Finite Group Databasebeta

← C101×#25422 #38807573

Subgroups — C101×#25422 #38807573

Order 25856.

1126 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C101C211yesmaximal, characteristic, complemented
2C2×#466×C101C211yesmaximal, characteristic, complemented
3C2×#465×C101C211yesmaximal, characteristic, complemented
4C2×#440×C101C211yesmaximal, characteristic, complemented
5C101×#2428C211yesmaximal, characteristic, complemented
6C101×#2426C211yesmaximal, characteristic, complemented
7C101×#2042C211yesmaximal, characteristic, complemented
8C101×#2041C211yesmaximal, characteristic, complemented
9C101×#2000C211yesmaximal, characteristic, complemented
10C101×#1999C211yesmaximal, characteristic, complemented
11C101×#1972C211yesmaximal, characteristic, complemented
12C101×#1943C211yesmaximal, characteristic, complemented
13C101×#1880C211yesmaximal, characteristic, complemented
14C101×#1879C211yesmaximal, characteristic, complemented
15C101×#1752C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×D8×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic
20C23×C8×C101C2211yescharacteristic
21C2×#127×C101C2211yescharacteristic
22C2×#124×C101C2211yescharacteristic
23C2×C22⋊Q8×C101C2211yescharacteristic
24C2×#121×C101—21no—
25C2×#121×C101C2211yescharacteristic
26C2×#121×C101C2211yescharacteristic
27C2×#121×C101C2211yescharacteristic
28C2×C4×Q8×C101C2211yescharacteristic
29C2×C4×D4×C101C2211yescharacteristic
30#496×C101—24no—
31#466×C101—24no—
32#465×C101—24no—
33#440×C101—24no—
34C2×#107×C101C2211yescharacteristic
35C2×#106×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×C22⋊C8×C101C2211yescharacteristic
45C2×#97×C101C2211yescharacteristic
46C2×#97×C101C2211yescharacteristic
47#396×C101—21no—
48#394×C101—21no—
49#394×C101—21no—
50#392×C101—21no—
51#390×C101—21no—
52#390×C101C2211yescharacteristic
53#390×C101C2211yescharacteristic
54#389×C101C2211yescharacteristic
55#389×C101C2211yescharacteristic
56#388×C101—21no—
57#386×C101—21no—
58C4×C22⋊C4×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C22×Q8×C101C2311yescharacteristic
64C22×D4×C101—21no—
65C22×D4×C101—21no—
66C22×D4×C101—21no—
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101C2311yescharacteristic
70C22×D4×C101C2311yescharacteristic
71C22×D4×C101C2311yescharacteristic
72C23×C4×C101—21no—
73C23×C4×C101C2311yescharacteristic
74C2×SD16×C101—22no—
75C2×SD16×C101—22no—
76C2×SD16×C101—22no—
77C2×SD16×C101—22no—
78C2×SD16×C101—41no—
79C2×SD16×C101D414yescomplemented
80C2×D8×C101—22no—
81C2×D8×C101—22no—
82C2×D8×C101—22no—
83C2×D8×C101—22no—
84C2×D8×C101—22no—
85C2×D8×C101—41no—
86C22×C8×C101—22no—
87C22×C8×C101—22no—
88C22×C8×C101—22no—
89C22×C8×C101C2311yescharacteristic
90C22×C8×C101C2311yescharacteristic
91C22×C8×C101C2311yescharacteristic
92C22×C8×C101C2311yescharacteristic
93#127×C101—22no—
94#127×C101—41no—
95#124×C101—22no—
96#124×C101—41no—
97C22⋊Q8×C101—22no—
98C22⋊Q8×C101—41no—
99#121×C101—22no—
100#121×C101—22no—
101#121×C101—22no—
102#121×C101—44no—
103#121×C101—41no—
104#121×C101—41no—
105#121×C101—41no—
106C4×Q8×C101—22no—
107C4×Q8×C101—41no—
108C4×D4×C101—22no—
109C4×D4×C101—41no—
110C2×C4⋊C4×C101—21no—
111C2×C4⋊C4×C101—21no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101—21no—
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C4⋊C4×C101C2311yescharacteristic
118C2×C22⋊C4×C101—21no—
119C2×C22⋊C4×C101—21no—
120C2×C22⋊C4×C101—21no—
121C2×C22⋊C4×C101—21no—
122C2×C22⋊C4×C101—21no—
123C2×C22⋊C4×C101—21no—
124C2×C22⋊C4×C101—21no—
125C2×C22⋊C4×C101—21no—
126C2×C22⋊C4×C101—21no—
127C2×C22⋊C4×C101—21no—
128C2×C22⋊C4×C101—21no—
129C2×C22⋊C4×C101D411yescharacteristic
130C2×C22⋊C4×C101D411yescharacteristic
131C2×C42×C101—21no—
132C2×C42×C101C2311yescharacteristic
133C2×C42×C101C2311yescharacteristic
134#107×C101D414yescomplemented
135#106×C101—22no—
136#103×C101—22no—
137#103×C101—22no—
138#102×C101—22no—
139#102×C101—22no—
140#102×C101—22no—
141#102×C101—22no—
142#102×C101—41no—
143#102×C101—41no—
144C22⋊C8×C101—22no—
145#97×C101—22no—
146#97×C101—22no—
147#95×C101—21no—
148#95×C101—21no—
149#95×C101D411yescharacteristic
150#95×C101D411yescharacteristic
151C24×C101—21no—
152C24×C101—21no—
153C24×C101—21no—
154C24×C101C2×D411yescharacteristic
155C2×Q8×C101—21no—
156C2×Q8×C101—21no—
157C2×Q8×C101—21no—
158C2×Q8×C101—21no—
159C2×Q8×C101—21no—
160C2×Q8×C101C2×D412yes—
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—21no—
170C2×D4×C101—21no—
171C2×D4×C101—21no—
172C2×D4×C101—21no—
173C2×D4×C101—21no—
174C2×D4×C101—21no—
175C2×D4×C101—21no—
176C2×D4×C101—21no—
177C2×D4×C101—21no—
178C2×D4×C101—42no—
179C2×D4×C101—42no—
180C2×D4×C101—42no—
181C2×D4×C101—42no—
182C2×D4×C101—42no—
183C2×D4×C101—42no—
184C2×D4×C101—42no—
185C2×D4×C101—42no—
186C2×D4×C101—42no—
187C2×D4×C101—42no—
188C2×D4×C101—81no—
189C2×D4×C101—81no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101—81no—
193C2×D4×C101C2×D412yes—
194C22×C4×C101—21no—
195C22×C4×C101—21no—
196C22×C4×C101—21no—
197C22×C4×C101—21no—
198C22×C4×C101—21no—
199C22×C4×C101—21no—
200C22×C4×C101—21no—
201C22×C4×C101—21no—
202C22×C4×C101—21no—
203C22×C4×C101—21no—
204C22×C4×C101—21no—
205C22×C4×C101—42no—
206C22×C4×C101—42no—
207C22×C4×C101—81no—
208C22×C4×C101C2×D411yescharacteristic
209C22×C4×C101C2×D411yescharacteristic
210C22×C4×C101C2×D411yescharacteristic
211C22×C4×C101C2×D411yescharacteristic
212C22×C4×C101C2×D411yescharacteristic
213C22×C4×C101C2411yescharacteristic
214SD16×C101—28no—
215SD16×C101—44no—
216D8×C101—44no—
217D8×C101—44no—
218C2×C8×C101—21no—
219C2×C8×C101—21no—
220C2×C8×C101—21no—
221C2×C8×C101—21no—
222C2×C8×C101—21no—
223C2×C8×C101—21no—
224C2×C8×C101—21no—
225C2×C8×C101—21no—
226C2×C8×C101—44no—
227C2×C8×C101C2×D412yes—
228C2×C8×C101C2×D412yes—
229C2×C8×C101#4112yes—
230C2×C8×C101#4112yes—
231C4⋊C4×C101—21no—
232C4⋊C4×C101—21no—
233C4⋊C4×C101—21no—
234C4⋊C4×C101—21no—
235C4⋊C4×C101—21no—
236C4⋊C4×C101—21no—
237C4⋊C4×C101—42no—
238C4⋊C4×C101—42no—
239C4⋊C4×C101—42no—
240C4⋊C4×C101—81no—
241C4⋊C4×C101C2×D412yes—
242C4⋊C4×C101C2×D412yes—
243C22⋊C4×C101—22no—
244C22⋊C4×C101—41no—
245C22⋊C4×C101—42no—
246C22⋊C4×C101—42no—
247C22⋊C4×C101—42no—
248C22⋊C4×C101—42no—
249C22⋊C4×C101—42no—
250C22⋊C4×C101—42no—
251C22⋊C4×C101—42no—
252C22⋊C4×C101—42no—
253C22⋊C4×C101—42no—
254C22⋊C4×C101—81no—
255C22⋊C4×C101—81no—
256C42×C101—21no—
257C42×C101—21no—
258C42×C101—21no—
259C42×C101—21no—
260C42×C101—42no—
261C23×C101—21no—
262C23×C101—21no—
263C23×C101—21no—
264C23×C101—21no—
265C23×C101—21no—
266C23×C101—21no—
267C23×C101—22no—
268C23×C101—41no—
269C23×C101—41no—
270C23×C101—41no—
271C23×C101—41no—
272C23×C101—41no—
273C23×C101—41no—
274C23×C101—41no—
275C23×C101—41no—
276C23×C101—41no—
277C23×C101—41no—
278C23×C101—41no—
279C23×C101—41no—
280C23×C101—41no—
281C23×C101—41no—
282C23×C101—41no—
283C23×C101—41no—
284C23×C101—41no—
285C23×C101—41no—
286C23×C101—41no—
287C23×C101—41no—
288C23×C101AGL(1,ℤ/8)12yes—
289C23×C101C22×D411yescharacteristic
290Q8×C101—22no—
291Q8×C101—22no—
292Q8×C101—41no—
293Q8×C101—41no—
294D4×C101—22no—
295D4×C101—22no—
296D4×C101—41no—
297D4×C101—41no—
298D4×C101—41no—
299D4×C101—41no—
300D4×C101—41no—
301D4×C101—41no—
302D4×C101—41no—
303D4×C101—41no—
304D4×C101—41no—
305D4×C101—41no—
306D4×C101—84no—
307D4×C101—84no—
308D4×C101—84no—
309D4×C101—84no—
310D4×C101—84no—
311C2×C4×C101—21no—
312C2×C4×C101—21no—
313C2×C4×C101—21no—
314C2×C4×C101—21no—
315C2×C4×C101—21no—
316C2×C4×C101—22no—
317C2×C4×C101—21no—
318C2×C4×C101—22no—
319C2×C4×C101—22no—
320C2×C4×C101—21no—
321C2×C4×C101—21no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—21no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—41no—
330C2×C4×C101—41no—
331C2×C4×C101—41no—
332C2×C4×C101—41no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—41no—
340C2×C4×C101—41no—
341C2×C4×C101—41no—
342C2×C4×C101—41no—
343C2×C4×C101—41no—
344C2×C4×C101—41no—
345C2×C4×C101—84no—
346C2×C4×C101C22×D411yescharacteristic
347C2×C4×C101C22×D411yescharacteristic
348C2×C4×C101C2×#4111yescharacteristic
349C2×C4×C101C2×#4111yescharacteristic
350C2×C4×C101H(5,𝔽2)11yescharacteristic
351C2×C4×C101H(5,𝔽2)11yescharacteristic
352C8×C101—22no—
353C8×C101—41no—
354C8×C101—41no—
355C8×C101#12114yescomplemented
356C22×C101—22no—
357C22×C101—22no—
358C22×C101—22no—
359C22×C101—41no—
360C22×C101—41no—
361C22×C101—41no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—42no—
365C22×C101—42no—
366C22×C101—81no—
367C22×C101—81no—
368C22×C101—81no—
369C22×C101—81no—
370C22×C101—81no—
371C22×C101—81no—
372C22×C101—81no—
373C22×C101—81no—
374C22×C101—81no—
375C22×C101—81no—
376C22×C101—81no—
377C22×C101—81no—
378C22×C101—81no—
379C22×C101—81no—
380C22×C101—81no—
381C22×C101—81no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101#53211yescharacteristic
385C22×C101D4211yescharacteristic
386C22×C101D4211yescharacteristic
387C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C101#57511yescharacteristic
389C22×C101#57611yescharacteristic
390C22×C101#57711yescharacteristic
391C4×C101—41no—
392C4×C101—42no—
393C4×C101—41no—
394C4×C101—42no—
395C4×C101—42no—
396C4×C101—41no—
397C4×C101—41no—
398C4×C101—41no—
399C4×C101—81no—
400C4×C101—81no—
401C4×C101C2×#12111yescharacteristic
402C4×C101#54011yescharacteristic
403C4×C101#54611yescharacteristic
404C4×C101#55011yescharacteristic
405#25422C10111yesmaximal, characteristic, direct product factor, Sylow
406C2×C101—42no—
407C2×C101—82no—
408C2×C101—161no—
409C2×C101—161no—
410C2×C101#242811yescharacteristic
411C2×C101#317911yescharacteristic
412C2×C101#318011yescharacteristic
413C2×C101#326411yescharacteristic
414C2×C101#326511yescharacteristic
415C2×C101#326811yescharacteristic
416C2×C101#327111yescharacteristic
417C2×#496C2×C10111yescharacteristic, complemented
418C2×#466C2×C10111yescharacteristic, complemented
419C2×#465C2×C10111yescharacteristic, complemented
420C2×#440C2×C10111yescharacteristic, complemented
421#2428C2×C10111yescharacteristic, complemented
422#2426C2×C10111yescharacteristic, complemented
423#2042C2×C10111yescharacteristic, complemented
424#2041C2×C10111yescharacteristic, complemented
425#2000C2×C10111yescharacteristic, complemented
426#1999C2×C10111yescharacteristic, complemented
427#1972C2×C10111yescharacteristic, complemented
428#1943C2×C10111yescharacteristic, complemented
429#1880C2×C10111yescharacteristic, complemented
430#1879C2×C10111yescharacteristic, complemented
431#1752C2×C10111yescharacteristic, complemented
432C101#2542211yescharacteristic, direct product factor, Sylow
433C22×SD16C22×C10111yescharacteristic
434C22×SD16C22×C10111yescharacteristic
435C22×D8C22×C10111yescharacteristic
436C22×D8C22×C10111yescharacteristic
437C23×C8C22×C10111yescharacteristic
438C2×#127C22×C10111yescharacteristic
439C2×#124C22×C10111yescharacteristic
440C2×C22⋊Q8C22×C10111yescharacteristic
441C2×#121—21no—
442C2×#121C22×C10111yescharacteristic
443C2×#121C22×C10111yescharacteristic
444C2×#121C22×C10111yescharacteristic
445C2×C4×Q8C22×C10111yescharacteristic
446C2×C4×D4C22×C10111yescharacteristic
447#496—24no—
448#466—24no—
449#465—24no—
450#440—24no—
451C2×#107C22×C10111yescharacteristic
452C2×#106C22×C10111yescharacteristic
453C2×#103C22×C10111yescharacteristic
454C2×#103C22×C10111yescharacteristic
455C2×#102C22×C10111yescharacteristic
456C2×#102C22×C10111yescharacteristic
457C2×#102C22×C10111yescharacteristic
458C2×#102C22×C10111yescharacteristic
459C2×#102C22×C10111yescharacteristic
460C2×#102C22×C10111yescharacteristic
461C2×C22⋊C8C22×C10111yescharacteristic
462C2×#97C22×C10111yescharacteristic
463C2×#97C22×C10111yescharacteristic
464#396—21no—
465#394—21no—
466#394—21no—
467#392—21no—
468#390—21no—
469#390C22×C10111yescharacteristic
470#390C22×C10111yescharacteristic
471#389C22×C10111yescharacteristic
472#389C22×C10111yescharacteristic
473#388—21no—
474#386—21no—
475C4×C22⋊C4C22×C10111yescharacteristic
476#340C22×C10111yescharacteristic
477#340C22×C10111yescharacteristic
478#336C22×C10111yescharacteristic
479#336C22×C10111yescharacteristic
480C22×Q8C23×C10111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4C23×C10111yescharacteristic
487C22×D4C23×C10111yescharacteristic
488C22×D4C23×C10111yescharacteristic
489C23×C4—21no—
490C23×C4C23×C10111yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—41no—
496C2×SD16D4×C10114yescomplemented
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—22no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—41no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8C23×C10111yescharacteristic
507C22×C8C23×C10111yescharacteristic
508C22×C8C23×C10111yescharacteristic
509C22×C8C23×C10111yescharacteristic
510#127—22no—
511#127—41no—
512#124—22no—
513#124—41no—
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—44no—
520#121—41no—
521#121—41no—
522#121—41no—
523C4×Q8—22no—
524C4×Q8—41no—
525C4×D4—22no—
526C4×D4—41no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4C23×C10111yescharacteristic
532C2×C4⋊C4C23×C10111yescharacteristic
533C2×C4⋊C4C23×C10111yescharacteristic
534C2×C4⋊C4C23×C10111yescharacteristic
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4D4×C10111yescharacteristic
547C2×C22⋊C4D4×C10111yescharacteristic
548C2×C42—21no—
549C2×C42C23×C10111yescharacteristic
550C2×C42C23×C10111yescharacteristic
551#107D4×C10114yescomplemented
552#106—22no—
553#103—22no—
554#103—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560#102—41no—
561C22⋊C8—22no—
562#97—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95D4×C10111yescharacteristic
567#95D4×C10111yescharacteristic
568C24—21no—
569C24—21no—
570C24—21no—
571C24C2×D4×C10111yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C10112yes—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4C2×D4×C10112yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—81no—
625C22×C4C2×D4×C10111yescharacteristic
626C22×C4C2×D4×C10111yescharacteristic
627C22×C4C2×D4×C10111yescharacteristic
628C22×C4C2×D4×C10111yescharacteristic
629C22×C4C2×D4×C10111yescharacteristic
630C22×C4C24×C10111yescharacteristic
631SD16—28no—
632SD16—44no—
633D8—44no—
634D8—44no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C10112yes—
645C2×C8C2×D4×C10112yes—
646C2×C8#41×C10112yes—
647C2×C8#41×C10112yes—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—81no—
658C4⋊C4C2×D4×C10112yes—
659C4⋊C4C2×D4×C10112yes—
660C22⋊C4—22no—
661C22⋊C4—41no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—81no—
672C22⋊C4—81no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—42no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C10112yes—
706C23C22×D4×C10111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727D4—84no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—84no—
763C2×C4C22×D4×C10111yescharacteristic
764C2×C4C22×D4×C10111yescharacteristic
765C2×C4C2×#41×C10111yescharacteristic
766C2×C4C2×#41×C10111yescharacteristic
767C2×C4H(5,𝔽2)×C10111yescharacteristic
768C2×C4H(5,𝔽2)×C10111yescharacteristic
769C8—22no—
770C8—41no—
771C8—41no—
772C8#121×C10114yescomplemented
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22#532×C10111yescharacteristic
802C22D42×C10111yescharacteristic
803C22D42×C10111yescharacteristic
804C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
805C22#575×C10111yescharacteristic
806C22#576×C10111yescharacteristic
807C22#577×C10111yescharacteristic
808C4—41no—
809C4—42no—
810C4—41no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4C2×#121×C10111yescharacteristic
819C4#540×C10111yescharacteristic
820C4#546×C10111yescharacteristic
821C4#550×C10111yescharacteristic
822C2—42no—
823C2—82no—
824C2—161no—
825C2—161no—
826C2C101×#242811yescharacteristic
827C2C101×#317911yescharacteristic
828C2C101×#318011yescharacteristic
829C2C101×#326411yescharacteristic
830C2C101×#326511yescharacteristic
831C2C101×#326811yescharacteristic
832C2C101×#327111yescharacteristic
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×#496×C101C2semidirect
2. C2×#466×C101C2semidirect
3. C2×#465×C101C2semidirect
4. C2×#440×C101C2semidirect
5. C101×#2428C2semidirect
6. C101×#2426C2semidirect
7. C101×#2042C2semidirect
8. C101×#2041C2semidirect
9. C101×#2000C2semidirect
10. C101×#1999C2semidirect
11. C101×#1972C2semidirect
12. C101×#1943C2semidirect
13. C101×#1880C2semidirect
14. C101×#1879C2semidirect
15. C101×#1752C2semidirect
79. C2×SD16×C101D4semidirect
134. #107×C101D4semidirect
355. C8×C101#121semidirect
405. #25422C101direct (N × H)
417. C2×#496C2×C101semidirect
418. C2×#466C2×C101semidirect
419. C2×#465C2×C101semidirect
420. C2×#440C2×C101semidirect
421. #2428C2×C101semidirect
422. #2426C2×C101semidirect
423. #2042C2×C101semidirect
424. #2041C2×C101semidirect
425. #2000C2×C101semidirect
426. #1999C2×C101semidirect
427. #1972C2×C101semidirect
428. #1943C2×C101semidirect
429. #1880C2×C101semidirect
430. #1879C2×C101semidirect
431. #1752C2×C101semidirect
432. C101#25422direct (N × H)
496. C2×SD16D4×C101semidirect
551. #107D4×C101semidirect
772. C8#121×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C1012
C2×#466×C1012
C2×#465×C1012
C2×#440×C1012
C101×#24282
C101×#24262
C101×#20422
C101×#20412
C101×#20002
C101×#19992
C101×#19722
C101×#19432
C101×#18802
C101×#18792
C101×#17522
#25422101