Finite Group Databasebeta

← C41×#22056 #23798257

Subgroups — C41×#22056 #23798257

Order 10496.

1136 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×C41×#447C211yesmaximal, characteristic
2C41×#2324C211yesmaximal, characteristic, complemented
3C41×#2309C211yesmaximal, characteristic, complemented
4C41×#1972C211yesmaximal, characteristic, complemented
5C41×#1970C211yesmaximal, characteristic, complemented
6C41×#1936C211yesmaximal, characteristic, complemented
7C41×#1934C211yesmaximal, characteristic, complemented
8C41×#1926C211yesmaximal, characteristic, complemented
9C41×#1925C211yesmaximal, characteristic, complemented
10C41×#1879C211yesmaximal, characteristic, complemented
11C41×#1879C211yesmaximal, characteristic, complemented
12C41×#1875C211yesmaximal, characteristic, complemented
13C41×#1854C211yesmaximal, characteristic, complemented
14C41×#1786C211yesmaximal, characteristic, complemented
15C41×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C22×D8×C41C2211yescharacteristic
19C2×#121×C41C2211yescharacteristic
20C2×C4×D4×C41C2211yescharacteristic, complemented
21C2×#117×C41C2211yescharacteristic
22C2×#117×C41C2211yescharacteristic
23C41×#447C418yescomplemented
24C2×#107×C41C2211yescharacteristic, complemented
25C2×#106×C41C2211yescharacteristic, complemented
26C2×#102×C41C2211yescharacteristic
27C2×#102×C41C2211yescharacteristic
28C2×#102×C41C2211yescharacteristic
29C2×#102×C41C2211yescharacteristic
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic, complemented
33C2×#102×C41C2211yescharacteristic, complemented
34C2×C22⋊C8×C41C2211yescharacteristic
35C2×C22⋊C8×C41C2211yescharacteristic
36C2×#97×C41C2211yescharacteristic, complemented
37C2×C4×C8×C41C2211yescharacteristic, complemented
38C41×#390—21no—
39C41×#390—21no—
40C41×#390—21no—
41C41×#390C2211yescharacteristic
42C41×#390C2211yescharacteristic
43C41×#390C2211yescharacteristic
44C41×#390C2211yescharacteristic
45C41×#390C2211yescharacteristic, complemented
46C41×#389C2211yescharacteristic, complemented
47C41×#388—21no—
48C41×#386—21no—
49C41×#385—21no—
50C41×#380C2211yescharacteristic
51C41×#379—21no—
52C41×#379—21no—
53C4×C4⋊C4×C41C2211yescharacteristic, complemented
54C41×#340C2211yescharacteristic, complemented
55C41×#340C2211yescharacteristic, complemented
56C41×#340C2211yescharacteristic, complemented
57C41×#340C2211yescharacteristic, complemented
58C41×#336C2211yescharacteristic, complemented
59C41×#336C2211yescharacteristic, complemented
60C25×C41—21no—
61C22×D4×C41—21no—
62C22×D4×C41—21no—
63C22×D4×C41—22no—
64C22×D4×C41—41no—
65C22×D4×C41—41no—
66C22×D4×C41—41no—
67C22×D4×C41—41no—
68C22×D4×C41C2×C414yescomplemented
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C22×D4×C41C2311yescharacteristic
72C23×C4×C41—21no—
73C23×C4×C41C2311yescharacteristic
74C2×D8×C41—41no—
75C2×D8×C41—41no—
76C2×D8×C41—41no—
77C2×D8×C41—41no—
78C2×D8×C41C2×C414yes—
79C2×D8×C41C2×C414yes—
80C22×C8×C41C2311yescharacteristic
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84#121×C41—22no—
85#121×C41C2×C414yes—
86C4×D4×C41—41no—
87C4×D4×C41—41no—
88#117×C41—41no—
89#117×C41—41no—
90#117×C41—41no—
91#117×C41—41no—
92C2×C4⋊C4×C41—21no—
93C2×C4⋊C4×C41D411yescharacteristic
94C2×C4⋊C4×C41D411yescharacteristic
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C4⋊C4×C41C2311yescharacteristic
97C2×C4⋊C4×C41C2311yescharacteristic
98C2×C4⋊C4×C41C2311yescharacteristic
99C2×C4⋊C4×C41C2311yescharacteristic
100C2×C22⋊C4×C41—21no—
101C2×C22⋊C4×C41—21no—
102C2×C22⋊C4×C41—21no—
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C22⋊C4×C41—21no—
109C2×C22⋊C4×C41—21no—
110C2×C22⋊C4×C41—21no—
111C2×C22⋊C4×C41—21no—
112C2×C22⋊C4×C41—21no—
113C2×C22⋊C4×C41—21no—
114C2×C22⋊C4×C41D411yescharacteristic
115C2×C22⋊C4×C41D411yescharacteristic
116C2×C42×C41—21no—
117C2×C42×C41—21no—
118C2×C42×C41C2311yescharacteristic
119C2×C42×C41C2311yescharacteristic
120#107×C41—41no—
121#106×C41—41no—
122#102×C41—41no—
123#102×C41—41no—
124#102×C41—41no—
125#102×C41—41no—
126#102×C41—41no—
127#102×C41—41no—
128#102×C41C2×C414yescomplemented
129#102×C41C2×C414yescomplemented
130C22⋊C8×C41—22no—
131C22⋊C8×C41C2×C414yescomplemented
132#97×C41—41no—
133C4×C8×C41—41no—
134#95×C41—21no—
135#95×C41—21no—
136#95×C41—21no—
137C24×C41—21no—
138C24×C41—21no—
139C24×C41—21no—
140C24×C41—24no—
141C24×C41—42no—
142C24×C41—42no—
143C24×C41—81no—
144C24×C41—81no—
145C24×C41—81no—
146C24×C41—81no—
147C24×C41C2×D411yescharacteristic
148C2×D4×C41—24no—
149C2×D4×C41—24no—
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—21no—
155C2×D4×C41—21no—
156C2×D4×C41—21no—
157C2×D4×C41—21no—
158C2×D4×C41—21no—
159C2×D4×C41—21no—
160C2×D4×C41—21no—
161C2×D4×C41—21no—
162C2×D4×C41—21no—
163C2×D4×C41—21no—
164C2×D4×C41—21no—
165C2×D4×C41—44no—
166C2×D4×C41—44no—
167C2×D4×C41—42no—
168C2×D4×C41—42no—
169C2×D4×C41—44no—
170C2×D4×C41—44no—
171C2×D4×C41—81no—
172C2×D4×C41—81no—
173C2×D4×C41C22×C412yes—
174C2×D4×C41C22×C412yes—
175C2×D4×C41C22×C412yes—
176C22×C4×C41—21no—
177C22×C4×C41—21no—
178C22×C4×C41—21no—
179C22×C4×C41—21no—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—42no—
186C22×C4×C41—81no—
187C22×C4×C41—81no—
188C22×C4×C41C22×C412yes—
189C22×C4×C41C2×D411yescharacteristic
190C22×C4×C41C2×D411yescharacteristic
191C22×C4×C41C2×D411yescharacteristic
192C22×C4×C41C2×D411yescharacteristic
193C22×C4×C41C2×D411yescharacteristic
194C22×C4×C41#4112yes—
195C22×C4×C41C2411yescharacteristic
196D8×C41—44no—
197D8×C41—44no—
198C2×C8×C41—21no—
199C2×C8×C41—21no—
200C2×C8×C41—21no—
201C2×C8×C41—21no—
202C2×C8×C41—21no—
203C2×C8×C41—21no—
204C2×C8×C41—21no—
205C2×C8×C41—21no—
206C2×C8×C41—21no—
207C2×C8×C41—21no—
208C2×C8×C41C22×C412yes—
209C2×C8×C41C22×C412yes—
210C4⋊C4×C41—21no—
211C4⋊C4×C41—21no—
212C4⋊C4×C41—21no—
213C4⋊C4×C41—21no—
214C4⋊C4×C41—21no—
215C4⋊C4×C41—21no—
216C4⋊C4×C41—21no—
217C4⋊C4×C41—21no—
218C4⋊C4×C41—21no—
219C4⋊C4×C41—41no—
220C4⋊C4×C41—41no—
221C4⋊C4×C41—81no—
222C4⋊C4×C41C22×C412yes—
223C22⋊C4×C41—24no—
224C22⋊C4×C41—41no—
225C22⋊C4×C41—41no—
226C22⋊C4×C41—42no—
227C22⋊C4×C41—42no—
228C22⋊C4×C41—81no—
229C22⋊C4×C41—81no—
230C22⋊C4×C41—81no—
231C22⋊C4×C41—81no—
232C22⋊C4×C41—81no—
233C22⋊C4×C41—81no—
234C22⋊C4×C41—81no—
235C22⋊C4×C41—81no—
236C22⋊C4×C41—81no—
237C22⋊C4×C41—81no—
238C22⋊C4×C41—81no—
239C42×C41—21no—
240C42×C41—21no—
241C42×C41—21no—
242C42×C41—21no—
243C42×C41—42no—
244C42×C41—81no—
245C23×C41—21no—
246C23×C41—21no—
247C23×C41—21no—
248C23×C41—21no—
249C23×C41—21no—
250C23×C41—21no—
251C23×C41—22no—
252C23×C41—22no—
253C23×C41—22no—
254C23×C41—48no—
255C23×C41—41no—
256C23×C41—41no—
257C23×C41—41no—
258C23×C41—41no—
259C23×C41—41no—
260C23×C41—41no—
261C23×C41—41no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—41no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—84no—
274C23×C41—84no—
275C23×C41—84no—
276C23×C41—84no—
277C23×C41—84no—
278C23×C41—84no—
279C23×C41C4×D412yes—
280C23×C41C22×D411yescharacteristic
281D4×C41—22no—
282D4×C41—22no—
283D4×C41—22no—
284D4×C41—22no—
285D4×C41—22no—
286D4×C41—22no—
287D4×C41—48no—
288D4×C41—41no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—84no—
295C2×C4×C41—21no—
296C2×C4×C41—21no—
297C2×C4×C41—22no—
298C2×C4×C41—22no—
299C2×C4×C41—22no—
300C2×C4×C41—22no—
301C2×C4×C41—22no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—21no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—41no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—84no—
329C2×C4×C41C4×D412yes—
330C2×C4×C41C23×C411yescharacteristic
331C2×C4×C41C2×#4111yescharacteristic
332C2×C4×C41H(5,𝔽2)11yescharacteristic
333C2×C4×C41H(5,𝔽2)11yescharacteristic
334C2×C4×C41H(5,𝔽2)11yescharacteristic
335C2×C4×C41H(5,𝔽2)11yescharacteristic
336C8×C41—22no—
337C8×C41—22no—
338C8×C41—41no—
339C8×C41—41no—
340#22056C4111yesmaximal, characteristic, direct product factor, Sylow
341C22×C41—22no—
342C22×C41—22no—
343C22×C41—22no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—41no—
347C22×C41—41no—
348C22×C41—42no—
349C22×C41—42no—
350C22×C41—42no—
351C22×C41—42no—
352C22×C41—42no—
353C22×C41—42no—
354C22×C41—42no—
355C22×C41—42no—
356C22×C41—42no—
357C22×C41—816no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41—81no—
363C22×C41—81no—
364C22×C41—81no—
365C22×C41—81no—
366C22×C41—81no—
367C22×C41—81no—
368C22×C41—81no—
369C22×C41—81no—
370C22×C41C2×C4×D411yescharacteristic
371C22×C41#53411yescharacteristic
372C22×C41#53511yescharacteristic
373C22×C41#57611yescharacteristic
374C22×C41#57611yescharacteristic
375C22×C41#57611yescharacteristic
376C22×C41#57711yescharacteristic
377C4×C41—22no—
378C4×C41—41no—
379C4×C41—41no—
380C4×C41—41no—
381C4×C41—41no—
382C4×C41—42no—
383C4×C41—81no—
384C4×C41—81no—
385C4×C41—81no—
386C4×C41—81no—
387C4×C41#51811yescharacteristic
388C4×C41#51811yescharacteristic
389C4×C41#53811yescharacteristic
390C4×C41#53811yescharacteristic
391C2×#447C2×C4111yescharacteristic
392#2324C2×C4111yescharacteristic, complemented
393#2309C2×C4111yescharacteristic, complemented
394#1972C2×C4111yescharacteristic, complemented
395#1970C2×C4111yescharacteristic, complemented
396#1936C2×C4111yescharacteristic, complemented
397#1934C2×C4111yescharacteristic, complemented
398#1926C2×C4111yescharacteristic, complemented
399#1925C2×C4111yescharacteristic, complemented
400#1879C2×C4111yescharacteristic, complemented
401#1879C2×C4111yescharacteristic, complemented
402#1875C2×C4111yescharacteristic, complemented
403#1854C2×C4111yescharacteristic, complemented
404#1786C2×C4111yescharacteristic, complemented
405#1750C2×C4111yescharacteristic, complemented
406C2×C41—42no—
407C2×C41—82no—
408C2×C41—82no—
409C2×C41—82no—
410C2×C41#232111yescharacteristic
411C2×C41#294611yescharacteristic
412C2×C41#294811yescharacteristic
413C2×C41#319811yescharacteristic
414C2×C41#319911yescharacteristic
415C2×C41#322011yescharacteristic
416C2×C41#322411yescharacteristic
417C23×D4C22×C4111yescharacteristic
418C22×D8C22×C4111yescharacteristic
419C22×D8C22×C4111yescharacteristic
420C2×#121C22×C4111yescharacteristic
421C2×C4×D4C22×C4111yescharacteristic, complemented
422C2×#117C22×C4111yescharacteristic
423C2×#117C22×C4111yescharacteristic
424#447C4×C4118yescomplemented
425C2×#107C22×C4111yescharacteristic, complemented
426C2×#106C22×C4111yescharacteristic, complemented
427C2×#102C22×C4111yescharacteristic
428C2×#102C22×C4111yescharacteristic
429C2×#102C22×C4111yescharacteristic
430C2×#102C22×C4111yescharacteristic
431C2×#102C22×C4111yescharacteristic
432C2×#102C22×C4111yescharacteristic
433C2×#102C22×C4111yescharacteristic, complemented
434C2×#102C22×C4111yescharacteristic, complemented
435C2×C22⋊C8C22×C4111yescharacteristic
436C2×C22⋊C8C22×C4111yescharacteristic
437C2×#97C22×C4111yescharacteristic, complemented
438C2×C4×C8C22×C4111yescharacteristic, complemented
439#390—21no—
440#390—21no—
441#390—21no—
442#390C22×C4111yescharacteristic
443#390C22×C4111yescharacteristic
444#390C22×C4111yescharacteristic
445#390C22×C4111yescharacteristic
446#390C22×C4111yescharacteristic, complemented
447#389C22×C4111yescharacteristic, complemented
448#388—21no—
449#386—21no—
450#385—21no—
451#380C22×C4111yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4C22×C4111yescharacteristic, complemented
455#340C22×C4111yescharacteristic, complemented
456#340C22×C4111yescharacteristic, complemented
457#340C22×C4111yescharacteristic, complemented
458#340C22×C4111yescharacteristic, complemented
459#336C22×C4111yescharacteristic, complemented
460#336C22×C4111yescharacteristic, complemented
461C41#2205611yescharacteristic, direct product factor, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×C4×C4114yescomplemented
471C22×D4C23×C4111yescharacteristic
472C22×D4C23×C4111yescharacteristic
473C22×D4C23×C4111yescharacteristic
474C23×C4—21no—
475C23×C4C23×C4111yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×C4×C4114yes—
481C2×D8C2×C4×C4114yes—
482C22×C8C23×C4111yescharacteristic
483C22×C8C23×C4111yescharacteristic
484C22×C8C23×C4111yescharacteristic
485C22×C8C23×C4111yescharacteristic
486#121—22no—
487#121C2×C4×C4114yes—
488C4×D4—41no—
489C4×D4—41no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4D4×C4111yescharacteristic
496C2×C4⋊C4D4×C4111yescharacteristic
497C2×C4⋊C4C23×C4111yescharacteristic
498C2×C4⋊C4C23×C4111yescharacteristic
499C2×C4⋊C4C23×C4111yescharacteristic
500C2×C4⋊C4C23×C4111yescharacteristic
501C2×C4⋊C4C23×C4111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C4111yescharacteristic
517C2×C22⋊C4D4×C4111yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C4111yescharacteristic
521C2×C42C23×C4111yescharacteristic
522#107—41no—
523#106—41no—
524#102—41no—
525#102—41no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102C2×C4×C4114yescomplemented
531#102C2×C4×C4114yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C4114yescomplemented
534#97—41no—
535C4×C8—41no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24C2×D4×C4111yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×C4×C4112yes—
576C2×D4C22×C4×C4112yes—
577C2×D4C22×C4×C4112yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—42no—
588C22×C4—81no—
589C22×C4—81no—
590C22×C4C22×C4×C4112yes—
591C22×C4C2×D4×C4111yescharacteristic
592C22×C4C2×D4×C4111yescharacteristic
593C22×C4C2×D4×C4111yescharacteristic
594C22×C4C2×D4×C4111yescharacteristic
595C22×C4C2×D4×C4111yescharacteristic
596C22×C4#41×C4112yes—
597C22×C4C24×C4111yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C22×C4×C4112yes—
611C2×C8C22×C4×C4112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—41no—
622C4⋊C4—41no—
623C4⋊C4—81no—
624C4⋊C4C22×C4×C4112yes—
625C22⋊C4—24no—
626C22⋊C4—41no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—81no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23C4×D4×C4112yes—
682C23C22×D4×C4111yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
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—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4C4×D4×C4112yes—
732C2×C4C23×C4×C4111yescharacteristic
733C2×C4C2×#41×C4111yescharacteristic
734C2×C4H(5,𝔽2)×C4111yescharacteristic
735C2×C4H(5,𝔽2)×C4111yescharacteristic
736C2×C4H(5,𝔽2)×C4111yescharacteristic
737C2×C4H(5,𝔽2)×C4111yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×C4×D4×C4111yescharacteristic
772C22C41×#53411yescharacteristic
773C22C41×#53511yescharacteristic
774C22C41×#57611yescharacteristic
775C22C41×#57611yescharacteristic
776C22C41×#57611yescharacteristic
777C22C41×#57711yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4C41×#51811yescharacteristic
789C4C41×#51811yescharacteristic
790C4C41×#53811yescharacteristic
791C4C41×#53811yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2C41×#232111yescharacteristic
797C2C41×#294611yescharacteristic
798C2C41×#294811yescharacteristic
799C2C41×#319811yescharacteristic
800C2C41×#319911yescharacteristic
801C2C41×#322011yescharacteristic
802C2C41×#322411yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#447C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×#117×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2324C2semidirect
3. C41×#2309C2semidirect
4. C41×#1972C2semidirect
5. C41×#1970C2semidirect
6. C41×#1936C2semidirect
7. C41×#1934C2semidirect
8. C41×#1926C2semidirect
9. C41×#1925C2semidirect
10. C41×#1879C2semidirect
11. C41×#1879C2semidirect
12. C41×#1875C2semidirect
13. C41×#1854C2semidirect
14. C41×#1786C2semidirect
15. C41×#1750C2semidirect
20. C2×C4×D4×C41C22semidirect
23. C41×#447C4semidirect
24. C2×#107×C41C22semidirect
25. C2×#106×C41C22semidirect
32. C2×#102×C41C22semidirect
33. C2×#102×C41C22semidirect
36. C2×#97×C41C22semidirect
37. C2×C4×C8×C41C22semidirect
45. C41×#390C22semidirect
46. C41×#389C22semidirect
53. C4×C4⋊C4×C41C22semidirect
54. C41×#340C22semidirect
55. C41×#340C22semidirect
56. C41×#340C22semidirect
57. C41×#340C22semidirect
58. C41×#336C22semidirect
59. C41×#336C22semidirect
68. C22×D4×C41C2×C4semidirect
128. #102×C41C2×C4semidirect
129. #102×C41C2×C4semidirect
131. C22⋊C8×C41C2×C4semidirect
340. #22056C41direct (N × H)
392. #2324C2×C41semidirect
393. #2309C2×C41semidirect
394. #1972C2×C41semidirect
395. #1970C2×C41semidirect
396. #1936C2×C41semidirect
397. #1934C2×C41semidirect
398. #1926C2×C41semidirect
399. #1925C2×C41semidirect
400. #1879C2×C41semidirect
401. #1879C2×C41semidirect
402. #1875C2×C41semidirect
403. #1854C2×C41semidirect
404. #1786C2×C41semidirect
405. #1750C2×C41semidirect
421. C2×C4×D4C22×C41semidirect
424. #447C4×C41semidirect
425. C2×#107C22×C41semidirect
426. C2×#106C22×C41semidirect
433. C2×#102C22×C41semidirect
434. C2×#102C22×C41semidirect
437. C2×#97C22×C41semidirect
438. C2×C4×C8C22×C41semidirect
446. #390C22×C41semidirect
447. #389C22×C41semidirect
454. C4×C4⋊C4C22×C41semidirect
455. #340C22×C41semidirect
456. #340C22×C41semidirect
457. #340C22×C41semidirect
458. #340C22×C41semidirect
459. #336C22×C41semidirect
460. #336C22×C41semidirect
461. C41#22056direct (N × H)
470. C22×D4C2×C4×C41semidirect
530. #102C2×C4×C41semidirect
531. #102C2×C4×C41semidirect
533. C22⋊C8C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4472
C41×#23242
C41×#23092
C41×#19722
C41×#19702
C41×#19362
C41×#19342
C41×#19262
C41×#19252
C41×#18792
C41×#18752
C41×#18542
C41×#17862
C41×#17502
#2205641