Finite Group Databasebeta

← C41×#24512 #23800713

Subgroups — C41×#24512 #23800713

Order 10496.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#447C211yesmaximal, characteristic
2C2×C41×#433C211yesmaximal, characteristic, complemented
3C41×#2624C211yesmaximal, characteristic, complemented
4C41×#2309C211yesmaximal, characteristic, complemented
5C41×#2067C211yesmaximal, characteristic, complemented
6C41×#2065C211yesmaximal, characteristic, complemented
7C41×#2054C211yesmaximal, characteristic, complemented
8C41×#2054C211yesmaximal, characteristic, complemented
9C41×#1972C211yesmaximal, characteristic, complemented
10C41×#1970C211yesmaximal, characteristic, complemented
11C41×#1936C211yesmaximal, characteristic, complemented
12C41×#1934C211yesmaximal, characteristic, complemented
13C41×#1875C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C41C2211yescharacteristic
17C22×D8×C41C2211yescharacteristic
18C22×D8×C41C2211yescharacteristic
19C2×#121×C41C2211yescharacteristic
20C2×#117×C41C2211yescharacteristic
21C2×#117×C41C2211yescharacteristic
22C41×#447—24no—
23C41×#433—24no—
24C2×#107×C41C2211yescharacteristic, complemented
25C2×#106×C41C2211yescharacteristic, complemented
26C2×C4⋊C8×C41C2211yescharacteristic, complemented
27C2×C4⋊C8×C41C2211yescharacteristic, complemented
28C2×#102×C41C2211yescharacteristic
29C2×#102×C41C2211yescharacteristic
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#102×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic, complemented
35C2×#102×C41C2211yescharacteristic, complemented
36C2×C22⋊C8×C41C2211yescharacteristic
37C2×C22⋊C8×C41C2211yescharacteristic
38C2×#97×C41C2211yescharacteristic, complemented
39C2×C4×C8×C41C2211yescharacteristic, complemented
40C41×#399—21no—
41C41×#397—21no—
42C41×#394—21no—
43C41×#394—21no—
44C41×#390—21no—
45C41×#390—21no—
46C41×#390C2211yescharacteristic
47C41×#390C2211yescharacteristic
48C41×#390C2211yescharacteristic
49C41×#390C2211yescharacteristic
50C41×#390C2211yescharacteristic, complemented
51C41×#390C2211yescharacteristic, complemented
52C41×#389C2211yescharacteristic, complemented
53C41×#389C2211yescharacteristic, complemented
54C41×#380C2211yescharacteristic
55C41×#379—21no—
56C41×#379—21no—
57C41×#340C2211yescharacteristic, complemented
58C41×#340C2211yescharacteristic, complemented
59C41×#340C2211yescharacteristic, complemented
60C41×#340C2211yescharacteristic, complemented
61C25×C41—21no—
62C22×D4×C41—22no—
63C22×D4×C41—22no—
64C22×D4×C41—21no—
65C22×D4×C41—21no—
66C22×D4×C41—22no—
67C22×D4×C41—22no—
68C22×D4×C41—41no—
69C22×D4×C41—41no—
70C22×D4×C41C2311yescharacteristic
71C22×D4×C41C2311yescharacteristic
72C22×D4×C41C2311yescharacteristic
73C23×C4×C41C2311yescharacteristic
74C2×D8×C41—22no—
75C2×D8×C41—22no—
76C2×D8×C41—22no—
77C2×D8×C41—22no—
78C2×D8×C41—41no—
79C2×D8×C41—41no—
80C22×C8×C41C2311yescharacteristic
81C22×C8×C41C2311yescharacteristic
82C22×C8×C41C2311yescharacteristic
83C22×C8×C41C2311yescharacteristic
84#121×C41—22no—
85#121×C41—22no—
86#117×C41—22no—
87#117×C41—22no—
88#117×C41—41no—
89#117×C41—41no—
90C2×C4⋊C4×C41—21no—
91C2×C4⋊C4×C41—21no—
92C2×C4⋊C4×C41D411yescharacteristic
93C2×C4⋊C4×C41D411yescharacteristic
94C2×C4⋊C4×C41C2311yescharacteristic
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C4⋊C4×C41C2311yescharacteristic
97C2×C4⋊C4×C41C2311yescharacteristic
98C2×C4⋊C4×C41C2311yescharacteristic
99C2×C22⋊C4×C41—21no—
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×C41C2311yescharacteristic
118C2×C42×C41C2311yescharacteristic
119#107×C41—41no—
120#106×C41—41no—
121C4⋊C8×C41—22no—
122C4⋊C8×C41—22no—
123#102×C41—22no—
124#102×C41—22no—
125#102×C41—22no—
126#102×C41—22no—
127#102×C41—41no—
128#102×C41—41no—
129#102×C41—41no—
130#102×C41—41no—
131C22⋊C8×C41—22no—
132C22⋊C8×C41D414yes—
133#97×C41—22no—
134C4×C8×C41—22no—
135#95×C41—21no—
136#95×C41—21no—
137#95×C41—21no—
138C24×C41—24no—
139C24×C41—21no—
140C24×C41—21no—
141C24×C41—21no—
142C24×C41—42no—
143C24×C41—42no—
144C24×C41—81no—
145C24×C41—81no—
146C24×C41—81no—
147C24×C41—81no—
148C24×C41C2×D411yescharacteristic
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—21no—
166C2×D4×C41—44no—
167C2×D4×C41—44no—
168C2×D4×C41—44no—
169C2×D4×C41—44no—
170C2×D4×C41—42no—
171C2×D4×C41—42no—
172C2×D4×C41—42no—
173C2×D4×C41—81no—
174C2×D4×C41—81no—
175C2×D4×C41#4112yes—
176C2×D4×C41#4112yes—
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—21no—
186C22×C4×C41C2×D411yescharacteristic
187C22×C4×C41C2×D411yescharacteristic
188C22×C4×C41C2×D411yescharacteristic
189C22×C4×C41C2×D411yescharacteristic
190C22×C4×C41C2×D411yescharacteristic
191C22×C4×C41C2×D412yes—
192C22×C4×C41#4112yes—
193C22×C4×C41C2411yescharacteristic
194D8×C41—44no—
195D8×C41—44no—
196C2×C8×C41—21no—
197C2×C8×C41—21no—
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×C41C2×D412yes—
207C2×C8×C41C2×D412yes—
208C4⋊C4×C41—22no—
209C4⋊C4×C41—22no—
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—21no—
220C4⋊C4×C41—81no—
221C4⋊C4×C41—81no—
222C22⋊C4×C41—22no—
223C22⋊C4×C41—22no—
224C22⋊C4×C41—42no—
225C22⋊C4×C41—42no—
226C22⋊C4×C41—81no—
227C22⋊C4×C41—81no—
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—
244C23×C41—21no—
245C23×C41—21no—
246C23×C41—21no—
247C23×C41—21no—
248C23×C41—21no—
249C23×C41—21no—
250C23×C41—22no—
251C23×C41—22no—
252C23×C41—48no—
253C23×C41—41no—
254C23×C41—41no—
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—84no—
273C23×C41—84no—
274C23×C41—84no—
275C23×C41—84no—
276C23×C41—84no—
277C23×C41—84no—
278C23×C41#12112yes—
279C23×C41C22×D411yescharacteristic
280D4×C41—22no—
281D4×C41—22no—
282D4×C41—22no—
283D4×C41—22no—
284D4×C41—48no—
285D4×C41—41no—
286D4×C41—41no—
287D4×C41—41no—
288D4×C41—41no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—84no—
294C2×C4×C41—21no—
295C2×C4×C41—21no—
296C2×C4×C41—22no—
297C2×C4×C41—22no—
298C2×C4×C41—22no—
299C2×C4×C41—22no—
300C2×C4×C41—21no—
301C2×C4×C41—21no—
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—41no—
313C2×C4×C41—41no—
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#12112yes—
328C2×C4×C41C22×D411yescharacteristic
329C2×C4×C41C2×#4111yescharacteristic
330C2×C4×C41C2×#4111yescharacteristic
331C2×C4×C41C2×#4111yescharacteristic
332C2×C4×C41H(5,𝔽2)11yescharacteristic
333C2×C4×C41H(5,𝔽2)11yescharacteristic
334C8×C41—22no—
335C8×C41—22no—
336C8×C41—41no—
337C8×C41—41no—
338#24512C4111yesmaximal, characteristic, direct product factor, Sylow
339C22×C41—22no—
340C22×C41—22no—
341C22×C41—22no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—42no—
347C22×C41—42no—
348C22×C41—42no—
349C22×C41—42no—
350C22×C41—42no—
351C22×C41—42no—
352C22×C41—816no—
353C22×C41—81no—
354C22×C41—81no—
355C22×C41—81no—
356C22×C41—81no—
357C22×C41—81no—
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×C41C2×#12111yescharacteristic
369C22×C41#52511yescharacteristic
370C22×C41#53511yescharacteristic
371C22×C41#57611yescharacteristic
372C22×C41#57611yescharacteristic
373C22×C41#57611yescharacteristic
374C22×C41#57711yescharacteristic
375C4×C41—22no—
376C4×C41—41no—
377C4×C41—41no—
378C4×C41—41no—
379C4×C41—41no—
380C4×C41—81no—
381C4×C41—81no—
382C4×C41—81no—
383C4×C41—81no—
384C4×C41—81no—
385C4×C41#54611yescharacteristic
386C4×C41#54611yescharacteristic
387C4×C41#55111yescharacteristic
388C4×C41#55111yescharacteristic
389C2×#447C2×C4111yescharacteristic
390C2×#433C2×C4111yescharacteristic, complemented
391#2624C2×C4111yescharacteristic, complemented
392#2309C2×C4111yescharacteristic, complemented
393#2067C2×C4111yescharacteristic, complemented
394#2065C2×C4111yescharacteristic, complemented
395#2054C2×C4111yescharacteristic, complemented
396#2054C2×C4111yescharacteristic, complemented
397#1972C2×C4111yescharacteristic, complemented
398#1970C2×C4111yescharacteristic, complemented
399#1936C2×C4111yescharacteristic, complemented
400#1934C2×C4111yescharacteristic, complemented
401#1875C2×C4111yescharacteristic, complemented
402#1854C2×C4111yescharacteristic, complemented
403#1786C2×C4111yescharacteristic, complemented
404C2×C41—42no—
405C2×C41—82no—
406C2×C41—82no—
407C2×C41—161no—
408C2×C41#241111yescharacteristic
409C2×C41#305811yescharacteristic
410C2×C41#306211yescharacteristic
411C2×C41#311811yescharacteristic
412C2×C41#312211yescharacteristic
413C2×C41#322011yescharacteristic
414C2×C41#322411yescharacteristic
415C23×D4C22×C4111yescharacteristic
416C22×D8C22×C4111yescharacteristic
417C22×D8C22×C4111yescharacteristic
418C2×#121C22×C4111yescharacteristic
419C2×#117C22×C4111yescharacteristic
420C2×#117C22×C4111yescharacteristic
421#447—24no—
422#433—24no—
423C2×#107C22×C4111yescharacteristic, complemented
424C2×#106C22×C4111yescharacteristic, complemented
425C2×C4⋊C8C22×C4111yescharacteristic, complemented
426C2×C4⋊C8C22×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#399—21no—
440#397—21no—
441#394—21no—
442#394—21no—
443#390—21no—
444#390—21no—
445#390C22×C4111yescharacteristic
446#390C22×C4111yescharacteristic
447#390C22×C4111yescharacteristic
448#390C22×C4111yescharacteristic
449#390C22×C4111yescharacteristic, complemented
450#390C22×C4111yescharacteristic, complemented
451#389C22×C4111yescharacteristic, complemented
452#389C22×C4111yescharacteristic, complemented
453#380C22×C4111yescharacteristic
454#379—21no—
455#379—21no—
456#340C22×C4111yescharacteristic, complemented
457#340C22×C4111yescharacteristic, complemented
458#340C22×C4111yescharacteristic, complemented
459#340C22×C4111yescharacteristic, complemented
460C41#2451211yescharacteristic, direct product factor, Sylow
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C23×C4111yescharacteristic
471C22×D4C23×C4111yescharacteristic
472C22×D4C23×C4111yescharacteristic
473C23×C4C23×C4111yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8C23×C4111yescharacteristic
481C22×C8C23×C4111yescharacteristic
482C22×C8C23×C4111yescharacteristic
483C22×C8C23×C4111yescharacteristic
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C4111yescharacteristic
493C2×C4⋊C4D4×C4111yescharacteristic
494C2×C4⋊C4C23×C4111yescharacteristic
495C2×C4⋊C4C23×C4111yescharacteristic
496C2×C4⋊C4C23×C4111yescharacteristic
497C2×C4⋊C4C23×C4111yescharacteristic
498C2×C4⋊C4C23×C4111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
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⋊C4D4×C4111yescharacteristic
515C2×C22⋊C4D4×C4111yescharacteristic
516C2×C42—21no—
517C2×C42C23×C4111yescharacteristic
518C2×C42C23×C4111yescharacteristic
519#107—41no—
520#106—41no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—22no—
532C22⋊C8D4×C4114yes—
533#97—22no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C4111yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
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—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C4112yes—
576C2×D4#41×C4112yes—
577C22×C4—21no—
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×C4C2×D4×C4111yescharacteristic
587C22×C4C2×D4×C4111yescharacteristic
588C22×C4C2×D4×C4111yescharacteristic
589C22×C4C2×D4×C4111yescharacteristic
590C22×C4C2×D4×C4111yescharacteristic
591C22×C4C2×D4×C4112yes—
592C22×C4#41×C4112yes—
593C22×C4C24×C4111yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8C2×D4×C4112yes—
607C2×C8C2×D4×C4112yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
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—81no—
621C4⋊C4—81no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
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—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
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—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#121×C4112yes—
679C23C22×D4×C4111yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
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—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
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#121×C4112yes—
728C2×C4C22×D4×C4111yescharacteristic
729C2×C4C2×#41×C4111yescharacteristic
730C2×C4C2×#41×C4111yescharacteristic
731C2×C4C2×#41×C4111yescharacteristic
732C2×C4H(5,𝔽2)×C4111yescharacteristic
733C2×C4H(5,𝔽2)×C4111yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C4111yescharacteristic
768C22C41×#52511yescharacteristic
769C22C41×#53511yescharacteristic
770C22C41×#57611yescharacteristic
771C22C41×#57611yescharacteristic
772C22C41×#57611yescharacteristic
773C22C41×#57711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C41×#54611yescharacteristic
785C4C41×#54611yescharacteristic
786C4C41×#55111yescharacteristic
787C4C41×#55111yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C41×#241111yescharacteristic
793C2C41×#305811yescharacteristic
794C2C41×#306211yescharacteristic
795C2C41×#311811yescharacteristic
796C2C41×#312211yescharacteristic
797C2C41×#322011yescharacteristic
798C2C41×#322411yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×C41×#447C2
LCSG ▷ C22×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. C2×C41×#433C2semidirect
3. C41×#2624C2semidirect
4. C41×#2309C2semidirect
5. C41×#2067C2semidirect
6. C41×#2065C2semidirect
7. C41×#2054C2semidirect
8. C41×#2054C2semidirect
9. C41×#1972C2semidirect
10. C41×#1970C2semidirect
11. C41×#1936C2semidirect
12. C41×#1934C2semidirect
13. C41×#1875C2semidirect
14. C41×#1854C2semidirect
15. C41×#1786C2semidirect
24. C2×#107×C41C22semidirect
25. C2×#106×C41C22semidirect
26. C2×C4⋊C8×C41C22semidirect
27. C2×C4⋊C8×C41C22semidirect
34. C2×#102×C41C22semidirect
35. C2×#102×C41C22semidirect
38. C2×#97×C41C22semidirect
39. C2×C4×C8×C41C22semidirect
50. C41×#390C22semidirect
51. C41×#390C22semidirect
52. C41×#389C22semidirect
53. C41×#389C22semidirect
57. C41×#340C22semidirect
58. C41×#340C22semidirect
59. C41×#340C22semidirect
60. C41×#340C22semidirect
338. #24512C41direct (N × H)
390. C2×#433C2×C41semidirect
391. #2624C2×C41semidirect
392. #2309C2×C41semidirect
393. #2067C2×C41semidirect
394. #2065C2×C41semidirect
395. #2054C2×C41semidirect
396. #2054C2×C41semidirect
397. #1972C2×C41semidirect
398. #1970C2×C41semidirect
399. #1936C2×C41semidirect
400. #1934C2×C41semidirect
401. #1875C2×C41semidirect
402. #1854C2×C41semidirect
403. #1786C2×C41semidirect
423. C2×#107C22×C41semidirect
424. C2×#106C22×C41semidirect
425. C2×C4⋊C8C22×C41semidirect
426. C2×C4⋊C8C22×C41semidirect
433. C2×#102C22×C41semidirect
434. C2×#102C22×C41semidirect
437. C2×#97C22×C41semidirect
438. C2×C4×C8C22×C41semidirect
449. #390C22×C41semidirect
450. #390C22×C41semidirect
451. #389C22×C41semidirect
452. #389C22×C41semidirect
456. #340C22×C41semidirect
457. #340C22×C41semidirect
458. #340C22×C41semidirect
459. #340C22×C41semidirect
460. C41#24512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4472
C2×C41×#4332
C41×#26242
C41×#23092
C41×#20672
C41×#20652
C41×#20542
C41×#19722
C41×#19702
C41×#19362
C41×#19342
C41×#18752
C41×#18542
C41×#17862
#2451241