Finite Group Databasebeta

← C101×#24886 #38807037

Subgroups — C101×#24886 #38807037

Order 25856.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C101C211yesmaximal, characteristic, complemented
2C2×#418×C101C211yesmaximal, characteristic, complemented
3C101×#2408C211yesmaximal, characteristic
4C101×#2354C211yesmaximal, characteristic, complemented
5C101×#2094C211yesmaximal, characteristic, complemented
6C101×#2071C211yesmaximal, characteristic, complemented
7C101×#2034C211yesmaximal, characteristic, complemented
8C101×#2033C211yesmaximal, characteristic, complemented
9C101×#1925C211yesmaximal, characteristic, complemented
10C101×#1925C211yesmaximal, characteristic, complemented
11C101×#1875C211yesmaximal, characteristic, complemented
12C101×#1870C211yesmaximal, characteristic, complemented
13C101×#1854C211yesmaximal, characteristic, complemented
14C101×#1809C211yesmaximal, characteristic, complemented
15C101×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×M16×C101C2211yescharacteristic
18C2×#121×C101C2211yescharacteristic
19C2×#121×C101C2211yescharacteristic
20C2×#120×C101—21no—
21C2×C4×D4×C101C2211yescharacteristic
22C2×#117×C101C2211yescharacteristic
23C2×#117×C101C2211yescharacteristic, complemented
24#482×C101—24no—
25C2×#107×C101C2211yescharacteristic, complemented
26C2×#107×C101C2211yescharacteristic, complemented
27C2×#106×C101C2211yescharacteristic, complemented
28C2×#106×C101C2211yescharacteristic, complemented
29#418×C101—24no—
30C2×#102×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×C22⋊C8×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic, complemented
40C2×C22⋊C8×C101C2211yescharacteristic, complemented
41#394×C101—21no—
42#392×C101—21no—
43#390×C101—21no—
44#390×C101C2211yescharacteristic
45#390×C101C2211yescharacteristic
46#388×C101—21no—
47#388×C101—21no—
48#384×C101C2211yescharacteristic, complemented
49#380×C101C2211yescharacteristic
50#380×C101C2211yescharacteristic
51#380×C101C2211yescharacteristic, complemented
52#379×C101—21no—
53C4×C4⋊C4×C101—21no—
54C4×C4⋊C4×C101C2211yescharacteristic, complemented
55#340×C101C2211yescharacteristic, complemented
56#340×C101C2211yescharacteristic, complemented
57#340×C101C2211yescharacteristic, complemented
58#340×C101C2211yescharacteristic, complemented
59#336×C101C2211yescharacteristic, complemented
60#336×C101C2211yescharacteristic, complemented
61C25×C101—21no—
62C22×D4×C101—22no—
63C22×D4×C101—22no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—22no—
68C22×D4×C101—22no—
69C22×D4×C101—41no—
70C22×D4×C101—41no—
71C22×D4×C101D411yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C22×D4×C101C2311yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C23×C4×C101C2311yescharacteristic
76C2×M16×C101—22no—
77C2×M16×C101—22no—
78C2×M16×C101—41no—
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83#121×C101—22no—
84#121×C101—22no—
85#121×C101—41no—
86#121×C101—41no—
87#120×C101—44no—
88C4×D4×C101—22no—
89C4×D4×C101—22no—
90#117×C101—22no—
91#117×C101—22no—
92#117×C101—41no—
93#117×C101—41no—
94C2×C4⋊C4×C101—21no—
95C2×C4⋊C4×C101—21no—
96C2×C4⋊C4×C101D411yescharacteristic
97C2×C4⋊C4×C101C2311yescharacteristic
98C2×C4⋊C4×C101C2311yescharacteristic
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C4⋊C4×C101C2311yescharacteristic
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C22⋊C4×C101—21no—
104C2×C22⋊C4×C101—21no—
105C2×C22⋊C4×C101—21no—
106C2×C22⋊C4×C101—21no—
107C2×C22⋊C4×C101—21no—
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101D411yescharacteristic
115C2×C22⋊C4×C101D411yescharacteristic
116C2×C42×C101—21no—
117C2×C42×C101—21no—
118C2×C42×C101—21no—
119C2×C42×C101C2311yescharacteristic
120#107×C101—22no—
121#107×C101—41no—
122#106×C101—22no—
123#106×C101—41no—
124#102×C101—22no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—22no—
129#102×C101—41no—
130#102×C101—41no—
131#102×C101D414yescomplemented
132C22⋊C8×C101—22no—
133C22⋊C8×C101—22no—
134C22⋊C8×C101—41no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101—21no—
138#95×C101—21no—
139C24×C101—21no—
140C24×C101—21no—
141C24×C101—42no—
142C24×C101—42no—
143C24×C101—42no—
144C24×C101—42no—
145C24×C101—42no—
146C24×C101—81no—
147C24×C101—81no—
148C24×C101C2×D411yescharacteristic
149C24×C101C2×D411yescharacteristic
150C2×D4×C101—28no—
151C2×D4×C101—22no—
152C2×D4×C101—22no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
163C2×D4×C101—44no—
164C2×D4×C101—44no—
165C2×D4×C101—41no—
166C2×D4×C101—42no—
167C2×D4×C101—42no—
168C2×D4×C101—44no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—42no—
173C2×D4×C101—42no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101C2×D412yes—
177C2×D4×C101#4112yes—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101C2×D411yescharacteristic
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101#4112yes—
199C22×C4×C101#4112yes—
200C22×C4×C101C2411yescharacteristic
201M16×C101—44no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—21no—
205C2×C8×C101—21no—
206C2×C8×C101—21no—
207C2×C8×C101—21no—
208C2×C8×C101—21no—
209C2×C8×C101—21no—
210C2×C8×C101—21no—
211C2×C8×C101—21no—
212C2×C8×C101—21no—
213C2×C8×C101C2×D412yes—
214C4⋊C4×C101—22no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—21no—
225C4⋊C4×C101—21no—
226C4⋊C4×C101—42no—
227C4⋊C4×C101—81no—
228C4⋊C4×C101C2×D412yes—
229C22⋊C4×C101—22no—
230C22⋊C4×C101—22no—
231C22⋊C4×C101—42no—
232C22⋊C4×C101—42no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—42no—
235C22⋊C4×C101—42no—
236C22⋊C4×C101—42no—
237C22⋊C4×C101—42no—
238C22⋊C4×C101—81no—
239C22⋊C4×C101—81no—
240C22⋊C4×C101—81no—
241C22⋊C4×C101—81no—
242C42×C101—21no—
243C42×C101—21no—
244C42×C101—42no—
245C42×C101—42no—
246C42×C101—42no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—21no—
255C23×C101—22no—
256C23×C101—22no—
257C23×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—48no—
263C23×C101—41no—
264C23×C101—41no—
265C23×C101—41no—
266C23×C101—41no—
267C23×C101—41no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101—84no—
276C23×C101—84no—
277C23×C101—84no—
278C23×C101—84no—
279C23×C101—84no—
280C23×C101—84no—
281C23×C101#12312yes—
282C23×C101C22×D411yescharacteristic
283D4×C101—22no—
284D4×C101—22no—
285D4×C101—22no—
286D4×C101—22no—
287D4×C101—44no—
288D4×C101—48no—
289D4×C101—41no—
290D4×C101—41no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—84no—
294D4×C101—84no—
295C2×C4×C101—21no—
296C2×C4×C101—21no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—22no—
300C2×C4×C101—22no—
301C2×C4×C101—22no—
302C2×C4×C101—22no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—22no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—41no—
311C2×C4×C101—41no—
312C2×C4×C101—41no—
313C2×C4×C101—41no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—41no—
326C2×C4×C101—41no—
327C2×C4×C101—41no—
328C2×C4×C101—41no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101#12312yes—
332C2×C4×C101AGL(1,ℤ/8)12yes—
333C2×C4×C101C22×D411yescharacteristic
334C2×C4×C101C2×#4111yescharacteristic
335C2×C4×C101C2×#4111yescharacteristic
336C2×C4×C101C2×#4111yescharacteristic
337C2×C4×C101H(5,𝔽2)11yescharacteristic
338C2×C4×C101H(5,𝔽2)11yescharacteristic
339C8×C101—22no—
340C8×C101—41no—
341C8×C101—41no—
342C8×C101—41no—
343C22×C101—22no—
344C22×C101—22no—
345C22×C101—22no—
346C22×C101—41no—
347C22×C101—41no—
348C22×C101—41no—
349C22×C101—41no—
350C22×C101—41no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101—42no—
354C22×C101—42no—
355C22×C101—41no—
356C22×C101—42no—
357C22×C101—41no—
358C22×C101—42no—
359C22×C101—41no—
360C22×C101—42no—
361C22×C101—41no—
362C22×C101—42no—
363C22×C101—816no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101—81no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101C2×#12311yescharacteristic
373C22×C101D4211yescharacteristic
374C22×C101#54611yescharacteristic
375C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C101#57511yescharacteristic
377C22×C101#57611yescharacteristic
378C22×C101#57711yescharacteristic
379C4×C101—22no—
380C4×C101—22no—
381C4×C101—41no—
382C4×C101—41no—
383C4×C101—42no—
384C4×C101—81no—
385C4×C101—81no—
386C4×C101—81no—
387C4×C101—81no—
388C4×C101—81no—
389C4×C101#52511yescharacteristic
390C4×C101#53811yescharacteristic
391C4×C101#54611yescharacteristic
392C4×C101#55111yescharacteristic
393#24886C10111yesmaximal, characteristic, direct product factor, Sylow
394C2×C101—42no—
395C2×C101—81no—
396C2×C101—82no—
397C2×C101—82no—
398C2×C101#241811yescharacteristic
399C2×C101#309411yescharacteristic
400C2×C101#309611yescharacteristic
401C2×C101#326811yescharacteristic
402C2×C101#327211yescharacteristic
403C2×C101#331111yescharacteristic
404C2×C101#332511yescharacteristic
405C2×#482C2×C10111yescharacteristic, complemented
406C2×#418C2×C10111yescharacteristic, complemented
407#2408C2×C10111yescharacteristic
408#2354C2×C10111yescharacteristic, complemented
409#2094C2×C10111yescharacteristic, complemented
410#2071C2×C10111yescharacteristic, complemented
411#2034C2×C10111yescharacteristic, complemented
412#2033C2×C10111yescharacteristic, complemented
413#1925C2×C10111yescharacteristic, complemented
414#1925C2×C10111yescharacteristic, complemented
415#1875C2×C10111yescharacteristic, complemented
416#1870C2×C10111yescharacteristic, complemented
417#1854C2×C10111yescharacteristic, complemented
418#1809C2×C10111yescharacteristic, complemented
419#1786C2×C10111yescharacteristic, complemented
420C101#2488611yescharacteristic, direct product factor, Sylow
421C23×D4C22×C10111yescharacteristic
422C22×M16C22×C10111yescharacteristic
423C2×#121C22×C10111yescharacteristic
424C2×#121C22×C10111yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C10111yescharacteristic
427C2×#117C22×C10111yescharacteristic
428C2×#117C22×C10111yescharacteristic, complemented
429#482—24no—
430C2×#107C22×C10111yescharacteristic, complemented
431C2×#107C22×C10111yescharacteristic, complemented
432C2×#106C22×C10111yescharacteristic, complemented
433C2×#106C22×C10111yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C10111yescharacteristic
436C2×#102C22×C10111yescharacteristic
437C2×#102C22×C10111yescharacteristic
438C2×#102C22×C10111yescharacteristic
439C2×#102C22×C10111yescharacteristic
440C2×#102C22×C10111yescharacteristic
441C2×#102C22×C10111yescharacteristic
442C2×#102C22×C10111yescharacteristic
443C2×C22⋊C8C22×C10111yescharacteristic
444C2×C22⋊C8C22×C10111yescharacteristic, complemented
445C2×C22⋊C8C22×C10111yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390—21no—
449#390C22×C10111yescharacteristic
450#390C22×C10111yescharacteristic
451#388—21no—
452#388—21no—
453#384C22×C10111yescharacteristic, complemented
454#380C22×C10111yescharacteristic
455#380C22×C10111yescharacteristic
456#380C22×C10111yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C22×C10111yescharacteristic, complemented
460#340C22×C10111yescharacteristic, complemented
461#340C22×C10111yescharacteristic, complemented
462#340C22×C10111yescharacteristic, complemented
463#340C22×C10111yescharacteristic, complemented
464#336C22×C10111yescharacteristic, complemented
465#336C22×C10111yescharacteristic, complemented
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C10111yescharacteristic
477C22×D4C23×C10111yescharacteristic
478C22×D4C23×C10111yescharacteristic
479C23×C4C23×C10111yescharacteristic
480C23×C4C23×C10111yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C10111yescharacteristic
485C22×C8C23×C10111yescharacteristic
486C22×C8C23×C10111yescharacteristic
487C22×C8C23×C10111yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C10111yescharacteristic
502C2×C4⋊C4C23×C10111yescharacteristic
503C2×C4⋊C4C23×C10111yescharacteristic
504C2×C4⋊C4C23×C10111yescharacteristic
505C2×C4⋊C4C23×C10111yescharacteristic
506C2×C4⋊C4C23×C10111yescharacteristic
507C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C10111yescharacteristic
520C2×C22⋊C4D4×C10111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C10111yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C10114yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C10111yescharacteristic
554C24C2×D4×C10111yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
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—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C10112yes—
582C2×D4#41×C10112yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4C2×D4×C10111yescharacteristic
600C22×C4C2×D4×C10111yescharacteristic
601C22×C4C2×D4×C10111yescharacteristic
602C22×C4C2×D4×C10111yescharacteristic
603C22×C4#41×C10112yes—
604C22×C4#41×C10112yes—
605C22×C4C24×C10111yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C10112yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C10112yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C10112yes—
687C23C22×D4×C10111yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
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—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4#123×C10112yes—
737C2×C4AGL(1,ℤ/8)×C10112yes—
738C2×C4C22×D4×C10111yescharacteristic
739C2×C4C2×#41×C10111yescharacteristic
740C2×C4C2×#41×C10111yescharacteristic
741C2×C4C2×#41×C10111yescharacteristic
742C2×C4H(5,𝔽2)×C10111yescharacteristic
743C2×C4H(5,𝔽2)×C10111yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C10111yescharacteristic
778C22D42×C10111yescharacteristic
779C22#546×C10111yescharacteristic
780C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
781C22#575×C10111yescharacteristic
782C22#576×C10111yescharacteristic
783C22#577×C10111yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4#525×C10111yescharacteristic
795C4#538×C10111yescharacteristic
796C4#546×C10111yescharacteristic
797C4#551×C10111yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2C101×#241811yescharacteristic
803C2C101×#309411yescharacteristic
804C2C101×#309611yescharacteristic
805C2C101×#326811yescharacteristic
806C2C101×#327211yescharacteristic
807C2C101×#331111yescharacteristic
808C2C101×#332511yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC101×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C101C2semidirect
2. C2×#418×C101C2semidirect
4. C101×#2354C2semidirect
5. C101×#2094C2semidirect
6. C101×#2071C2semidirect
7. C101×#2034C2semidirect
8. C101×#2033C2semidirect
9. C101×#1925C2semidirect
10. C101×#1925C2semidirect
11. C101×#1875C2semidirect
12. C101×#1870C2semidirect
13. C101×#1854C2semidirect
14. C101×#1809C2semidirect
15. C101×#1786C2semidirect
23. C2×#117×C101C22semidirect
25. C2×#107×C101C22semidirect
26. C2×#107×C101C22semidirect
27. C2×#106×C101C22semidirect
28. C2×#106×C101C22semidirect
39. C2×C22⋊C8×C101C22semidirect
40. C2×C22⋊C8×C101C22semidirect
48. #384×C101C22semidirect
51. #380×C101C22semidirect
54. C4×C4⋊C4×C101C22semidirect
55. #340×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #340×C101C22semidirect
59. #336×C101C22semidirect
60. #336×C101C22semidirect
131. #102×C101D4semidirect
393. #24886C101direct (N × H)
405. C2×#482C2×C101semidirect
406. C2×#418C2×C101semidirect
408. #2354C2×C101semidirect
409. #2094C2×C101semidirect
410. #2071C2×C101semidirect
411. #2034C2×C101semidirect
412. #2033C2×C101semidirect
413. #1925C2×C101semidirect
414. #1925C2×C101semidirect
415. #1875C2×C101semidirect
416. #1870C2×C101semidirect
417. #1854C2×C101semidirect
418. #1809C2×C101semidirect
419. #1786C2×C101semidirect
420. C101#24886direct (N × H)
428. C2×#117C22×C101semidirect
430. C2×#107C22×C101semidirect
431. C2×#107C22×C101semidirect
432. C2×#106C22×C101semidirect
433. C2×#106C22×C101semidirect
444. C2×C22⋊C8C22×C101semidirect
445. C2×C22⋊C8C22×C101semidirect
453. #384C22×C101semidirect
456. #380C22×C101semidirect
459. C4×C4⋊C4C22×C101semidirect
460. #340C22×C101semidirect
461. #340C22×C101semidirect
462. #340C22×C101semidirect
463. #340C22×C101semidirect
464. #336C22×C101semidirect
465. #336C22×C101semidirect
536. #102D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1012
C2×#418×C1012
C101×#24082
C101×#23542
C101×#20942
C101×#20712
C101×#20342
C101×#20332
C101×#19252
C101×#18752
C101×#18702
C101×#18542
C101×#18092
C101×#17862
#24886101