Finite Group Databasebeta

← C41×#22578 #23798779

Subgroups — C41×#22578 #23798779

Order 10496.

1010 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#417C211yesmaximal, characteristic
2C41×#2345C211yesmaximal, characteristic, complemented
3C41×#2339C211yesmaximal, characteristic
4C41×#1935C211yesmaximal, characteristic, complemented
5C41×#1933C211yesmaximal, characteristic, complemented
6C41×#1928C211yesmaximal, characteristic, complemented
7C41×#1927C211yesmaximal, characteristic, complemented
8C41×#1864C211yesmaximal, characteristic, complemented
9C41×#1862C211yesmaximal, characteristic, complemented
10C41×#1823C211yesmaximal, characteristic, complemented
11C41×#1809C211yesmaximal, characteristic, complemented
12C41×#1788C211yesmaximal, characteristic
13C41×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C41C211yesmaximal, characteristic, complemented
15C41×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C41C2211yescharacteristic
17C22×M16×C41C2211yescharacteristic
18C2×C4×D4×C41C2211yescharacteristic
19C2×C4×D4×C41C2211yescharacteristic
20C22×C4⋊C4×C41C2211yescharacteristic
21C2×#107×C41C2211yescharacteristic
22C2×#106×C41C2211yescharacteristic
23C41×#417C418yescomplemented
24C2×#103×C41C2211yescharacteristic
25C2×#103×C41C2211yescharacteristic
26C2×#103×C41C2211yescharacteristic
27C2×#103×C41C2211yescharacteristic
28C2×#102×C41C2211yescharacteristic
29C2×#102×C41C2211yescharacteristic
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×C22⋊C8×C41C2211yescharacteristic
33C2×#97×C41C2211yescharacteristic
34C2×C4×C8×C41C2211yescharacteristic
35C41×#391C2211yescharacteristic
36C41×#391C2211yescharacteristic
37C41×#389C2211yescharacteristic
38C41×#389C2211yescharacteristic
39C41×#387—21no—
40C41×#387—21no—
41C41×#386—21no—
42C41×#386—21no—
43C41×#381—21no—
44C41×#380—21no—
45C41×#380C2211yescharacteristic
46C41×#380C2211yescharacteristic
47C4×C4⋊C4×C41C2211yescharacteristic
48C4×C4⋊C4×C41C2211yescharacteristic
49C4×C22⋊C4×C41—21no—
50C4×C22⋊C4×C41C2211yescharacteristic
51C2×#95×C41—21no—
52C41×#340C2211yescharacteristic
53C41×#340C2211yescharacteristic
54C41×#340C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#336C2211yescharacteristic
59C41×#336C2211yescharacteristic
60C2×#41×C41—22no—
61C2×#41×C41—22no—
62C2×#41×C41—22no—
63C2×#41×C41—41no—
64C2×#41×C41—41no—
65C2×#41×C41C2×C414yes—
66C22×Q8×C41C2311yescharacteristic
67C22×D4×C41—21no—
68C22×D4×C41C2311yescharacteristic
69C23×C4×C41—21no—
70C23×C4×C41—21no—
71C23×C4×C41—21no—
72C23×C4×C41—21no—
73C23×C4×C41C2311yescharacteristic
74C2×M16×C41—41no—
75C2×M16×C41—41no—
76C2×M16×C41C2×C414yescomplemented
77C22×C8×C41C2311yescharacteristic
78C22×C8×C41C2311yescharacteristic
79C22×C8×C41C2311yescharacteristic
80C22×C8×C41C2311yescharacteristic
81C4×D4×C41—22no—
82C4×D4×C41—22no—
83C4×D4×C41—41no—
84C4×D4×C41—41no—
85C2×C4⋊C4×C41—21no—
86C2×C4⋊C4×C41—22no—
87C2×C4⋊C4×C41—21no—
88C2×C4⋊C4×C41—21no—
89C2×C4⋊C4×C41C2×C414yescomplemented
90C2×C4⋊C4×C41C2311yescharacteristic
91C2×C4⋊C4×C41C2311yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C4⋊C4×C41C2311yescharacteristic
94C2×C4⋊C4×C41C2311yescharacteristic
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C22⋊C4×C41—21no—
97C2×C22⋊C4×C41—21no—
98C2×C22⋊C4×C41—21no—
99C2×C22⋊C4×C41—21no—
100C2×C22⋊C4×C41D411yescharacteristic
101C2×C22⋊C4×C41D411yescharacteristic
102C2×C42×C41—21no—
103C2×C42×C41—21no—
104C2×C42×C41C2311yescharacteristic
105C2×C42×C41C2311yescharacteristic
106#107×C41—41no—
107#106×C41—41no—
108#103×C41—41no—
109#103×C41—41no—
110#103×C41C2×C414yescomplemented
111#103×C41C2×C414yescomplemented
112#102×C41—22no—
113#102×C41—22no—
114#102×C41C2×C414yes—
115#102×C41C2×C414yes—
116C22⋊C8×C41—22no—
117#97×C41—41no—
118C4×C8×C41—41no—
119#95×C41—21no—
120#95×C41—21no—
121#95×C41—21no—
122#95×C41—21no—
123#95×C41—21no—
124#95×C41—21no—
125#95×C41—21no—
126#95×C41—21no—
127#95×C41—21no—
128#95×C41—21no—
129#95×C41D411yescharacteristic
130#95×C41D411yescharacteristic
131C24×C41—21no—
132C24×C41C2×D411yescharacteristic
133#41×C41—28no—
134#41×C41—44no—
135#41×C41—44no—
136#41×C41—44no—
137C2×Q8×C41—21no—
138C2×Q8×C41—21no—
139C2×Q8×C41—21no—
140C2×Q8×C41—21no—
141C2×Q8×C41—21no—
142C2×Q8×C41C22×C412yes—
143C2×D4×C41—24no—
144C2×D4×C41—21no—
145C2×D4×C41—21no—
146C2×D4×C41—21no—
147C2×D4×C41—42no—
148C2×D4×C41—42no—
149C2×D4×C41C22×C412yes—
150C2×D4×C41#4112yes—
151C2×D4×C41#4112yes—
152C22×C4×C41—21no—
153C22×C4×C41—21no—
154C22×C4×C41—21no—
155C22×C4×C41—21no—
156C22×C4×C41—21no—
157C22×C4×C41—21no—
158C22×C4×C41—21no—
159C22×C4×C41—24no—
160C22×C4×C41—24no—
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—42no—
166C22×C4×C41—42no—
167C22×C4×C41—42no—
168C22×C4×C41—42no—
169C22×C4×C41—42no—
170C22×C4×C41—42no—
171C22×C4×C41—81no—
172C22×C4×C41—81no—
173C22×C4×C41—81no—
174C22×C4×C41—81no—
175C22×C4×C41C22×C412yes—
176C22×C4×C41C2×D411yescharacteristic
177C22×C4×C41C2×D411yescharacteristic
178C22×C4×C41C2×D411yescharacteristic
179C22×C4×C41C2×D411yescharacteristic
180C22×C4×C41C2×D411yescharacteristic
181C22×C4×C41#4112yes—
182C22×C4×C41C2411yescharacteristic
183M16×C41—44no—
184C2×C8×C41—21no—
185C2×C8×C41—21no—
186C2×C8×C41—21no—
187C2×C8×C41—21no—
188C2×C8×C41—21no—
189C2×C8×C41—21no—
190C2×C8×C41—21no—
191C2×C8×C41—21no—
192C2×C8×C41—21no—
193C2×C8×C41—21no—
194C2×C8×C41C22×C412yes—
195C2×C8×C41C22×C412yes—
196C4⋊C4×C41—24no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—21no—
203C4⋊C4×C41—21no—
204C4⋊C4×C41—21no—
205C4⋊C4×C41—21no—
206C4⋊C4×C41—21no—
207C4⋊C4×C41—81no—
208C4⋊C4×C41—81no—
209C4⋊C4×C41C22×C412yes—
210C4⋊C4×C41C22×C412yes—
211C22⋊C4×C41—22no—
212C22⋊C4×C41—41no—
213C22⋊C4×C41—42no—
214C22⋊C4×C41—42no—
215C22⋊C4×C41—42no—
216C22⋊C4×C41—81no—
217C42×C41—21no—
218C42×C41—21no—
219C42×C41—21no—
220C42×C41—21no—
221C42×C41—81no—
222C42×C41—81no—
223C23×C41—22no—
224C23×C41—22no—
225C23×C41—22no—
226C23×C41—21no—
227C23×C41—21no—
228C23×C41—21no—
229C23×C41—21no—
230C23×C41—21no—
231C23×C41—21no—
232C23×C41—41no—
233C23×C41—41no—
234C23×C41—41no—
235C23×C41—41no—
236C23×C41C4×D412yes—
237C23×C41C22×D411yescharacteristic
238Q8×C41—22no—
239Q8×C41—22no—
240Q8×C41—41no—
241Q8×C41—41no—
242D4×C41—22no—
243D4×C41—22no—
244D4×C41—22no—
245D4×C41—48no—
246D4×C41#11714yes—
247C2×C4×C41—21no—
248C2×C4×C41—21no—
249C2×C4×C41—21no—
250C2×C4×C41—21no—
251C2×C4×C41—22no—
252C2×C4×C41—22no—
253C2×C4×C41—22no—
254C2×C4×C41—22no—
255C2×C4×C41—22no—
256C2×C4×C41—22no—
257C2×C4×C41—22no—
258C2×C4×C41—21no—
259C2×C4×C41—21no—
260C2×C4×C41—21no—
261C2×C4×C41—21no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—21no—
266C2×C4×C41—21no—
267C2×C4×C41—48no—
268C2×C4×C41—41no—
269C2×C4×C41—41no—
270C2×C4×C41—41no—
271C2×C4×C41—41no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—41no—
278C2×C4×C41—41no—
279C2×C4×C41—41no—
280C2×C4×C41—41no—
281C2×C4×C41—41no—
282C2×C4×C41—41no—
283C2×C4×C41—41no—
284C2×C4×C41—41no—
285C2×C4×C41—41no—
286C2×C4×C41—84no—
287C2×C4×C41—84no—
288C2×C4×C41—84no—
289C2×C4×C41C4×D412yes—
290C2×C4×C41#13712yes—
291C2×C4×C41C23×C411yescharacteristic
292C2×C4×C41C2×#4111yescharacteristic
293C2×C4×C41C2×#4111yescharacteristic
294C2×C4×C41C2×#4111yescharacteristic
295C2×C4×C41H(5,𝔽2)11yescharacteristic
296C2×C4×C41H(5,𝔽2)11yescharacteristic
297C8×C41—22no—
298C8×C41—22no—
299C8×C41—41no—
300C8×C41—41no—
301#22578C4111yesmaximal, characteristic, direct product factor, Sylow
302C22×C41—22no—
303C22×C41—24no—
304C22×C41—22no—
305C22×C41—22no—
306C22×C41—41no—
307C22×C41—42no—
308C22×C41—42no—
309C22×C41—42no—
310C22×C41—41no—
311C22×C41—42no—
312C22×C41—42no—
313C22×C41—41no—
314C22×C41—42no—
315C22×C41—41no—
316C22×C41C2×C4×D411yescharacteristic
317C22×C41#54611yescharacteristic
318C22×C41#54611yescharacteristic
319C22×C41C2×#13711yescharacteristic
320C22×C41#57511yescharacteristic
321C22×C41#57611yescharacteristic
322C22×C41#57711yescharacteristic
323C4×C41—22no—
324C4×C41—22no—
325C4×C41—41no—
326C4×C41—42no—
327C4×C41—42no—
328C4×C41—42no—
329C4×C41—41no—
330C4×C41—41no—
331C4×C41—81no—
332C4×C41—81no—
333C4×C41—81no—
334C4×C41—81no—
335C4×C41C2×#11711yescharacteristic
336C4×C41#51811yescharacteristic
337C4×C41#55111yescharacteristic
338C4×C41#55111yescharacteristic
339C2×#417C2×C4111yescharacteristic
340#2345C2×C4111yescharacteristic, complemented
341#2339C2×C4111yescharacteristic
342#1935C2×C4111yescharacteristic, complemented
343#1933C2×C4111yescharacteristic, complemented
344#1928C2×C4111yescharacteristic, complemented
345#1927C2×C4111yescharacteristic, complemented
346#1864C2×C4111yescharacteristic, complemented
347#1862C2×C4111yescharacteristic, complemented
348#1823C2×C4111yescharacteristic, complemented
349#1809C2×C4111yescharacteristic, complemented
350#1788C2×C4111yescharacteristic
351#1762C2×C4111yescharacteristic, complemented
352C4×#102C2×C4111yescharacteristic, complemented
353#1753C2×C4111yescharacteristic, complemented
354C2×C41—42no—
355C2×C41—44no—
356C2×C41#234211yescharacteristic
357C2×C41C4×#13711yescharacteristic
358C2×C41#294611yescharacteristic
359C2×C41#330711yescharacteristic
360C2×C41#331411yescharacteristic
361C2×C41#332211yescharacteristic
362C2×C41#333111yescharacteristic
363C22×#41C22×C4111yescharacteristic
364C22×M16C22×C4111yescharacteristic
365C2×C4×D4C22×C4111yescharacteristic
366C2×C4×D4C22×C4111yescharacteristic
367C22×C4⋊C4C22×C4111yescharacteristic
368C2×#107C22×C4111yescharacteristic
369C2×#106C22×C4111yescharacteristic
370#417C4×C4118yescomplemented
371C2×#103C22×C4111yescharacteristic
372C2×#103C22×C4111yescharacteristic
373C2×#103C22×C4111yescharacteristic
374C2×#103C22×C4111yescharacteristic
375C2×#102C22×C4111yescharacteristic
376C2×#102C22×C4111yescharacteristic
377C2×#102C22×C4111yescharacteristic
378C2×#102C22×C4111yescharacteristic
379C2×C22⋊C8C22×C4111yescharacteristic
380C2×#97C22×C4111yescharacteristic
381C2×C4×C8C22×C4111yescharacteristic
382#391C22×C4111yescharacteristic
383#391C22×C4111yescharacteristic
384#389C22×C4111yescharacteristic
385#389C22×C4111yescharacteristic
386#387—21no—
387#387—21no—
388#386—21no—
389#386—21no—
390#381—21no—
391#380—21no—
392#380C22×C4111yescharacteristic
393#380C22×C4111yescharacteristic
394C4×C4⋊C4C22×C4111yescharacteristic
395C4×C4⋊C4C22×C4111yescharacteristic
396C4×C22⋊C4—21no—
397C4×C22⋊C4C22×C4111yescharacteristic
398C2×#95—21no—
399#340C22×C4111yescharacteristic
400#340C22×C4111yescharacteristic
401#340C22×C4111yescharacteristic
402#340C22×C4111yescharacteristic
403#340C22×C4111yescharacteristic
404#340C22×C4111yescharacteristic
405#336C22×C4111yescharacteristic
406#336C22×C4111yescharacteristic
407C41#2257811yescharacteristic, direct product factor, Sylow
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—41no—
412C2×#41—41no—
413C2×#41C2×C4×C4114yes—
414C22×Q8C23×C4111yescharacteristic
415C22×D4—21no—
416C22×D4C23×C4111yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C23×C4111yescharacteristic
422C2×M16—41no—
423C2×M16—41no—
424C2×M16C2×C4×C4114yescomplemented
425C22×C8C23×C4111yescharacteristic
426C22×C8C23×C4111yescharacteristic
427C22×C8C23×C4111yescharacteristic
428C22×C8C23×C4111yescharacteristic
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—41no—
432C4×D4—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4C2×C4×C4114yescomplemented
438C2×C4⋊C4C23×C4111yescharacteristic
439C2×C4⋊C4C23×C4111yescharacteristic
440C2×C4⋊C4C23×C4111yescharacteristic
441C2×C4⋊C4C23×C4111yescharacteristic
442C2×C4⋊C4C23×C4111yescharacteristic
443C2×C4⋊C4C23×C4111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C4111yescharacteristic
449C2×C22⋊C4D4×C4111yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C4111yescharacteristic
453C2×C42C23×C4111yescharacteristic
454#107—41no—
455#106—41no—
456#103—41no—
457#103—41no—
458#103C2×C4×C4114yescomplemented
459#103C2×C4×C4114yescomplemented
460#102—22no—
461#102—22no—
462#102C2×C4×C4114yes—
463#102C2×C4×C4114yes—
464C22⋊C8—22no—
465#97—41no—
466C4×C8—41no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95D4×C4111yescharacteristic
478#95D4×C4111yescharacteristic
479C24—21no—
480C24C2×D4×C4111yescharacteristic
481#41—28no—
482#41—44no—
483#41—44no—
484#41—44no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C22×C4×C4112yes—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C22×C4×C4112yes—
498C2×D4#41×C4112yes—
499C2×D4#41×C4112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4C22×C4×C4112yes—
524C22×C4C2×D4×C4111yescharacteristic
525C22×C4C2×D4×C4111yescharacteristic
526C22×C4C2×D4×C4111yescharacteristic
527C22×C4C2×D4×C4111yescharacteristic
528C22×C4C2×D4×C4111yescharacteristic
529C22×C4#41×C4112yes—
530C22×C4C24×C4111yescharacteristic
531M16—44no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8C22×C4×C4112yes—
543C2×C8C22×C4×C4112yes—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4C22×C4×C4112yes—
558C4⋊C4C22×C4×C4112yes—
559C22⋊C4—22no—
560C22⋊C4—41no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—81no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23C4×D4×C4112yes—
585C23C22×D4×C4111yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4#117×C4114yes—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4—84no—
637C2×C4C4×D4×C4112yes—
638C2×C4#137×C4112yes—
639C2×C4C23×C4×C4111yescharacteristic
640C2×C4C2×#41×C4111yescharacteristic
641C2×C4C2×#41×C4111yescharacteristic
642C2×C4C2×#41×C4111yescharacteristic
643C2×C4H(5,𝔽2)×C4111yescharacteristic
644C2×C4H(5,𝔽2)×C4111yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—24no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22C2×C4×D4×C4111yescharacteristic
664C22C41×#54611yescharacteristic
665C22C41×#54611yescharacteristic
666C22C2×#137×C4111yescharacteristic
667C22C41×#57511yescharacteristic
668C22C41×#57611yescharacteristic
669C22C41×#57711yescharacteristic
670C4—22no—
671C4—22no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C2×#117×C4111yescharacteristic
683C4C41×#51811yescharacteristic
684C4C41×#55111yescharacteristic
685C4C41×#55111yescharacteristic
686C2—42no—
687C2—44no—
688C2C41×#234211yescharacteristic
689C2C4×#137×C4111yescharacteristic
690C2C41×#294611yescharacteristic
691C2C41×#330711yescharacteristic
692C2C41×#331411yescharacteristic
693C2C41×#332211yescharacteristic
694C2C41×#333111yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutatorC2×C4C23×C4×C41
Frattini, cosocleC22×C4C24×C41
prime radicalC22×#41×C41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#2345C2semidirect
4. C41×#1935C2semidirect
5. C41×#1933C2semidirect
6. C41×#1928C2semidirect
7. C41×#1927C2semidirect
8. C41×#1864C2semidirect
9. C41×#1862C2semidirect
10. C41×#1823C2semidirect
11. C41×#1809C2semidirect
13. C41×#1762C2semidirect
14. C4×#102×C41C2semidirect
15. C41×#1753C2semidirect
23. C41×#417C4semidirect
76. C2×M16×C41C2×C4semidirect
89. C2×C4⋊C4×C41C2×C4semidirect
110. #103×C41C2×C4semidirect
111. #103×C41C2×C4semidirect
301. #22578C41direct (N × H)
340. #2345C2×C41semidirect
342. #1935C2×C41semidirect
343. #1933C2×C41semidirect
344. #1928C2×C41semidirect
345. #1927C2×C41semidirect
346. #1864C2×C41semidirect
347. #1862C2×C41semidirect
348. #1823C2×C41semidirect
349. #1809C2×C41semidirect
351. #1762C2×C41semidirect
352. C4×#102C2×C41semidirect
353. #1753C2×C41semidirect
370. #417C4×C41semidirect
407. C41#22578direct (N × H)
424. C2×M16C2×C4×C41semidirect
437. C2×C4⋊C4C2×C4×C41semidirect
458. #103C2×C4×C41semidirect
459. #103C2×C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4172
C41×#23452
C41×#23392
C41×#19352
C41×#19332
C41×#19282
C41×#19272
C41×#18642
C41×#18622
C41×#18232
C41×#18092
C41×#17882
C41×#17622
C4×#102×C412
C41×#17532
#2257841