Finite Group Databasebeta

← C101×#22334 #38804485

Subgroups — C101×#22334 #38804485

Order 25856.

806 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2392C211yesmaximal, characteristic
2C101×#1955C211yesmaximal, characteristic, complemented
3C101×#1954C211yesmaximal, characteristic, complemented
4C101×#1924C211yesmaximal, characteristic, complemented
5C101×#1924C211yesmaximal, characteristic, complemented
6C101×#1917C211yesmaximal, characteristic, complemented
7C101×#1916C211yesmaximal, characteristic, complemented
8C101×#1870C211yesmaximal, characteristic, complemented
9C101×#1870C211yesmaximal, characteristic, complemented
10C101×#1869C211yesmaximal, characteristic, complemented
11C101×#1869C211yesmaximal, characteristic, complemented
12C101×#1818C211yesmaximal, characteristic, complemented
13C101×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C101C211yesmaximal, characteristic, complemented
15C101×#1750C211yesmaximal, characteristic, complemented
16C22×M16×C101C2211yescharacteristic
17C23×C8×C101C2211yescharacteristic
18C2×C4×D4×C101C2211yescharacteristic
19C2×C4×D4×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic
21C2×#117×C101C2211yescharacteristic
22C2×C4⋊C8×C101C2211yescharacteristic
23C2×C4⋊C8×C101C2211yescharacteristic
24C2×C22⋊C8×C101C2211yescharacteristic
25C2×C22⋊C8×C101C2211yescharacteristic
26C2×C22⋊C8×C101C2211yescharacteristic
27C2×C22⋊C8×C101C2211yescharacteristic
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×#97×C101C2211yescharacteristic
35C2×#97×C101C2211yescharacteristic
36C2×C4×C8×C101C2211yescharacteristic
37C2×C4×C8×C101C2211yescharacteristic
38#398×C101C411yescharacteristic
39#397×C101C411yescharacteristic
40#396×C101C411yescharacteristic
41#396×C101C411yescharacteristic
42#394×C101C411yescharacteristic
43#394×C101C411yescharacteristic
44#394×C101C411yescharacteristic
45#392×C101C411yescharacteristic
46C4×C4⋊C4×C101C2211yescharacteristic
47C4×C22⋊C4×C101C2211yescharacteristic
48C4×C22⋊C4×C101C2211yescharacteristic
49#336×C101C2211yescharacteristic
50#336×C101C2211yescharacteristic
51#336×C101C2211yescharacteristic
52#336×C101C2211yescharacteristic
53#336×C101C2211yescharacteristic
54#336×C101C2211yescharacteristic
55#336×C101C2211yescharacteristic
56#336×C101C2211yescharacteristic
57#336×C101C2211yescharacteristic
58#336×C101C2211yescharacteristic
59C22×D4×C101C2×C411yescharacteristic
60C22×D4×C101C2×C411yescharacteristic
61C22×D4×C101C2×C411yescharacteristic
62C23×C4×C101C2311yescharacteristic
63C23×C4×C101C2311yescharacteristic
64C23×C4×C101C2311yescharacteristic
65C2×M16×C101—22no—
66C2×M16×C101—41no—
67C2×M16×C101—41no—
68C22×C8×C101—22no—
69C22×C8×C101—41no—
70C22×C8×C101—41no—
71C22×C8×C101C2311yescharacteristic
72C22×C8×C101C2311yescharacteristic
73C22×C8×C101C2311yescharacteristic
74C22×C8×C101C2311yescharacteristic
75C22×C8×C101C2311yescharacteristic
76C22×C8×C101C2311yescharacteristic
77C22×C8×C101C2311yescharacteristic
78C22×C8×C101C2311yescharacteristic
79C4×D4×C101—41no—
80C4×D4×C101—41no—
81C4×D4×C101—41no—
82C4×D4×C101—41no—
83C4×D4×C101—41no—
84C4×D4×C101—41no—
85#117×C101—41no—
86#117×C101—41no—
87C2×C4⋊C4×C101C2×C411yescharacteristic
88C2×C4⋊C4×C101C2×C411yescharacteristic
89C2×C4⋊C4×C101C2×C411yescharacteristic
90C2×C4⋊C4×C101C2×C411yescharacteristic
91C2×C4⋊C4×C101C2×C411yescharacteristic
92C2×C4⋊C4×C101C2×C411yescharacteristic
93C2×C4⋊C4×C101C2×C411yescharacteristic
94C2×C22⋊C4×C101C2×C411yescharacteristic
95C2×C22⋊C4×C101C2×C411yescharacteristic
96C2×C22⋊C4×C101C2×C411yescharacteristic
97C2×C22⋊C4×C101C2×C411yescharacteristic
98C2×C22⋊C4×C101C2×C411yescharacteristic
99C2×C22⋊C4×C101C2×C411yescharacteristic
100C2×C22⋊C4×C101C2×C411yescharacteristic
101C2×C22⋊C4×C101C2×C411yescharacteristic
102C2×C22⋊C4×C101C2×C411yescharacteristic
103C2×C22⋊C4×C101C2×C411yescharacteristic
104C2×C22⋊C4×C101C2×C411yescharacteristic
105C2×C22⋊C4×C101C2×C411yescharacteristic
106C2×C42×C101C2311yescharacteristic
107C2×C42×C101C2311yescharacteristic
108C2×C42×C101C2311yescharacteristic
109C2×C42×C101C2311yescharacteristic
110C4⋊C8×C101—41no—
111C4⋊C8×C101—41no—
112C22⋊C8×C101—22no—
113C22⋊C8×C101—22no—
114C22⋊C8×C101—22no—
115C22⋊C8×C101—22no—
116C22⋊C8×C101—41no—
117C22⋊C8×C101—41no—
118C22⋊C8×C101—41no—
119C22⋊C8×C101—41no—
120C22⋊C8×C101—41no—
121C22⋊C8×C101—41no—
122#97×C101—41no—
123#97×C101—41no—
124C4×C8×C101—41no—
125C4×C8×C101—41no—
126#95×C101C2×C411yescharacteristic
127#95×C101C2×C411yescharacteristic
128#95×C101C2×C411yescharacteristic
129#95×C101C2×C411yescharacteristic
130#95×C101C2×C411yescharacteristic
131#95×C101C2×C411yescharacteristic
132C24×C101C22×C411yescharacteristic
133C24×C101C22×C411yescharacteristic
134C24×C101C22×C411yescharacteristic
135C2×D4×C101—22no—
136C2×D4×C101—22no—
137C2×D4×C101—22no—
138C2×D4×C101—41no—
139C2×D4×C101—41no—
140C2×D4×C101—41no—
141C2×D4×C101—41no—
142C2×D4×C101—41no—
143C2×D4×C101—41no—
144C22×C4×C101—21no—
145C22×C4×C101—21no—
146C22×C4×C101—21no—
147C22×C4×C101—21no—
148C22×C4×C101—21no—
149C22×C4×C101—21no—
150C22×C4×C101—21no—
151C22×C4×C101—21no—
152C22×C4×C101—21no—
153C22×C4×C101—21no—
154C22×C4×C101—21no—
155C22×C4×C101—21no—
156C22×C4×C101—21no—
157C22×C4×C101—21no—
158C22×C4×C101—21no—
159C22×C4×C101—21no—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101C22×C411yescharacteristic
163C22×C4×C101C22×C411yescharacteristic
164C22×C4×C101C22×C411yescharacteristic
165C22×C4×C101C22×C411yescharacteristic
166C22×C4×C101C22×C411yescharacteristic
167C22×C4×C101C22×C411yescharacteristic
168C22×C4×C101C22×C411yescharacteristic
169C22×C4×C101C22×C411yescharacteristic
170C22×C4×C101C22×C411yescharacteristic
171C22×C4×C101C22×C411yescharacteristic
172C22×C4×C101C22×C411yescharacteristic
173C22×C4×C101C2411yescharacteristic
174M16×C101—44no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101—21no—
191C2×C8×C101—21no—
192C2×C8×C101—21no—
193C2×C8×C101—21no—
194C2×C8×C101—21no—
195C2×C8×C101—21no—
196C2×C8×C101—21no—
197C2×C8×C101—44no—
198C2×C8×C101#4112yes—
199C2×C8×C101#4112yes—
200C4⋊C4×C101—22no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101—41no—
204C4⋊C4×C101—41no—
205C4⋊C4×C101—41no—
206C4⋊C4×C101—41no—
207C22⋊C4×C101—22no—
208C22⋊C4×C101—22no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C22⋊C4×C101—41no—
215C22⋊C4×C101—41no—
216C22⋊C4×C101—41no—
217C22⋊C4×C101—41no—
218C22⋊C4×C101—41no—
219C42×C101—21no—
220C42×C101—21no—
221C42×C101—21no—
222C42×C101—21no—
223C42×C101—21no—
224C42×C101—21no—
225C42×C101—21no—
226C42×C101—21no—
227C23×C101—21no—
228C23×C101—21no—
229C23×C101—21no—
230C23×C101—21no—
231C23×C101—21no—
232C23×C101—21no—
233C23×C101—21no—
234C23×C101—21no—
235C23×C101—21no—
236C23×C101—21no—
237C23×C101—21no—
238C23×C101—21no—
239C23×C101—21no—
240C23×C101—21no—
241C23×C101—21no—
242C23×C101—21no—
243C23×C101—21no—
244C23×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101#13112yes—
248C23×C101C23×C411yescharacteristic
249D4×C101—44no—
250D4×C101—44no—
251D4×C101—44no—
252C2×C4×C101—21no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
255C2×C4×C101—21no—
256C2×C4×C101—21no—
257C2×C4×C101—21no—
258C2×C4×C101—21no—
259C2×C4×C101—21no—
260C2×C4×C101—21no—
261C2×C4×C101—21no—
262C2×C4×C101—21no—
263C2×C4×C101—21no—
264C2×C4×C101—21no—
265C2×C4×C101—21no—
266C2×C4×C101—21no—
267C2×C4×C101—21no—
268C2×C4×C101—21no—
269C2×C4×C101—21no—
270C2×C4×C101—21no—
271C2×C4×C101—21no—
272C2×C4×C101—21no—
273C2×C4×C101—21no—
274C2×C4×C101—21no—
275C2×C4×C101—21no—
276C2×C4×C101—21no—
277C2×C4×C101—21no—
278C2×C4×C101—21no—
279C2×C4×C101—21no—
280C2×C4×C101—21no—
281C2×C4×C101—21no—
282C2×C4×C101—21no—
283C2×C4×C101—21no—
284C2×C4×C101—41no—
285C2×C4×C101—41no—
286C2×C4×C101—41no—
287C2×C4×C101—41no—
288C2×C4×C101—41no—
289C2×C4×C101—41no—
290C2×C4×C101—41no—
291C2×C4×C101—41no—
292C2×C4×C101—41no—
293C2×C4×C101—41no—
294C2×C4×C101—41no—
295C2×C4×C101—41no—
296C2×C4×C101#13112yes—
297C2×C4×C101C2×#4111yescharacteristic
298C2×C4×C101C2×#4111yescharacteristic
299C2×C4×C101H(5,𝔽2)11yescharacteristic
300C2×C4×C101H(5,𝔽2)11yescharacteristic
301C2×C4×C101H(5,𝔽2)11yescharacteristic
302C2×C4×C101H(5,𝔽2)11yescharacteristic
303C8×C101—22no—
304C8×C101—22no—
305C8×C101—41no—
306C8×C101—41no—
307C8×C101—41no—
308C8×C101—41no—
309C8×C101—41no—
310C8×C101—41no—
311C22×C101—22no—
312C22×C101—22no—
313C22×C101—22no—
314C22×C101—41no—
315C22×C101—41no—
316C22×C101—41no—
317C22×C101—41no—
318C22×C101—41no—
319C22×C101—41no—
320C22×C101—41no—
321C22×C101—41no—
322C22×C101—41no—
323C22×C101—41no—
324C22×C101—41no—
325C22×C101—41no—
326C22×C101—41no—
327C22×C101—41no—
328C22×C101—41no—
329C22×C101—41no—
330C22×C101—41no—
331C22×C101—41no—
332C22×C101C4×#4111yescharacteristic
333C22×C101#51811yescharacteristic
334C22×C101#51811yescharacteristic
335C22×C101C2×#13111yescharacteristic
336C22×C101C2×#13111yescharacteristic
337C22×C101#56811yescharacteristic
338C22×C101#56811yescharacteristic
339C4×C101—22no—
340C4×C101—41no—
341C4×C101—41no—
342C4×C101—41no—
343C4×C101—41no—
344C4×C101—41no—
345C4×C101—41no—
346C4×C101—41no—
347C4×C101—41no—
348C4×C101—41no—
349C4×C101—41no—
350C4×C101#53811yescharacteristic
351C4×C101#53811yescharacteristic
352C4×C101#54011yescharacteristic
353C4×C101#54011yescharacteristic
354#22334C10111yesmaximal, characteristic, direct product factor, Sylow
355C2×C101—42no—
356C2×C101—81no—
357C2×C101—81no—
358C2×C101#233311yescharacteristic
359C2×C101#296611yescharacteristic
360C2×C101#296711yescharacteristic
361C2×C101#297611yescharacteristic
362C2×C101#297611yescharacteristic
363C2×C101#297611yescharacteristic
364C2×C101#298111yescharacteristic
365#2392C2×C10111yescharacteristic
366#1955C2×C10111yescharacteristic, complemented
367#1954C2×C10111yescharacteristic, complemented
368#1924C2×C10111yescharacteristic, complemented
369#1924C2×C10111yescharacteristic, complemented
370#1917C2×C10111yescharacteristic, complemented
371#1916C2×C10111yescharacteristic, complemented
372#1870C2×C10111yescharacteristic, complemented
373#1870C2×C10111yescharacteristic, complemented
374#1869C2×C10111yescharacteristic, complemented
375#1869C2×C10111yescharacteristic, complemented
376#1818C2×C10111yescharacteristic, complemented
377#1753C2×C10111yescharacteristic, complemented
378C8×C22⋊C4C2×C10111yescharacteristic, complemented
379#1750C2×C10111yescharacteristic, complemented
380C101#2233411yescharacteristic, direct product factor, Sylow
381C22×M16C22×C10111yescharacteristic
382C23×C8C22×C10111yescharacteristic
383C2×C4×D4C22×C10111yescharacteristic
384C2×C4×D4C22×C10111yescharacteristic
385C2×C4×D4C22×C10111yescharacteristic
386C2×#117C22×C10111yescharacteristic
387C2×C4⋊C8C22×C10111yescharacteristic
388C2×C4⋊C8C22×C10111yescharacteristic
389C2×C22⋊C8C22×C10111yescharacteristic
390C2×C22⋊C8C22×C10111yescharacteristic
391C2×C22⋊C8C22×C10111yescharacteristic
392C2×C22⋊C8C22×C10111yescharacteristic
393C2×C22⋊C8C22×C10111yescharacteristic
394C2×C22⋊C8C22×C10111yescharacteristic
395C2×C22⋊C8C22×C10111yescharacteristic
396C2×C22⋊C8C22×C10111yescharacteristic
397C2×C22⋊C8C22×C10111yescharacteristic
398C2×C22⋊C8C22×C10111yescharacteristic
399C2×#97C22×C10111yescharacteristic
400C2×#97C22×C10111yescharacteristic
401C2×C4×C8C22×C10111yescharacteristic
402C2×C4×C8C22×C10111yescharacteristic
403#398C4×C10111yescharacteristic
404#397C4×C10111yescharacteristic
405#396C4×C10111yescharacteristic
406#396C4×C10111yescharacteristic
407#394C4×C10111yescharacteristic
408#394C4×C10111yescharacteristic
409#394C4×C10111yescharacteristic
410#392C4×C10111yescharacteristic
411C4×C4⋊C4C22×C10111yescharacteristic
412C4×C22⋊C4C22×C10111yescharacteristic
413C4×C22⋊C4C22×C10111yescharacteristic
414#336C22×C10111yescharacteristic
415#336C22×C10111yescharacteristic
416#336C22×C10111yescharacteristic
417#336C22×C10111yescharacteristic
418#336C22×C10111yescharacteristic
419#336C22×C10111yescharacteristic
420#336C22×C10111yescharacteristic
421#336C22×C10111yescharacteristic
422#336C22×C10111yescharacteristic
423#336C22×C10111yescharacteristic
424C22×D4C2×C4×C10111yescharacteristic
425C22×D4C2×C4×C10111yescharacteristic
426C22×D4C2×C4×C10111yescharacteristic
427C23×C4C23×C10111yescharacteristic
428C23×C4C23×C10111yescharacteristic
429C23×C4C23×C10111yescharacteristic
430C2×M16—22no—
431C2×M16—41no—
432C2×M16—41no—
433C22×C8—22no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8C23×C10111yescharacteristic
437C22×C8C23×C10111yescharacteristic
438C22×C8C23×C10111yescharacteristic
439C22×C8C23×C10111yescharacteristic
440C22×C8C23×C10111yescharacteristic
441C22×C8C23×C10111yescharacteristic
442C22×C8C23×C10111yescharacteristic
443C22×C8C23×C10111yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×C4×C10111yescharacteristic
453C2×C4⋊C4C2×C4×C10111yescharacteristic
454C2×C4⋊C4C2×C4×C10111yescharacteristic
455C2×C4⋊C4C2×C4×C10111yescharacteristic
456C2×C4⋊C4C2×C4×C10111yescharacteristic
457C2×C4⋊C4C2×C4×C10111yescharacteristic
458C2×C4⋊C4C2×C4×C10111yescharacteristic
459C2×C22⋊C4C2×C4×C10111yescharacteristic
460C2×C22⋊C4C2×C4×C10111yescharacteristic
461C2×C22⋊C4C2×C4×C10111yescharacteristic
462C2×C22⋊C4C2×C4×C10111yescharacteristic
463C2×C22⋊C4C2×C4×C10111yescharacteristic
464C2×C22⋊C4C2×C4×C10111yescharacteristic
465C2×C22⋊C4C2×C4×C10111yescharacteristic
466C2×C22⋊C4C2×C4×C10111yescharacteristic
467C2×C22⋊C4C2×C4×C10111yescharacteristic
468C2×C22⋊C4C2×C4×C10111yescharacteristic
469C2×C22⋊C4C2×C4×C10111yescharacteristic
470C2×C22⋊C4C2×C4×C10111yescharacteristic
471C2×C42C23×C10111yescharacteristic
472C2×C42C23×C10111yescharacteristic
473C2×C42C23×C10111yescharacteristic
474C2×C42C23×C10111yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C22⋊C8—22no—
478C22⋊C8—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487#97—41no—
488#97—41no—
489C4×C8—41no—
490C4×C8—41no—
491#95C2×C4×C10111yescharacteristic
492#95C2×C4×C10111yescharacteristic
493#95C2×C4×C10111yescharacteristic
494#95C2×C4×C10111yescharacteristic
495#95C2×C4×C10111yescharacteristic
496#95C2×C4×C10111yescharacteristic
497C24C22×C4×C10111yescharacteristic
498C24C22×C4×C10111yescharacteristic
499C24C22×C4×C10111yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C10111yescharacteristic
528C22×C4C22×C4×C10111yescharacteristic
529C22×C4C22×C4×C10111yescharacteristic
530C22×C4C22×C4×C10111yescharacteristic
531C22×C4C22×C4×C10111yescharacteristic
532C22×C4C22×C4×C10111yescharacteristic
533C22×C4C22×C4×C10111yescharacteristic
534C22×C4C22×C4×C10111yescharacteristic
535C22×C4C22×C4×C10111yescharacteristic
536C22×C4C22×C4×C10111yescharacteristic
537C22×C4C22×C4×C10111yescharacteristic
538C22×C4C24×C10111yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—44no—
563C2×C8#41×C10112yes—
564C2×C8#41×C10112yes—
565C4⋊C4—22no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#131×C10112yes—
613C23C23×C4×C10111yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4#131×C10112yes—
662C2×C4C2×#41×C10111yescharacteristic
663C2×C4C2×#41×C10111yescharacteristic
664C2×C4H(5,𝔽2)×C10111yescharacteristic
665C2×C4H(5,𝔽2)×C10111yescharacteristic
666C2×C4H(5,𝔽2)×C10111yescharacteristic
667C2×C4H(5,𝔽2)×C10111yescharacteristic
668C8—22no—
669C8—22no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22C4×#41×C10111yescharacteristic
698C22#518×C10111yescharacteristic
699C22#518×C10111yescharacteristic
700C22C2×#131×C10111yescharacteristic
701C22C2×#131×C10111yescharacteristic
702C22#568×C10111yescharacteristic
703C22#568×C10111yescharacteristic
704C4—22no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4#538×C10111yescharacteristic
716C4#538×C10111yescharacteristic
717C4#540×C10111yescharacteristic
718C4#540×C10111yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2C101×#233311yescharacteristic
723C2C101×#296611yescharacteristic
724C2C101×#296711yescharacteristic
725C2C101×#297611yescharacteristic
726C2C101×#297611yescharacteristic
727C2C101×#297611yescharacteristic
728C2C101×#298111yescharacteristic
subgroupG/H
centerC22×C4×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC22×C4C24×C101
socleC23×C101C23×C4
prime radical#392×C101C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1955C2semidirect
3. C101×#1954C2semidirect
4. C101×#1924C2semidirect
5. C101×#1924C2semidirect
6. C101×#1917C2semidirect
7. C101×#1916C2semidirect
8. C101×#1870C2semidirect
9. C101×#1870C2semidirect
10. C101×#1869C2semidirect
11. C101×#1869C2semidirect
12. C101×#1818C2semidirect
13. C101×#1753C2semidirect
14. C8×C22⋊C4×C101C2semidirect
15. C101×#1750C2semidirect
354. #22334C101direct (N × H)
366. #1955C2×C101semidirect
367. #1954C2×C101semidirect
368. #1924C2×C101semidirect
369. #1924C2×C101semidirect
370. #1917C2×C101semidirect
371. #1916C2×C101semidirect
372. #1870C2×C101semidirect
373. #1870C2×C101semidirect
374. #1869C2×C101semidirect
375. #1869C2×C101semidirect
376. #1818C2×C101semidirect
377. #1753C2×C101semidirect
378. C8×C22⋊C4C2×C101semidirect
379. #1750C2×C101semidirect
380. C101#22334direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#23922
C101×#19552
C101×#19542
C101×#19242
C101×#19172
C101×#19162
C101×#18702
C101×#18692
C101×#18182
C101×#17532
C8×C22⋊C4×C1012
C101×#17502
#22334101