Finite Group Databasebeta

← C101×#22144 #38804295

Subgroups — C101×#22144 #38804295

Order 25856.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C101C211yesmaximal, characteristic, complemented
2C2×#433×C101C211yesmaximal, characteristic, complemented
3C101×#2392C211yesmaximal, characteristic
4C101×#1955C211yesmaximal, characteristic, complemented
5C101×#1954C211yesmaximal, characteristic, complemented
6C101×#1954C211yesmaximal, characteristic, complemented
7C101×#1939C211yesmaximal, characteristic, complemented
8C101×#1924C211yesmaximal, characteristic, complemented
9C101×#1923C211yesmaximal, characteristic, complemented
10C101×#1870C211yesmaximal, characteristic, complemented
11C101×#1869C211yesmaximal, characteristic, complemented
12C101×#1851C211yesmaximal, characteristic, complemented
13C101×#1850C211yesmaximal, characteristic, complemented
14C101×#1798C211yesmaximal, characteristic, complemented
15C101×#1771C211yesmaximal, characteristic, complemented
16C22×M16×C101C2211yescharacteristic
17C23×C8×C101C2211yescharacteristic
18C2×C4×D4×C101C2211yescharacteristic
19C2×C4×D4×C101C2211yescharacteristic
20C2×C4×D4×C101C2211yescharacteristic
21C2×#117×C101C2211yescharacteristic
22#435×C101—24no—
23#433×C101—24no—
24C2×C4⋊C8×C101C2211yescharacteristic
25C2×C4⋊C8×C101C2211yescharacteristic
26C2×C4⋊C8×C101C2211yescharacteristic
27C2×C4⋊C8×C101C2211yescharacteristic
28C2×C4⋊C8×C101C2211yescharacteristic
29C2×C4⋊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×#97×C101C2211yescharacteristic
41C2×#97×C101C2211yescharacteristic
42C2×C4×C8×C101C2211yescharacteristic
43C2×C4×C8×C101C2211yescharacteristic
44#398×C101C411yescharacteristic
45#397×C101C411yescharacteristic
46#396×C101C411yescharacteristic
47#396×C101C411yescharacteristic
48#394×C101C411yescharacteristic
49#394×C101C411yescharacteristic
50#394×C101C411yescharacteristic
51#392×C101C411yescharacteristic
52C4×C4⋊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
61C22×D4×C101C2×C411yescharacteristic
62C22×D4×C101C2×C411yescharacteristic
63C22×D4×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
81C4×D4×C101—22no—
82C4×D4×C101—22no—
83C4×D4×C101—41no—
84C4×D4×C101—41no—
85C4×D4×C101—41no—
86C4×D4×C101—41no—
87#117×C101—22no—
88#117×C101—22no—
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×C4⋊C4×C101C2×C411yescharacteristic
95C2×C4⋊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×C22⋊C4×C101C2×C411yescharacteristic
107C2×C22⋊C4×C101C2×C411yescharacteristic
108C2×C42×C101C2311yescharacteristic
109C2×C42×C101C2311yescharacteristic
110C2×C42×C101C2311yescharacteristic
111C2×C42×C101C2311yescharacteristic
112C4⋊C8×C101—22no—
113C4⋊C8×C101—22no—
114C4⋊C8×C101—22no—
115C4⋊C8×C101—22no—
116C4⋊C8×C101—41no—
117C4⋊C8×C101—41no—
118C22⋊C8×C101—22no—
119C22⋊C8×C101—22no—
120C22⋊C8×C101—22no—
121C22⋊C8×C101—22no—
122C22⋊C8×C101—41no—
123C22⋊C8×C101—41no—
124C22⋊C8×C101—41no—
125C22⋊C8×C101—41no—
126C22⋊C8×C101—41no—
127C22⋊C8×C101—41no—
128#97×C101—41no—
129#97×C101D414yescomplemented
130C4×C8×C101—22no—
131C4×C8×C101—41no—
132#95×C101C2×C411yescharacteristic
133#95×C101C2×C411yescharacteristic
134#95×C101C2×C411yescharacteristic
135#95×C101C2×C411yescharacteristic
136#95×C101C2×C411yescharacteristic
137#95×C101C2×C411yescharacteristic
138C24×C101C22×C411yescharacteristic
139C24×C101C22×C411yescharacteristic
140C24×C101C22×C411yescharacteristic
141C2×D4×C101—22no—
142C2×D4×C101—22no—
143C2×D4×C101—22no—
144C2×D4×C101—22no—
145C2×D4×C101—41no—
146C2×D4×C101—41no—
147C2×D4×C101—41no—
148C2×D4×C101—41no—
149C2×D4×C101—41no—
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—21no—
168C22×C4×C101C22×C411yescharacteristic
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×C101C2411yescharacteristic
180M16×C101—44no—
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—21no—
198C2×C8×C101—21no—
199C2×C8×C101—21no—
200C2×C8×C101—21no—
201C2×C8×C101—21no—
202C2×C8×C101—21no—
203C2×C8×C101—44no—
204C2×C8×C101C2×D412yes—
205C2×C8×C101C2×D412yes—
206C4⋊C4×C101—22no—
207C4⋊C4×C101—22no—
208C4⋊C4×C101—22no—
209C4⋊C4×C101—22no—
210C4⋊C4×C101—41no—
211C4⋊C4×C101—41no—
212C4⋊C4×C101—41no—
213C22⋊C4×C101—22no—
214C22⋊C4×C101—22no—
215C22⋊C4×C101—22no—
216C22⋊C4×C101—22no—
217C22⋊C4×C101—22no—
218C22⋊C4×C101—22no—
219C22⋊C4×C101—41no—
220C22⋊C4×C101—41no—
221C22⋊C4×C101—41no—
222C22⋊C4×C101—41no—
223C22⋊C4×C101—41no—
224C22⋊C4×C101—41no—
225C42×C101—21no—
226C42×C101—21no—
227C42×C101—21no—
228C42×C101—21no—
229C42×C101—21no—
230C42×C101—21no—
231C42×C101C2×D412yes—
232C42×C101#4112yes—
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×C101—21no—
252C23×C101—21no—
253C23×C101#13112yes—
254C23×C101C23×C411yescharacteristic
255D4×C101—44no—
256D4×C101—44no—
257D4×C101—44no—
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—21no—
287C2×C4×C101—21no—
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×C101C4×D412yes—
301C2×C4×C101C4×D412yes—
302C2×C4×C101#13112yes—
303C2×C4×C101C22×D411yescharacteristic
304C2×C4×C101C2×#4111yescharacteristic
305C2×C4×C101H(5,𝔽2)11yescharacteristic
306C2×C4×C101H(5,𝔽2)11yescharacteristic
307C2×C4×C101H(5,𝔽2)11yescharacteristic
308C2×C4×C1012−1+411yescharacteristic
309C8×C101—22no—
310C8×C101—22no—
311C8×C101—41no—
312C8×C101—41no—
313C8×C101—41no—
314C8×C101—41no—
315C8×C101—41no—
316C8×C101—41no—
317C22×C101—22no—
318C22×C101—22no—
319C22×C101—22no—
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×C101—41no—
333C22×C101—41no—
334C22×C101—41no—
335C22×C101—41no—
336C22×C101—41no—
337C22×C101—41no—
338C22×C101C2×C4×D411yescharacteristic
339C22×C101#51811yescharacteristic
340C22×C101#52011yescharacteristic
341C22×C101C2×#13111yescharacteristic
342C22×C101C2×#13111yescharacteristic
343C22×C101#56811yescharacteristic
344C22×C101#56811yescharacteristic
345C4×C101—22no—
346C4×C101—22no—
347C4×C101—22no—
348C4×C101—41no—
349C4×C101—41no—
350C4×C101—41no—
351C4×C101—41no—
352C4×C101—41no—
353C4×C101—41no—
354C4×C101—41no—
355C4×C101—41no—
356C4×C101#53511yescharacteristic
357C4×C101#53711yescharacteristic
358C4×C101#54011yescharacteristic
359C4×C101#54211yescharacteristic
360#22144C10111yesmaximal, characteristic, direct product factor, Sylow
361C2×C101—42no—
362C2×C101—81no—
363C2×C101—81no—
364C2×C101#232411yescharacteristic
365C2×C101#293311yescharacteristic
366C2×C101#293511yescharacteristic
367C2×C101#297711yescharacteristic
368C2×C101#297811yescharacteristic
369C2×C101#299211yescharacteristic
370C2×C101#299311yescharacteristic
371C2×#435C2×C10111yescharacteristic, complemented
372C2×#433C2×C10111yescharacteristic, complemented
373#2392C2×C10111yescharacteristic
374#1955C2×C10111yescharacteristic, complemented
375#1954C2×C10111yescharacteristic, complemented
376#1954C2×C10111yescharacteristic, complemented
377#1939C2×C10111yescharacteristic, complemented
378#1924C2×C10111yescharacteristic, complemented
379#1923C2×C10111yescharacteristic, complemented
380#1870C2×C10111yescharacteristic, complemented
381#1869C2×C10111yescharacteristic, complemented
382#1851C2×C10111yescharacteristic, complemented
383#1850C2×C10111yescharacteristic, complemented
384#1798C2×C10111yescharacteristic, complemented
385#1771C2×C10111yescharacteristic, complemented
386C101#2214411yescharacteristic, direct product factor, Sylow
387C22×M16C22×C10111yescharacteristic
388C23×C8C22×C10111yescharacteristic
389C2×C4×D4C22×C10111yescharacteristic
390C2×C4×D4C22×C10111yescharacteristic
391C2×C4×D4C22×C10111yescharacteristic
392C2×#117C22×C10111yescharacteristic
393#435—24no—
394#433—24no—
395C2×C4⋊C8C22×C10111yescharacteristic
396C2×C4⋊C8C22×C10111yescharacteristic
397C2×C4⋊C8C22×C10111yescharacteristic
398C2×C4⋊C8C22×C10111yescharacteristic
399C2×C4⋊C8C22×C10111yescharacteristic
400C2×C4⋊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×C22⋊C8C22×C10111yescharacteristic
408C2×C22⋊C8C22×C10111yescharacteristic
409C2×C22⋊C8C22×C10111yescharacteristic
410C2×C22⋊C8C22×C10111yescharacteristic
411C2×#97C22×C10111yescharacteristic
412C2×#97C22×C10111yescharacteristic
413C2×C4×C8C22×C10111yescharacteristic
414C2×C4×C8C22×C10111yescharacteristic
415#398C4×C10111yescharacteristic
416#397C4×C10111yescharacteristic
417#396C4×C10111yescharacteristic
418#396C4×C10111yescharacteristic
419#394C4×C10111yescharacteristic
420#394C4×C10111yescharacteristic
421#394C4×C10111yescharacteristic
422#392C4×C10111yescharacteristic
423C4×C4⋊C4C22×C10111yescharacteristic
424C4×C22⋊C4C22×C10111yescharacteristic
425C4×C22⋊C4C22×C10111yescharacteristic
426#336C22×C10111yescharacteristic
427#336C22×C10111yescharacteristic
428#336C22×C10111yescharacteristic
429#336C22×C10111yescharacteristic
430#336C22×C10111yescharacteristic
431#336C22×C10111yescharacteristic
432C22×D4C2×C4×C10111yescharacteristic
433C22×D4C2×C4×C10111yescharacteristic
434C22×D4C2×C4×C10111yescharacteristic
435C23×C4C23×C10111yescharacteristic
436C23×C4C23×C10111yescharacteristic
437C23×C4C23×C10111yescharacteristic
438C2×M16—22no—
439C2×M16—41no—
440C2×M16—41no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8C23×C10111yescharacteristic
445C22×C8C23×C10111yescharacteristic
446C22×C8C23×C10111yescharacteristic
447C22×C8C23×C10111yescharacteristic
448C22×C8C23×C10111yescharacteristic
449C22×C8C23×C10111yescharacteristic
450C22×C8C23×C10111yescharacteristic
451C22×C8C23×C10111yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458#117—22no—
459#117—22no—
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×C4⋊C4C2×C4×C10111yescharacteristic
466C2×C4⋊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×C22⋊C4C2×C4×C10111yescharacteristic
476C2×C22⋊C4C2×C4×C10111yescharacteristic
477C2×C22⋊C4C2×C4×C10111yescharacteristic
478C2×C22⋊C4C2×C4×C10111yescharacteristic
479C2×C42C23×C10111yescharacteristic
480C2×C42C23×C10111yescharacteristic
481C2×C42C23×C10111yescharacteristic
482C2×C42C23×C10111yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—41no—
488C4⋊C8—41no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497C22⋊C8—41no—
498C22⋊C8—41no—
499#97—41no—
500#97D4×C10114yescomplemented
501C4×C8—22no—
502C4×C8—41no—
503#95C2×C4×C10111yescharacteristic
504#95C2×C4×C10111yescharacteristic
505#95C2×C4×C10111yescharacteristic
506#95C2×C4×C10111yescharacteristic
507#95C2×C4×C10111yescharacteristic
508#95C2×C4×C10111yescharacteristic
509C24C22×C4×C10111yescharacteristic
510C24C22×C4×C10111yescharacteristic
511C24C22×C4×C10111yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
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×C4C22×C4×C10111yescharacteristic
540C22×C4C22×C4×C10111yescharacteristic
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×C4C24×C10111yescharacteristic
551M16—44no—
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—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—44no—
575C2×C8C2×D4×C10112yes—
576C2×C8C2×D4×C10112yes—
577C4⋊C4—22no—
578C4⋊C4—22no—
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—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42C2×D4×C10112yes—
603C42#41×C10112yes—
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—
623C23—21no—
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—21no—
659C2×C4—41no—
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×C4C4×D4×C10112yes—
672C2×C4C4×D4×C10112yes—
673C2×C4#131×C10112yes—
674C2×C4C22×D4×C10111yescharacteristic
675C2×C4C2×#41×C10111yescharacteristic
676C2×C4H(5,𝔽2)×C10111yescharacteristic
677C2×C4H(5,𝔽2)×C10111yescharacteristic
678C2×C4H(5,𝔽2)×C10111yescharacteristic
679C2×C42−1+4×C10111yescharacteristic
680C8—22no—
681C8—22no—
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
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—
709C22C2×C4×D4×C10111yescharacteristic
710C22#518×C10111yescharacteristic
711C22#520×C10111yescharacteristic
712C22C2×#131×C10111yescharacteristic
713C22C2×#131×C10111yescharacteristic
714C22#568×C10111yescharacteristic
715C22#568×C10111yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4#535×C10111yescharacteristic
728C4#537×C10111yescharacteristic
729C4#540×C10111yescharacteristic
730C4#542×C10111yescharacteristic
731C2—42no—
732C2—81no—
733C2—81no—
734C2C101×#232411yescharacteristic
735C2C101×#293311yescharacteristic
736C2C101×#293511yescharacteristic
737C2C101×#297711yescharacteristic
738C2C101×#297811yescharacteristic
739C2C101×#299211yescharacteristic
740C2C101×#299311yescharacteristic
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
1. C2×#435×C101C2semidirect
2. C2×#433×C101C2semidirect
4. C101×#1955C2semidirect
5. C101×#1954C2semidirect
6. C101×#1954C2semidirect
7. C101×#1939C2semidirect
8. C101×#1924C2semidirect
9. C101×#1923C2semidirect
10. C101×#1870C2semidirect
11. C101×#1869C2semidirect
12. C101×#1851C2semidirect
13. C101×#1850C2semidirect
14. C101×#1798C2semidirect
15. C101×#1771C2semidirect
129. #97×C101D4semidirect
360. #22144C101direct (N × H)
371. C2×#435C2×C101semidirect
372. C2×#433C2×C101semidirect
374. #1955C2×C101semidirect
375. #1954C2×C101semidirect
376. #1954C2×C101semidirect
377. #1939C2×C101semidirect
378. #1924C2×C101semidirect
379. #1923C2×C101semidirect
380. #1870C2×C101semidirect
381. #1869C2×C101semidirect
382. #1851C2×C101semidirect
383. #1850C2×C101semidirect
384. #1798C2×C101semidirect
385. #1771C2×C101semidirect
386. C101#22144direct (N × H)
500. #97D4×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×#433×C1012
C101×#23922
C101×#19552
C101×#19542
C101×#19392
C101×#19242
C101×#19232
C101×#18702
C101×#18692
C101×#18512
C101×#18502
C101×#17982
C101×#17712
#22144101