Finite Group Databasebeta

← #25112687

Subgroups — #25112687

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582977C211yesmaximal, characteristic, complemented
2C2×#14582971C211yesmaximal, characteristic, complemented
3#19135536C211yesmaximal, characteristic, complemented
4#19135532C211yesmaximal, characteristic, complemented
5#19134893C211yesmaximal, characteristic, complemented
6#19134893C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic, complemented
8#19134888C211yesmaximal, characteristic, complemented
9#19134666C211yesmaximal, characteristic, complemented
10#19134663C211yesmaximal, characteristic, complemented
11#19134579C211yesmaximal, characteristic, complemented
12#19134361C211yesmaximal, characteristic, complemented
13#19134292C211yesmaximal, characteristic, complemented
14#19134289C211yesmaximal, characteristic, complemented
15C2×C43×#529C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14582977—24no—
21#14582971—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582654C2211yescharacteristic
35#14582654C2211yescharacteristic
36#14582654C2211yescharacteristic
37#14582654C2211yescharacteristic
38#14582654C2211yescharacteristic
39#14582654C2211yescharacteristic
40#14582654C2211yescharacteristic
41#14582654C2211yescharacteristic
42#14582654C2211yescharacteristic
43#14582654C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46C43×#529—24no—
47C43×#529—24no—
48C2×#126×C43C411yescharacteristic
49C2×#126×C43C411yescharacteristic
50C2×#125×C43C411yescharacteristic
51C2×#124×C43C411yescharacteristic
52C2×#123×C43C411yescharacteristic
53C2×#123×C43C411yescharacteristic
54C2×C22⋊Q8×C43C411yescharacteristic
55C2×#121×C43C411yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×#117×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C22×C42×C43C2211yescharacteristic
63C2×#10621877—22no—
64C2×#10621877—22no—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—22no—
68C2×#10621877—22no—
69C2×#10621877—41no—
70C2×#10621877—41no—
71C2×#10621877—41no—
72C22×C43⋊C8—22no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C4⋊(C43⋊C8)—22no—
84C4⋊(C43⋊C8)—22no—
85C22⋊(C43⋊C8)—22no—
86C22⋊(C43⋊C8)—22no—
87C22⋊(C43⋊C8)—22no—
88C22⋊(C43⋊C8)—22no—
89C22⋊(C43⋊C8)—22no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—41no—
92C22⋊(C43⋊C8)—41no—
93#13063236—22no—
94C4×C43⋊C8—22no—
95C22×Q8×C43C2×C411yescharacteristic
96C22×D4×C43C2×C411yescharacteristic
97C22×D4×C43C2×C411yescharacteristic
98C22×D4×C43C2×C411yescharacteristic
99C23×C4×C43C2×C411yescharacteristic
100C23×C4×C43C2×C411yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C23×C4×C43C2311yescharacteristic
103C23×C4×C43C2311yescharacteristic
104#126×C43—24no—
105#126×C43—24no—
106#125×C43—24no—
107#124×C43—24no—
108#123×C43—24no—
109#123×C43—24no—
110C22⋊Q8×C43—24no—
111#121×C43—24no—
112C4×Q8×C43—22no—
113C4×Q8×C43—22no—
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C4×D4×C43D414yes—
119C4×D4×C43D414yes—
120#117×C43—22no—
121#117×C43—22no—
122#117×C43—22no—
123#117×C43—22no—
124C2×C4⋊C4×C43C2×C411yescharacteristic
125C2×C4⋊C4×C43C2×C411yescharacteristic
126C2×C4⋊C4×C43C2×C411yescharacteristic
127C2×C4⋊C4×C43C2×C411yescharacteristic
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43C2×C411yescharacteristic
135C2×C22⋊C4×C43C2×C411yescharacteristic
136C2×C22⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2×C411yescharacteristic
138C2×C22⋊C4×C43C2×C411yescharacteristic
139C2×C22⋊C4×C43C2×C411yescharacteristic
140C2×C22⋊C4×C43C2×C411yescharacteristic
141C2×C22⋊C4×C43C2×C411yescharacteristic
142C2×C22⋊C4×C43C2×C411yescharacteristic
143C2×C22⋊C4×C43C2×C411yescharacteristic
144C2×C42×C43—22no—
145C2×C42×C43—22no—
146C2×C42×C43C2×C411yescharacteristic
147C2×C42×C43C2×C411yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150C2×C42×C43C2311yescharacteristic
151C2×C42×C43C2311yescharacteristic
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C24×C43C22×C411yescharacteristic
155C2×Q8×C43—22no—
156C2×Q8×C43—22no—
157C2×Q8×C43—41no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—41no—
162C2×D4×C43—41no—
163C2×D4×C43—41no—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43C22⋊C414yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—22no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—41no—
185C22×C4×C43—41no—
186C22×C4×C43—41no—
187C22×C4×C43C22×C411yescharacteristic
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C22×C411yescharacteristic
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C22×C411yescharacteristic
195C22×C4×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C22×C411yescharacteristic
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2411yescharacteristic
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—22no—
206C4⋊C4×C43—22no—
207C4⋊C4×C43—22no—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—22no—
211C4⋊C4×C43—22no—
212C4⋊C4×C43C22⋊C414yes—
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—22no—
221C22⋊C4×C43C22⋊C414yes—
222C22⋊C4×C43C22⋊C414yes—
223C42×C43—22no—
224C42×C43—22no—
225C42×C43—21no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C42×C43—21no—
231C42×C43C2×D412yes—
232C42×C43C2×D412yes—
233#10621877—44no—
234#10621877—44no—
235#10621877—44no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—44no—
259C2×C43⋊C8#4112yes—
260C2×C43⋊C8#4112yes—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43C2×C22⋊C412yes—
281C23×C43C2×C22⋊C412yes—
282C23×C43C23×C411yescharacteristic
283Q8×C43—44no—
284D4×C43—44no—
285D4×C43—44no—
286D4×C43—44no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—44no—
324C2×C4×C43—44no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43C2×C22⋊C412yes—
330C2×C4×C43C2×C22⋊C412yes—
331C2×C4×C43C2×C22⋊C412yes—
332C2×C4×C43C2×C22⋊C412yes—
333C2×C4×C43#13112yes—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C2×C4×C432−1+411yescharacteristic
340C43⋊C8—22no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347C43⋊C8—41no—
348#22472—431nomaximal, Sylow
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43C22×C22⋊C411yescharacteristic
371C22×C43C4×#4111yescharacteristic
372C22×C43#52011yescharacteristic
373C22×C43C2×#13111yescharacteristic
374C22×C43#56811yescharacteristic
375C22×C43#56811yescharacteristic
376C22×C43#56811yescharacteristic
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—22no—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—41no—
383C4×C43—41no—
384C4×C43—41no—
385C4×C43—41no—
386C4×C43—41no—
387C4×C43—41no—
388C4×C43#54611yescharacteristic
389C4×C43#54611yescharacteristic
390C4×C43#54711yescharacteristic
391C4×C43#54711yescharacteristic
392C2×#529D4311yescharacteristic
393C2×#436—431no—
394C2×#435—431no—
395#1985—431no—
396#1984—431no—
397#1870—431no—
398#1870—431no—
399#1870—431no—
400#1869—431no—
401#1818—431no—
402#1817—431no—
403#1798—431no—
404#1750—431no—
405#1729—431no—
406#1728—431no—
407C2×C43—42no—
408C2×C43—42no—
409C2×C43—81no—
410C2×C43#233911yescharacteristic
411C2×C43#287911yescharacteristic
412C2×C43#288011yescharacteristic
413C2×C43#296711yescharacteristic
414C2×C43#296911yescharacteristic
415C2×C43#299311yescharacteristic
416C2×C43#299511yescharacteristic
417C22×M16—431no—
418C22×M16—431no—
419C22×M16—431no—
420C23×C8—431no—
421#529—24no—
422#529—24no—
423C2×#126Dic4311yescharacteristic
424C2×#126Dic4311yescharacteristic
425C2×#125Dic4311yescharacteristic
426C2×#124Dic4311yescharacteristic
427C2×#123Dic4311yescharacteristic
428C2×#123Dic4311yescharacteristic
429C2×C22⋊Q8Dic4311yescharacteristic
430C2×#121Dic4311yescharacteristic
431C2×C4×Q8C2×D4311yescharacteristic
432C2×C4×D4C2×D4311yescharacteristic
433C2×C4×D4C2×D4311yescharacteristic
434C2×C4×D4C2×D4311yescharacteristic
435C2×#117C2×D4311yescharacteristic
436C2×#117C2×D4311yescharacteristic
437C22×C42C2×D4311yescharacteristic
438#436—864no—
439#435—864no—
440C2×C4⋊C8—431no—
441C2×C4⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8—431no—
450C2×#97—431no—
451C2×C4×C8—431no—
452#336—431no—
453#336—431no—
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336—431no—
460#336—431no—
461#336—431no—
462#336—431no—
463#336—431no—
464C43#2247211yescharacteristic, complemented, Sylow
465C22×Q8C2×Dic4311yescharacteristic
466C22×D4C2×Dic4311yescharacteristic
467C22×D4C2×Dic4311yescharacteristic
468C22×D4C2×Dic4311yescharacteristic
469C23×C4C2×Dic4311yescharacteristic
470C23×C4C2×Dic4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C2×M16—862no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—862no—
480C2×M16—1721no—
481C2×M16—1721no—
482C2×M16—1721no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—862no—
492C22×C8—862no—
493C22×C8—1721no—
494#126—24no—
495#126—24no—
496#125—24no—
497#124—24no—
498#123—24no—
499#123—24no—
500C22⋊Q8—24no—
501#121—24no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4C22⋊D4314yes—
509C4×D4C22⋊D4314yes—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—22no—
514C2×C4⋊C4C2×Dic4311yescharacteristic
515C2×C4⋊C4C2×Dic4311yescharacteristic
516C2×C4⋊C4C2×Dic4311yescharacteristic
517C2×C4⋊C4C2×Dic4311yescharacteristic
518C2×C4⋊C4C2×Dic4311yescharacteristic
519C2×C4⋊C4C2×Dic4311yescharacteristic
520C2×C4⋊C4C2×Dic4311yescharacteristic
521C2×C4⋊C4C2×Dic4311yescharacteristic
522C2×C4⋊C4C2×Dic4311yescharacteristic
523C2×C4⋊C4C2×Dic4311yescharacteristic
524C2×C22⋊C4C2×Dic4311yescharacteristic
525C2×C22⋊C4C2×Dic4311yescharacteristic
526C2×C22⋊C4C2×Dic4311yescharacteristic
527C2×C22⋊C4C2×Dic4311yescharacteristic
528C2×C22⋊C4C2×Dic4311yescharacteristic
529C2×C22⋊C4C2×Dic4311yescharacteristic
530C2×C22⋊C4C2×Dic4311yescharacteristic
531C2×C22⋊C4C2×Dic4311yescharacteristic
532C2×C22⋊C4C2×Dic4311yescharacteristic
533C2×C22⋊C4C2×Dic4311yescharacteristic
534C2×C42—22no—
535C2×C42—22no—
536C2×C42C2×Dic4311yescharacteristic
537C2×C42C2×Dic4311yescharacteristic
538C2×C42C22×D4311yescharacteristic
539C2×C42C22×D4311yescharacteristic
540C2×C42C22×D4311yescharacteristic
541C2×C42C22×D4311yescharacteristic
542C4⋊C8—862no—
543C4⋊C8—862no—
544C22⋊C8—862no—
545C22⋊C8—862no—
546C22⋊C8—862no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549C22⋊C8—862no—
550C22⋊C8—1721no—
551C22⋊C8—1721no—
552#97—862no—
553C4×C8—862no—
554C24C22×Dic4311yescharacteristic
555C24C22×Dic4311yescharacteristic
556C24C22×Dic4311yescharacteristic
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—41no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4C22⋊Dic4314yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic4311yescharacteristic
590C22×C4C22×Dic4311yescharacteristic
591C22×C4C22×Dic4311yescharacteristic
592C22×C4C22×Dic4311yescharacteristic
593C22×C4C22×Dic4311yescharacteristic
594C22×C4C22×Dic4311yescharacteristic
595C22×C4C22×Dic4311yescharacteristic
596C22×C4C22×Dic4311yescharacteristic
597C22×C4C22×Dic4311yescharacteristic
598C22×C4C22×Dic4311yescharacteristic
599C22×C4C22×Dic4311yescharacteristic
600C22×C4C2×C22⋊D4312yes—
601C22×C4C2×C22⋊D4312yes—
602C22×C4C2×C22⋊D4312yes—
603C22×C4C2×C22⋊D4312yes—
604C22×C4C23×D4311yescharacteristic
605M16—1724no—
606M16—1724no—
607M16—1724no—
608C2×C8—432no—
609C2×C8—432no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—1724no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4C22⋊Dic4314yes—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4C22⋊Dic4314yes—
652C22⋊C4C22⋊Dic4314yes—
653C42—22no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42C2×C22⋊D4312yes—
662C42C2×C22⋊D4312yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23C2×C22⋊Dic4312yes—
683C23C2×C22⋊Dic4312yes—
684C23C23×Dic4311yescharacteristic
685Q8—44no—
686D4—44no—
687D4—44no—
688D4—44no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4C2×C22⋊Dic4312yes—
732C2×C4C2×C22⋊Dic4312yes—
733C2×C4C2×C22⋊Dic4312yes—
734C2×C4C2×C22⋊Dic4312yes—
735C2×C4#1306333212yes—
736C2×C4C22×C22⋊D4311yescharacteristic
737C2×C4C22×C22⋊D4311yescharacteristic
738C2×C4#41×D4311yescharacteristic
739C2×C4#41×D4311yescharacteristic
740C2×C4#1306337111yescharacteristic
741C2×C4#1306337211yescharacteristic
742C8—862no—
743C8—862no—
744C8—1721no—
745C8—1721no—
746C8—1721no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22C22×C22⋊Dic4311yescharacteristic
772C22#41×Dic4311yescharacteristic
773C22#1458338211yescharacteristic
774C22C2×#1306333211yescharacteristic
775C22#1458366611yescharacteristic
776C22#1458366611yescharacteristic
777C22#1458366611yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4#1458353711yescharacteristic
790C4#1458353711yescharacteristic
791C4#1458354811yescharacteristic
792C4#1458354811yescharacteristic
793C2—42no—
794C2—42no—
795C2—81no—
796C2#1913742511yescharacteristic
797C2#1914304011yescharacteristic
798C2#1914304411yescharacteristic
799C2#1914358211yescharacteristic
800C2#1914360011yescharacteristic
801C2#1914374411yescharacteristic
802C2#1914376511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#529C2
prime radicalC2×#121×C43C4
cosocleC22×C4×C43C24
hypercenterC2×#529D43
hypocenterC43#22472
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#14582977C2semidirect
2. C2×#14582971C2semidirect
3. #19135536C2semidirect
4. #19135532C2semidirect
5. #19134893C2semidirect
6. #19134893C2semidirect
7. #19134893C2semidirect
8. #19134888C2semidirect
9. #19134666C2semidirect
10. #19134663C2semidirect
11. #19134579C2semidirect
12. #19134361C2semidirect
13. #19134292C2semidirect
14. #19134289C2semidirect
464. C43#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#145829772
C2×#145829712
#191355362
#191355322
#191348932
#191348882
#191346662
#191346632
#191345792
#191343612
#191342922
#191342892
C2×C43×#5292
#2247243