Finite Group Databasebeta

← C101×#26961 #38809112

Subgroups — C101×#26961 #38809112

Order 25856.

1068 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C101C211yesmaximal, characteristic, complemented
2C2×C4×D8×C101C211yesmaximal, characteristic, complemented
3C101×#2428C211yesmaximal, characteristic, complemented
4C101×#2422C211yesmaximal, characteristic, complemented
5C101×#2083C211yesmaximal, characteristic, complemented
6C101×#2033C211yesmaximal, characteristic, complemented
7C101×#2011C211yesmaximal, characteristic, complemented
8C101×#1999C211yesmaximal, characteristic, complemented
9C101×#1957C211yesmaximal, characteristic, complemented
10C101×#1934C211yesmaximal, characteristic, complemented
11C101×#1934C211yesmaximal, characteristic, complemented
12C101×#1893C211yesmaximal, characteristic, complemented
13C101×#1879C211yesmaximal, characteristic, complemented
14C101×#1862C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C101C211yesmaximal, characteristic, complemented
16C22×D8×C101C2211yescharacteristic
17C22×D8×C101C2211yescharacteristic
18C23×C8×C101C2211yescharacteristic
19C2×#127×C101C2211yescharacteristic
20C2×#123×C101—21no—
21C2×#121×C101—21no—
22C2×#121×C101C2211yescharacteristic
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×C4×D4×C101C2211yescharacteristic
26C2×C4×D4×C101C2211yescharacteristic
27#466×C101—24no—
28C4×D8×C101—24no—
29C2×#107×C101C2211yescharacteristic
30C2×#107×C101C2211yescharacteristic
31C2×#102×C101C2211yescharacteristic
32C2×#102×C101C2211yescharacteristic
33C2×#102×C101C2211yescharacteristic
34C2×#102×C101C2211yescharacteristic
35C2×#102×C101C2211yescharacteristic
36C2×#102×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×C22⋊C8×C101C2211yescharacteristic
40C2×C4×C8×C101C2211yescharacteristic
41C2×C4×C8×C101C2211yescharacteristic
42#397×C101—21no—
43#394×C101—21no—
44#394×C101—21no—
45#392×C101—21no—
46#390×C101C2211yescharacteristic
47#390×C101C2211yescharacteristic
48#389×C101C2211yescharacteristic
49#389×C101C2211yescharacteristic
50#386×C101—21no—
51#385×C101—21no—
52#384×C101C2211yescharacteristic
53#380×C101C2211yescharacteristic
54C4×C22⋊C4×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#336×C101C2211yescharacteristic
60#336×C101C2211yescharacteristic
61C22×D4×C101—21no—
62C22×D4×C101—21no—
63C22×D4×C101—21no—
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101C2311yescharacteristic
67C22×D4×C101C2311yescharacteristic
68C22×D4×C101C2311yescharacteristic
69C23×C4×C101—21no—
70C23×C4×C101—21no—
71C23×C4×C101C2311yescharacteristic
72C2×D8×C101—22no—
73C2×D8×C101—22no—
74C2×D8×C101—22no—
75C2×D8×C101—22no—
76C2×D8×C101—22no—
77C2×D8×C101—41no—
78C22×C8×C101—22no—
79C22×C8×C101—22no—
80C22×C8×C101—41no—
81C22×C8×C101C2311yescharacteristic
82C22×C8×C101C2311yescharacteristic
83C22×C8×C101C2311yescharacteristic
84C22×C8×C101C2311yescharacteristic
85#127×C101—22no—
86#127×C101—41no—
87#123×C101—44no—
88#121×C101—22no—
89#121×C101—22no—
90#121×C101—22no—
91#121×C101—41no—
92#121×C101—41no—
93#121×C101—41no—
94#121×C101—44no—
95C4×D4×C101—22no—
96C4×D4×C101—22no—
97C4×D4×C101—41no—
98C4×D4×C101—41no—
99C2×C4⋊C4×C101—21no—
100C2×C4⋊C4×C101—21no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101C2311yescharacteristic
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×C22⋊C4×C101—21no—
116C2×C22⋊C4×C101—21no—
117C2×C22⋊C4×C101—21no—
118C2×C22⋊C4×C101D411yescharacteristic
119C2×C22⋊C4×C101D411yescharacteristic
120C2×C42×C101C2311yescharacteristic
121C2×C42×C101C2311yescharacteristic
122#107×C101—22no—
123#107×C101—22no—
124#102×C101—22no—
125#102×C101—22no—
126#102×C101—22no—
127#102×C101—22no—
128#102×C101—41no—
129#102×C101—41no—
130#102×C101—41no—
131#102×C101D414yescomplemented
132C22⋊C8×C101—22no—
133C4×C8×C101—22no—
134C4×C8×C101—41no—
135#95×C101—21no—
136#95×C101—21no—
137#95×C101—21no—
138#95×C101D411yescharacteristic
139#95×C101D411yescharacteristic
140C24×C101—21no—
141C24×C101—21no—
142C24×C101—21no—
143C24×C101C2×D411yescharacteristic
144C2×D4×C101—21no—
145C2×D4×C101—21no—
146C2×D4×C101—21no—
147C2×D4×C101—21no—
148C2×D4×C101—21no—
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—42no—
161C2×D4×C101—42no—
162C2×D4×C101—42no—
163C2×D4×C101—42no—
164C2×D4×C101—42no—
165C2×D4×C101—42no—
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×C101C2×D412yes—
176C2×D4×C101#4112yes—
177C22×C4×C101—21no—
178C22×C4×C101—21no—
179C22×C4×C101—21no—
180C22×C4×C101—21no—
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—42no—
189C22×C4×C101—42no—
190C22×C4×C101—42no—
191C22×C4×C101—42no—
192C22×C4×C101—81no—
193C22×C4×C101—81no—
194C22×C4×C101C2×D411yescharacteristic
195C22×C4×C101C2×D411yescharacteristic
196C22×C4×C101C2×D411yescharacteristic
197C22×C4×C101C2×D411yescharacteristic
198C22×C4×C101C2×D411yescharacteristic
199C22×C4×C101C2411yescharacteristic
200D8×C101—28no—
201D8×C101—44no—
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—44no—
212C2×C8×C101C2×D412yes—
213C2×C8×C101#4112yes—
214C2×C8×C101#4112yes—
215C4⋊C4×C101—21no—
216C4⋊C4×C101—21no—
217C4⋊C4×C101—21no—
218C4⋊C4×C101—21no—
219C4⋊C4×C101—21no—
220C4⋊C4×C101—21no—
221C4⋊C4×C101—21no—
222C4⋊C4×C101—21no—
223C4⋊C4×C101—21no—
224C4⋊C4×C101—42no—
225C4⋊C4×C101—42no—
226C4⋊C4×C101—42no—
227C4⋊C4×C101—81no—
228C4⋊C4×C101C2×D412yes—
229C22⋊C4×C101—22no—
230C22⋊C4×C101—42no—
231C22⋊C4×C101—42no—
232C22⋊C4×C101—42no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—42no—
235C22⋊C4×C101—42no—
236C22⋊C4×C101—42no—
237C22⋊C4×C101—42no—
238C22⋊C4×C101—42no—
239C22⋊C4×C101—81no—
240C22⋊C4×C101D814yescomplemented
241C42×C101—21no—
242C42×C101—21no—
243C42×C101—21no—
244C42×C101—21no—
245C23×C101—21no—
246C23×C101—21no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—21no—
250C23×C101—21no—
251C23×C101—22no—
252C23×C101—22no—
253C23×C101—41no—
254C23×C101—41no—
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×C101C2×D812yes—
273C23×C101C22×D411yescharacteristic
274D4×C101—22no—
275D4×C101—22no—
276D4×C101—22no—
277D4×C101—22no—
278D4×C101—41no—
279D4×C101—41no—
280D4×C101—41no—
281D4×C101—41no—
282D4×C101—41no—
283D4×C101—41no—
284D4×C101—41no—
285D4×C101—41no—
286D4×C101—84no—
287D4×C101—84no—
288D4×C101—84no—
289D4×C101—84no—
290D4×C101—84no—
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—22no—
301C2×C4×C101—21no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—41no—
305C2×C4×C101—41no—
306C2×C4×C101—41no—
307C2×C4×C101—41no—
308C2×C4×C101—41no—
309C2×C4×C101—41no—
310C2×C4×C101—41no—
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—84no—
323C2×C4×C101—84no—
324C2×C4×C101C2×D812yes—
325C2×C4×C101C2×D812yes—
326C2×C4×C101#13512yes—
327C2×C4×C101C22×D411yescharacteristic
328C2×C4×C101C2×#4111yescharacteristic
329C2×C4×C101C2×#4111yescharacteristic
330C2×C4×C101C2×#4111yescharacteristic
331C2×C4×C101H(5,𝔽2)11yescharacteristic
332C2×C4×C101H(5,𝔽2)11yescharacteristic
333C8×C101—22no—
334C8×C101—22no—
335C8×C101—22no—
336C8×C101—41no—
337C22×C101—22no—
338C22×C101—22no—
339C22×C101—22no—
340C22×C101—41no—
341C22×C101—41no—
342C22×C101—41no—
343C22×C101—41no—
344C22×C101—42no—
345C22×C101—42no—
346C22×C101—42no—
347C22×C101—42no—
348C22×C101—42no—
349C22×C101—42no—
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#53211yescharacteristic
366C22×C101D4211yescharacteristic
367C22×C101#54611yescharacteristic
368C22×C101C22×D811yescharacteristic
369C22×C101C2×#13511yescharacteristic
370C22×C101#57611yescharacteristic
371C22×C101#57711yescharacteristic
372C4×C101—22no—
373C4×C101—22no—
374C4×C101—22no—
375C4×C101—41no—
376C4×C101—42no—
377C4×C101—41no—
378C4×C101—81no—
379C4×C101—81no—
380C4×C101—81no—
381C4×C101—81no—
382C4×C101#52511yescharacteristic
383C4×C101#54011yescharacteristic
384C4×C101#54611yescharacteristic
385C4×C101#55311yescharacteristic
386#26961C10111yesmaximal, characteristic, direct product factor, Sylow
387C2×C101—42no—
388C2×C101—82no—
389C2×C101—82no—
390C2×C101—161no—
391C2×C101#246411yescharacteristic
392C2×C101#316911yescharacteristic
393C2×C101#317911yescharacteristic
394C2×C101D4×D811yescharacteristic
395C2×C101#328411yescharacteristic
396C2×C101#329411yescharacteristic
397C2×C101#329711yescharacteristic
398C2×#466C2×C10111yescharacteristic, complemented
399C2×C4×D8C2×C10111yescharacteristic, complemented
400#2428C2×C10111yescharacteristic, complemented
401#2422C2×C10111yescharacteristic, complemented
402#2083C2×C10111yescharacteristic, complemented
403#2033C2×C10111yescharacteristic, complemented
404#2011C2×C10111yescharacteristic, complemented
405#1999C2×C10111yescharacteristic, complemented
406#1957C2×C10111yescharacteristic, complemented
407#1934C2×C10111yescharacteristic, complemented
408#1934C2×C10111yescharacteristic, complemented
409#1893C2×C10111yescharacteristic, complemented
410#1879C2×C10111yescharacteristic, complemented
411#1862C2×C10111yescharacteristic, complemented
412C8×C22⋊C4C2×C10111yescharacteristic, complemented
413C101#2696111yescharacteristic, direct product factor, Sylow
414C22×D8C22×C10111yescharacteristic
415C22×D8C22×C10111yescharacteristic
416C23×C8C22×C10111yescharacteristic
417C2×#127C22×C10111yescharacteristic
418C2×#123—21no—
419C2×#121—21no—
420C2×#121C22×C10111yescharacteristic
421C2×#121C22×C10111yescharacteristic
422C2×#121C22×C10111yescharacteristic
423C2×C4×D4C22×C10111yescharacteristic
424C2×C4×D4C22×C10111yescharacteristic
425#466—24no—
426C4×D8—24no—
427C2×#107C22×C10111yescharacteristic
428C2×#107C22×C10111yescharacteristic
429C2×#102C22×C10111yescharacteristic
430C2×#102C22×C10111yescharacteristic
431C2×#102C22×C10111yescharacteristic
432C2×#102C22×C10111yescharacteristic
433C2×#102C22×C10111yescharacteristic
434C2×#102C22×C10111yescharacteristic
435C2×#102C22×C10111yescharacteristic
436C2×#102C22×C10111yescharacteristic
437C2×C22⋊C8C22×C10111yescharacteristic
438C2×C4×C8C22×C10111yescharacteristic
439C2×C4×C8C22×C10111yescharacteristic
440#397—21no—
441#394—21no—
442#394—21no—
443#392—21no—
444#390C22×C10111yescharacteristic
445#390C22×C10111yescharacteristic
446#389C22×C10111yescharacteristic
447#389C22×C10111yescharacteristic
448#386—21no—
449#385—21no—
450#384C22×C10111yescharacteristic
451#380C22×C10111yescharacteristic
452C4×C22⋊C4C22×C10111yescharacteristic
453#340C22×C10111yescharacteristic
454#340C22×C10111yescharacteristic
455#340C22×C10111yescharacteristic
456#340C22×C10111yescharacteristic
457#336C22×C10111yescharacteristic
458#336C22×C10111yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C10111yescharacteristic
465C22×D4C23×C10111yescharacteristic
466C22×D4C23×C10111yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C10111yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C22×C8—22no—
477C22×C8—22no—
478C22×C8—41no—
479C22×C8C23×C10111yescharacteristic
480C22×C8C23×C10111yescharacteristic
481C22×C8C23×C10111yescharacteristic
482C22×C8C23×C10111yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—41no—
490#121—41no—
491#121—41no—
492#121—44no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C10111yescharacteristic
502C2×C4⋊C4C23×C10111yescharacteristic
503C2×C4⋊C4C23×C10111yescharacteristic
504C2×C4⋊C4C23×C10111yescharacteristic
505C2×C4⋊C4C23×C10111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
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⋊C4D4×C10111yescharacteristic
517C2×C22⋊C4D4×C10111yescharacteristic
518C2×C42C23×C10111yescharacteristic
519C2×C42C23×C10111yescharacteristic
520#107—22no—
521#107—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C10114yescomplemented
530C22⋊C8—22no—
531C4×C8—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C10111yescharacteristic
537#95D4×C10111yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C10111yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
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—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C10112yes—
574C2×D4#41×C10112yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C10111yescharacteristic
593C22×C4C2×D4×C10111yescharacteristic
594C22×C4C2×D4×C10111yescharacteristic
595C22×C4C2×D4×C10111yescharacteristic
596C22×C4C2×D4×C10111yescharacteristic
597C22×C4C24×C10111yescharacteristic
598D8—28no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—44no—
610C2×C8C2×D4×C10112yes—
611C2×C8#41×C10112yes—
612C2×C8#41×C10112yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C10112yes—
627C22⋊C4—22no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—81no—
638C22⋊C4D8×C10114yescomplemented
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—22no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
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—
670C23C2×D8×C10112yes—
671C23C22×D4×C10111yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
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—84no—
721C2×C4—84no—
722C2×C4C2×D8×C10112yes—
723C2×C4C2×D8×C10112yes—
724C2×C4#135×C10112yes—
725C2×C4C22×D4×C10111yescharacteristic
726C2×C4C2×#41×C10111yescharacteristic
727C2×C4C2×#41×C10111yescharacteristic
728C2×C4C2×#41×C10111yescharacteristic
729C2×C4H(5,𝔽2)×C10111yescharacteristic
730C2×C4H(5,𝔽2)×C10111yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
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#532×C10111yescharacteristic
764C22D42×C10111yescharacteristic
765C22#546×C10111yescharacteristic
766C22C22×D8×C10111yescharacteristic
767C22C2×#135×C10111yescharacteristic
768C22#576×C10111yescharacteristic
769C22#577×C10111yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4#525×C10111yescharacteristic
781C4#540×C10111yescharacteristic
782C4#546×C10111yescharacteristic
783C4#553×C10111yescharacteristic
784C2—42no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C101×#246411yescharacteristic
789C2C101×#316911yescharacteristic
790C2C101×#317911yescharacteristic
791C2D4×D8×C10111yescharacteristic
792C2C101×#328411yescharacteristic
793C2C101×#329411yescharacteristic
794C2C101×#329711yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C22⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C101C2semidirect
2. C2×C4×D8×C101C2semidirect
3. C101×#2428C2semidirect
4. C101×#2422C2semidirect
5. C101×#2083C2semidirect
6. C101×#2033C2semidirect
7. C101×#2011C2semidirect
8. C101×#1999C2semidirect
9. C101×#1957C2semidirect
10. C101×#1934C2semidirect
11. C101×#1934C2semidirect
12. C101×#1893C2semidirect
13. C101×#1879C2semidirect
14. C101×#1862C2semidirect
15. C8×C22⋊C4×C101C2semidirect
131. #102×C101D4semidirect
240. C22⋊C4×C101D8semidirect
386. #26961C101direct (N × H)
398. C2×#466C2×C101semidirect
399. C2×C4×D8C2×C101semidirect
400. #2428C2×C101semidirect
401. #2422C2×C101semidirect
402. #2083C2×C101semidirect
403. #2033C2×C101semidirect
404. #2011C2×C101semidirect
405. #1999C2×C101semidirect
406. #1957C2×C101semidirect
407. #1934C2×C101semidirect
408. #1934C2×C101semidirect
409. #1893C2×C101semidirect
410. #1879C2×C101semidirect
411. #1862C2×C101semidirect
412. C8×C22⋊C4C2×C101semidirect
413. C101#26961direct (N × H)
529. #102D4×C101semidirect
638. C22⋊C4D8×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1012
C2×C4×D8×C1012
C101×#24282
C101×#24222
C101×#20832
C101×#20332
C101×#20112
C101×#19992
C101×#19572
C101×#19342
C101×#18932
C101×#18792
C101×#18622
C8×C22⋊C4×C1012
#26961101