Finite Group Databasebeta

← C101×#24539 #38806690

Subgroups — C101×#24539 #38806690

Order 25856.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C101C211yesmaximal, characteristic
2C2×#418×C101C211yesmaximal, characteristic, complemented
3C101×#2500C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
5C101×#2073C211yesmaximal, characteristic, complemented
6C101×#2071C211yesmaximal, characteristic, complemented
7C101×#2054C211yesmaximal, characteristic, complemented
8C101×#2054C211yesmaximal, characteristic, complemented
9C101×#1895C211yesmaximal, characteristic, complemented
10C101×#1879C211yesmaximal, characteristic, complemented
11C101×#1879C211yesmaximal, characteristic, complemented
12C101×#1851C211yesmaximal, characteristic, complemented
13C101×#1825C211yesmaximal, characteristic, complemented
14C101×#1804C211yesmaximal, characteristic, complemented
15C101×#1802C211yesmaximal, characteristic, complemented
16C23×D4×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×M16×C101C2211yescharacteristic
20C2×#121×C101C2211yescharacteristic
21C2×C4×D4×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C2×#117×C101C2211yescharacteristic
24C22×C22⋊C4×C101—21no—
25#447×C101—24no—
26C2×C4⋊C8×C101C2211yescharacteristic, complemented
27C2×C4⋊C8×C101C2211yescharacteristic, complemented
28#418×C101—24no—
29C2×#102×C101C2211yescharacteristic
30C2×#102×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic, complemented
36C2×#102×C101C2211yescharacteristic, complemented
37C2×C22⋊C8×C101C2211yescharacteristic
38#394×C101—21no—
39#394×C101—21no—
40#390×C101C2211yescharacteristic
41#390×C101C2211yescharacteristic
42#390×C101C2211yescharacteristic, complemented
43#390×C101C2211yescharacteristic, complemented
44#388×C101—21no—
45#388×C101—21no—
46#386×C101—21no—
47#386×C101—21no—
48#384×C101C2211yescharacteristic, complemented
49#382×C101C2211yescharacteristic, complemented
50#380×C101C2211yescharacteristic
51#379×C101—21no—
52C4×C22⋊C4×C101C2211yescharacteristic
53#340×C101C2211yescharacteristic, complemented
54#340×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—22no—
67C22×D4×C101—41no—
68C22×D4×C101—41no—
69C22×D4×C101D414yes—
70C22×D4×C101C2311yescharacteristic
71C22×D4×C101C2311yescharacteristic
72C22×D4×C101C2311yescharacteristic
73C23×C4×C101—21no—
74C23×C4×C101—21no—
75C23×C4×C101C2311yescharacteristic
76C2×D8×C101—22no—
77C2×D8×C101—22no—
78C2×D8×C101—22no—
79C2×D8×C101—22no—
80C2×D8×C101—41no—
81C2×D8×C101—41no—
82C2×M16×C101—22no—
83C2×M16×C101—41no—
84C2×M16×C101—41no—
85C22×C8×C101C2311yescharacteristic
86C22×C8×C101C2311yescharacteristic
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89#121×C101—22no—
90#121×C101—22no—
91C4×D4×C101—22no—
92C4×D4×C101—22no—
93C4×D4×C101—41no—
94C4×D4×C101—41no—
95#117×C101—22no—
96#117×C101—22no—
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101C2311yescharacteristic
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C4⋊C4×C101C2311yescharacteristic
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C4⋊C4×C101C2311yescharacteristic
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×C101—21no—
115C2×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—44no—
118C2×C22⋊C4×C101D411yescharacteristic
119C2×C22⋊C4×C101D411yescharacteristic
120C2×C42×C101—21no—
121C2×C42×C101C2311yescharacteristic
122C2×C42×C101C2311yescharacteristic
123C4⋊C8×C101—41no—
124C4⋊C8×C101—41no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—22no—
129#102×C101—22no—
130#102×C101—22no—
131#102×C101—41no—
132#102×C101—41no—
133C22⋊C8×C101—22no—
134#95×C101—21no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101D411yescharacteristic
138#95×C101D411yescharacteristic
139C24×C101—21no—
140C24×C101—21no—
141C24×C101—24no—
142C24×C101—21no—
143C24×C101—42no—
144C24×C101—42no—
145C24×C101—42no—
146C24×C101—42no—
147C24×C101—81no—
148C24×C101—81no—
149C24×C101C2×D411yescharacteristic
150C2×D4×C101—28no—
151C2×D4×C101—24no—
152C2×D4×C101—21no—
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—21no—
164C2×D4×C101—21no—
165C2×D4×C101—21no—
166C2×D4×C101—44no—
167C2×D4×C101—44no—
168C2×D4×C101—44no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—81no—
173C2×D4×C101—81no—
174C2×D4×C101C2×D412yes—
175C2×D4×C101C2×D412yes—
176C2×D4×C101#4112yes—
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—42no—
188C22×C4×C101—42no—
189C22×C4×C101—42no—
190C22×C4×C101—42no—
191C22×C4×C101—81no—
192C22×C4×C101—81no—
193C22×C4×C101C2×D411yescharacteristic
194C22×C4×C101C2×D411yescharacteristic
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2×D412yes—
198C22×C4×C101C2×D411yescharacteristic
199C22×C4×C101#4112yes—
200C22×C4×C101C2411yescharacteristic
201D8×C101—44no—
202D8×C101—44no—
203M16×C101—44no—
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×C101—21no—
214C2×C8×C101—21no—
215C2×C8×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—81no—
227C4⋊C4×C101—81no—
228C22⋊C4×C101—22no—
229C22⋊C4×C101—41no—
230C22⋊C4×C101—42no—
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—42no—
239C22⋊C4×C101—81no—
240C22⋊C4×C101—81no—
241C22⋊C4×C101—81no—
242C22⋊C4×C101—81no—
243C42×C101—21no—
244C42×C101—21no—
245C42×C101—21no—
246C42×C101—21no—
247C42×C101—42no—
248C23×C101—22no—
249C23×C101—22no—
250C23×C101—22no—
251C23×C101—21no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—21no—
255C23×C101—21no—
256C23×C101—21no—
257C23×C101—22no—
258C23×C101—48no—
259C23×C101—48no—
260C23×C101—41no—
261C23×C101—41no—
262C23×C101—41no—
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—41no—
276C23×C101—41no—
277C23×C101—84no—
278C23×C101—84no—
279C23×C101—84no—
280C23×C101—84no—
281C23×C101—84no—
282C23×C101#12112yes—
283C23×C101C22×D411yescharacteristic
284D4×C101—22no—
285D4×C101—22no—
286D4×C101—22no—
287D4×C101—22no—
288D4×C101—22no—
289D4×C101—48no—
290D4×C101—41no—
291D4×C101—41no—
292D4×C101—41no—
293D4×C101—41no—
294D4×C101—41no—
295D4×C101—41no—
296D4×C101—84no—
297D4×C101#12314yes—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—22no—
303C2×C4×C101—22no—
304C2×C4×C101—22no—
305C2×C4×C101—22no—
306C2×C4×C101—21no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
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—84no—
331C2×C4×C101—84no—
332C2×C4×C101#12112yes—
333C2×C4×C101AGL(1,ℤ/8)12yes—
334C2×C4×C101C22×D411yescharacteristic
335C2×C4×C101C2×#4111yescharacteristic
336C2×C4×C101C2×#4111yescharacteristic
337C2×C4×C101C2×#4111yescharacteristic
338C2×C4×C101H(5,𝔽2)11yescharacteristic
339C2×C4×C101H(5,𝔽2)11yescharacteristic
340C8×C101—41no—
341C8×C101—41no—
342C8×C101—41no—
343C8×C101—41no—
344C22×C101—22no—
345C22×C101—24no—
346C22×C101—22no—
347C22×C101—22no—
348C22×C101—42no—
349C22×C101—42no—
350C22×C101—42no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101—42no—
354C22×C101—41no—
355C22×C101—42no—
356C22×C101—42no—
357C22×C101—41no—
358C22×C101—42no—
359C22×C101—42no—
360C22×C101—42no—
361C22×C101—816no—
362C22×C101—81no—
363C22×C101—81no—
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×C101—81no—
373C22×C101C2×#12111yescharacteristic
374C22×C101#54611yescharacteristic
375C22×C101#54611yescharacteristic
376C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C101#57511yescharacteristic
378C22×C101#57611yescharacteristic
379C22×C101#57611yescharacteristic
380C4×C101—22no—
381C4×C101—22no—
382C4×C101—41no—
383C4×C101—41no—
384C4×C101—41no—
385C4×C101—81no—
386C4×C101—81no—
387C4×C101—81no—
388C4×C101—81no—
389C4×C101—81no—
390C4×C101C2×#12311yescharacteristic
391C4×C101#53411yescharacteristic
392C4×C101#55111yescharacteristic
393C4×C101#55111yescharacteristic
394#24539C10111yesmaximal, characteristic, direct product factor, Sylow
395C2×C101—42no—
396C2×C101—44no—
397C2×C101—82no—
398C2×C101—161no—
399C2×C101#241211yescharacteristic
400C2×C101#303611yescharacteristic
401C2×C101#304111yescharacteristic
402C2×C101#331811yescharacteristic
403C2×C101#331911yescharacteristic
404C2×C101#332211yescharacteristic
405C2×C101#332511yescharacteristic
406C2×#447C2×C10111yescharacteristic
407C2×#418C2×C10111yescharacteristic, complemented
408#2500C2×C10111yescharacteristic, complemented
409D4×C22⋊C4C2×C10111yescharacteristic, complemented
410#2073C2×C10111yescharacteristic, complemented
411#2071C2×C10111yescharacteristic, complemented
412#2054C2×C10111yescharacteristic, complemented
413#2054C2×C10111yescharacteristic, complemented
414#1895C2×C10111yescharacteristic, complemented
415#1879C2×C10111yescharacteristic, complemented
416#1879C2×C10111yescharacteristic, complemented
417#1851C2×C10111yescharacteristic, complemented
418#1825C2×C10111yescharacteristic, complemented
419#1804C2×C10111yescharacteristic, complemented
420#1802C2×C10111yescharacteristic, complemented
421C101#2453911yescharacteristic, direct product factor, Sylow
422C23×D4C22×C10111yescharacteristic
423C22×D8C22×C10111yescharacteristic
424C22×D8C22×C10111yescharacteristic
425C22×M16C22×C10111yescharacteristic
426C2×#121C22×C10111yescharacteristic
427C2×C4×D4C22×C10111yescharacteristic
428C2×C4×D4C22×C10111yescharacteristic
429C2×#117C22×C10111yescharacteristic
430C22×C22⋊C4—21no—
431#447—24no—
432C2×C4⋊C8C22×C10111yescharacteristic, complemented
433C2×C4⋊C8C22×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, complemented
442C2×#102C22×C10111yescharacteristic, complemented
443C2×C22⋊C8C22×C10111yescharacteristic
444#394—21no—
445#394—21no—
446#390C22×C10111yescharacteristic
447#390C22×C10111yescharacteristic
448#390C22×C10111yescharacteristic, complemented
449#390C22×C10111yescharacteristic, complemented
450#388—21no—
451#388—21no—
452#386—21no—
453#386—21no—
454#384C22×C10111yescharacteristic, complemented
455#382C22×C10111yescharacteristic, complemented
456#380C22×C10111yescharacteristic
457#379—21no—
458C4×C22⋊C4C22×C10111yescharacteristic
459#340C22×C10111yescharacteristic, complemented
460#340C22×C10111yescharacteristic, complemented
461#340C22×C10111yescharacteristic, complemented
462#340C22×C10111yescharacteristic, complemented
463#340C22×C10111yescharacteristic, complemented
464#340C22×C10111yescharacteristic, complemented
465#336C22×C10111yescharacteristic, complemented
466#336C22×C10111yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4D4×C10114yes—
476C22×D4C23×C10111yescharacteristic
477C22×D4C23×C10111yescharacteristic
478C22×D4C23×C10111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C10111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—41no—
487C2×D8—41no—
488C2×M16—22no—
489C2×M16—41no—
490C2×M16—41no—
491C22×C8C23×C10111yescharacteristic
492C22×C8C23×C10111yescharacteristic
493C22×C8C23×C10111yescharacteristic
494C22×C8C23×C10111yescharacteristic
495#121—22no—
496#121—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—41no—
500C4×D4—41no—
501#117—22no—
502#117—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C10111yescharacteristic
506C2×C4⋊C4C23×C10111yescharacteristic
507C2×C4⋊C4C23×C10111yescharacteristic
508C2×C4⋊C4C23×C10111yescharacteristic
509C2×C4⋊C4C23×C10111yescharacteristic
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⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—44no—
524C2×C22⋊C4D4×C10111yescharacteristic
525C2×C22⋊C4D4×C10111yescharacteristic
526C2×C42—21no—
527C2×C42C23×C10111yescharacteristic
528C2×C42C23×C10111yescharacteristic
529C4⋊C8—41no—
530C4⋊C8—41no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539C22⋊C8—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C10111yescharacteristic
544#95D4×C10111yescharacteristic
545C24—21no—
546C24—21no—
547C24—24no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C10111yescharacteristic
556C2×D4—28no—
557C2×D4—24no—
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—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C10112yes—
581C2×D4C2×D4×C10112yes—
582C2×D4#41×C10112yes—
583C2×D4#41×C10112yes—
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—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4—81no—
599C22×C4C2×D4×C10111yescharacteristic
600C22×C4C2×D4×C10111yescharacteristic
601C22×C4C2×D4×C10111yescharacteristic
602C22×C4C2×D4×C10111yescharacteristic
603C22×C4C2×D4×C10112yes—
604C22×C4C2×D4×C10111yescharacteristic
605C22×C4#41×C10112yes—
606C22×C4C24×C10111yescharacteristic
607D8—44no—
608D8—44no—
609M16—44no—
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×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—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—21no—
632C4⋊C4—81no—
633C4⋊C4—81no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
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—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23#121×C10112yes—
689C23C22×D4×C10111yescharacteristic
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4#123×C10114yes—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
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—84no—
737C2×C4—84no—
738C2×C4#121×C10112yes—
739C2×C4AGL(1,ℤ/8)×C10112yes—
740C2×C4C22×D4×C10111yescharacteristic
741C2×C4C2×#41×C10111yescharacteristic
742C2×C4C2×#41×C10111yescharacteristic
743C2×C4C2×#41×C10111yescharacteristic
744C2×C4H(5,𝔽2)×C10111yescharacteristic
745C2×C4H(5,𝔽2)×C10111yescharacteristic
746C8—41no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—816no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#121×C10111yescharacteristic
780C22#546×C10111yescharacteristic
781C22#546×C10111yescharacteristic
782C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
783C22#575×C10111yescharacteristic
784C22#576×C10111yescharacteristic
785C22#576×C10111yescharacteristic
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C10111yescharacteristic
797C4#534×C10111yescharacteristic
798C4#551×C10111yescharacteristic
799C4#551×C10111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—161no—
804C2C101×#241211yescharacteristic
805C2C101×#303611yescharacteristic
806C2C101×#304111yescharacteristic
807C2C101×#331811yescharacteristic
808C2C101×#331911yescharacteristic
809C2C101×#332211yescharacteristic
810C2C101×#332511yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#447×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#418×C101C2semidirect
3. C101×#2500C2semidirect
4. D4×C22⋊C4×C101C2semidirect
5. C101×#2073C2semidirect
6. C101×#2071C2semidirect
7. C101×#2054C2semidirect
8. C101×#2054C2semidirect
9. C101×#1895C2semidirect
10. C101×#1879C2semidirect
11. C101×#1879C2semidirect
12. C101×#1851C2semidirect
13. C101×#1825C2semidirect
14. C101×#1804C2semidirect
15. C101×#1802C2semidirect
26. C2×C4⋊C8×C101C22semidirect
27. C2×C4⋊C8×C101C22semidirect
35. C2×#102×C101C22semidirect
36. C2×#102×C101C22semidirect
42. #390×C101C22semidirect
43. #390×C101C22semidirect
48. #384×C101C22semidirect
49. #382×C101C22semidirect
53. #340×C101C22semidirect
54. #340×C101C22semidirect
55. #340×C101C22semidirect
56. #340×C101C22semidirect
57. #340×C101C22semidirect
58. #340×C101C22semidirect
59. #336×C101C22semidirect
60. #336×C101C22semidirect
394. #24539C101direct (N × H)
407. C2×#418C2×C101semidirect
408. #2500C2×C101semidirect
409. D4×C22⋊C4C2×C101semidirect
410. #2073C2×C101semidirect
411. #2071C2×C101semidirect
412. #2054C2×C101semidirect
413. #2054C2×C101semidirect
414. #1895C2×C101semidirect
415. #1879C2×C101semidirect
416. #1879C2×C101semidirect
417. #1851C2×C101semidirect
418. #1825C2×C101semidirect
419. #1804C2×C101semidirect
420. #1802C2×C101semidirect
421. C101#24539direct (N × H)
432. C2×C4⋊C8C22×C101semidirect
433. C2×C4⋊C8C22×C101semidirect
441. C2×#102C22×C101semidirect
442. C2×#102C22×C101semidirect
448. #390C22×C101semidirect
449. #390C22×C101semidirect
454. #384C22×C101semidirect
455. #382C22×C101semidirect
459. #340C22×C101semidirect
460. #340C22×C101semidirect
461. #340C22×C101semidirect
462. #340C22×C101semidirect
463. #340C22×C101semidirect
464. #340C22×C101semidirect
465. #336C22×C101semidirect
466. #336C22×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1012
C2×#418×C1012
C101×#25002
D4×C22⋊C4×C1012
C101×#20732
C101×#20712
C101×#20542
C101×#18952
C101×#18792
C101×#18512
C101×#18252
C101×#18042
C101×#18022
#24539101