
119C4⋊C4×D43C2×C418yes—
120C2×C22⋊Dic43C2×C411yescharacteristic
121C2×C22⋊Dic43C2×C411yescharacteristic
122C2×(C2×D43)⋊C4C2×C411yescharacteristic
123C2×(C2×D43)⋊C4C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C22⋊C4×D43C2×C418yes—
127C22⋊C4×D43C2×C418yes—
128C2×C4×Dic43C2×C411yescharacteristic
129C2×C4×Dic43C2×C411yescharacteristic
130C2×C4×Dic43C2×C411yescharacteristic
131C2×C4×Dic43C2×C411yescharacteristic
132C2×C4×Dic43C2311yescharacteristic
133C2×C4×Dic43C2311yescharacteristic
134C42×D43C2×C414yes—
135C42×D43C2×C414yes—
136C42×D43C2314yes—
137C42×D43C2314yes—
138C4⋊(C43⋊C8)C2314yescomplemented
139C4⋊(C43⋊C8)C2314yescomplemented
140Dic43⋊C8C2314yescomplemented
141Dic43⋊C8C2314yescomplemented
142Dic43⋊C8C2314yescomplemented
143Dic43⋊C8C2314yescomplemented
144C22⋊(C43⋊C8)C2314yes—
145C22⋊(C43⋊C8)C2314yes—
146(C2×D43)⋊C8C2314yes—
147(C2×D43)⋊C8C2314yes—
148(C2×D43)⋊C8C2314yes—
149(C2×D43)⋊C8C2314yes—
150#13063236C2314yescomplemented
151#13063235C2314yescomplemented
152#13063235C2314yescomplemented
153C4×C43⋊C8C2314yescomplemented
154C8×Dic43C2314yescomplemented
155C8×Dic43C2314yescomplemented
156C23×C4×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C22×C8×C43C2311yescharacteristic
159C22×C8×C43C2311yescharacteristic
160C22×C8×C43C2311yescharacteristic
161#117×C43C2×C414yes—
162#117×C43C2314yes—
163C2×C4⋊C4×C43C2×C411yescharacteristic
164C2×C4⋊C4×C43C2×C411yescharacteristic
165C2×C22⋊C4×C43C2×C411yescharacteristic
166C2×C22⋊C4×C43C2×C411yescharacteristic
167C2×C42×C43C2311yescharacteristic
168C2×C42×C43C2311yescharacteristic
169C4⋊C8×C43C2314yescomplemented
170C4⋊C8×C43C2314yescomplemented
171C22⋊C8×C43C2314yes—
172C22⋊C8×C43C2314yes—
173#97×C43C2314yescomplemented
174C4×C8×C43C2314yescomplemented
175C24×C43C22×C411yescharacteristic
176C23×D43—24no—
177C23×D43—24no—
178C23×D43—42no—
179C23×D43C22×C414yes—
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C22×C411yescharacteristic
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2411yescharacteristic
192C22×Dic43—24no—
193C22×Dic43C22×C411yescharacteristic
194C22×Dic43C22×C411yescharacteristic
195C22×Dic43C22×C411yescharacteristic
196C22×Dic43C22×C411yescharacteristic
197C22×Dic43C22×C411yescharacteristic
198C22×Dic43C22×C414yes—
199C22×Dic43C22×C411yescharacteristic
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—24no—
203C2×C4×D43—216no—
204C2×C4×D43—28no—
205C2×C4×D43—28no—
206C2×C4×D43—24no—
207C2×C4×D43—24no—
208C2×C4×D43—24no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43C22×C412yes—
212C2×C4×D43C22×C414yes—
213C2×C4×D43C22×C414yes—
214C2×C4×D43C22×C414yes—
215C2×C4×D43C22×C414yes—
216C2×C4×D43C22×C414yes—
217C2×C4×D43C22×C414yes—
218C2×C4×D43C22×C412yes—
219C2×C4×D43#4114yes—
220C2×C4×D43#4114yes—
221C2×C4×D43C2412yes—
222C2×C4×D43C2412yes—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43C2412yes—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C2×C8×C43C2412yes—
231C4⋊C4×C43C22×C414yes—
232C4⋊C4×C43C22×C414yes—
233C22⋊C4×C43C22×C414yes—
234C22⋊C4×C43C22×C414yes—
235C42×C43C22×C412yes—
236C42×C43C22×C412yes—
237C42×C43C2412yes—
238C42×C43C2412yes—
239C22⋊Dic43C22×C414yes—
240C22⋊Dic43C22×C414yes—
241(C2×D43)⋊C4C22×C414yes—
242(C2×D43)⋊C4C22×C414yes—
243(C2×D43)⋊C4C22×C414yes—
244(C2×D43)⋊C4C22×C414yes—
245C4⋊Dic43C22×C414yes—
246C4⋊Dic43C22×C414yes—
247Dic43⋊C4C22×C414yes—
248Dic43⋊C4C22×C414yes—
249Dic43⋊C4C22×C414yes—
250Dic43⋊C4C22×C414yes—
251C4×Dic43C22×C412yes—
252C4×Dic43C22×C412yes—
253C4×Dic43C22×C414yes—
254C4×Dic43C22×C414yes—
255C4×Dic43C22×C414yes—
256C4×Dic43C22×C414yes—
257C4×Dic43C2412yes—
258C4×Dic43C2412yes—
259C2×C43⋊C8—22no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8C2412yes—
264C2×C43⋊C8C2412yes—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267#10621872—28no—
268#10621872—28no—
269C8×D43—28no—
270C8×D43—28no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43C23×C412yes—
275C23×C43C23×C411yescharacteristic
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—28no—
281C22×D43—28no—
282C22×D43—44no—
283C22×D43—416no—
284C22×D43#11714yes—
285C22×D43#13114yes—
286C22×D43C23×C412yes—
287C22×D43C23×C412yes—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—24no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43C23×C412yes—
297C2×C4×C43C23×C412yes—
298C2×C4×C43C23×C412yes—
299C2×C4×C43C23×C412yes—
300C2×C4×C43C23×C412yes—
301C2×C4×C43C23×C411yescharacteristic
302C2×C4×C43C2×#4112yes—
303C2×C4×C43C2×#4112yes—
304C2×C4×C43C2511yescharacteristic
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—28no—
311C2×Dic43#11714yes—
312C2×Dic43C23×C412yes—
313C2×Dic43C23×C412yes—
314C2×Dic43C23×C412yes—
315C2×Dic43C23×C412yes—
316C2×Dic43C23×C412yes—
317C2×Dic43C23×C412yes—
318C4×D43—28no—
319C4×D43—28no—
320C4×D43—28no—
321C4×D43—24no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—28no—
325C4×D43—44no—
326C4×D43—44no—
327C4×D43#11718yes—
328C4×D43C2×#4114yes—
329C4×D43C2×#4114yes—
330C8×C43—22no—
331C8×C43—22no—
332C8×C43—22no—
333C8×C43—22no—
334C43⋊C8—22no—
335C43⋊C8—22no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C2×#2924—431nomaximal, Sylow
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—44no—
343C22×C43C2×#11712yes—
344C22×C43C2×#13112yes—
345C22×C43#56812yes—
346C22×C43C24×C411yescharacteristic
347C2×D43—22no—
348C2×D43—28no—
349C2×D43—28no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—416no—
354C2×D43C2×#11714yes—
355C2×D43C2×#13114yes—
356C4×C43—22no—
357C4×C43—22no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43C2×#11712yes—
362C4×C43C22×#4111yescharacteristic
363C4×C43C22×#4111yescharacteristic
364Dic43—22no—
365Dic43—22no—
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43C2×#11714yes—
370C22×#117—431no—
371#2924—4316no—
372C2×#433—431no—
373C2×#433—431no—
374C2×#433—431no—
375C2×#433D4311yescharacteristic, complemented
376C2×#432—431no—
377C2×#432—431no—
378C2×#431—431no—
379C2×#431—431no—
380C2×#424—431no—
381C2×#424—431no—
382C2×#407—431no—
383C22×C22⋊C8—431no—
384C2×#405—431no—
385C2×#405—431no—
386C2×C43—42no—
387C2×C43#292414yescomplemented
388C2×C43C22×#11711yescharacteristic
389C2×C43C22×#13111yescharacteristic
390C2×C43C2×#56811yescharacteristic
391D43—24no—
392D43—24no—
393C24×C4—431no—
394C22×M16—431no—
395C22×M16—431no—
396C23×C8—431no—
397C23×C8—431no—
398C2×#117—431no—
399C2×#117—438no—
400C2×#117—438no—
401C2×#117—431no—
402C2×#117—431no—
403C2×#117—431no—
404C2×#117—431no—
405C2×#117—431no—
406C2×#117—431no—
407C2×#117C2×D4311yescharacteristic
408C22×C4⋊C4—431no—
409C22×C4⋊C4—431no—
410C22×C22⋊C4—431no—
411C22×C22⋊C4—431no—
412C22×C42—431no—
413C22×C42—431no—
414#433—438no—
415#433—438no—
416#433—438no—
417#433C2×D4318yescomplemented
418#432—438no—
419#432—438no—
420#431—438no—
421#431—438no—
422#424—438no—
423#424—438no—
424C2×C4⋊C8—431no—
425C2×C4⋊C8—431no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×C4⋊C8—431no—
429C2×C4⋊C8—431no—
430C2×C4⋊C8C2×D4311yescharacteristic, complemented
431C2×C4⋊C8C2×D4311yescharacteristic, complemented
432#407—438no—
433C2×C22⋊C8—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8—431no—
436C2×C22⋊C8—431no—
437C2×C22⋊C8—431no—
438C2×C22⋊C8—431no—
439C2×C22⋊C8—438no—
440C2×C22⋊C8C2×D4311yescharacteristic
441C2×C22⋊C8C2×D4311yescharacteristic
442#405—438no—
443#405—438no—
444C2×#97—431no—
445C2×#97—431no—
446C2×#97—431no—
447C2×#97C2×D4311yescharacteristic, complemented
448C2×C4×C8—431no—
449C2×C4×C8—431no—
450C2×C4×C8—431no—
451C2×C4×C8C2×D4311yescharacteristic, complemented
452C43C2×#292411yescharacteristic, complemented, Sylow
453C25—431no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—431no—
459C23×C4—434no—
460C23×C4—431no—
461C23×C4—434no—
462C23×C4—431no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—864no—
466C23×C4—864no—
467C23×C4C22×D4311yescharacteristic
468C2×M16—434no—
469C2×M16—434no—
470C2×M16—864no—
471C2×M16—864no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—434no—
477C22×C8—434no—
478C22×C8—864no—
479C22×C8—864no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484#117—434no—
485#117—434no—
486#117—438no—
487#117—438no—
488#117—438no—
489#117—438no—
490#117—434no—
491#117—434no—
492#117—434no—
493#117—434no—
494#117C4×D4314yes—
495#117C22×D4314yes—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—438no—
503C2×C4⋊C4—438no—
504C2×C4⋊C4C4×D4311yescharacteristic
505C2×C4⋊C4C4×D4311yescharacteristic
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—431no—
509C2×C22⋊C4—431no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—438no—
513C2×C22⋊C4—438no—
514C2×C22⋊C4C4×D4311yescharacteristic
515C2×C22⋊C4C4×D4311yescharacteristic
516C2×C42—431no—
517C2×C42—431no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—434no—
523C2×C42—434no—
524C2×C42—434no—
525C2×C42—434no—
526C2×C42C22×D4311yescharacteristic
527C2×C42C22×D4311yescharacteristic
528C4⋊C8—434no—
529C4⋊C8—434no—
530C4⋊C8—434no—
531C4⋊C8—434no—
532C4⋊C8—434no—
533C4⋊C8—434no—
534C4⋊C8C22×D4314yescomplemented
535C4⋊C8C22×D4314yescomplemented
536C22⋊C8—434no—
537C22⋊C8—434no—
538C22⋊C8—434no—
539C22⋊C8—434no—
540C22⋊C8—434no—
541C22⋊C8—434no—
542C22⋊C8C22×D4314yes—
543C22⋊C8C22×D4314yes—
544#97—434no—
545#97—434no—
546#97—434no—
547#97C22×D4314yescomplemented
548C4×C8—434no—
549C4×C8—434no—
550C4×C8—434no—
551C4×C8C22×D4314yescomplemented
552C24—431no—
553C24—431no—
554C24—434no—
555C24—864no—
556C24—864no—
557C24—1722no—
558C24C2×C4×D4311yescharacteristic
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—431no—
562C22×C4—432no—
563C22×C4—434no—
564C22×C4—434no—
565C22×C4—432no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—434no—
572C22×C4—432no—
573C22×C4—434no—
574C22×C4—434no—
575C22×C4—434no—
576C22×C4—434no—
577C22×C4—432no—
578C22×C4—434no—
579C22×C4—434no—
580C22×C4—864no—
581C22×C4—8616no—
582C22×C4—868no—
583C22×C4—868no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—864no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4C2×C4×D4311yescharacteristic
593C22×C4C2×C4×D4311yescharacteristic
594C22×C4C2×C4×D4311yescharacteristic
595C22×C4C2×C4×D4311yescharacteristic
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×C4×D4312yes—
598C22×C4C23×D4312yes—
599C22×C4C23×D4311yescharacteristic
600M16—868no—
601M16—868no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—868no—
611C2×C8—868no—
612C2×C8—862no—
613C2×C8—862no—
614C2×C8—862no—
615C2×C8—862no—
616C2×C8C23×D4312yes—
617C2×C8C23×D4312yes—
618C2×C8C23×D4312yes—
619C2×C8C23×D4312yes—
620C4⋊C4—434no—
621C4⋊C4—434no—
622C4⋊C4—434no—
623C4⋊C4—434no—
624C4⋊C4—434no—
625C4⋊C4—434no—
626C4⋊C4C2×C4×D4314yes—
627C4⋊C4C2×C4×D4314yes—
628C22⋊C4—434no—
629C22⋊C4—434no—
630C22⋊C4—434no—
631C22⋊C4—434no—
632C22⋊C4—434no—
633C22⋊C4—434no—
634C22⋊C4C2×C4×D4314yes—
635C22⋊C4C2×C4×D4314yes—
636C42—434no—
637C42—434no—
638C42—434no—
639C42—434no—
640C42—432no—
641C42—432no—
642C42—432no—
643C42—432no—
644C42C2×C4×D4312yes—
645C42C2×C4×D4312yes—
646C42C23×D4312yes—
647C42C23×D4312yes—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—434no—
652C23—434no—
653C23—432no—
654C23—432no—
655C23—868no—
656C23—868no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—1724no—
662C23—17216no—
663C23C22×C4×D4312yes—
664C23C22×C4×D4311yescharacteristic
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—434no—
674C2×C4—432no—
675C2×C4—438no—
676C2×C4—434no—
677C2×C4—434no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—868no—
684C2×C4—868no—
685C2×C4—868no—
686C2×C4—868no—
687C2×C4—868no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—864no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4C22×C4×D4312yes—
699C2×C4C22×C4×D4312yes—
700C2×C4C22×C4×D4312yes—
701C2×C4C22×C4×D4312yes—
702C2×C4C22×C4×D4312yes—
703C2×C4C22×C4×D4311yescharacteristic
704C2×C4#41×D4312yes—
705C2×C4#41×D4312yes—
706C2×C4C24×D4311yescharacteristic
707C8—22no—
708C8—22no—
709C8—22no—
710C8—22no—
711C8—862no—
712C8—862no—
713C8—862no—
714C8—862no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—44no—
719C22—434no—
720C22—434no—
721C22—868no—
722C22—868no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—17216no—
728C22#117×D4312yes—
729C22#131×D4312yes—
730C22#1458366412yes—
731C22C23×C4×D4311yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—22no—
736C4—22no—
737C4—434no—
738C4—862no—
739C4—862no—
740C4—862no—
741C4—862no—
742C4—862no—
743C4#117×D4312yes—
744C4C2×#41×D4311yescharacteristic
745C4C2×#41×D4311yescharacteristic
746C2—42no—
747C2—864no—
748C2—864no—
749C2#1914325114yesdirect product factor
750C2C2×#117×D4311yescharacteristic
751C2C2×#131×D4311yescharacteristic
752C2C2×#1458366411yescharacteristic
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#433C2
socleC23×C43C23×C4
prime radicalC24×D43C2×C4
cosocleC2×C4×C43C25
hypercenterC2×#433D43
hypocenterC43C2×#2924
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #19143251C2direct (N × H)
3. C2×#14582960C2semidirect
4. C2×#14582957C2semidirect
5. C2×#14582957C2semidirect
6. C2×#14582955C2semidirect
7. C2×#14582954C2semidirect
8. C2×#14582951C2semidirect
9. C2×#14582950C2semidirect
10. C2×#14582924C2semidirect
11. C2×#14582924C2semidirect
14. C2×#14582856C2semidirect
15. C2×#14582853C2semidirect
16. C2×C43×#433C2semidirect
37. #14582960C22semidirect
38. #14582957C22semidirect
39. #14582957C22semidirect
40. #14582955C22semidirect
41. #14582954C22semidirect
42. #14582951C22semidirect
43. #14582950C22semidirect
44. #14582924C22semidirect
45. #14582924C22semidirect
46. C2×C4⋊(C43⋊C8)C22semidirect
47. C2×C4⋊(C43⋊C8)C22semidirect
48. C2×Dic43⋊C8C22semidirect
49. C2×Dic43⋊C8C22semidirect
50. C2×Dic43⋊C8C22semidirect
51. C2×Dic43⋊C8C22semidirect
60. #14582856C22semidirect
61. #14582853C22semidirect
62. C2×#13063236C22semidirect
63. C2×#13063235C22semidirect
64. C2×#13063235C22semidirect
65. C2×C4×C43⋊C8C22semidirect
66. C2×C8×Dic43C22semidirect
67. C2×C8×Dic43C22semidirect
69. C43×#433C22semidirect
70. C2×C4⋊C8×C43C22semidirect
71. C2×C4⋊C8×C43C22semidirect
74. C2×#97×C43C22semidirect
75. C2×C4×C8×C43C22semidirect
138. C4⋊(C43⋊C8)C23semidirect
139. C4⋊(C43⋊C8)C23semidirect
140. Dic43⋊C8C23semidirect
141. Dic43⋊C8C23semidirect
142. Dic43⋊C8C23semidirect
143. Dic43⋊C8C23semidirect
150. #13063236C23semidirect
151. #13063235C23semidirect
152. #13063235C23semidirect
153. C4×C43⋊C8C23semidirect
154. C8×Dic43C23semidirect
155. C8×Dic43C23semidirect
169. C4⋊C8×C43C23semidirect
170. C4⋊C8×C43C23semidirect
173. #97×C43C23semidirect
174. C4×C8×C43C23semidirect
375. C2×#433D43semidirect
387. C2×C43#2924semidirect
417. #433C2×D43semidirect
430. C2×C4⋊C8C2×D43semidirect
431. C2×C4⋊C8C2×D43semidirect
447. C2×#97C2×D43semidirect
451. C2×C4×C8C2×D43semidirect
452. C43C2×#2924semidirect
534. C4⋊C8C22×D43semidirect
535. C4⋊C8C22×D43semidirect
547. #97C22×D43semidirect
551. C4×C8C22×D43semidirect
749. C2#19143251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117×D432
#191432512
C2×#145829602
C2×#145829572
C2×#145829552
C2×#145829542
C2×#145829512
C2×#145829502
C2×#145829242
C2×#145828612
C2×C22⋊C8×D432
C2×#145828562
C2×#145828532
C2×C43×#4332
C2×#292443