Finite Group Databasebeta

← C101×#22558 #38804709

Subgroups — C101×#22558 #38804709

Order 25856.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C101C211yesmaximal, characteristic, complemented
2C22×C22⋊C8×C101C211yesmaximal, characteristic
3C101×#2280C211yesmaximal, characteristic
4C101×#1924C211yesmaximal, characteristic, complemented
5C101×#1924C211yesmaximal, characteristic, complemented
6C101×#1923C211yesmaximal, characteristic, complemented
7C101×#1923C211yesmaximal, characteristic, complemented
8C101×#1850C211yesmaximal, characteristic, complemented
9C101×#1850C211yesmaximal, characteristic, complemented
10C101×#1818C211yesmaximal, characteristic, complemented
11C101×#1798C211yesmaximal, characteristic, complemented
12C101×#1779C211yesmaximal, characteristic
13C101×#1752C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C101C211yesmaximal, characteristic, complemented
15C101×#1750C211yesmaximal, characteristic, complemented
16C24×C4×C101C2211yescharacteristic
17C23×C8×C101C2211yescharacteristic
18C23×C8×C101C2211yescharacteristic
19C2×#117×C101C2211yescharacteristic
20C2×#117×C101C2211yescharacteristic
21#433×C101—24no—
22C2×C4⋊C8×C101C2211yescharacteristic, complemented
23C2×C4⋊C8×C101C2211yescharacteristic, complemented
24C2×C4⋊C8×C101C2211yescharacteristic, complemented
25C2×C4⋊C8×C101C2211yescharacteristic, complemented
26C2×C22⋊C8×C101—24no—
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×C22⋊C8×C101C2211yescharacteristic
36C2×C22⋊C8×C101C2211yescharacteristic
37C2×#97×C101C2211yescharacteristic, complemented
38C2×#97×C101C2211yescharacteristic, complemented
39C2×C4×C8×C101C2211yescharacteristic, complemented
40C2×C4×C8×C101C2211yescharacteristic, complemented
41#381×C101C411yescharacteristic
42#381×C101C411yescharacteristic
43#380×C101C411yescharacteristic
44#380×C101C411yescharacteristic
45#380×C101C411yescharacteristic
46#380×C101C411yescharacteristic
47#379×C101C411yescharacteristic
48#379×C101C411yescharacteristic
49C4×C22⋊C4×C101C2211yescharacteristic
50C4×C22⋊C4×C101C2211yescharacteristic
51C4×C22⋊C4×C101C2211yescharacteristic
52C4×C22⋊C4×C101C2211yescharacteristic
53#336×C101C2211yescharacteristic, complemented
54#336×C101C2211yescharacteristic, complemented
55#336×C101C2211yescharacteristic, complemented
56#336×C101C2211yescharacteristic, complemented
57#336×C101C2211yescharacteristic, complemented
58#336×C101C2211yescharacteristic, complemented
59#336×C101C2211yescharacteristic, complemented
60#336×C101C2211yescharacteristic, complemented
61C25×C101C2×C411yescharacteristic
62C23×C4×C101—22no—
63C23×C4×C101—22no—
64C23×C4×C101—22no—
65C23×C4×C101—22no—
66C23×C4×C101—41no—
67C23×C4×C101—41no—
68C23×C4×C101C2×C411yescharacteristic
69C23×C4×C101C2×C411yescharacteristic
70C23×C4×C101C2×C411yescharacteristic
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2311yescharacteristic
73C23×C4×C101C2311yescharacteristic
74C22×C8×C101—22no—
75C22×C8×C101—22no—
76C22×C8×C101—22no—
77C22×C8×C101—22no—
78C22×C8×C101—41no—
79C22×C8×C101—41no—
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84C22×C8×C101C2311yescharacteristic
85C22×C8×C101C2311yescharacteristic
86C22×C8×C101C2311yescharacteristic
87C22×C8×C101C2311yescharacteristic
88#117×C101—22no—
89#117×C101—22no—
90#117×C101—41no—
91#117×C101—41no—
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—41no—
115C4⋊C8×C101—41no—
116C22⋊C8×C101—22no—
117C22⋊C8×C101—22no—
118C22⋊C8×C101—22no—
119C22⋊C8×C101—22no—
120C22⋊C8×C101—22no—
121C22⋊C8×C101—22no—
122C22⋊C8×C101—22no—
123C22⋊C8×C101—41no—
124C22⋊C8×C101—41no—
125C22⋊C8×C101D414yes—
126#97×C101—22no—
127#97×C101—41no—
128C4×C8×C101—22no—
129C4×C8×C101—41no—
130#95×C101C2×C411yescharacteristic
131#95×C101C2×C411yescharacteristic
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×C101—22no—
139C24×C101—22no—
140C24×C101—22no—
141C24×C101—22no—
142C24×C101—22no—
143C24×C101—41no—
144C24×C101—41no—
145C24×C101C22×C411yescharacteristic
146C24×C101C22×C411yescharacteristic
147C24×C101C22×C411yescharacteristic
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—22no—
157C22×C4×C101—22no—
158C22×C4×C101—22no—
159C22×C4×C101—22no—
160C22×C4×C101—22no—
161C22×C4×C101—22no—
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×C101—41no—
169C22×C4×C101—41no—
170C22×C4×C101—41no—
171C22×C4×C101—44no—
172C22×C4×C101—44no—
173C22×C4×C101—44no—
174C22×C4×C101—44no—
175C22×C4×C101C22×C411yescharacteristic
176C22×C4×C101C22×C411yescharacteristic
177C22×C4×C101C22×C411yescharacteristic
178C22×C4×C101C22×C411yescharacteristic
179C22×C4×C101C22×C411yescharacteristic
180C22×C4×C101C22×C411yescharacteristic
181C22×C4×C101C22×C411yescharacteristic
182C22×C4×C101C22×C411yescharacteristic
183C22×C4×C101C22×C411yescharacteristic
184C22×C4×C101C22×C411yescharacteristic
185C22×C4×C101C22×C411yescharacteristic
186C22×C4×C101C2×D412yes—
187C22×C4×C101#4112yes—
188C22×C4×C101#4112yes—
189C22×C4×C101#4112yes—
190C22×C4×C101C2411yescharacteristic
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—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—44no—
214C2×C8×C101—44no—
215C2×C8×C101C2×D412yes—
216C2×C8×C101C2×D412yes—
217C4⋊C4×C101—22no—
218C4⋊C4×C101—22no—
219C4⋊C4×C101—41no—
220C4⋊C4×C101—41no—
221C22⋊C4×C101—22no—
222C22⋊C4×C101—22no—
223C22⋊C4×C101—22no—
224C22⋊C4×C101—22no—
225C22⋊C4×C101—22no—
226C22⋊C4×C101—22no—
227C22⋊C4×C101—22no—
228C22⋊C4×C101—22no—
229C22⋊C4×C101—41no—
230C22⋊C4×C101—41no—
231C22⋊C4×C101—41no—
232C22⋊C4×C101—41no—
233C42×C101—21no—
234C42×C101—21no—
235C42×C101—21no—
236C42×C101—21no—
237C42×C101—21no—
238C42×C101—21no—
239C42×C101—21no—
240C42×C101—21no—
241C23×C101—21no—
242C23×C101—21no—
243C23×C101—21no—
244C23×C101—21no—
245C23×C101—28no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—21no—
255C23×C101—21no—
256C23×C101—21no—
257C23×C101—21no—
258C23×C101—44no—
259C23×C101—44no—
260C23×C101—44no—
261C23×C101—44no—
262C23×C101—44no—
263C23×C101—44no—
264C23×C101#11712yes—
265C23×C101C4×D412yes—
266C23×C101#13112yes—
267C23×C101#13112yes—
268C23×C101#13112yes—
269C23×C101C23×C411yescharacteristic
270C2×C4×C101—21no—
271C2×C4×C101—21no—
272C2×C4×C101—21no—
273C2×C4×C101—21no—
274C2×C4×C101—22no—
275C2×C4×C101—22no—
276C2×C4×C101—22no—
277C2×C4×C101—22no—
278C2×C4×C101—22no—
279C2×C4×C101—22no—
280C2×C4×C101—22no—
281C2×C4×C101—22no—
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—21no—
289C2×C4×C101—21no—
290C2×C4×C101—21no—
291C2×C4×C101—21no—
292C2×C4×C101—21no—
293C2×C4×C101—21no—
294C2×C4×C101—21no—
295C2×C4×C101—21no—
296C2×C4×C101—21no—
297C2×C4×C101—21no—
298C2×C4×C101—21no—
299C2×C4×C101—21no—
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—44no—
310C2×C4×C101—44no—
311C2×C4×C101—44no—
312C2×C4×C101—41no—
313C2×C4×C101—41no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101#11712yes—
317C2×C4×C101C4×D412yes—
318C2×C4×C101C22×D411yescharacteristic
319C2×C4×C101C2×#4111yescharacteristic
320C2×C4×C101C2×#4111yescharacteristic
321C2×C4×C101C2×#4111yescharacteristic
322C2×C4×C101H(5,𝔽2)11yescharacteristic
323C2×C4×C101H(5,𝔽2)11yescharacteristic
324C8×C101—22no—
325C8×C101—22no—
326C8×C101—41no—
327C8×C101—41no—
328C8×C101—41no—
329C8×C101—41no—
330C8×C101—41no—
331C8×C101—41no—
332C22×C101—22no—
333C22×C101—22no—
334C22×C101—22no—
335C22×C101—22no—
336C22×C101—22no—
337C22×C101—22no—
338C22×C101—22no—
339C22×C101—22no—
340C22×C101—22no—
341C22×C101—22no—
342C22×C101—22no—
343C22×C101—22no—
344C22×C101—416no—
345C22×C101—41no—
346C22×C101—41no—
347C22×C101—41no—
348C22×C101—41no—
349C22×C101—41no—
350C22×C101—41no—
351C22×C101—41no—
352C22×C101—41no—
353C22×C101#43314yescomplemented
354C22×C101C2×#11711yescharacteristic
355C22×C101C2×C4×D411yescharacteristic
356C22×C101#51811yescharacteristic
357C22×C101C2×#13111yescharacteristic
358C22×C101C2×#13111yescharacteristic
359C22×C101C2×#13111yescharacteristic
360C22×C101#56811yescharacteristic
361C4×C101—22no—
362C4×C101—22no—
363C4×C101—41no—
364C4×C101—41no—
365C4×C101—41no—
366C4×C101—41no—
367C4×C101—41no—
368C4×C101—41no—
369C4×C101—41no—
370C4×C101—41no—
371C4×C101—41no—
372C4×C101#54611yescharacteristic
373C4×C101#54611yescharacteristic
374C4×C101#55111yescharacteristic
375C4×C101#55111yescharacteristic
376#22558C10111yesmaximal, characteristic, direct product factor, Sylow
377C2×C101—24no—
378C2×C101—42no—
379C2×C101—42no—
380C2×C101#234211yescharacteristic
381C2×C101C2×#43311yescharacteristic
382C2×C101#292411yescharacteristic
383C2×C101#292911yescharacteristic
384C2×C101#293311yescharacteristic
385C2×C101#297611yescharacteristic
386C2×C101#297711yescharacteristic
387C2×#433C2×C10111yescharacteristic, complemented
388C22×C22⋊C8C2×C10111yescharacteristic
389#2280C2×C10111yescharacteristic
390#1924C2×C10111yescharacteristic, complemented
391#1924C2×C10111yescharacteristic, complemented
392#1923C2×C10111yescharacteristic, complemented
393#1923C2×C10111yescharacteristic, complemented
394#1850C2×C10111yescharacteristic, complemented
395#1850C2×C10111yescharacteristic, complemented
396#1818C2×C10111yescharacteristic, complemented
397#1798C2×C10111yescharacteristic, complemented
398#1779C2×C10111yescharacteristic
399#1752C2×C10111yescharacteristic, complemented
400C8×C22⋊C4C2×C10111yescharacteristic, complemented
401#1750C2×C10111yescharacteristic, complemented
402C101#2255811yescharacteristic, direct product factor, Sylow
403C24×C4C22×C10111yescharacteristic
404C23×C8C22×C10111yescharacteristic
405C23×C8C22×C10111yescharacteristic
406C2×#117C22×C10111yescharacteristic
407C2×#117C22×C10111yescharacteristic
408#433—24no—
409C2×C4⋊C8C22×C10111yescharacteristic, complemented
410C2×C4⋊C8C22×C10111yescharacteristic, complemented
411C2×C4⋊C8C22×C10111yescharacteristic, complemented
412C2×C4⋊C8C22×C10111yescharacteristic, complemented
413C2×C22⋊C8—24no—
414C2×C22⋊C8C22×C10111yescharacteristic
415C2×C22⋊C8C22×C10111yescharacteristic
416C2×C22⋊C8C22×C10111yescharacteristic
417C2×C22⋊C8C22×C10111yescharacteristic
418C2×C22⋊C8C22×C10111yescharacteristic
419C2×C22⋊C8C22×C10111yescharacteristic
420C2×C22⋊C8C22×C10111yescharacteristic
421C2×C22⋊C8C22×C10111yescharacteristic
422C2×C22⋊C8C22×C10111yescharacteristic
423C2×C22⋊C8C22×C10111yescharacteristic
424C2×#97C22×C10111yescharacteristic, complemented
425C2×#97C22×C10111yescharacteristic, complemented
426C2×C4×C8C22×C10111yescharacteristic, complemented
427C2×C4×C8C22×C10111yescharacteristic, complemented
428#381C4×C10111yescharacteristic
429#381C4×C10111yescharacteristic
430#380C4×C10111yescharacteristic
431#380C4×C10111yescharacteristic
432#380C4×C10111yescharacteristic
433#380C4×C10111yescharacteristic
434#379C4×C10111yescharacteristic
435#379C4×C10111yescharacteristic
436C4×C22⋊C4C22×C10111yescharacteristic
437C4×C22⋊C4C22×C10111yescharacteristic
438C4×C22⋊C4C22×C10111yescharacteristic
439C4×C22⋊C4C22×C10111yescharacteristic
440#336C22×C10111yescharacteristic, complemented
441#336C22×C10111yescharacteristic, complemented
442#336C22×C10111yescharacteristic, complemented
443#336C22×C10111yescharacteristic, complemented
444#336C22×C10111yescharacteristic, complemented
445#336C22×C10111yescharacteristic, complemented
446#336C22×C10111yescharacteristic, complemented
447#336C22×C10111yescharacteristic, complemented
448C25C2×C4×C10111yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C2×C4×C10111yescharacteristic
456C23×C4C2×C4×C10111yescharacteristic
457C23×C4C2×C4×C10111yescharacteristic
458C23×C4C23×C10111yescharacteristic
459C23×C4C23×C10111yescharacteristic
460C23×C4C23×C10111yescharacteristic
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—22no—
464C22×C8—22no—
465C22×C8—41no—
466C22×C8—41no—
467C22×C8C23×C10111yescharacteristic
468C22×C8C23×C10111yescharacteristic
469C22×C8C23×C10111yescharacteristic
470C22×C8C23×C10111yescharacteristic
471C22×C8C23×C10111yescharacteristic
472C22×C8C23×C10111yescharacteristic
473C22×C8C23×C10111yescharacteristic
474C22×C8C23×C10111yescharacteristic
475#117—22no—
476#117—22no—
477#117—41no—
478#117—41no—
479C2×C4⋊C4C2×C4×C10111yescharacteristic
480C2×C4⋊C4C2×C4×C10111yescharacteristic
481C2×C4⋊C4C2×C4×C10111yescharacteristic
482C2×C4⋊C4C2×C4×C10111yescharacteristic
483C2×C22⋊C4C2×C4×C10111yescharacteristic
484C2×C22⋊C4C2×C4×C10111yescharacteristic
485C2×C22⋊C4C2×C4×C10111yescharacteristic
486C2×C22⋊C4C2×C4×C10111yescharacteristic
487C2×C22⋊C4C2×C4×C10111yescharacteristic
488C2×C22⋊C4C2×C4×C10111yescharacteristic
489C2×C22⋊C4C2×C4×C10111yescharacteristic
490C2×C22⋊C4C2×C4×C10111yescharacteristic
491C2×C22⋊C4C2×C4×C10111yescharacteristic
492C2×C22⋊C4C2×C4×C10111yescharacteristic
493C2×C22⋊C4C2×C4×C10111yescharacteristic
494C2×C22⋊C4C2×C4×C10111yescharacteristic
495C2×C42C23×C10111yescharacteristic
496C2×C42C23×C10111yescharacteristic
497C2×C42C23×C10111yescharacteristic
498C2×C42C23×C10111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—41no—
502C4⋊C8—41no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512C22⋊C8D4×C10114yes—
513#97—22no—
514#97—41no—
515C4×C8—22no—
516C4×C8—41no—
517#95C2×C4×C10111yescharacteristic
518#95C2×C4×C10111yescharacteristic
519#95C2×C4×C10111yescharacteristic
520#95C2×C4×C10111yescharacteristic
521#95C2×C4×C10111yescharacteristic
522#95C2×C4×C10111yescharacteristic
523#95C2×C4×C10111yescharacteristic
524#95C2×C4×C10111yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24C22×C4×C10111yescharacteristic
533C24C22×C4×C10111yescharacteristic
534C24C22×C4×C10111yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4C22×C4×C10111yescharacteristic
563C22×C4C22×C4×C10111yescharacteristic
564C22×C4C22×C4×C10111yescharacteristic
565C22×C4C22×C4×C10111yescharacteristic
566C22×C4C22×C4×C10111yescharacteristic
567C22×C4C22×C4×C10111yescharacteristic
568C22×C4C22×C4×C10111yescharacteristic
569C22×C4C22×C4×C10111yescharacteristic
570C22×C4C22×C4×C10111yescharacteristic
571C22×C4C22×C4×C10111yescharacteristic
572C22×C4C22×C4×C10111yescharacteristic
573C22×C4C2×D4×C10112yes—
574C22×C4#41×C10112yes—
575C22×C4#41×C10112yes—
576C22×C4#41×C10112yes—
577C22×C4C24×C10111yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—44no—
601C2×C8—44no—
602C2×C8C2×D4×C10112yes—
603C2×C8C2×D4×C10112yes—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—28no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23#117×C10112yes—
652C23C4×D4×C10112yes—
653C23#131×C10112yes—
654C23#131×C10112yes—
655C23#131×C10112yes—
656C23C23×C4×C10111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4#117×C10112yes—
704C2×C4C4×D4×C10112yes—
705C2×C4C22×D4×C10111yescharacteristic
706C2×C4C2×#41×C10111yescharacteristic
707C2×C4C2×#41×C10111yescharacteristic
708C2×C4C2×#41×C10111yescharacteristic
709C2×C4H(5,𝔽2)×C10111yescharacteristic
710C2×C4H(5,𝔽2)×C10111yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—416no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22#433×C10114yescomplemented
741C22C2×#117×C10111yescharacteristic
742C22C2×C4×D4×C10111yescharacteristic
743C22#518×C10111yescharacteristic
744C22C2×#131×C10111yescharacteristic
745C22C2×#131×C10111yescharacteristic
746C22C2×#131×C10111yescharacteristic
747C22#568×C10111yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4#546×C10111yescharacteristic
760C4#546×C10111yescharacteristic
761C4#551×C10111yescharacteristic
762C4#551×C10111yescharacteristic
763C2—24no—
764C2—42no—
765C2—42no—
766C2C101×#234211yescharacteristic
767C2C2×#433×C10111yescharacteristic
768C2C101×#292411yescharacteristic
769C2C101×#292911yescharacteristic
770C2C101×#293311yescharacteristic
771C2C101×#297611yescharacteristic
772C2C101×#297711yescharacteristic
subgroupG/H
centerC22×C4×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC22×C4C24×C101
socleC23×C101C23×C4
prime radicalC25×C101C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#433×C101C2semidirect
4. C101×#1924C2semidirect
5. C101×#1924C2semidirect
6. C101×#1923C2semidirect
7. C101×#1923C2semidirect
8. C101×#1850C2semidirect
9. C101×#1850C2semidirect
10. C101×#1818C2semidirect
11. C101×#1798C2semidirect
13. C101×#1752C2semidirect
14. C8×C22⋊C4×C101C2semidirect
15. C101×#1750C2semidirect
22. C2×C4⋊C8×C101C22semidirect
23. C2×C4⋊C8×C101C22semidirect
24. C2×C4⋊C8×C101C22semidirect
25. C2×C4⋊C8×C101C22semidirect
37. C2×#97×C101C22semidirect
38. C2×#97×C101C22semidirect
39. C2×C4×C8×C101C22semidirect
40. C2×C4×C8×C101C22semidirect
53. #336×C101C22semidirect
54. #336×C101C22semidirect
55. #336×C101C22semidirect
56. #336×C101C22semidirect
57. #336×C101C22semidirect
58. #336×C101C22semidirect
59. #336×C101C22semidirect
60. #336×C101C22semidirect
353. C22×C101#433semidirect
376. #22558C101direct (N × H)
387. C2×#433C2×C101semidirect
390. #1924C2×C101semidirect
391. #1924C2×C101semidirect
392. #1923C2×C101semidirect
393. #1923C2×C101semidirect
394. #1850C2×C101semidirect
395. #1850C2×C101semidirect
396. #1818C2×C101semidirect
397. #1798C2×C101semidirect
399. #1752C2×C101semidirect
400. C8×C22⋊C4C2×C101semidirect
401. #1750C2×C101semidirect
402. C101#22558direct (N × H)
409. C2×C4⋊C8C22×C101semidirect
410. C2×C4⋊C8C22×C101semidirect
411. C2×C4⋊C8C22×C101semidirect
412. C2×C4⋊C8C22×C101semidirect
424. C2×#97C22×C101semidirect
425. C2×#97C22×C101semidirect
426. C2×C4×C8C22×C101semidirect
427. C2×C4×C8C22×C101semidirect
440. #336C22×C101semidirect
441. #336C22×C101semidirect
442. #336C22×C101semidirect
443. #336C22×C101semidirect
444. #336C22×C101semidirect
445. #336C22×C101semidirect
446. #336C22×C101semidirect
447. #336C22×C101semidirect
740. C22#433×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#433×C1012
C22×C22⋊C8×C1012
C101×#22802
C101×#19242
C101×#19232
C101×#18502
C101×#18182
C101×#17982
C101×#17792
C101×#17522
C8×C22⋊C4×C1012
C101×#17502
#22558101