Finite Group Databasebeta

← C101×#22333 #38804484

Subgroups — C101×#22333 #38804484

Order 25856.

884 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C101C211yesmaximal, characteristic
2C101×#1955C211yesmaximal, characteristic, complemented
3C101×#1954C211yesmaximal, characteristic, complemented
4C101×#1923C211yesmaximal, characteristic, complemented
5C101×#1923C211yesmaximal, 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×#1817C211yesmaximal, characteristic, complemented
13C101×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C101C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C101C211yesmaximal, characteristic, complemented
16C22×M16×C101C2211yescharacteristic
17C23×C8×C101C2211yescharacteristic
18C2×#121×C101C411yescharacteristic
19C2×C4×D4×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic
21C2×C4×D4×C101C2211yescharacteristic
22C22×C42×C101C2211yescharacteristic
23C2×C4⋊C8×C101C2211yescharacteristic
24C2×C4⋊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×C22⋊C8×C101C2211yescharacteristic
35C2×#97×C101C2211yescharacteristic
36C2×C4×C8×C101C2211yescharacteristic
37C2×C4×C8×C101C2211yescharacteristic
38C2×C4×C8×C101C2211yescharacteristic
39#390×C101C411yescharacteristic
40#389×C101C411yescharacteristic
41#388×C101C411yescharacteristic
42#388×C101C411yescharacteristic
43#386×C101C411yescharacteristic
44#386×C101C411yescharacteristic
45#380×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×C101C2×C411yescharacteristic
63C23×C4×C101C2×C411yescharacteristic
64C23×C4×C101C2311yescharacteristic
65C23×C4×C101C2311yescharacteristic
66C23×C4×C101C2311yescharacteristic
67C2×M16×C101—22no—
68C2×M16×C101—41no—
69C2×M16×C101—41no—
70C22×C8×C101—22no—
71C22×C8×C101—41no—
72C22×C8×C101—41no—
73C22×C8×C101C2311yescharacteristic
74C22×C8×C101C2311yescharacteristic
75C22×C8×C101C2311yescharacteristic
76C22×C8×C101C2311yescharacteristic
77C22×C8×C101C2311yescharacteristic
78C22×C8×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81#121×C101—24no—
82C4×D4×C101—41no—
83C4×D4×C101—41no—
84C4×D4×C101—41no—
85C4×D4×C101—41no—
86C4×D4×C101—41no—
87C4×D4×C101—41no—
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×C22⋊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×C42×C101—41no—
104C2×C42×C101—41no—
105C2×C42×C101C2×C411yescharacteristic
106C2×C42×C101C2×C411yescharacteristic
107C2×C42×C101C2311yescharacteristic
108C2×C42×C101C2311yescharacteristic
109C2×C42×C101C2311yescharacteristic
110C2×C42×C101C2311yescharacteristic
111C4⋊C8×C101—41no—
112C4⋊C8×C101—41no—
113C22⋊C8×C101—22no—
114C22⋊C8×C101—22no—
115C22⋊C8×C101—22no—
116C22⋊C8×C101—22no—
117C22⋊C8×C101—41no—
118C22⋊C8×C101—41no—
119C22⋊C8×C101—41no—
120C22⋊C8×C101—41no—
121C22⋊C8×C101—41no—
122C22⋊C8×C101—41no—
123#97×C101—41no—
124C4×C8×C101—41no—
125C4×C8×C101—41no—
126C4×C8×C101—41no—
127#95×C101C2×C411yescharacteristic
128#95×C101C2×C411yescharacteristic
129#95×C101C2×C411yescharacteristic
130#95×C101C2×C411yescharacteristic
131#95×C101C2×C411yescharacteristic
132#95×C101C2×C411yescharacteristic
133C24×C101C22×C411yescharacteristic
134C24×C101C22×C411yescharacteristic
135C24×C101C22×C411yescharacteristic
136C2×D4×C101—22no—
137C2×D4×C101—22no—
138C2×D4×C101—22no—
139C2×D4×C101—22no—
140C2×D4×C101—22no—
141C2×D4×C101—22no—
142C2×D4×C101—41no—
143C2×D4×C101—41no—
144C2×D4×C101—41no—
145C22×C4×C101—22no—
146C22×C4×C101—22no—
147C22×C4×C101—22no—
148C22×C4×C101—22no—
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×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169C22×C4×C101C22×C411yescharacteristic
170C22×C4×C101C22×C411yescharacteristic
171C22×C4×C101C22×C411yescharacteristic
172C22×C4×C101C22×C411yescharacteristic
173C22×C4×C101C22×C411yescharacteristic
174C22×C4×C101C22×C411yescharacteristic
175C22×C4×C101C22×C411yescharacteristic
176C22×C4×C101C22×C411yescharacteristic
177C22×C4×C101C22×C411yescharacteristic
178C22×C4×C101C22×C411yescharacteristic
179C22×C4×C101C22×C411yescharacteristic
180C22×C4×C101C2411yescharacteristic
181M16×C101—44no—
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—21no—
198C2×C8×C101—21no—
199C2×C8×C101—21no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—21no—
204C2×C8×C101—44no—
205C2×C8×C101#4112yes—
206C2×C8×C101#4112yes—
207C4⋊C4×C101—22no—
208C4⋊C4×C101—22no—
209C4⋊C4×C101—41no—
210C4⋊C4×C101—41no—
211C4⋊C4×C101—41no—
212C22⋊C4×C101—22no—
213C22⋊C4×C101—22no—
214C22⋊C4×C101—22no—
215C22⋊C4×C101—41no—
216C22⋊C4×C101—41no—
217C22⋊C4×C101—41no—
218C22⋊C4×C101—41no—
219C22⋊C4×C101—41no—
220C22⋊C4×C101—41no—
221C22⋊C4×C101M1614yescomplemented
222C42×C101—21no—
223C42×C101—21no—
224C42×C101—21no—
225C42×C101—21no—
226C42×C101—21no—
227C42×C101—21no—
228C42×C101—21no—
229C42×C101—21no—
230C42×C101—41no—
231C42×C101—41no—
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—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101C2×M1612yes—
252C23×C101#13112yes—
253C23×C101C23×C411yescharacteristic
254D4×C101—44no—
255D4×C101—44no—
256D4×C101—44no—
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—21no—
285C2×C4×C101—21no—
286C2×C4×C101—44no—
287C2×C4×C101—44no—
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—41no—
297C2×C4×C101—41no—
298C2×C4×C101—41no—
299C2×C4×C101—41no—
300C2×C4×C101C2×M1612yes—
301C2×C4×C101C2×M1612yes—
302C2×C4×C101#13112yes—
303C2×C4×C101#13112yes—
304C2×C4×C101C2×#4111yescharacteristic
305C2×C4×C101C2×#4111yescharacteristic
306C2×C4×C101H(5,𝔽2)11yescharacteristic
307C2×C4×C101H(5,𝔽2)11yescharacteristic
308C2×C4×C101H(5,𝔽2)11yescharacteristic
309C2×C4×C101H(5,𝔽2)11yescharacteristic
310C8×C101—22no—
311C8×C101—22no—
312C8×C101—41no—
313C8×C101—41no—
314C8×C101—41no—
315C8×C101—41no—
316C8×C101—41no—
317C8×C101—41no—
318C22×C101—22no—
319C22×C101—22no—
320C22×C101—22no—
321C22×C101—22no—
322C22×C101—22no—
323C22×C101—22no—
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×C101—41no—
333C22×C101—41no—
334C22×C101—41no—
335C22×C101—41no—
336C22×C101—41no—
337C22×C101—41no—
338C22×C101—41no—
339C22×C101C4×#4111yescharacteristic
340C22×C101#51811yescharacteristic
341C22×C101#51811yescharacteristic
342C22×C101C22×M1611yescharacteristic
343C22×C101C2×#13111yescharacteristic
344C22×C101C2×#13111yescharacteristic
345C22×C101C2×#13111yescharacteristic
346C4×C101—22no—
347C4×C101—22no—
348C4×C101—22no—
349C4×C101—22no—
350C4×C101—41no—
351C4×C101—41no—
352C4×C101—41no—
353C4×C101—41no—
354C4×C101—41no—
355C4×C101—41no—
356C4×C101—41no—
357C4×C101#53811yescharacteristic
358C4×C101#53811yescharacteristic
359C4×C101#54011yescharacteristic
360C4×C101#54011yescharacteristic
361#22333C10111yesmaximal, characteristic, direct product factor, Sylow
362C2×C101—42no—
363C2×C101—42no—
364C2×C101—81no—
365C2×C101#233311yescharacteristic
366C2×C101#296511yescharacteristic
367C2×C101#296611yescharacteristic
368C2×C101#297411yescharacteristic
369C2×C101#297411yescharacteristic
370C2×C101#297711yescharacteristic
371C2×C101#297911yescharacteristic
372C4×#121C2×C10111yescharacteristic
373#1955C2×C10111yescharacteristic, complemented
374#1954C2×C10111yescharacteristic, complemented
375#1923C2×C10111yescharacteristic, complemented
376#1923C2×C10111yescharacteristic, complemented
377#1917C2×C10111yescharacteristic, complemented
378#1916C2×C10111yescharacteristic, complemented
379#1870C2×C10111yescharacteristic, complemented
380#1870C2×C10111yescharacteristic, complemented
381#1869C2×C10111yescharacteristic, complemented
382#1869C2×C10111yescharacteristic, complemented
383#1817C2×C10111yescharacteristic, complemented
384#1753C2×C10111yescharacteristic, complemented
385C8×C22⋊C4C2×C10111yescharacteristic, complemented
386C4×C22⋊C8C2×C10111yescharacteristic, complemented
387C101#2233311yescharacteristic, direct product factor, Sylow
388C22×M16C22×C10111yescharacteristic
389C23×C8C22×C10111yescharacteristic
390C2×#121C4×C10111yescharacteristic
391C2×C4×D4C22×C10111yescharacteristic
392C2×C4×D4C22×C10111yescharacteristic
393C2×C4×D4C22×C10111yescharacteristic
394C22×C42C22×C10111yescharacteristic
395C2×C4⋊C8C22×C10111yescharacteristic
396C2×C4⋊C8C22×C10111yescharacteristic
397C2×C22⋊C8C22×C10111yescharacteristic
398C2×C22⋊C8C22×C10111yescharacteristic
399C2×C22⋊C8C22×C10111yescharacteristic
400C2×C22⋊C8C22×C10111yescharacteristic
401C2×C22⋊C8C22×C10111yescharacteristic
402C2×C22⋊C8C22×C10111yescharacteristic
403C2×C22⋊C8C22×C10111yescharacteristic
404C2×C22⋊C8C22×C10111yescharacteristic
405C2×C22⋊C8C22×C10111yescharacteristic
406C2×C22⋊C8C22×C10111yescharacteristic
407C2×#97C22×C10111yescharacteristic
408C2×C4×C8C22×C10111yescharacteristic
409C2×C4×C8C22×C10111yescharacteristic
410C2×C4×C8C22×C10111yescharacteristic
411#390C4×C10111yescharacteristic
412#389C4×C10111yescharacteristic
413#388C4×C10111yescharacteristic
414#388C4×C10111yescharacteristic
415#386C4×C10111yescharacteristic
416#386C4×C10111yescharacteristic
417#380C4×C10111yescharacteristic
418C4×C4⋊C4C22×C10111yescharacteristic
419C4×C22⋊C4C22×C10111yescharacteristic
420C4×C22⋊C4C22×C10111yescharacteristic
421#336C22×C10111yescharacteristic
422#336C22×C10111yescharacteristic
423#336C22×C10111yescharacteristic
424#336C22×C10111yescharacteristic
425#336C22×C10111yescharacteristic
426#336C22×C10111yescharacteristic
427#336C22×C10111yescharacteristic
428#336C22×C10111yescharacteristic
429#336C22×C10111yescharacteristic
430#336C22×C10111yescharacteristic
431C22×D4C2×C4×C10111yescharacteristic
432C22×D4C2×C4×C10111yescharacteristic
433C22×D4C2×C4×C10111yescharacteristic
434C23×C4C2×C4×C10111yescharacteristic
435C23×C4C2×C4×C10111yescharacteristic
436C23×C4C23×C10111yescharacteristic
437C23×C4C23×C10111yescharacteristic
438C23×C4C23×C10111yescharacteristic
439C2×M16—22no—
440C2×M16—41no—
441C2×M16—41no—
442C22×C8—22no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C10111yescharacteristic
446C22×C8C23×C10111yescharacteristic
447C22×C8C23×C10111yescharacteristic
448C22×C8C23×C10111yescharacteristic
449C22×C8C23×C10111yescharacteristic
450C22×C8C23×C10111yescharacteristic
451C22×C8C23×C10111yescharacteristic
452C22×C8C23×C10111yescharacteristic
453#121—24no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C4×D4—41no—
460C2×C4⋊C4C2×C4×C10111yescharacteristic
461C2×C4⋊C4C2×C4×C10111yescharacteristic
462C2×C4⋊C4C2×C4×C10111yescharacteristic
463C2×C4⋊C4C2×C4×C10111yescharacteristic
464C2×C4⋊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×C22⋊C4C2×C4×C10111yescharacteristic
472C2×C22⋊C4C2×C4×C10111yescharacteristic
473C2×C22⋊C4C2×C4×C10111yescharacteristic
474C2×C22⋊C4C2×C4×C10111yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C10111yescharacteristic
478C2×C42C2×C4×C10111yescharacteristic
479C2×C42C23×C10111yescharacteristic
480C2×C42C23×C10111yescharacteristic
481C2×C42C23×C10111yescharacteristic
482C2×C42C23×C10111yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C22⋊C8—22no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495#97—41no—
496C4×C8—41no—
497C4×C8—41no—
498C4×C8—41no—
499#95C2×C4×C10111yescharacteristic
500#95C2×C4×C10111yescharacteristic
501#95C2×C4×C10111yescharacteristic
502#95C2×C4×C10111yescharacteristic
503#95C2×C4×C10111yescharacteristic
504#95C2×C4×C10111yescharacteristic
505C24C22×C4×C10111yescharacteristic
506C24C22×C4×C10111yescharacteristic
507C24C22×C4×C10111yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4C22×C4×C10111yescharacteristic
542C22×C4C22×C4×C10111yescharacteristic
543C22×C4C22×C4×C10111yescharacteristic
544C22×C4C22×C4×C10111yescharacteristic
545C22×C4C22×C4×C10111yescharacteristic
546C22×C4C22×C4×C10111yescharacteristic
547C22×C4C22×C4×C10111yescharacteristic
548C22×C4C22×C4×C10111yescharacteristic
549C22×C4C22×C4×C10111yescharacteristic
550C22×C4C22×C4×C10111yescharacteristic
551C22×C4C22×C4×C10111yescharacteristic
552C22×C4C24×C10111yescharacteristic
553M16—44no—
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—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—44no—
577C2×C8#41×C10112yes—
578C2×C8#41×C10112yes—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4M16×C10114yescomplemented
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—41no—
603C42—41no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×M16×C10112yes—
624C23#131×C10112yes—
625C23C23×C4×C10111yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
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—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4C2×M16×C10112yes—
673C2×C4C2×M16×C10112yes—
674C2×C4#131×C10112yes—
675C2×C4#131×C10112yes—
676C2×C4C2×#41×C10111yescharacteristic
677C2×C4C2×#41×C10111yescharacteristic
678C2×C4H(5,𝔽2)×C10111yescharacteristic
679C2×C4H(5,𝔽2)×C10111yescharacteristic
680C2×C4H(5,𝔽2)×C10111yescharacteristic
681C2×C4H(5,𝔽2)×C10111yescharacteristic
682C8—22no—
683C8—22no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C4×#41×C10111yescharacteristic
712C22#518×C10111yescharacteristic
713C22#518×C10111yescharacteristic
714C22C22×M16×C10111yescharacteristic
715C22C2×#131×C10111yescharacteristic
716C22C2×#131×C10111yescharacteristic
717C22C2×#131×C10111yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—22no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4#538×C10111yescharacteristic
730C4#538×C10111yescharacteristic
731C4#540×C10111yescharacteristic
732C4#540×C10111yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2C101×#233311yescharacteristic
737C2C101×#296511yescharacteristic
738C2C101×#296611yescharacteristic
739C2C101×#297411yescharacteristic
740C2C101×#297411yescharacteristic
741C2C101×#297711yescharacteristic
742C2C101×#297911yescharacteristic
subgroupG/H
centerC22×C4×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC22×C4C24×C101
socleC23×C101C23×C4
prime radicalC2×#121×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×#1923C2semidirect
5. C101×#1923C2semidirect
6. C101×#1917C2semidirect
7. C101×#1916C2semidirect
8. C101×#1870C2semidirect
9. C101×#1870C2semidirect
10. C101×#1869C2semidirect
11. C101×#1869C2semidirect
12. C101×#1817C2semidirect
13. C101×#1753C2semidirect
14. C8×C22⋊C4×C101C2semidirect
15. C4×C22⋊C8×C101C2semidirect
221. C22⋊C4×C101M16semidirect
361. #22333C101direct (N × H)
373. #1955C2×C101semidirect
374. #1954C2×C101semidirect
375. #1923C2×C101semidirect
376. #1923C2×C101semidirect
377. #1917C2×C101semidirect
378. #1916C2×C101semidirect
379. #1870C2×C101semidirect
380. #1870C2×C101semidirect
381. #1869C2×C101semidirect
382. #1869C2×C101semidirect
383. #1817C2×C101semidirect
384. #1753C2×C101semidirect
385. C8×C22⋊C4C2×C101semidirect
386. C4×C22⋊C8C2×C101semidirect
387. C101#22333direct (N × H)
593. C22⋊C4M16×C101semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1012
C101×#19552
C101×#19542
C101×#19232
C101×#19172
C101×#19162
C101×#18702
C101×#18692
C101×#18172
C101×#17532
C8×C22⋊C4×C1012
C4×C22⋊C8×C1012
#22333101