Finite Group Databasebeta

← C101×#22037 #38804188

Subgroups — C101×#22037 #38804188

Order 25856.

1034 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C101C211yesmaximal, characteristic, complemented
2C2×#408×C101C211yesmaximal, characteristic, complemented
3C101×#2388C211yesmaximal, characteristic
4C101×#1955C211yesmaximal, characteristic, complemented
5C101×#1954C211yesmaximal, characteristic, complemented
6C101×#1924C211yesmaximal, characteristic, complemented
7C101×#1924C211yesmaximal, characteristic, complemented
8C101×#1924C211yesmaximal, characteristic, complemented
9C101×#1923C211yesmaximal, characteristic, complemented
10C101×#1869C211yesmaximal, characteristic, complemented
11C101×#1869C211yesmaximal, characteristic, complemented
12C101×#1869C211yesmaximal, characteristic, complemented
13C101×#1850C211yesmaximal, characteristic, complemented
14C101×#1780C211yesmaximal, characteristic, complemented
15C101×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×M16×C101C2211yescharacteristic
18C23×C8×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic
21C2×C4×D4×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23#435×C101—24no—
24C2×C4⋊C8×C101C2211yescharacteristic
25C2×C4⋊C8×C101C2211yescharacteristic
26C2×C4⋊C8×C101C2211yescharacteristic
27#408×C101—24no—
28C2×C22⋊C8×C101C2211yescharacteristic
29C2×C22⋊C8×C101C2211yescharacteristic
30C2×C22⋊C8×C101C2211yescharacteristic
31C2×C22⋊C8×C101C2211yescharacteristic
32C2×C22⋊C8×C101C2211yescharacteristic
33C2×C22⋊C8×C101C2211yescharacteristic
34C2×C22⋊C8×C101C2211yescharacteristic
35C2×C22⋊C8×C101C2211yescharacteristic
36C2×C22⋊C8×C101C2211yescharacteristic
37C2×C22⋊C8×C101C2211yescharacteristic
38C2×C22⋊C8×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×C22⋊C8×C101C2211yescharacteristic
41C2×#97×C101C2211yescharacteristic
42C2×#97×C101C2211yescharacteristic
43C2×C4×C8×C101C2211yescharacteristic
44#395×C101C411yescharacteristic
45#394×C101C411yescharacteristic
46#394×C101C411yescharacteristic
47#394×C101C411yescharacteristic
48#393×C101C411yescharacteristic
49#392×C101C411yescharacteristic
50#392×C101C411yescharacteristic
51#392×C101C411yescharacteristic
52C4×C22⋊C4×C101C2211yescharacteristic
53C4×C22⋊C4×C101C2211yescharacteristic
54C4×C22⋊C4×C101C2211yescharacteristic
55#336×C101C2211yescharacteristic
56#336×C101C2211yescharacteristic
57#336×C101C2211yescharacteristic
58#336×C101C2211yescharacteristic
59#336×C101C2211yescharacteristic
60#336×C101C2211yescharacteristic
61C2×#41×C101—22no—
62C2×#41×C101—22no—
63C2×#41×C101—41no—
64C2×#41×C101—41no—
65C2×#41×C101—41no—
66C2×#41×C101—41no—
67C22×Q8×C101C2×C411yescharacteristic
68C22×D4×C101C2×C411yescharacteristic
69C22×D4×C101C2×C411yescharacteristic
70C22×D4×C101C2×C411yescharacteristic
71C22×D4×C101C2×C411yescharacteristic
72C22×D4×C101C2×C411yescharacteristic
73C22×D4×C101C2×C411yescharacteristic
74C23×C4×C101C2311yescharacteristic
75C23×C4×C101C2311yescharacteristic
76C23×C4×C101C2311yescharacteristic
77C23×C4×C101C2311yescharacteristic
78C2×M16×C101—41no—
79C2×M16×C101—41no—
80C2×M16×C101D414yescomplemented
81C22×C8×C101—22no—
82C22×C8×C101—22no—
83C22×C8×C101—41no—
84C22×C8×C101—41no—
85C22×C8×C101—41no—
86C22×C8×C101—41no—
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93C22×C8×C101C2311yescharacteristic
94C22×C8×C101C2311yescharacteristic
95C4×D4×C101—22no—
96C4×D4×C101—22no—
97C4×D4×C101—41no—
98C4×D4×C101—41no—
99C4×D4×C101—41no—
100C4×D4×C101—41no—
101C2×C4⋊C4×C101C2×C411yescharacteristic
102C2×C4⋊C4×C101C2×C411yescharacteristic
103C2×C4⋊C4×C101C2×C411yescharacteristic
104C2×C22⋊C4×C101C2×C411yescharacteristic
105C2×C22⋊C4×C101C2×C411yescharacteristic
106C2×C22⋊C4×C101C2×C411yescharacteristic
107C2×C22⋊C4×C101C2×C411yescharacteristic
108C2×C22⋊C4×C101C2×C411yescharacteristic
109C2×C22⋊C4×C101C2×C411yescharacteristic
110C2×C22⋊C4×C101C2×C411yescharacteristic
111C2×C22⋊C4×C101C2×C411yescharacteristic
112C2×C22⋊C4×C101C2×C411yescharacteristic
113C2×C22⋊C4×C101C2×C411yescharacteristic
114C2×C22⋊C4×C101C2×C411yescharacteristic
115C2×C22⋊C4×C101C2×C411yescharacteristic
116C2×C42×C101C2311yescharacteristic
117C2×C42×C101C2311yescharacteristic
118C2×C42×C101C2311yescharacteristic
119C4⋊C8×C101—22no—
120C4⋊C8×C101—41no—
121C4⋊C8×C101—41no—
122C22⋊C8×C101—22no—
123C22⋊C8×C101—22no—
124C22⋊C8×C101—22no—
125C22⋊C8×C101—22no—
126C22⋊C8×C101—22no—
127C22⋊C8×C101—22no—
128C22⋊C8×C101—22no—
129C22⋊C8×C101—41no—
130C22⋊C8×C101—41no—
131C22⋊C8×C101—41no—
132C22⋊C8×C101—41no—
133C22⋊C8×C101—41no—
134C22⋊C8×C101—41no—
135#97×C101—22no—
136#97×C101—41no—
137C4×C8×C101—41no—
138#95×C101C2×C411yescharacteristic
139#95×C101C2×C411yescharacteristic
140#95×C101C2×C411yescharacteristic
141#95×C101C2×C411yescharacteristic
142#95×C101C2×C411yescharacteristic
143#95×C101C2×C411yescharacteristic
144C24×C101C22×C411yescharacteristic
145C24×C101C22×C411yescharacteristic
146C24×C101C22×C411yescharacteristic
147C24×C101C22×C411yescharacteristic
148#41×C101—44no—
149#41×C101—44no—
150#41×C101—44no—
151#41×C101—44no—
152C2×Q8×C101—22no—
153C2×Q8×C101—41no—
154C2×Q8×C101—41no—
155C2×D4×C101—22no—
156C2×D4×C101—22no—
157C2×D4×C101—22no—
158C2×D4×C101—22no—
159C2×D4×C101—22no—
160C2×D4×C101—22no—
161C2×D4×C101—22no—
162C2×D4×C101—22no—
163C2×D4×C101—41no—
164C2×D4×C101—41no—
165C2×D4×C101—41no—
166C2×D4×C101—41no—
167C2×D4×C101—41no—
168C2×D4×C101—41no—
169C2×D4×C101—41no—
170C2×D4×C101—41no—
171C2×D4×C101—41no—
172C2×D4×C101—41no—
173C22×C4×C101—21no—
174C22×C4×C101—21no—
175C22×C4×C101—21no—
176C22×C4×C101—21no—
177C22×C4×C101—21no—
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×C101—21no—
195C22×C4×C101C22×C411yescharacteristic
196C22×C4×C101C22×C411yescharacteristic
197C22×C4×C101C22×C411yescharacteristic
198C22×C4×C101C22×C411yescharacteristic
199C22×C4×C101C22×C411yescharacteristic
200C22×C4×C101C22×C411yescharacteristic
201C22×C4×C101C22×C411yescharacteristic
202C22×C4×C101C22×C411yescharacteristic
203C22×C4×C101C22×C411yescharacteristic
204C22×C4×C101C22×C411yescharacteristic
205C22×C4×C101C2×D412yes—
206C22×C4×C101#4112yes—
207C22×C4×C101C2411yescharacteristic
208M16×C101—44no—
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—
216C2×C8×C101—21no—
217C2×C8×C101—21no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—21no—
227C2×C8×C101—21no—
228C2×C8×C101—21no—
229C2×C8×C101—21no—
230C2×C8×C101—21no—
231C2×C8×C101—44no—
232C2×C8×C101—44no—
233C2×C8×C101C2×D412yes—
234C2×C8×C101C2×D412yes—
235C4⋊C4×C101—22no—
236C4⋊C4×C101—41no—
237C4⋊C4×C101—41no—
238C22⋊C4×C101—22no—
239C22⋊C4×C101—22no—
240C22⋊C4×C101—22no—
241C22⋊C4×C101—22no—
242C22⋊C4×C101—41no—
243C22⋊C4×C101—41no—
244C22⋊C4×C101—41no—
245C22⋊C4×C101—41no—
246C22⋊C4×C101—41no—
247C22⋊C4×C101—41no—
248C22⋊C4×C101—41no—
249C22⋊C4×C101—41no—
250C42×C101—21no—
251C42×C101—21no—
252C42×C101—21no—
253C42×C101—21no—
254C42×C101—21no—
255C42×C101—21no—
256C23×C101—21no—
257C23×C101—21no—
258C23×C101—21no—
259C23×C101—21no—
260C23×C101—21no—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—21no—
268C23×C101—21no—
269C23×C101—21no—
270C23×C101—21no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
277C23×C101—21no—
278C23×C101—21no—
279C23×C101—21no—
280C23×C101—21no—
281C23×C101—21no—
282C23×C101C4×D412yes—
283C23×C101#13112yes—
284C23×C101C23×C411yescharacteristic
285Q8×C101—44no—
286D4×C101—44no—
287D4×C101—44no—
288D4×C101—44no—
289D4×C101—44no—
290D4×C101—44no—
291D4×C101—44no—
292C2×C4×C101—21no—
293C2×C4×C101—21no—
294C2×C4×C101—21no—
295C2×C4×C101—21no—
296C2×C4×C101—22no—
297C2×C4×C101—22no—
298C2×C4×C101—22no—
299C2×C4×C101—22no—
300C2×C4×C101—21no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
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—21no—
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
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—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101C4×D412yes—
337C2×C4×C101#13112yes—
338C2×C4×C101C22×D411yescharacteristic
339C2×C4×C101C2×#4111yescharacteristic
340C2×C4×C101H(5,𝔽2)11yescharacteristic
341C2×C4×C101H(5,𝔽2)11yescharacteristic
342C2×C4×C101H(5,𝔽2)11yescharacteristic
343C2×C4×C101H(5,𝔽2)11yescharacteristic
344C8×C101—22no—
345C8×C101—22no—
346C8×C101—41no—
347C8×C101—41no—
348C8×C101—41no—
349C8×C101—41no—
350C8×C101—41no—
351C8×C101—41no—
352C22×C101—22no—
353C22×C101—22no—
354C22×C101—22no—
355C22×C101—22no—
356C22×C101—22no—
357C22×C101—22no—
358C22×C101—41no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—41no—
364C22×C101—41no—
365C22×C101—41no—
366C22×C101—41no—
367C22×C101—41no—
368C22×C101—41no—
369C22×C101—41no—
370C22×C101—41no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—41no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—41no—
378C22×C101—41no—
379C22×C101—41no—
380C22×C101C2×C4×D411yescharacteristic
381C22×C101#51811yescharacteristic
382C22×C101#51811yescharacteristic
383C22×C101C2×#13111yescharacteristic
384C22×C101C2×#13111yescharacteristic
385C22×C101#56811yescharacteristic
386C22×C101#56811yescharacteristic
387C4×C101—22no—
388C4×C101—22no—
389C4×C101—41no—
390C4×C101—41no—
391C4×C101—41no—
392C4×C101—41no—
393C4×C101—41no—
394C4×C101—41no—
395C4×C101—41no—
396C4×C101—41no—
397C4×C101#53411yescharacteristic
398C4×C101#53511yescharacteristic
399C4×C101#53811yescharacteristic
400C4×C101#53811yescharacteristic
401#22037C10111yesmaximal, characteristic, direct product factor, Sylow
402C2×C101—42no—
403C2×C101—42no—
404C2×C101—81no—
405C2×C101—81no—
406C2×C101#232111yescharacteristic
407C2×C101#293311yescharacteristic
408C2×C101#293511yescharacteristic
409C2×C101#297611yescharacteristic
410C2×C101#297711yescharacteristic
411C2×C101#298011yescharacteristic
412C2×C101#298111yescharacteristic
413C2×#435C2×C10111yescharacteristic, complemented
414C2×#408C2×C10111yescharacteristic, complemented
415#2388C2×C10111yescharacteristic
416#1955C2×C10111yescharacteristic, complemented
417#1954C2×C10111yescharacteristic, complemented
418#1924C2×C10111yescharacteristic, complemented
419#1924C2×C10111yescharacteristic, complemented
420#1924C2×C10111yescharacteristic, complemented
421#1923C2×C10111yescharacteristic, complemented
422#1869C2×C10111yescharacteristic, complemented
423#1869C2×C10111yescharacteristic, complemented
424#1869C2×C10111yescharacteristic, complemented
425#1850C2×C10111yescharacteristic, complemented
426#1780C2×C10111yescharacteristic, complemented
427#1753C2×C10111yescharacteristic, complemented
428C101#2203711yescharacteristic, direct product factor, Sylow
429C22×#41C22×C10111yescharacteristic
430C22×M16C22×C10111yescharacteristic
431C23×C8C22×C10111yescharacteristic
432C23×C8C22×C10111yescharacteristic
433C2×C4×D4C22×C10111yescharacteristic
434C2×C4×D4C22×C10111yescharacteristic
435C2×C4×D4C22×C10111yescharacteristic
436#435—24no—
437C2×C4⋊C8C22×C10111yescharacteristic
438C2×C4⋊C8C22×C10111yescharacteristic
439C2×C4⋊C8C22×C10111yescharacteristic
440#408—24no—
441C2×C22⋊C8C22×C10111yescharacteristic
442C2×C22⋊C8C22×C10111yescharacteristic
443C2×C22⋊C8C22×C10111yescharacteristic
444C2×C22⋊C8C22×C10111yescharacteristic
445C2×C22⋊C8C22×C10111yescharacteristic
446C2×C22⋊C8C22×C10111yescharacteristic
447C2×C22⋊C8C22×C10111yescharacteristic
448C2×C22⋊C8C22×C10111yescharacteristic
449C2×C22⋊C8C22×C10111yescharacteristic
450C2×C22⋊C8C22×C10111yescharacteristic
451C2×C22⋊C8C22×C10111yescharacteristic
452C2×C22⋊C8C22×C10111yescharacteristic
453C2×C22⋊C8C22×C10111yescharacteristic
454C2×#97C22×C10111yescharacteristic
455C2×#97C22×C10111yescharacteristic
456C2×C4×C8C22×C10111yescharacteristic
457#395C4×C10111yescharacteristic
458#394C4×C10111yescharacteristic
459#394C4×C10111yescharacteristic
460#394C4×C10111yescharacteristic
461#393C4×C10111yescharacteristic
462#392C4×C10111yescharacteristic
463#392C4×C10111yescharacteristic
464#392C4×C10111yescharacteristic
465C4×C22⋊C4C22×C10111yescharacteristic
466C4×C22⋊C4C22×C10111yescharacteristic
467C4×C22⋊C4C22×C10111yescharacteristic
468#336C22×C10111yescharacteristic
469#336C22×C10111yescharacteristic
470#336C22×C10111yescharacteristic
471#336C22×C10111yescharacteristic
472#336C22×C10111yescharacteristic
473#336C22×C10111yescharacteristic
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C2×C4×C10111yescharacteristic
481C22×D4C2×C4×C10111yescharacteristic
482C22×D4C2×C4×C10111yescharacteristic
483C22×D4C2×C4×C10111yescharacteristic
484C22×D4C2×C4×C10111yescharacteristic
485C22×D4C2×C4×C10111yescharacteristic
486C22×D4C2×C4×C10111yescharacteristic
487C23×C4C23×C10111yescharacteristic
488C23×C4C23×C10111yescharacteristic
489C23×C4C23×C10111yescharacteristic
490C23×C4C23×C10111yescharacteristic
491C2×M16—41no—
492C2×M16—41no—
493C2×M16D4×C10114yescomplemented
494C22×C8—22no—
495C22×C8—22no—
496C22×C8—41no—
497C22×C8—41no—
498C22×C8—41no—
499C22×C8—41no—
500C22×C8C23×C10111yescharacteristic
501C22×C8C23×C10111yescharacteristic
502C22×C8C23×C10111yescharacteristic
503C22×C8C23×C10111yescharacteristic
504C22×C8C23×C10111yescharacteristic
505C22×C8C23×C10111yescharacteristic
506C22×C8C23×C10111yescharacteristic
507C22×C8C23×C10111yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513C4×D4—41no—
514C2×C4⋊C4C2×C4×C10111yescharacteristic
515C2×C4⋊C4C2×C4×C10111yescharacteristic
516C2×C4⋊C4C2×C4×C10111yescharacteristic
517C2×C22⋊C4C2×C4×C10111yescharacteristic
518C2×C22⋊C4C2×C4×C10111yescharacteristic
519C2×C22⋊C4C2×C4×C10111yescharacteristic
520C2×C22⋊C4C2×C4×C10111yescharacteristic
521C2×C22⋊C4C2×C4×C10111yescharacteristic
522C2×C22⋊C4C2×C4×C10111yescharacteristic
523C2×C22⋊C4C2×C4×C10111yescharacteristic
524C2×C22⋊C4C2×C4×C10111yescharacteristic
525C2×C22⋊C4C2×C4×C10111yescharacteristic
526C2×C22⋊C4C2×C4×C10111yescharacteristic
527C2×C22⋊C4C2×C4×C10111yescharacteristic
528C2×C22⋊C4C2×C4×C10111yescharacteristic
529C2×C42C23×C10111yescharacteristic
530C2×C42C23×C10111yescharacteristic
531C2×C42C23×C10111yescharacteristic
532C4⋊C8—22no—
533C4⋊C8—41no—
534C4⋊C8—41no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548#97—22no—
549#97—41no—
550C4×C8—41no—
551#95C2×C4×C10111yescharacteristic
552#95C2×C4×C10111yescharacteristic
553#95C2×C4×C10111yescharacteristic
554#95C2×C4×C10111yescharacteristic
555#95C2×C4×C10111yescharacteristic
556#95C2×C4×C10111yescharacteristic
557C24C22×C4×C10111yescharacteristic
558C24C22×C4×C10111yescharacteristic
559C24C22×C4×C10111yescharacteristic
560C24C22×C4×C10111yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
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×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4C22×C4×C10111yescharacteristic
609C22×C4C22×C4×C10111yescharacteristic
610C22×C4C22×C4×C10111yescharacteristic
611C22×C4C22×C4×C10111yescharacteristic
612C22×C4C22×C4×C10111yescharacteristic
613C22×C4C22×C4×C10111yescharacteristic
614C22×C4C22×C4×C10111yescharacteristic
615C22×C4C22×C4×C10111yescharacteristic
616C22×C4C22×C4×C10111yescharacteristic
617C22×C4C22×C4×C10111yescharacteristic
618C22×C4C2×D4×C10112yes—
619C22×C4#41×C10112yes—
620C22×C4C24×C10111yescharacteristic
621M16—44no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—44no—
645C2×C8—44no—
646C2×C8C2×D4×C10112yes—
647C2×C8C2×D4×C10112yes—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23C4×D4×C10112yes—
696C23#131×C10112yes—
697C23C23×C4×C10111yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
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—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4C4×D4×C10112yes—
750C2×C4#131×C10112yes—
751C2×C4C22×D4×C10111yescharacteristic
752C2×C4C2×#41×C10111yescharacteristic
753C2×C4H(5,𝔽2)×C10111yescharacteristic
754C2×C4H(5,𝔽2)×C10111yescharacteristic
755C2×C4H(5,𝔽2)×C10111yescharacteristic
756C2×C4H(5,𝔽2)×C10111yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—41no—
762C8—41no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×C4×D4×C10111yescharacteristic
794C22#518×C10111yescharacteristic
795C22#518×C10111yescharacteristic
796C22C2×#131×C10111yescharacteristic
797C22C2×#131×C10111yescharacteristic
798C22#568×C10111yescharacteristic
799C22#568×C10111yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4#534×C10111yescharacteristic
811C4#535×C10111yescharacteristic
812C4#538×C10111yescharacteristic
813C4#538×C10111yescharacteristic
814C2—42no—
815C2—42no—
816C2—81no—
817C2—81no—
818C2C101×#232111yescharacteristic
819C2C101×#293311yescharacteristic
820C2C101×#293511yescharacteristic
821C2C101×#297611yescharacteristic
822C2C101×#297711yescharacteristic
823C2C101×#298011yescharacteristic
824C2C101×#298111yescharacteristic
subgroupG/H
centerC22×C4×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC22×C4C24×C101
socleC23×C101C23×C4
prime radicalC101×#2388C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C101C2semidirect
2. C2×#408×C101C2semidirect
4. C101×#1955C2semidirect
5. C101×#1954C2semidirect
6. C101×#1924C2semidirect
7. C101×#1924C2semidirect
8. C101×#1924C2semidirect
9. C101×#1923C2semidirect
10. C101×#1869C2semidirect
11. C101×#1869C2semidirect
12. C101×#1869C2semidirect
13. C101×#1850C2semidirect
14. C101×#1780C2semidirect
15. C101×#1753C2semidirect
80. C2×M16×C101D4semidirect
401. #22037C101direct (N × H)
413. C2×#435C2×C101semidirect
414. C2×#408C2×C101semidirect
416. #1955C2×C101semidirect
417. #1954C2×C101semidirect
418. #1924C2×C101semidirect
419. #1924C2×C101semidirect
420. #1924C2×C101semidirect
421. #1923C2×C101semidirect
422. #1869C2×C101semidirect
423. #1869C2×C101semidirect
424. #1869C2×C101semidirect
425. #1850C2×C101semidirect
426. #1780C2×C101semidirect
427. #1753C2×C101semidirect
428. C101#22037direct (N × H)
493. C2×M16D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1012
C2×#408×C1012
C101×#23882
C101×#19552
C101×#19542
C101×#19242
C101×#19232
C101×#18692
C101×#18502
C101×#17802
C101×#17532
#22037101