Finite Group Databasebeta

← C101×#24734 #38806885

Subgroups — C101×#24734 #38806885

Order 25856.

988 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
1C2×#464×C101C211yesmaximal, characteristic, complemented
2C2×#464×C101C211yesmaximal, characteristic, complemented
3C2×#460×C101C211yesmaximal, characteristic
4C2×C4×SD16×C101C211yesmaximal, characteristic, complemented
5C101×#2544C211yesmaximal, characteristic
6C101×#2351C211yesmaximal, characteristic, complemented
7C101×#2066C211yesmaximal, characteristic, complemented
8C101×#2065C211yesmaximal, characteristic, complemented
9C101×#2042C211yesmaximal, characteristic, complemented
10C101×#2041C211yesmaximal, characteristic
11C101×#1958C211yesmaximal, characteristic, complemented
12C101×#1939C211yesmaximal, characteristic, complemented
13C101×#1880C211yesmaximal, characteristic, complemented
14C101×#1878C211yesmaximal, characteristic, complemented
15C101×#1804C211yesmaximal, characteristic, complemented
16C22×Q16×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C2×#127×C101C2211yescharacteristic
20C2×#124×C101C2211yescharacteristic
21C2×#124×C101C2211yescharacteristic
22C2×C4×Q8×C101C2211yescharacteristic
23C2×C4×Q8×C101C2211yescharacteristic
24C2×C4×Q8×C101C2211yescharacteristic
25C2×C4×D4×C101C2211yescharacteristic
26#464×C101—24no—
27#464×C101—24no—
28#460×C101—24no—
29C4×SD16×C101—24no—
30C2×#106×C101C2211yescharacteristic
31C2×C4⋊C8×C101C2211yescharacteristic
32C2×C4⋊C8×C101C2211yescharacteristic
33C2×C4⋊C8×C101C2211yescharacteristic
34C2×#103×C101C2211yescharacteristic
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#103×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44C2×C4×C8×C101C2211yescharacteristic
45#394×C101—21no—
46#394×C101—21no—
47#391×C101C2211yescharacteristic
48#390×C101C2211yescharacteristic
49#389×C101—21no—
50#389×C101—21no—
51#389×C101C2211yescharacteristic
52#389×C101C2211yescharacteristic
53#386×C101—21no—
54#386×C101—21no—
55#382×C101—21no—
56#382×C101C2211yescharacteristic
57C4×C4⋊C4×C101—21no—
58C4×C4⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C22×Q8×C101C2311yescharacteristic
64C22×Q8×C101C2311yescharacteristic
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101C2311yescharacteristic
68C22×D4×C101C2311yescharacteristic
69C23×C4×C101—21no—
70C2×Q16×C101—22no—
71C2×Q16×C101—22no—
72C2×Q16×C101—22no—
73C2×SD16×C101—22no—
74C2×SD16×C101—22no—
75C2×SD16×C101—22no—
76C2×SD16×C101—22no—
77C2×SD16×C101—22no—
78C2×SD16×C101D414yes—
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83#127×C101—22no—
84#127×C101—41no—
85#124×C101—22no—
86#124×C101—22no—
87#124×C101—22no—
88#124×C101—41no—
89C4×Q8×C101—22no—
90C4×Q8×C101—22no—
91C4×Q8×C101—22no—
92C4×Q8×C101—41no—
93C4×Q8×C101—41no—
94C4×Q8×C101D414yescomplemented
95C4×D4×C101—22no—
96C4×D4×C101—22no—
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101—21no—
100C2×C4⋊C4×C101—21no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101D411yescharacteristic
103C2×C4⋊C4×C101D411yescharacteristic
104C2×C4⋊C4×C101C2311yescharacteristic
105C2×C4⋊C4×C101C2311yescharacteristic
106C2×C4⋊C4×C101C2311yescharacteristic
107C2×C4⋊C4×C101C2311yescharacteristic
108C2×C22⋊C4×C101—21no—
109C2×C22⋊C4×C101—21no—
110C2×C22⋊C4×C101—21no—
111C2×C22⋊C4×C101—21no—
112C2×C22⋊C4×C101—21no—
113C2×C22⋊C4×C101—21no—
114C2×C22⋊C4×C101—21no—
115C2×C42×C101—21no—
116C2×C42×C101—21no—
117C2×C42×C101—21no—
118C2×C42×C101C2311yescharacteristic
119C2×C42×C101C2311yescharacteristic
120C2×C42×C101C2311yescharacteristic
121#106×C101—22no—
122C4⋊C8×C101—22no—
123C4⋊C8×C101—22no—
124C4⋊C8×C101—22no—
125#103×C101—22no—
126#103×C101—22no—
127#103×C101—22no—
128#103×C101—41no—
129#102×C101—22no—
130#102×C101—22no—
131#102×C101—22no—
132#102×C101—22no—
133#102×C101—22no—
134#102×C101—41no—
135C4×C8×C101—22no—
136#95×C101—21no—
137#95×C101—21no—
138#95×C101—21no—
139#95×C101—21no—
140#95×C101—21no—
141#95×C101—21no—
142#95×C101D411yescharacteristic
143#95×C101D411yescharacteristic
144C24×C101—21no—
145C24×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101—21no—
154C2×Q8×C101—21no—
155C2×Q8×C101C2×D412yes—
156C2×Q8×C101C2×D412yes—
157C2×Q8×C101#4112yes—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
163C2×D4×C101—21no—
164C2×D4×C101—21no—
165C2×D4×C101—21no—
166C2×D4×C101—21no—
167C2×D4×C101—21no—
168C2×D4×C101—21no—
169C2×D4×C101—42no—
170C2×D4×C101—42no—
171C2×D4×C101—42no—
172C2×D4×C101—42no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101C2×D412yes—
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—42no—
183C22×C4×C101—81no—
184C22×C4×C101—81no—
185C22×C4×C101C2×D411yescharacteristic
186C22×C4×C101C2×D411yescharacteristic
187C22×C4×C101C2×D411yescharacteristic
188C22×C4×C101C2×D411yescharacteristic
189C22×C4×C101C2×D411yescharacteristic
190C22×C4×C101C2×D411yescharacteristic
191C22×C4×C101C2411yescharacteristic
192Q16×C101—44no—
193SD16×C101—28no—
194SD16×C101—44no—
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×C101C2×D412yes—
207C4⋊C4×C101—24no—
208C4⋊C4×C101—22no—
209C4⋊C4×C101—21no—
210C4⋊C4×C101—21no—
211C4⋊C4×C101—21no—
212C4⋊C4×C101—21no—
213C4⋊C4×C101—21no—
214C4⋊C4×C101—21no—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—41no—
217C4⋊C4×C101—42no—
218C4⋊C4×C101—42no—
219C4⋊C4×C101—42no—
220C4⋊C4×C101—42no—
221C4⋊C4×C101C2×D412yes—
222C22⋊C4×C101—42no—
223C22⋊C4×C101—42no—
224C22⋊C4×C101—42no—
225C22⋊C4×C101—42no—
226C22⋊C4×C101—42no—
227C22⋊C4×C101—81no—
228C22⋊C4×C101—81no—
229C42×C101—24no—
230C42×C101—21no—
231C42×C101—21no—
232C42×C101—21no—
233C42×C101—21no—
234C42×C101—42no—
235C42×C101—42no—
236C42×C101C2×D412yes—
237C42×C101#4112yes—
238C23×C101—22no—
239C23×C101—41no—
240C23×C101—41no—
241C23×C101—41no—
242C23×C101—41no—
243C23×C101—41no—
244C23×C101—41no—
245C23×C101—41no—
246C23×C101—41no—
247C23×C101—41no—
248C23×C101—41no—
249C23×C101—41no—
250C23×C101—41no—
251C23×C101—41no—
252C23×C101C22×D411yescharacteristic
253Q8×C101—22no—
254Q8×C101—22no—
255Q8×C101—22no—
256Q8×C101—41no—
257Q8×C101—41no—
258Q8×C101—41no—
259Q8×C101—41no—
260Q8×C101#12114yes—
261D4×C101—22no—
262D4×C101—22no—
263D4×C101—41no—
264D4×C101—41no—
265D4×C101—41no—
266D4×C101—41no—
267D4×C101—41no—
268D4×C101—41no—
269D4×C101—84no—
270D4×C101—84no—
271C2×C4×C101—22no—
272C2×C4×C101—21no—
273C2×C4×C101—22no—
274C2×C4×C101—22no—
275C2×C4×C101—21no—
276C2×C4×C101—21no—
277C2×C4×C101—21no—
278C2×C4×C101—21no—
279C2×C4×C101—21no—
280C2×C4×C101—22no—
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—21no—
289C2×C4×C101—21no—
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×C101—41no—
301C2×C4×C101—41no—
302C2×C4×C101—41no—
303C2×C4×C101—41no—
304C2×C4×C101—84no—
305C2×C4×C101#12112yes—
306C2×C4×C101#12112yes—
307C2×C4×C101#13512yes—
308C2×C4×C101C22×D411yescharacteristic
309C2×C4×C101C22×D411yescharacteristic
310C2×C4×C101C2×#4111yescharacteristic
311C2×C4×C101C2×#4111yescharacteristic
312C2×C4×C101H(5,𝔽2)11yescharacteristic
313C2×C4×C1012−1+411yescharacteristic
314C8×C101—22no—
315C8×C101—41no—
316C8×C101—41no—
317C8×C101—41no—
318C22×C101—42no—
319C22×C101—42no—
320C22×C101—42no—
321C22×C101—81no—
322C22×C101—81no—
323C22×C101—81no—
324C22×C101—81no—
325C22×C101—81no—
326C22×C101—81no—
327C22×C101—81no—
328C22×C101—81no—
329C22×C101—81no—
330C22×C101—81no—
331C22×C101—81no—
332C22×C101C2×#12111yescharacteristic
333C22×C101D4211yescharacteristic
334C22×C101#54811yescharacteristic
335C22×C101C2×#13511yescharacteristic
336C22×C101#57511yescharacteristic
337C22×C101#57711yescharacteristic
338C22×C101#57711yescharacteristic
339C4×C101—24no—
340C4×C101—22no—
341C4×C101—22no—
342C4×C101—22no—
343C4×C101—41no—
344C4×C101—41no—
345C4×C101—41no—
346C4×C101—42no—
347C4×C101—81no—
348C4×C101—81no—
349C4×C101—81no—
350C4×C101—81no—
351C4×C101C2×#12111yescharacteristic
352C4×C101#53711yescharacteristic
353C4×C101#54711yescharacteristic
354C4×C101#55311yescharacteristic
355#24734C10111yesmaximal, characteristic, direct product factor, Sylow
356C2×C101—82no—
357C2×C101—161no—
358C2×C101#241611yescharacteristic
359C2×C101#303511yescharacteristic
360C2×C101#304311yescharacteristic
361C2×C101#327511yescharacteristic
362C2×C101#328211yescharacteristic
363C2×C101#336511yescharacteristic
364C2×C101#337111yescharacteristic
365C2×#464C2×C10111yescharacteristic, complemented
366C2×#464C2×C10111yescharacteristic, complemented
367C2×#460C2×C10111yescharacteristic
368C2×C4×SD16C2×C10111yescharacteristic, complemented
369#2544C2×C10111yescharacteristic
370#2351C2×C10111yescharacteristic, complemented
371#2066C2×C10111yescharacteristic, complemented
372#2065C2×C10111yescharacteristic, complemented
373#2042C2×C10111yescharacteristic, complemented
374#2041C2×C10111yescharacteristic
375#1958C2×C10111yescharacteristic, complemented
376#1939C2×C10111yescharacteristic, complemented
377#1880C2×C10111yescharacteristic, complemented
378#1878C2×C10111yescharacteristic, complemented
379#1804C2×C10111yescharacteristic, complemented
380C101#2473411yescharacteristic, direct product factor, Sylow
381C22×Q16C22×C10111yescharacteristic
382C22×SD16C22×C10111yescharacteristic
383C22×SD16C22×C10111yescharacteristic
384C2×#127C22×C10111yescharacteristic
385C2×#124C22×C10111yescharacteristic
386C2×#124C22×C10111yescharacteristic
387C2×C4×Q8C22×C10111yescharacteristic
388C2×C4×Q8C22×C10111yescharacteristic
389C2×C4×Q8C22×C10111yescharacteristic
390C2×C4×D4C22×C10111yescharacteristic
391#464—24no—
392#464—24no—
393#460—24no—
394C4×SD16—24no—
395C2×#106C22×C10111yescharacteristic
396C2×C4⋊C8C22×C10111yescharacteristic
397C2×C4⋊C8C22×C10111yescharacteristic
398C2×C4⋊C8C22×C10111yescharacteristic
399C2×#103C22×C10111yescharacteristic
400C2×#103C22×C10111yescharacteristic
401C2×#103C22×C10111yescharacteristic
402C2×#103C22×C10111yescharacteristic
403C2×#102C22×C10111yescharacteristic
404C2×#102C22×C10111yescharacteristic
405C2×#102C22×C10111yescharacteristic
406C2×#102C22×C10111yescharacteristic
407C2×#102C22×C10111yescharacteristic
408C2×#102C22×C10111yescharacteristic
409C2×C4×C8C22×C10111yescharacteristic
410#394—21no—
411#394—21no—
412#391C22×C10111yescharacteristic
413#390C22×C10111yescharacteristic
414#389—21no—
415#389—21no—
416#389C22×C10111yescharacteristic
417#389C22×C10111yescharacteristic
418#386—21no—
419#386—21no—
420#382—21no—
421#382C22×C10111yescharacteristic
422C4×C4⋊C4—21no—
423C4×C4⋊C4C22×C10111yescharacteristic
424#340C22×C10111yescharacteristic
425#340C22×C10111yescharacteristic
426#336C22×C10111yescharacteristic
427#336C22×C10111yescharacteristic
428C22×Q8C23×C10111yescharacteristic
429C22×Q8C23×C10111yescharacteristic
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C23×C10111yescharacteristic
433C22×D4C23×C10111yescharacteristic
434C23×C4—21no—
435C2×Q16—22no—
436C2×Q16—22no—
437C2×Q16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—22no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16D4×C10114yes—
444C22×C8C23×C10111yescharacteristic
445C22×C8C23×C10111yescharacteristic
446C22×C8C23×C10111yescharacteristic
447C22×C8C23×C10111yescharacteristic
448#127—22no—
449#127—41no—
450#124—22no—
451#124—22no—
452#124—22no—
453#124—41no—
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—22no—
457C4×Q8—41no—
458C4×Q8—41no—
459C4×Q8D4×C10114yescomplemented
460C4×D4—22no—
461C4×D4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4D4×C10111yescharacteristic
468C2×C4⋊C4D4×C10111yescharacteristic
469C2×C4⋊C4C23×C10111yescharacteristic
470C2×C4⋊C4C23×C10111yescharacteristic
471C2×C4⋊C4C23×C10111yescharacteristic
472C2×C4⋊C4C23×C10111yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42C23×C10111yescharacteristic
484C2×C42C23×C10111yescharacteristic
485C2×C42C23×C10111yescharacteristic
486#106—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—22no—
498#102—22no—
499#102—41no—
500C4×C8—22no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95D4×C10111yescharacteristic
508#95D4×C10111yescharacteristic
509C24—21no—
510C24—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8C2×D4×C10112yes—
521C2×Q8C2×D4×C10112yes—
522C2×Q8#41×C10112yes—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4C2×D4×C10112yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4C2×D4×C10111yescharacteristic
551C22×C4C2×D4×C10111yescharacteristic
552C22×C4C2×D4×C10111yescharacteristic
553C22×C4C2×D4×C10111yescharacteristic
554C22×C4C2×D4×C10111yescharacteristic
555C22×C4C2×D4×C10111yescharacteristic
556C22×C4C24×C10111yescharacteristic
557Q16—44no—
558SD16—28no—
559SD16—44no—
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×C8C2×D4×C10112yes—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—41no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4C2×D4×C10112yes—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C42—24no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C42—42no—
601C42C2×D4×C10112yes—
602C42#41×C10112yes—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C10111yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8#121×C10114yes—
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
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—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
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—84no—
670C2×C4#121×C10112yes—
671C2×C4#121×C10112yes—
672C2×C4#135×C10112yes—
673C2×C4C22×D4×C10111yescharacteristic
674C2×C4C22×D4×C10111yescharacteristic
675C2×C4C2×#41×C10111yescharacteristic
676C2×C4C2×#41×C10111yescharacteristic
677C2×C4H(5,𝔽2)×C10111yescharacteristic
678C2×C42−1+4×C10111yescharacteristic
679C8—22no—
680C8—41no—
681C8—41no—
682C8—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C2×#121×C10111yescharacteristic
698C22D42×C10111yescharacteristic
699C22#548×C10111yescharacteristic
700C22C2×#135×C10111yescharacteristic
701C22#575×C10111yescharacteristic
702C22#577×C10111yescharacteristic
703C22#577×C10111yescharacteristic
704C4—24no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4C2×#121×C10111yescharacteristic
717C4#537×C10111yescharacteristic
718C4#547×C10111yescharacteristic
719C4#553×C10111yescharacteristic
720C2—82no—
721C2—161no—
722C2C101×#241611yescharacteristic
723C2C101×#303511yescharacteristic
724C2C101×#304311yescharacteristic
725C2C101×#327511yescharacteristic
726C2C101×#328211yescharacteristic
727C2C101×#336511yescharacteristic
728C2C101×#337111yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#127×C101C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C4⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#464×C101C2semidirect
2. C2×#464×C101C2semidirect
4. C2×C4×SD16×C101C2semidirect
6. C101×#2351C2semidirect
7. C101×#2066C2semidirect
8. C101×#2065C2semidirect
9. C101×#2042C2semidirect
11. C101×#1958C2semidirect
12. C101×#1939C2semidirect
13. C101×#1880C2semidirect
14. C101×#1878C2semidirect
15. C101×#1804C2semidirect
94. C4×Q8×C101D4semidirect
355. #24734C101direct (N × H)
365. C2×#464C2×C101semidirect
366. C2×#464C2×C101semidirect
368. C2×C4×SD16C2×C101semidirect
370. #2351C2×C101semidirect
371. #2066C2×C101semidirect
372. #2065C2×C101semidirect
373. #2042C2×C101semidirect
375. #1958C2×C101semidirect
376. #1939C2×C101semidirect
377. #1880C2×C101semidirect
378. #1878C2×C101semidirect
379. #1804C2×C101semidirect
380. C101#24734direct (N × H)
459. C4×Q8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#464×C1012
C2×#460×C1012
C2×C4×SD16×C1012
C101×#25442
C101×#23512
C101×#20662
C101×#20652
C101×#20422
C101×#20412
C101×#19582
C101×#19392
C101×#18802
C101×#18782
C101×#18042
#24734101