Finite Group Databasebeta

← C101×#24762 #38806913

Subgroups — C101×#24762 #38806913

Order 25856.

1060 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C101C211yesmaximal, characteristic, complemented
2C2×#466×C101C211yesmaximal, characteristic, complemented
3C2×#459×C101C211yesmaximal, characteristic, complemented
4C2×#424×C101C211yesmaximal, characteristic, complemented
5C101×#2619C211yesmaximal, characteristic, complemented
6C101×#2324C211yesmaximal, characteristic, complemented
7C101×#2067C211yesmaximal, characteristic, complemented
8C101×#2065C211yesmaximal, characteristic, complemented
9C101×#2054C211yesmaximal, characteristic, complemented
10C101×#2054C211yesmaximal, characteristic, complemented
11C101×#1982C211yesmaximal, characteristic, complemented
12C101×#1949C211yesmaximal, characteristic, complemented
13C101×#1895C211yesmaximal, characteristic, complemented
14C101×#1893C211yesmaximal, characteristic, complemented
15C101×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C22×M16×C101C2211yescharacteristic
19C23×C8×C101C2211yescharacteristic
20C2×#127×C101C2211yescharacteristic
21C2×#121×C101C2211yescharacteristic
22C2×#121×C101C2211yescharacteristic
23C2×#121×C101C2211yescharacteristic
24C2×C4×D4×C101C2211yescharacteristic
25C2×#117×C101C2211yescharacteristic
26#469×C101—24no—
27#466×C101—24no—
28#459×C101—24no—
29C2×#107×C101C2211yescharacteristic
30C2×#106×C101C2211yescharacteristic
31#424×C101—24no—
32C2×C4⋊C8×C101C2211yescharacteristic
33C2×C4⋊C8×C101C2211yescharacteristic
34C2×C4⋊C8×C101C2211yescharacteristic
35C2×C4⋊C8×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×#102×C101C2211yescharacteristic
44#394×C101—21no—
45#394×C101—21no—
46#392×C101—21no—
47#392×C101—21no—
48#390×C101—21no—
49#390×C101C2211yescharacteristic
50#390×C101C2211yescharacteristic
51#390×C101C2211yescharacteristic
52#389×C101C2211yescharacteristic
53#388×C101—21no—
54#386×C101—21no—
55#385×C101—21no—
56#382×C101C2211yescharacteristic
57#380×C101C2211yescharacteristic
58C4×C4⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#340×C101C2211yescharacteristic
62#340×C101C2211yescharacteristic
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101C2311yescharacteristic
69C22×D4×C101C2311yescharacteristic
70C22×D4×C101C2311yescharacteristic
71C23×C4×C101—21no—
72C23×C4×C101C2311yescharacteristic
73C2×D8×C101—22no—
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C2×D8×C101—41no—
78C2×D8×C101—41no—
79C2×M16×C101—22no—
80C2×M16×C101—22no—
81C2×M16×C101—41no—
82C22×C8×C101—22no—
83C22×C8×C101—22no—
84C22×C8×C101—41no—
85C22×C8×C101C2311yescharacteristic
86C22×C8×C101C2311yescharacteristic
87C22×C8×C101C2311yescharacteristic
88C22×C8×C101C2311yescharacteristic
89#127×C101—22no—
90#127×C101—22no—
91#121×C101—22no—
92#121×C101—22no—
93#121×C101—22no—
94#121×C101—22no—
95#121×C101—22no—
96#121×C101D414yescomplemented
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99#117×C101—22no—
100#117×C101—22no—
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×C4⋊C4×C101C2311yescharacteristic
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×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101D411yescharacteristic
121C2×C22⋊C4×C101D411yescharacteristic
122C2×C42×C101—21no—
123C2×C42×C101C2311yescharacteristic
124C2×C42×C101C2311yescharacteristic
125#107×C101—22no—
126#106×C101—22no—
127C4⋊C8×C101—22no—
128C4⋊C8×C101—22no—
129C4⋊C8×C101—22no—
130C4⋊C8×C101D414yescomplemented
131#102×C101—22no—
132#102×C101—22no—
133#102×C101—22no—
134#102×C101—22no—
135#102×C101—22no—
136#102×C101—22no—
137#102×C101—41no—
138#102×C101—41no—
139#95×C101—21no—
140#95×C101—21no—
141#95×C101—21no—
142#95×C101—21no—
143#95×C101—21no—
144C24×C101—21no—
145C24×C101—21no—
146C24×C101—21no—
147C24×C101C2×D411yescharacteristic
148C2×D4×C101—24no—
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
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—42no—
167C2×D4×C101—42no—
168C2×D4×C101—42no—
169C2×D4×C101—42no—
170C2×D4×C101—81no—
171C2×D4×C101—81no—
172C2×D4×C101—81no—
173C2×D4×C101—81no—
174C2×D4×C101—81no—
175C2×D4×C101—81no—
176C2×D4×C101—81no—
177C2×D4×C101—81no—
178C2×D4×C101—81no—
179C2×D4×C101—81no—
180C2×D4×C101C2×D412yes—
181C22×C4×C101—21no—
182C22×C4×C101—21no—
183C22×C4×C101—21no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—21no—
187C22×C4×C101—21no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—42no—
191C22×C4×C101—81no—
192C22×C4×C101—81no—
193C22×C4×C101C2×D411yescharacteristic
194C22×C4×C101C2×D411yescharacteristic
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101C2×D412yes—
199C22×C4×C101#4112yes—
200C22×C4×C101C2411yescharacteristic
201D8×C101—44no—
202D8×C101—44no—
203M16×C101—44no—
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—21no—
214C2×C8×C101—44no—
215C2×C8×C101C2×D412yes—
216C2×C8×C101C2×D412yes—
217C4⋊C4×C101—22no—
218C4⋊C4×C101—22no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—21no—
225C4⋊C4×C101—21no—
226C4⋊C4×C101—21no—
227C4⋊C4×C101—21no—
228C4⋊C4×C101—81no—
229C4⋊C4×C101C2×D412yes—
230C22⋊C4×C101—24no—
231C22⋊C4×C101—22no—
232C22⋊C4×C101—22no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—42no—
235C22⋊C4×C101—42no—
236C22⋊C4×C101—81no—
237C22⋊C4×C101—81no—
238C22⋊C4×C101—81no—
239C22⋊C4×C101—81no—
240C22⋊C4×C101—81no—
241C22⋊C4×C101—81no—
242C22⋊C4×C101—81no—
243C42×C101—21no—
244C42×C101—21no—
245C42×C101—81no—
246C42×C101C2×D412yes—
247C42×C101#4112yes—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—21no—
253C23×C101—21no—
254C23×C101—22no—
255C23×C101—41no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—41no—
260C23×C101—41no—
261C23×C101—41no—
262C23×C101—41no—
263C23×C101—41no—
264C23×C101—41no—
265C23×C101—41no—
266C23×C101—41no—
267C23×C101—41no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101#12112yes—
276C23×C101C22×D411yescharacteristic
277D4×C101—22no—
278D4×C101—22no—
279D4×C101—41no—
280D4×C101—41no—
281D4×C101—41no—
282D4×C101—41no—
283D4×C101—41no—
284D4×C101—41no—
285D4×C101—41no—
286D4×C101—41no—
287D4×C101—41no—
288D4×C101—41no—
289D4×C101—84no—
290D4×C101—84no—
291D4×C101—84no—
292D4×C101—84no—
293D4×C101—84no—
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—22no—
301C2×C4×C101—22no—
302C2×C4×C101—22no—
303C2×C4×C101—22no—
304C2×C4×C101—21no—
305C2×C4×C101—21no—
306C2×C4×C101—22no—
307C2×C4×C101—21no—
308C2×C4×C101—21no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—41no—
312C2×C4×C101—41no—
313C2×C4×C101—41no—
314C2×C4×C101—41no—
315C2×C4×C101—41no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—41no—
319C2×C4×C101—41no—
320C2×C4×C101—41no—
321C2×C4×C101—41no—
322C2×C4×C101—41no—
323C2×C4×C101—41no—
324C2×C4×C101—41no—
325C2×C4×C101—84no—
326C2×C4×C101#12112yes—
327C2×C4×C101#12112yes—
328C2×C4×C101#12112yes—
329C2×C4×C101C22×D411yescharacteristic
330C2×C4×C101C22×D411yescharacteristic
331C2×C4×C101C2×#4111yescharacteristic
332C2×C4×C101C2×#4111yescharacteristic
333C2×C4×C101H(5,𝔽2)11yescharacteristic
334C2×C4×C1012−1+411yescharacteristic
335C8×C101—22no—
336C8×C101—22no—
337C8×C101—41no—
338C8×C101—41no—
339C22×C101—22no—
340C22×C101—22no—
341C22×C101—22no—
342C22×C101—41no—
343C22×C101—41no—
344C22×C101—41no—
345C22×C101—41no—
346C22×C101—42no—
347C22×C101—42no—
348C22×C101—42no—
349C22×C101—81no—
350C22×C101—81no—
351C22×C101—81no—
352C22×C101—81no—
353C22×C101—81no—
354C22×C101—81no—
355C22×C101—81no—
356C22×C101—81no—
357C22×C101—81no—
358C22×C101—81no—
359C22×C101—81no—
360C22×C101—81no—
361C22×C101—81no—
362C22×C101—81no—
363C22×C101—81no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101—81no—
367C22×C101C2×#12111yescharacteristic
368C22×C101C2×#12111yescharacteristic
369C22×C101#53711yescharacteristic
370C22×C101#57611yescharacteristic
371C22×C101#57611yescharacteristic
372C22×C101#57611yescharacteristic
373C22×C101#57711yescharacteristic
374C4×C101—22no—
375C4×C101—22no—
376C4×C101—22no—
377C4×C101—42no—
378C4×C101—41no—
379C4×C101—41no—
380C4×C101—81no—
381C4×C101—81no—
382C4×C101—81no—
383C4×C101—81no—
384C4×C101D4211yescharacteristic
385C4×C101#54711yescharacteristic
386C4×C101#54811yescharacteristic
387C4×C101#55311yescharacteristic
388#24762C10111yesmaximal, characteristic, direct product factor, Sylow
389C2×C101—42no—
390C2×C101—82no—
391C2×C101—161no—
392C2×C101—161no—
393C2×C101#241611yescharacteristic
394C2×C101#304111yescharacteristic
395C2×C101#304511yescharacteristic
396C2×C101#305811yescharacteristic
397C2×C101#306211yescharacteristic
398C2×C101#325711yescharacteristic
399C2×C101#325911yescharacteristic
400C2×#469C2×C10111yescharacteristic, complemented
401C2×#466C2×C10111yescharacteristic, complemented
402C2×#459C2×C10111yescharacteristic, complemented
403C2×#424C2×C10111yescharacteristic, complemented
404#2619C2×C10111yescharacteristic, complemented
405#2324C2×C10111yescharacteristic, complemented
406#2067C2×C10111yescharacteristic, complemented
407#2065C2×C10111yescharacteristic, complemented
408#2054C2×C10111yescharacteristic, complemented
409#2054C2×C10111yescharacteristic, complemented
410#1982C2×C10111yescharacteristic, complemented
411#1949C2×C10111yescharacteristic, complemented
412#1895C2×C10111yescharacteristic, complemented
413#1893C2×C10111yescharacteristic, complemented
414#1804C2×C10111yescharacteristic, complemented
415C101#2476211yescharacteristic, direct product factor, Sylow
416C22×D8C22×C10111yescharacteristic
417C22×D8C22×C10111yescharacteristic
418C22×M16C22×C10111yescharacteristic
419C23×C8C22×C10111yescharacteristic
420C2×#127C22×C10111yescharacteristic
421C2×#121C22×C10111yescharacteristic
422C2×#121C22×C10111yescharacteristic
423C2×#121C22×C10111yescharacteristic
424C2×C4×D4C22×C10111yescharacteristic
425C2×#117C22×C10111yescharacteristic
426#469—24no—
427#466—24no—
428#459—24no—
429C2×#107C22×C10111yescharacteristic
430C2×#106C22×C10111yescharacteristic
431#424—24no—
432C2×C4⋊C8C22×C10111yescharacteristic
433C2×C4⋊C8C22×C10111yescharacteristic
434C2×C4⋊C8C22×C10111yescharacteristic
435C2×C4⋊C8C22×C10111yescharacteristic
436C2×#102C22×C10111yescharacteristic
437C2×#102C22×C10111yescharacteristic
438C2×#102C22×C10111yescharacteristic
439C2×#102C22×C10111yescharacteristic
440C2×#102C22×C10111yescharacteristic
441C2×#102C22×C10111yescharacteristic
442C2×#102C22×C10111yescharacteristic
443C2×#102C22×C10111yescharacteristic
444#394—21no—
445#394—21no—
446#392—21no—
447#392—21no—
448#390—21no—
449#390C22×C10111yescharacteristic
450#390C22×C10111yescharacteristic
451#390C22×C10111yescharacteristic
452#389C22×C10111yescharacteristic
453#388—21no—
454#386—21no—
455#385—21no—
456#382C22×C10111yescharacteristic
457#380C22×C10111yescharacteristic
458C4×C4⋊C4C22×C10111yescharacteristic
459#340C22×C10111yescharacteristic
460#340C22×C10111yescharacteristic
461#340C22×C10111yescharacteristic
462#340C22×C10111yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4C23×C10111yescharacteristic
469C22×D4C23×C10111yescharacteristic
470C22×D4C23×C10111yescharacteristic
471C23×C4—21no—
472C23×C4C23×C10111yescharacteristic
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C2×D8—41no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C10111yescharacteristic
486C22×C8C23×C10111yescharacteristic
487C22×C8C23×C10111yescharacteristic
488C22×C8C23×C10111yescharacteristic
489#127—22no—
490#127—22no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—22no—
496#121D4×C10114yescomplemented
497C4×D4—22no—
498C4×D4—22no—
499#117—22no—
500#117—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4D4×C10111yescharacteristic
503C2×C4⋊C4D4×C10111yescharacteristic
504C2×C4⋊C4C23×C10111yescharacteristic
505C2×C4⋊C4C23×C10111yescharacteristic
506C2×C4⋊C4C23×C10111yescharacteristic
507C2×C4⋊C4C23×C10111yescharacteristic
508C2×C4⋊C4C23×C10111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C10111yescharacteristic
521C2×C22⋊C4D4×C10111yescharacteristic
522C2×C42—21no—
523C2×C42C23×C10111yescharacteristic
524C2×C42C23×C10111yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8D4×C10114yescomplemented
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—41no—
538#102—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24C2×D4×C10111yescharacteristic
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4C2×D4×C10112yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C10111yescharacteristic
594C22×C4C2×D4×C10111yescharacteristic
595C22×C4C2×D4×C10111yescharacteristic
596C22×C4C2×D4×C10111yescharacteristic
597C22×C4C2×D4×C10111yescharacteristic
598C22×C4C2×D4×C10112yes—
599C22×C4#41×C10112yes—
600C22×C4C24×C10111yescharacteristic
601D8—44no—
602D8—44no—
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—44no—
615C2×C8C2×D4×C10112yes—
616C2×C8C2×D4×C10112yes—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—81no—
629C4⋊C4C2×D4×C10112yes—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C42—21no—
644C42—21no—
645C42—81no—
646C42C2×D4×C10112yes—
647C42#41×C10112yes—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23#121×C10112yes—
676C23C22×D4×C10111yescharacteristic
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—84no—
690D4—84no—
691D4—84no—
692D4—84no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4#121×C10112yes—
727C2×C4#121×C10112yes—
728C2×C4#121×C10112yes—
729C2×C4C22×D4×C10111yescharacteristic
730C2×C4C22×D4×C10111yescharacteristic
731C2×C4C2×#41×C10111yescharacteristic
732C2×C4C2×#41×C10111yescharacteristic
733C2×C4H(5,𝔽2)×C10111yescharacteristic
734C2×C42−1+4×C10111yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C10111yescharacteristic
768C22C2×#121×C10111yescharacteristic
769C22#537×C10111yescharacteristic
770C22#576×C10111yescharacteristic
771C22#576×C10111yescharacteristic
772C22#576×C10111yescharacteristic
773C22#577×C10111yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4D42×C10111yescharacteristic
785C4#547×C10111yescharacteristic
786C4#548×C10111yescharacteristic
787C4#553×C10111yescharacteristic
788C2—42no—
789C2—82no—
790C2—161no—
791C2—161no—
792C2C101×#241611yescharacteristic
793C2C101×#304111yescharacteristic
794C2C101×#304511yescharacteristic
795C2C101×#305811yescharacteristic
796C2C101×#306211yescharacteristic
797C2C101×#325711yescharacteristic
798C2C101×#325911yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#469×C101C2semidirect
2. C2×#466×C101C2semidirect
3. C2×#459×C101C2semidirect
4. C2×#424×C101C2semidirect
5. C101×#2619C2semidirect
6. C101×#2324C2semidirect
7. C101×#2067C2semidirect
8. C101×#2065C2semidirect
9. C101×#2054C2semidirect
10. C101×#2054C2semidirect
11. C101×#1982C2semidirect
12. C101×#1949C2semidirect
13. C101×#1895C2semidirect
14. C101×#1893C2semidirect
15. C101×#1804C2semidirect
96. #121×C101D4semidirect
130. C4⋊C8×C101D4semidirect
388. #24762C101direct (N × H)
400. C2×#469C2×C101semidirect
401. C2×#466C2×C101semidirect
402. C2×#459C2×C101semidirect
403. C2×#424C2×C101semidirect
404. #2619C2×C101semidirect
405. #2324C2×C101semidirect
406. #2067C2×C101semidirect
407. #2065C2×C101semidirect
408. #2054C2×C101semidirect
409. #2054C2×C101semidirect
410. #1982C2×C101semidirect
411. #1949C2×C101semidirect
412. #1895C2×C101semidirect
413. #1893C2×C101semidirect
414. #1804C2×C101semidirect
415. C101#24762direct (N × H)
496. #121D4×C101semidirect
530. C4⋊C8D4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1012
C2×#466×C1012
C2×#459×C1012
C2×#424×C1012
C101×#26192
C101×#23242
C101×#20672
C101×#20652
C101×#20542
C101×#19822
C101×#19492
C101×#18952
C101×#18932
C101×#18042
#24762101