Finite Group Databasebeta

← C41×#11189 #23787390

Subgroups — C41×#11189 #23787390

Order 10496.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#102×C41C211yesmaximal, characteristic
2C22×#102×C41C211yesmaximal, characteristic
3C2×C41×#390C211yesmaximal, characteristic
4C2×C41×#340C211yesmaximal, characteristic, complemented
5C2×C41×#340C211yesmaximal, characteristic, complemented
6C2×C41×#336C211yesmaximal, characteristic, complemented
7C41×C4⋊#95C211yesmaximal, characteristic, complemented
8C23×D4×C41C2211yescharacteristic
9C23×C8×C41C2211yescharacteristic
10C23×C8×C41C2211yescharacteristic
11C22×C4⋊C4×C41C2211yescharacteristic
12C22×C4⋊C4×C41C2211yescharacteristic
13C22×C4⋊C4×C41C2211yescharacteristic
14C22×C22⋊C4×C41—21no—
15C22×C22⋊C4×C41—21no—
16C22×C42×C41C2211yescharacteristic
17C2×#102×C41—22no—
18C2×#102×C41—22no—
19C2×#102×C41—22no—
20C2×#102×C41—22no—
21C2×#102×C41—22no—
22C2×#102×C41C414yescomplemented
23C41×#390—22no—
24C41×#390—22no—
25C2×#95×C41—21no—
26C2×#95×C41—21no—
27C41×#340—22no—
28C41×#340—22no—
29C41×#336—22no—
30C25×C41—21no—
31C22×D4×C41—21no—
32C22×D4×C41—21no—
33C22×D4×C41—21no—
34C22×D4×C41—21no—
35C22×D4×C41—21no—
36C22×D4×C41—21no—
37C22×D4×C41—21no—
38C22×D4×C41—21no—
39C22×D4×C41—21no—
40C22×D4×C41—21no—
41C22×D4×C41—21no—
42C22×D4×C41C2×C412yes—
43C22×D4×C41D412yes—
44C22×D4×C41D412yes—
45C23×C4×C41—21no—
46C23×C4×C41—21no—
47C23×C4×C41—21no—
48C23×C4×C41D411yescharacteristic
49C23×C4×C41D411yescharacteristic
50C23×C4×C41C2311yescharacteristic
51C22×C8×C41—21no—
52C22×C8×C41—21no—
53C22×C8×C41—21no—
54C22×C8×C41—21no—
55C22×C8×C41—21no—
56C22×C8×C41—21no—
57C22×C8×C41—21no—
58C22×C8×C41—21no—
59C22×C8×C41—21no—
60C22×C8×C41—21no—
61C22×C8×C41—21no—
62C22×C8×C41—21no—
63C22×C8×C41C2×C412yes—
64C22×C8×C41D412yes—
65C2×C4⋊C4×C41—21no—
66C2×C4⋊C4×C41—21no—
67C2×C4⋊C4×C41—21no—
68C2×C4⋊C4×C41—21no—
69C2×C4⋊C4×C41—21no—
70C2×C4⋊C4×C41—21no—
71C2×C4⋊C4×C41—21no—
72C2×C4⋊C4×C41—21no—
73C2×C4⋊C4×C41—21no—
74C2×C4⋊C4×C41—21no—
75C2×C4⋊C4×C41—21no—
76C2×C4⋊C4×C41—21no—
77C2×C4⋊C4×C41—21no—
78C2×C4⋊C4×C41—21no—
79C2×C4⋊C4×C41—21no—
80C2×C4⋊C4×C41C2×C412yes—
81C2×C4⋊C4×C41D412yes—
82C2×C4⋊C4×C41D412yes—
83C2×C22⋊C4×C41—24no—
84C2×C22⋊C4×C41—24no—
85C2×C22⋊C4×C41—42no—
86C2×C22⋊C4×C41—42no—
87C2×C22⋊C4×C41—42no—
88C2×C22⋊C4×C41—42no—
89C2×C42×C41—21no—
90C2×C42×C41—21no—
91C2×C42×C41—21no—
92C2×C42×C41—21no—
93C2×C42×C41—21no—
94C2×C42×C41—21no—
95#102×C41—28no—
96#102×C41—28no—
97#95×C41—42no—
98#95×C41—42no—
99C24×C41—22no—
100C24×C41—22no—
101C24×C41—22no—
102C24×C41—41no—
103C24×C41—41no—
104C24×C41—41no—
105C24×C41—41no—
106C24×C41—41no—
107C24×C41—41no—
108C24×C41—41no—
109C24×C41—41no—
110C24×C41—41no—
111C24×C41—41no—
112C24×C41—41no—
113C24×C41—41no—
114C24×C41C2×D411yescharacteristic
115C2×D4×C41—22no—
116C2×D4×C41—22no—
117C2×D4×C41—22no—
118C2×D4×C41—22no—
119C2×D4×C41—22no—
120C2×D4×C41—22no—
121C2×D4×C41—22no—
122C2×D4×C41—22no—
123C2×D4×C41—22no—
124C2×D4×C41—22no—
125C2×D4×C41—22no—
126C2×D4×C41—22no—
127C2×D4×C41—22no—
128C2×D4×C41—22no—
129C2×D4×C41—22no—
130C2×D4×C41—41no—
131C2×D4×C41—41no—
132C2×D4×C41—41no—
133C2×D4×C41—41no—
134C2×D4×C41—41no—
135C2×D4×C41—41no—
136C2×D4×C41—41no—
137C2×D4×C41—41no—
138C2×D4×C41—41no—
139C2×D4×C41—41no—
140C2×D4×C41—41no—
141C2×D4×C41—41no—
142C2×D4×C41C22⋊C414yes—
143C22×C4×C41—21no—
144C22×C4×C41—21no—
145C22×C4×C41—21no—
146C22×C4×C41—21no—
147C22×C4×C41—21no—
148C22×C4×C41—21no—
149C22×C4×C41—21no—
150C22×C4×C41—21no—
151C22×C4×C41—21no—
152C22×C4×C41—21no—
153C22×C4×C41—21no—
154C22×C4×C41—21no—
155C22×C4×C41—22no—
156C22×C4×C41—22no—
157C22×C4×C41—22no—
158C22×C4×C41—41no—
159C22×C4×C41—41no—
160C22×C4×C41—41no—
161C22×C4×C41—41no—
162C22×C4×C41—41no—
163C22×C4×C41—41no—
164C22×C4×C41—41no—
165C22×C4×C41—41no—
166C22×C4×C41—41no—
167C22×C4×C41—41no—
168C22×C4×C41—41no—
169C22×C4×C41—41no—
170C22×C4×C41—41no—
171C22×C4×C41—41no—
172C22×C4×C41—41no—
173C22×C4×C41—41no—
174C22×C4×C41—41no—
175C22×C4×C41—41no—
176C22×C4×C41D812yes—
177C22×C4×C41SD1612yes—
178C22×C4×C41C22×C411yescharacteristic
179C22×C4×C41C2×D411yescharacteristic
180C22×C4×C41C2×D411yescharacteristic
181C22×C4×C41C2×D411yescharacteristic
182C22×C4×C41C2×D411yescharacteristic
183C22×C4×C41C2×D411yescharacteristic
184C22×C4×C41#4111yescharacteristic
185C22×C4×C41#4111yescharacteristic
186C22×C4×C41#4111yescharacteristic
187C22×C4×C41#4111yescharacteristic
188C22×C4×C41#4111yescharacteristic
189C22×C4×C41#4111yescharacteristic
190C22×C4×C41#4111yescharacteristic
191C22×C4×C41#4111yescharacteristic
192C2×C8×C41—22no—
193C2×C8×C41—22no—
194C2×C8×C41—22no—
195C2×C8×C41—22no—
196C2×C8×C41—22no—
197C2×C8×C41—22no—
198C2×C8×C41—41no—
199C2×C8×C41—41no—
200C2×C8×C41—41no—
201C2×C8×C41—41no—
202C2×C8×C41—41no—
203C2×C8×C41—41no—
204C2×C8×C41—41no—
205C2×C8×C41—41no—
206C4⋊C4×C41—22no—
207C4⋊C4×C41—22no—
208C4⋊C4×C41—22no—
209C4⋊C4×C41—22no—
210C4⋊C4×C41—22no—
211C4⋊C4×C41—22no—
212C4⋊C4×C41—41no—
213C4⋊C4×C41—41no—
214C4⋊C4×C41—41no—
215C4⋊C4×C41—41no—
216C4⋊C4×C41—41no—
217C4⋊C4×C41—41no—
218C22⋊C4×C41—48no—
219C22⋊C4×C41—48no—
220C42×C41—41no—
221C42×C41—41no—
222C42×C41—41no—
223C42×C41—41no—
224C23×C41—24no—
225C23×C41—42no—
226C23×C41—42no—
227C23×C41—42no—
228C23×C41—42no—
229C23×C41—42no—
230C23×C41—42no—
231C23×C41—42no—
232C23×C41—42no—
233C23×C41—42no—
234C23×C41—42no—
235C23×C41—42no—
236C23×C41—42no—
237C23×C41—42no—
238C23×C41—42no—
239C23×C41—42no—
240C23×C41—42no—
241C23×C41—42no—
242C23×C41—42no—
243C23×C41—81no—
244C23×C41—81no—
245C23×C41—81no—
246C23×C41—81no—
247C23×C41—81no—
248C23×C41—81no—
249C23×C41—81no—
250C23×C41—81no—
251C23×C41—81no—
252C23×C41—81no—
253C23×C41—81no—
254C23×C41—81no—
255C23×C41—81no—
256C23×C41—81no—
257C23×C41—81no—
258C23×C41—81no—
259C23×C41C4×D411yescharacteristic
260C23×C41#12011yescharacteristic
261C23×C41#12111yescharacteristic
262C23×C41#12111yescharacteristic
263C23×C41#12111yescharacteristic
264C23×C41#12311yescharacteristic
265C23×C41#12411yescharacteristic
266C23×C41C2×D811yescharacteristic
267C23×C41C2×SD1611yescharacteristic
268C23×C41#13511yescharacteristic
269C23×C41#13511yescharacteristic
270C23×C41AGL(1,ℤ/8)11yescharacteristic
271C23×C41AGL(1,ℤ/8)11yescharacteristic
272C23×C41AGL(1,ℤ/8)11yescharacteristic
273C23×C41#13711yescharacteristic
274D4×C41—24no—
275D4×C41—24no—
276D4×C41—42no—
277D4×C41—42no—
278D4×C41—42no—
279D4×C41—42no—
280D4×C41—42no—
281D4×C41—42no—
282C2×C4×C41—22no—
283C2×C4×C41—22no—
284C2×C4×C41—22no—
285C2×C4×C41—22no—
286C2×C4×C41—22no—
287C2×C4×C41—22no—
288C2×C4×C41—41no—
289C2×C4×C41—41no—
290C2×C4×C41—41no—
291C2×C4×C41—41no—
292C2×C4×C41—41no—
293C2×C4×C41—41no—
294C2×C4×C41—41no—
295C2×C4×C41—41no—
296C2×C4×C41—42no—
297C2×C4×C41—42no—
298C2×C4×C41—42no—
299C2×C4×C41—42no—
300C2×C4×C41—42no—
301C2×C4×C41—42no—
302C2×C4×C41—42no—
303C2×C4×C41—42no—
304C2×C4×C41—42no—
305C2×C4×C41—81no—
306C2×C4×C41—81no—
307C2×C4×C41—81no—
308C2×C4×C41—81no—
309C2×C4×C41—81no—
310C2×C4×C41—81no—
311C2×C4×C41—81no—
312C2×C4×C41—81no—
313C2×C4×C41—81no—
314C2×C4×C41—81no—
315C2×C4×C41—81no—
316C2×C4×C41—81no—
317C2×C4×C41C2×C22⋊C411yescharacteristic
318C2×C4×C41#11711yescharacteristic
319C2×C4×C41#11711yescharacteristic
320C2×C4×C41C4×D411yescharacteristic
321C2×C4×C41C4×D411yescharacteristic
322C2×C4×C41C4×D411yescharacteristic
323C2×C4×C41#12011yescharacteristic
324C2×C4×C41#12111yescharacteristic
325C2×C4×C41#12111yescharacteristic
326C2×C4×C41#12111yescharacteristic
327C2×C4×C41#12111yescharacteristic
328C2×C4×C41#12111yescharacteristic
329C2×C4×C41#12311yescharacteristic
330C2×C4×C41#12311yescharacteristic
331C2×C4×C41#12311yescharacteristic
332C2×C4×C41#12311yescharacteristic
333C2×C4×C41#12311yescharacteristic
334C2×C4×C41#12311yescharacteristic
335C2×C4×C41#12311yescharacteristic
336C2×C4×C41#12311yescharacteristic
337C2×C4×C41#12311yescharacteristic
338C2×C4×C41#12411yescharacteristic
339C2×C4×C41#12411yescharacteristic
340C2×C4×C41#12411yescharacteristic
341C2×C4×C41#12611yescharacteristic
342C2×C4×C41#12611yescharacteristic
343C2×C4×C41#12611yescharacteristic
344C2×C4×C41#12611yescharacteristic
345C8×C41—42no—
346C8×C41—42no—
347#11189C4111yesmaximal, characteristic, direct product factor, Sylow
348C22×C41—44no—
349C22×C41—44no—
350C22×C41—44no—
351C22×C41—82no—
352C22×C41—82no—
353C22×C41—82no—
354C22×C41—82no—
355C22×C41—82no—
356C22×C41—82no—
357C22×C41—82no—
358C22×C41—82no—
359C22×C41—82no—
360C22×C41—82no—
361C22×C41—82no—
362C22×C41—82no—
363C22×C41#38611yescharacteristic
364C22×C41#38811yescharacteristic
365C22×C41#38811yescharacteristic
366C22×C41#39411yescharacteristic
367C22×C41#39411yescharacteristic
368C22×C41#39411yescharacteristic
369C22×C41#39711yescharacteristic
370C22×C41C4×D811yescharacteristic
371C22×C41C4×SD1611yescharacteristic
372C22×C41#44011yescharacteristic
373C22×C41#44211yescharacteristic
374C22×C41#44711yescharacteristic
375C22×C41#44911yescharacteristic
376C22×C41#45011yescharacteristic
377C22×C41#45211yescharacteristic
378C22×C41#45911yescharacteristic
379C22×C41#45911yescharacteristic
380C22×C41#46011yescharacteristic
381C22×C41#46111yescharacteristic
382C22×C41#46311yescharacteristic
383C22×C41#46311yescharacteristic
384C22×C41#46311yescharacteristic
385C22×C41#46411yescharacteristic
386C22×C41#46511yescharacteristic
387C22×C41#46611yescharacteristic
388C22×C41#46811yescharacteristic
389C22×C41#46911yescharacteristic
390C22×C41#48011yescharacteristic
391C22×C41#48111yescharacteristic
392C22×C41#48211yescharacteristic
393C22×C41#48211yescharacteristic
394C22×C41#48611yescharacteristic
395C22×C41#48811yescharacteristic
396C22×C41#48911yescharacteristic
397C22×C41#49011yescharacteristic
398C4×C41—42no—
399C4×C41—42no—
400C4×C41—82no—
401C4×C41—82no—
402C4×C41—82no—
403C4×C41#38111yescharacteristic
404C4×C41#38611yescharacteristic
405C4×C41#38811yescharacteristic
406C4×C41#38811yescharacteristic
407C4×C41#39411yescharacteristic
408C4×C41#39711yescharacteristic
409C4×C41#39711yescharacteristic
410C4×C41#39711yescharacteristic
411C22×#102C2×C4111yescharacteristic
412C22×#102C2×C4111yescharacteristic
413C2×#390C2×C4111yescharacteristic
414C2×#340C2×C4111yescharacteristic, complemented
415C2×#340C2×C4111yescharacteristic, complemented
416C2×#336C2×C4111yescharacteristic, complemented
417C4⋊#95C2×C4111yescharacteristic, complemented
418C2×C41—84no—
419C2×C41#144011yescharacteristic
420C2×C41#187711yescharacteristic
421C2×C41#187911yescharacteristic
422C2×C41#192511yescharacteristic
423C2×C41#192611yescharacteristic
424C2×C41#193411yescharacteristic
425C2×C41#193611yescharacteristic
426C2×C41#203311yescharacteristic
427C2×C41#203411yescharacteristic
428C2×C41#204111yescharacteristic
429C2×C41#204211yescharacteristic
430C2×C41#205411yescharacteristic
431C2×C41#205511yescharacteristic
432C2×C41#207111yescharacteristic
433C2×C41#207311yescharacteristic
434C23×D4C22×C4111yescharacteristic
435C23×C8C22×C4111yescharacteristic
436C23×C8C22×C4111yescharacteristic
437C22×C4⋊C4C22×C4111yescharacteristic
438C22×C4⋊C4C22×C4111yescharacteristic
439C22×C4⋊C4C22×C4111yescharacteristic
440C22×C22⋊C4—21no—
441C22×C22⋊C4—21no—
442C22×C42C22×C4111yescharacteristic
443C2×#102—22no—
444C2×#102—22no—
445C2×#102—22no—
446C2×#102—22no—
447C2×#102—22no—
448C2×#102C4×C4114yescomplemented
449#390—22no—
450#390—22no—
451C2×#95—21no—
452C2×#95—21no—
453#340—22no—
454#340—22no—
455#336—22no—
456C41#1118911yescharacteristic, direct product factor, Sylow
457C25—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4C2×C4×C4112yes—
470C22×D4D4×C4112yes—
471C22×D4D4×C4112yes—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4D4×C4111yescharacteristic
476C23×C4D4×C4111yescharacteristic
477C23×C4C23×C4111yescharacteristic
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—21no—
489C22×C8—21no—
490C22×C8C2×C4×C4112yes—
491C22×C8D4×C4112yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4C2×C4×C4112yes—
508C2×C4⋊C4D4×C4112yes—
509C2×C4⋊C4D4×C4112yes—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—21no—
522#102—28no—
523#102—28no—
524#95—42no—
525#95—42no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—41no—
535C24—41no—
536C24—41no—
537C24—41no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24C2×D4×C4111yescharacteristic
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4C22⋊C4×C4114yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4D8×C4112yes—
604C22×C4SD16×C4112yes—
605C22×C4C22×C4×C4111yescharacteristic
606C22×C4C2×D4×C4111yescharacteristic
607C22×C4C2×D4×C4111yescharacteristic
608C22×C4C2×D4×C4111yescharacteristic
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611C22×C4#41×C4111yescharacteristic
612C22×C4#41×C4111yescharacteristic
613C22×C4#41×C4111yescharacteristic
614C22×C4#41×C4111yescharacteristic
615C22×C4#41×C4111yescharacteristic
616C22×C4#41×C4111yescharacteristic
617C22×C4#41×C4111yescharacteristic
618C22×C4#41×C4111yescharacteristic
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23C4×D4×C4111yescharacteristic
687C23#120×C4111yescharacteristic
688C23#121×C4111yescharacteristic
689C23#121×C4111yescharacteristic
690C23#121×C4111yescharacteristic
691C23#123×C4111yescharacteristic
692C23#124×C4111yescharacteristic
693C23C2×D8×C4111yescharacteristic
694C23C2×SD16×C4111yescharacteristic
695C23#135×C4111yescharacteristic
696C23#135×C4111yescharacteristic
697C23AGL(1,ℤ/8)×C4111yescharacteristic
698C23AGL(1,ℤ/8)×C4111yescharacteristic
699C23AGL(1,ℤ/8)×C4111yescharacteristic
700C23#137×C4111yescharacteristic
701D4—24no—
702D4—24no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
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—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4C2×C22⋊C4×C4111yescharacteristic
745C2×C4#117×C4111yescharacteristic
746C2×C4#117×C4111yescharacteristic
747C2×C4C4×D4×C4111yescharacteristic
748C2×C4C4×D4×C4111yescharacteristic
749C2×C4C4×D4×C4111yescharacteristic
750C2×C4#120×C4111yescharacteristic
751C2×C4#121×C4111yescharacteristic
752C2×C4#121×C4111yescharacteristic
753C2×C4#121×C4111yescharacteristic
754C2×C4#121×C4111yescharacteristic
755C2×C4#121×C4111yescharacteristic
756C2×C4#123×C4111yescharacteristic
757C2×C4#123×C4111yescharacteristic
758C2×C4#123×C4111yescharacteristic
759C2×C4#123×C4111yescharacteristic
760C2×C4#123×C4111yescharacteristic
761C2×C4#123×C4111yescharacteristic
762C2×C4#123×C4111yescharacteristic
763C2×C4#123×C4111yescharacteristic
764C2×C4#123×C4111yescharacteristic
765C2×C4#124×C4111yescharacteristic
766C2×C4#124×C4111yescharacteristic
767C2×C4#124×C4111yescharacteristic
768C2×C4#126×C4111yescharacteristic
769C2×C4#126×C4111yescharacteristic
770C2×C4#126×C4111yescharacteristic
771C2×C4#126×C4111yescharacteristic
772C8—42no—
773C8—42no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22C41×#38611yescharacteristic
790C22C41×#38811yescharacteristic
791C22C41×#38811yescharacteristic
792C22C41×#39411yescharacteristic
793C22C41×#39411yescharacteristic
794C22C41×#39411yescharacteristic
795C22C41×#39711yescharacteristic
796C22C4×D8×C4111yescharacteristic
797C22C4×SD16×C4111yescharacteristic
798C22C41×#44011yescharacteristic
799C22C41×#44211yescharacteristic
800C22C41×#44711yescharacteristic
801C22C41×#44911yescharacteristic
802C22C41×#45011yescharacteristic
803C22C41×#45211yescharacteristic
804C22C41×#45911yescharacteristic
805C22C41×#45911yescharacteristic
806C22C41×#46011yescharacteristic
807C22C41×#46111yescharacteristic
808C22C41×#46311yescharacteristic
809C22C41×#46311yescharacteristic
810C22C41×#46311yescharacteristic
811C22C41×#46411yescharacteristic
812C22C41×#46511yescharacteristic
813C22C41×#46611yescharacteristic
814C22C41×#46811yescharacteristic
815C22C41×#46911yescharacteristic
816C22C41×#48011yescharacteristic
817C22C41×#48111yescharacteristic
818C22C41×#48211yescharacteristic
819C22C41×#48211yescharacteristic
820C22C41×#48611yescharacteristic
821C22C41×#48811yescharacteristic
822C22C41×#48911yescharacteristic
823C22C41×#49011yescharacteristic
824C4—42no—
825C4—42no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4C41×#38111yescharacteristic
830C4C41×#38611yescharacteristic
831C4C41×#38811yescharacteristic
832C4C41×#38811yescharacteristic
833C4C41×#39411yescharacteristic
834C4C41×#39711yescharacteristic
835C4C41×#39711yescharacteristic
836C4C41×#39711yescharacteristic
837C2—84no—
838C2C41×#144011yescharacteristic
839C2C41×#187711yescharacteristic
840C2C41×#187911yescharacteristic
841C2C41×#192511yescharacteristic
842C2C41×#192611yescharacteristic
843C2C41×#193411yescharacteristic
844C2C41×#193611yescharacteristic
845C2C41×#203311yescharacteristic
846C2C41×#203411yescharacteristic
847C2C41×#204111yescharacteristic
848C2C41×#204211yescharacteristic
849C2C41×#205411yescharacteristic
850C2C41×#205511yescharacteristic
851C2C41×#207111yescharacteristic
852C2C41×#207311yescharacteristic
subgroupG/H
center, socleC24×C41C2×D4
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC23×D4×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C41 ◁ C22×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C41×#340C2semidirect
5. C2×C41×#340C2semidirect
6. C2×C41×#336C2semidirect
7. C41×C4⋊#95C2semidirect
22. C2×#102×C41C4semidirect
347. #11189C41direct (N × H)
414. C2×#340C2×C41semidirect
415. C2×#340C2×C41semidirect
416. C2×#336C2×C41semidirect
417. C4⋊#95C2×C41semidirect
448. C2×#102C4×C41semidirect
456. C41#11189direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#102×C412
C2×C41×#3902
C2×C41×#3402
C2×C41×#3362
C41×C4⋊#952
#1118941