Finite Group Databasebeta

← C101×#18252 #38800403

Subgroups — C101×#18252 #38800403

Order 25856.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3534C211yesmaximal, characteristic, complemented
2C101×#3006C211yesmaximal, characteristic, complemented
3C101×#3002C211yesmaximal, characteristic, complemented
4C101×#2430C211yesmaximal, characteristic, complemented
5C101×#1606C211yesmaximal, characteristic, complemented
6C101×#1604C211yesmaximal, characteristic, complemented
7C101×#1603C211yesmaximal, characteristic, complemented
8C101×#1601C211yesmaximal, characteristic, complemented
9C101×#1600C211yesmaximal, characteristic, complemented
10C101×#1598C211yesmaximal, characteristic, complemented
11C101×#1597C211yesmaximal, characteristic, complemented
12C101×#1595C211yesmaximal, characteristic, complemented
13C101×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C101C211yesmaximal, characteristic, complemented
15C101×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C101—21no—
18C2×#135×C101—21no—
19#562×C101—21no—
20#560×C101—21no—
21#553×C101—21no—
22#551×C101—21no—
23#546×C101—21no—
24#546×C101—21no—
25#546×C101—21no—
26D42×C101—21no—
27#540×C101—21no—
28#539×C101—21no—
29#539×C101C2211yescharacteristic
30#538×C101—21no—
31#538×C101C2211yescharacteristic
32#537×C101C2211yescharacteristic
33#534×C101—21no—
34#534×C101C2211yescharacteristic
35#525×C101C2211yescharacteristic
36C2×#123×C101C2211yescharacteristic
37C2×#121×C101—21no—
38C2×#121×C101C2211yescharacteristic
39#452×C101—21no—
40#451×C101C2211yescharacteristic, complemented
41#450×C101C2211yescharacteristic, complemented
42#449×C101—21no—
43#449×C101—21no—
44#449×C101—21no—
45#448×C101C2211yescharacteristic
46#448×C101C2211yescharacteristic, complemented
47#448×C101C2211yescharacteristic, complemented
48#447×C101C2211yescharacteristic
49#447×C101C2211yescharacteristic, complemented
50#447×C101C2211yescharacteristic, complemented
51#417×C101—21no—
52#416×C101—21no—
53#407×C101C2211yescharacteristic, complemented
54C2×C22⋊C8×C101C2211yescharacteristic, complemented
55#395×C101C2211yescharacteristic, complemented
56#394×C101C2211yescharacteristic, complemented
57#393×C101C2211yescharacteristic, complemented
58#392×C101C2211yescharacteristic, complemented
59#386×C101—21no—
60#386×C101—21no—
61#385×C101—21no—
62C2×#95×C101C2211yescharacteristic, complemented
63#328×C101C2211yescharacteristic, complemented
64#328×C101C2211yescharacteristic, complemented
65#327×C101C2211yescharacteristic
66#327×C101C2211yescharacteristic
67#327×C101C2211yescharacteristic, complemented
68#327×C101C2211yescharacteristic, complemented
69#327×C101C2211yescharacteristic, complemented
70#327×C101C2211yescharacteristic, complemented
71#324×C101C2211yescharacteristic, complemented
72#324×C101C2211yescharacteristic, complemented
73#323×C101C2211yescharacteristic, complemented
74#323×C101C2211yescharacteristic, complemented
75C2×#41×C101—21no—
76C2×#41×C101—21no—
77C2×#41×C101—21no—
78C2×#41×C101—21no—
79C2×#41×C101—21no—
80C2×#41×C101—44no—
81C2×#41×C101D411yescharacteristic, complemented
82C22×Q8×C101C2311yescharacteristic
83C22×D4×C101—21no—
84C22×D4×C101—21no—
85C22×D4×C101—21no—
86C22×D4×C101—21no—
87C22×D4×C101—21no—
88C22×D4×C101D411yescharacteristic
89C22×D4×C101D411yescharacteristic, complemented
90C22×D4×C101C2311yescharacteristic
91C23×C4×C101—21no—
92C23×C4×C101—21no—
93C23×C4×C101C2311yescharacteristic
94AGL(1,ℤ/8)×C101—44no—
95#135×C101—44no—
96C2×Q16×C101—21no—
97C2×SD16×C101—21no—
98C2×SD16×C101—21no—
99C2×SD16×C101—21no—
100C2×SD16×C101—21no—
101C2×D8×C101—21no—
102C2×D8×C101—21no—
103C2×D8×C101—21no—
104C2×M16×C101—21no—
105C22×C8×C101—21no—
106#127×C101—21no—
107#126×C101—21no—
108#126×C101—21no—
109#126×C101—21no—
110#126×C101—21no—
111#125×C101—21no—
112#125×C101—21no—
113#124×C101—21no—
114#124×C101—21no—
115#124×C101—21no—
116#123×C101—21no—
117#123×C101—21no—
118#123×C101—21no—
119#123×C101—21no—
120#123×C101—21no—
121#123×C101—21no—
122#123×C101—21no—
123#123×C101—21no—
124#123×C101—21no—
125#123×C101—21no—
126#123×C101—21no—
127#123×C101—21no—
128#123×C101—21no—
129#123×C101—21no—
130C22⋊Q8×C101—21no—
131C22⋊Q8×C101—21no—
132C22⋊Q8×C101—21no—
133C22⋊Q8×C101—21no—
134C22⋊Q8×C101—21no—
135C22⋊Q8×C101D411yescharacteristic, complemented
136C22⋊Q8×C101C2311yescharacteristic
137#121×C101—21no—
138#121×C101—21no—
139#121×C101—21no—
140#121×C101—21no—
141#121×C101—21no—
142#121×C101—21no—
143#121×C101—21no—
144#121×C101—21no—
145#121×C101—21no—
146#121×C101—21no—
147#121×C101—21no—
148#121×C101—21no—
149#121×C101—21no—
150#121×C101—21no—
151#121×C101—21no—
152#121×C101—44no—
153#121×C101D411yescharacteristic, complemented
154#121×C101D411yescharacteristic, complemented
155#121×C101D411yescharacteristic, complemented
156#121×C101C2311yescharacteristic
157#121×C101C2311yescharacteristic
158#121×C101C2311yescharacteristic
159#120×C101—21no—
160#120×C101—21no—
161#120×C101—21no—
162#120×C101—21no—
163#120×C101—21no—
164#120×C101—21no—
165#120×C101—21no—
166#120×C101—21no—
167C4×D4×C101—21no—
168C4×D4×C101—21no—
169C4×D4×C101—21no—
170C4×D4×C101—21no—
171C4×D4×C101—21no—
172C4×D4×C101—21no—
173C4×D4×C101—21no—
174C4×D4×C101—21no—
175#117×C101—21no—
176#117×C101D411yescharacteristic, complemented
177C2×C4⋊C4×C101—21no—
178C2×C4⋊C4×C101D411yescharacteristic
179C2×C4⋊C4×C101D411yescharacteristic, complemented
180C2×C4⋊C4×C101C2311yescharacteristic
181C2×C22⋊C4×C101—21no—
182C2×C22⋊C4×C101—21no—
183C2×C22⋊C4×C101—21no—
184C2×C22⋊C4×C101—21no—
185C2×C22⋊C4×C101—21no—
186C2×C22⋊C4×C101—21no—
187C2×C22⋊C4×C101—21no—
188C2×C22⋊C4×C101D411yescharacteristic
189C2×C22⋊C4×C101D411yescharacteristic
190C2×C22⋊C4×C101C2311yescharacteristic
191#103×C101—21no—
192#103×C101—21no—
193#103×C101—21no—
194#103×C101—21no—
195#102×C101—21no—
196#102×C101—21no—
197#102×C101—21no—
198#102×C101—21no—
199C22⋊C8×C101—21no—
200C22⋊C8×C101—21no—
201C22⋊C8×C101C2311yescharacteristic
202C22⋊C8×C101C2311yescharacteristic
203C22⋊C8×C101C2311yescharacteristic
204C22⋊C8×C101C2311yescharacteristic
205#95×C101—21no—
206#95×C101—21no—
207#95×C101—21no—
208#95×C101C2311yescharacteristic
209#95×C101C2311yescharacteristic
210C24×C101—21no—
211C24×C101—21no—
212C24×C101—21no—
213C24×C101C2×D411yescharacteristic
214C24×C101C2×D411yescharacteristic
215#41×C101—24no—
216#41×C101—24no—
217#41×C101—42no—
218#41×C101—42no—
219#41×C101—42no—
220#41×C101—42no—
221#41×C101—42no—
222#41×C101—42no—
223#41×C101—42no—
224#41×C101—81no—
225#41×C101—81no—
226C2×Q8×C101—21no—
227C2×Q8×C101—21no—
228C2×Q8×C101—21no—
229C2×Q8×C101—42no—
230C2×Q8×C101C2×D411yescharacteristic
231C2×D4×C101—24no—
232C2×D4×C101—21no—
233C2×D4×C101—21no—
234C2×D4×C101—21no—
235C2×D4×C101—21no—
236C2×D4×C101—21no—
237C2×D4×C101—21no—
238C2×D4×C101—21no—
239C2×D4×C101—21no—
240C2×D4×C101—21no—
241C2×D4×C101—21no—
242C2×D4×C101—21no—
243C2×D4×C101—21no—
244C2×D4×C101—21no—
245C2×D4×C101—21no—
246C2×D4×C101—21no—
247C2×D4×C101—21no—
248C2×D4×C101—21no—
249C2×D4×C101—21no—
250C2×D4×C101—21no—
251C2×D4×C101—42no—
252C2×D4×C101—42no—
253C2×D4×C101—42no—
254C2×D4×C101—42no—
255C2×D4×C101—41no—
256C2×D4×C101—41no—
257C2×D4×C101—42no—
258C2×D4×C101—42no—
259C2×D4×C101—81no—
260C2×D4×C101—81no—
261C2×D4×C101—81no—
262C2×D4×C101—81no—
263C2×D4×C101—81no—
264C2×D4×C101—82no—
265C2×D4×C101C2×D411yescharacteristic
266C2×D4×C101C2×D411yescharacteristic
267C2×D4×C101C2×D411yescharacteristic
268C22×C4×C101—21no—
269C22×C4×C101—21no—
270C22×C4×C101—21no—
271C22×C4×C101—21no—
272C22×C4×C101—21no—
273C22×C4×C101—21no—
274C22×C4×C101—21no—
275C22×C4×C101—21no—
276C22×C4×C101—21no—
277C22×C4×C101—21no—
278C22×C4×C101—42no—
279C22×C4×C101—42no—
280C22×C4×C101—42no—
281C22×C4×C101—42no—
282C22×C4×C101—41no—
283C22×C4×C101—41no—
284C22×C4×C101—42no—
285C22×C4×C101—81no—
286C22×C4×C101C2×D411yescharacteristic
287C22×C4×C101C2×D411yescharacteristic
288C22×C4×C101C2×D411yescharacteristic
289C22×C4×C101C2×D411yescharacteristic
290C22×C4×C101C2×D411yescharacteristic
291C22×C4×C101C2×D411yescharacteristic
292C22×C4×C101C2×D411yescharacteristic
293C22×C4×C101C2×D411yescharacteristic
294C22×C4×C101C2411yescharacteristic
295Q16×C101—42no—
296SD16×C101—42no—
297SD16×C101—42no—
298SD16×C101—42no—
299SD16×C101—42no—
300D8×C101—42no—
301D8×C101—42no—
302D8×C101—42no—
303M16×C101—42no—
304C2×C8×C101—21no—
305C2×C8×C101—21no—
306C2×C8×C101—21no—
307C2×C8×C101—21no—
308C2×C8×C101—42no—
309C4⋊C4×C101—21no—
310C4⋊C4×C101—21no—
311C4⋊C4×C101—21no—
312C4⋊C4×C101—21no—
313C4⋊C4×C101—21no—
314C4⋊C4×C101—21no—
315C4⋊C4×C101—21no—
316C4⋊C4×C101—21no—
317C4⋊C4×C101—21no—
318C4⋊C4×C101—21no—
319C4⋊C4×C101—21no—
320C4⋊C4×C101—21no—
321C4⋊C4×C101—21no—
322C4⋊C4×C101—42no—
323C4⋊C4×C101C2×D411yescharacteristic
324C4⋊C4×C101C2×D411yescharacteristic
325C4⋊C4×C101C2×D411yescharacteristic
326C4⋊C4×C101C2×D411yescharacteristic
327C22⋊C4×C101—21no—
328C22⋊C4×C101—21no—
329C22⋊C4×C101—21no—
330C22⋊C4×C101—21no—
331C22⋊C4×C101—21no—
332C22⋊C4×C101—21no—
333C22⋊C4×C101—21no—
334C22⋊C4×C101—21no—
335C22⋊C4×C101—21no—
336C22⋊C4×C101—21no—
337C22⋊C4×C101—21no—
338C22⋊C4×C101—21no—
339C22⋊C4×C101—21no—
340C22⋊C4×C101—21no—
341C22⋊C4×C101—21no—
342C22⋊C4×C101—21no—
343C22⋊C4×C101—21no—
344C22⋊C4×C101—21no—
345C22⋊C4×C101—21no—
346C22⋊C4×C101—21no—
347C22⋊C4×C101—21no—
348C22⋊C4×C101—21no—
349C22⋊C4×C101—21no—
350C22⋊C4×C101—21no—
351C22⋊C4×C101—21no—
352C22⋊C4×C101—42no—
353C22⋊C4×C101—42no—
354C22⋊C4×C101—42no—
355C22⋊C4×C101—81no—
356C42×C101—21no—
357C42×C101—21no—
358C42×C101—21no—
359C23×C101—21no—
360C23×C101—21no—
361C23×C101—22no—
362C23×C101—22no—
363C23×C101—21no—
364C23×C101—21no—
365C23×C101—21no—
366C23×C101—21no—
367C23×C101—21no—
368C23×C101—21no—
369C23×C101—41no—
370C23×C101—41no—
371C23×C101—41no—
372C23×C101—41no—
373C23×C101—41no—
374C23×C101—41no—
375C23×C101—41no—
376C23×C101—41no—
377C23×C101—41no—
378C23×C101—42no—
379C23×C101—81no—
380C23×C101—81no—
381C23×C101—81no—
382C23×C101—81no—
383C23×C101—81no—
384C23×C101#12011yescharacteristic
385C23×C101#12011yescharacteristic
386C23×C101C22×D411yescharacteristic
387Q8×C101—22no—
388Q8×C101—22no—
389Q8×C101—41no—
390Q8×C101—41no—
391Q8×C101—41no—
392Q8×C101—81no—
393D4×C101—22no—
394D4×C101—22no—
395D4×C101—41no—
396D4×C101—41no—
397D4×C101—41no—
398D4×C101—41no—
399D4×C101—41no—
400D4×C101—44no—
401D4×C101—41no—
402D4×C101—41no—
403D4×C101—41no—
404D4×C101—41no—
405D4×C101—41no—
406D4×C101—41no—
407D4×C101—44no—
408D4×C101—42no—
409D4×C101—42no—
410D4×C101—81no—
411D4×C101—81no—
412D4×C101—81no—
413D4×C101—81no—
414D4×C101—81no—
415D4×C101—81no—
416D4×C101—81no—
417D4×C101—81no—
418D4×C101—81no—
419D4×C101—81no—
420D4×C101—81no—
421D4×C101—81no—
422D4×C101—84no—
423C2×C4×C101—22no—
424C2×C4×C101—22no—
425C2×C4×C101—22no—
426C2×C4×C101—22no—
427C2×C4×C101—21no—
428C2×C4×C101—21no—
429C2×C4×C101—21no—
430C2×C4×C101—21no—
431C2×C4×C101—21no—
432C2×C4×C101—21no—
433C2×C4×C101—21no—
434C2×C4×C101—21no—
435C2×C4×C101—21no—
436C2×C4×C101—21no—
437C2×C4×C101—41no—
438C2×C4×C101—41no—
439C2×C4×C101—41no—
440C2×C4×C101—41no—
441C2×C4×C101—44no—
442C2×C4×C101—44no—
443C2×C4×C101—41no—
444C2×C4×C101—41no—
445C2×C4×C101—41no—
446C2×C4×C101—41no—
447C2×C4×C101—41no—
448C2×C4×C101—41no—
449C2×C4×C101—41no—
450C2×C4×C101—41no—
451C2×C4×C101—41no—
452C2×C4×C101—81no—
453C2×C4×C101—81no—
454C2×C4×C101—81no—
455C2×C4×C101—81no—
456C2×C4×C101—81no—
457C2×C4×C101—81no—
458C2×C4×C101—81no—
459C2×C4×C101—84no—
460C2×C4×C101#12011yescharacteristic
461C2×C4×C101#12011yescharacteristic
462C2×C4×C101C22×D411yescharacteristic
463C2×C4×C101C22×D411yescharacteristic
464C8×C101—41no—
465C8×C101—41no—
466C8×C101—41no—
467C8×C101—41no—
468C22×C101—21no—
469C22×C101—21no—
470C22×C101—21no—
471C22×C101—21no—
472C22×C101—21no—
473C22×C101—21no—
474C22×C101—21no—
475C22×C101—42no—
476C22×C101—42no—
477C22×C101—42no—
478C22×C101—42no—
479C22×C101—41no—
480C22×C101—41no—
481C22×C101—41no—
482C22×C101—41no—
483C22×C101—41no—
484C22×C101—41no—
485C22×C101—41no—
486C22×C101—41no—
487C22×C101—42no—
488C22×C101—41no—
489C22×C101—41no—
490C22×C101—41no—
491C22×C101—41no—
492C22×C101—81no—
493C22×C101—81no—
494C22×C101—81no—
495C22×C101—81no—
496C22×C101—81no—
497C22×C101—81no—
498C22×C101—162no—
499C22×C101—162no—
500C22×C101B(4,𝔽2)12yes—
501C22×C101C2×#12011yescharacteristic
502C22×C101#57611yescharacteristic
503C22×C101#57711yescharacteristic
504C4×C101—21no—
505C4×C101—21no—
506C4×C101—21no—
507C4×C101—21no—
508C4×C101—42no—
509C4×C101—41no—
510C4×C101—41no—
511C4×C101—41no—
512C4×C101—41no—
513C4×C101—41no—
514C4×C101—41no—
515C4×C101—42no—
516C4×C101—41no—
517C4×C101—41no—
518C4×C101—81no—
519#18252C10111yesmaximal, characteristic, direct product factor, Sylow
520C2×C101—21no—
521C2×C101—21no—
522C2×C101—22no—
523C2×C101—41no—
524C2×C101—82no—
525C2×C101—81no—
526C2×C101—81no—
527C2×C101—81no—
528C2×C101—81no—
529C2×C101#301211yescharacteristic
530C2×C101#301811yescharacteristic
531C2×C101C2×B(4,𝔽2)11yescharacteristic
532#3534C2×C10111yescharacteristic, complemented
533#3006C2×C10111yescharacteristic, complemented
534#3002C2×C10111yescharacteristic, complemented
535#2430C2×C10111yescharacteristic, complemented
536#1606C2×C10111yescharacteristic, complemented
537#1604C2×C10111yescharacteristic, complemented
538#1603C2×C10111yescharacteristic, complemented
539#1601C2×C10111yescharacteristic, complemented
540#1600C2×C10111yescharacteristic, complemented
541#1598C2×C10111yescharacteristic, complemented
542#1597C2×C10111yescharacteristic, complemented
543#1595C2×C10111yescharacteristic, complemented
544#1504C2×C10111yescharacteristic, complemented
545C2×#327C2×C10111yescharacteristic, complemented
546#1468C2×C10111yescharacteristic, complemented
547C101#1825211yescharacteristic, direct product factor, Sylow
548C22×#41C22×C10111yescharacteristic, complemented
549C2×AGL(1,ℤ/8)—21no—
550C2×#135—21no—
551#562—21no—
552#560—21no—
553#553—21no—
554#551—21no—
555#546—21no—
556#546—21no—
557#546—21no—
558D42—21no—
559#540—21no—
560#539—21no—
561#539C22×C10111yescharacteristic
562#538—21no—
563#538C22×C10111yescharacteristic
564#537C22×C10111yescharacteristic
565#534—21no—
566#534C22×C10111yescharacteristic
567#525C22×C10111yescharacteristic
568C2×#123C22×C10111yescharacteristic
569C2×#121—21no—
570C2×#121C22×C10111yescharacteristic
571#452—21no—
572#451C22×C10111yescharacteristic, complemented
573#450C22×C10111yescharacteristic, complemented
574#449—21no—
575#449—21no—
576#449—21no—
577#448C22×C10111yescharacteristic
578#448C22×C10111yescharacteristic, complemented
579#448C22×C10111yescharacteristic, complemented
580#447C22×C10111yescharacteristic
581#447C22×C10111yescharacteristic, complemented
582#447C22×C10111yescharacteristic, complemented
583#417—21no—
584#416—21no—
585#407C22×C10111yescharacteristic, complemented
586C2×C22⋊C8C22×C10111yescharacteristic, complemented
587#395C22×C10111yescharacteristic, complemented
588#394C22×C10111yescharacteristic, complemented
589#393C22×C10111yescharacteristic, complemented
590#392C22×C10111yescharacteristic, complemented
591#386—21no—
592#386—21no—
593#385—21no—
594C2×#95C22×C10111yescharacteristic, complemented
595#328C22×C10111yescharacteristic, complemented
596#328C22×C10111yescharacteristic, complemented
597#327C22×C10111yescharacteristic
598#327C22×C10111yescharacteristic
599#327C22×C10111yescharacteristic, complemented
600#327C22×C10111yescharacteristic, complemented
601#327C22×C10111yescharacteristic, complemented
602#327C22×C10111yescharacteristic, complemented
603#324C22×C10111yescharacteristic, complemented
604#324C22×C10111yescharacteristic, complemented
605#323C22×C10111yescharacteristic, complemented
606#323C22×C10111yescharacteristic, complemented
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C10111yescharacteristic, complemented
614C22×Q8C23×C10111yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C10111yescharacteristic
621C22×D4D4×C10111yescharacteristic, complemented
622C22×D4C23×C10111yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C10111yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C10111yescharacteristic, complemented
668C22⋊Q8C23×C10111yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C10111yescharacteristic, complemented
686#121D4×C10111yescharacteristic, complemented
687#121D4×C10111yescharacteristic, complemented
688#121C23×C10111yescharacteristic
689#121C23×C10111yescharacteristic
690#121C23×C10111yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C10111yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C10111yescharacteristic
711C2×C4⋊C4D4×C10111yescharacteristic, complemented
712C2×C4⋊C4C23×C10111yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C10111yescharacteristic
721C2×C22⋊C4D4×C10111yescharacteristic
722C2×C22⋊C4C23×C10111yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C10111yescharacteristic
734C22⋊C8C23×C10111yescharacteristic
735C22⋊C8C23×C10111yescharacteristic
736C22⋊C8C23×C10111yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C10111yescharacteristic
741#95C23×C10111yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C10111yescharacteristic
746C24C2×D4×C10111yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C10111yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C10111yescharacteristic
798C2×D4C2×D4×C10111yescharacteristic
799C2×D4C2×D4×C10111yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C10111yescharacteristic
819C22×C4C2×D4×C10111yescharacteristic
820C22×C4C2×D4×C10111yescharacteristic
821C22×C4C2×D4×C10111yescharacteristic
822C22×C4C2×D4×C10111yescharacteristic
823C22×C4C2×D4×C10111yescharacteristic
824C22×C4C2×D4×C10111yescharacteristic
825C22×C4C2×D4×C10111yescharacteristic
826C22×C4C24×C10111yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C10111yescharacteristic
856C4⋊C4C2×D4×C10111yescharacteristic
857C4⋊C4C2×D4×C10111yescharacteristic
858C4⋊C4C2×D4×C10111yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C10111yescharacteristic
917C23#120×C10111yescharacteristic
918C23C22×D4×C10111yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C10111yescharacteristic
993C2×C4#120×C10111yescharacteristic
994C2×C4C22×D4×C10111yescharacteristic
995C2×C4C22×D4×C10111yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22B(4,𝔽2)×C10112yes—
1033C22C2×#120×C10111yescharacteristic
1034C22#576×C10111yescharacteristic
1035C22#577×C10111yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C101×#301211yescharacteristic
1061C2C101×#301811yescharacteristic
1062C2C2×B(4,𝔽2)×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC22×C4C24×C101
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3534C2semidirect
2. C101×#3006C2semidirect
3. C101×#3002C2semidirect
4. C101×#2430C2semidirect
5. C101×#1606C2semidirect
6. C101×#1604C2semidirect
7. C101×#1603C2semidirect
8. C101×#1601C2semidirect
9. C101×#1600C2semidirect
10. C101×#1598C2semidirect
11. C101×#1597C2semidirect
12. C101×#1595C2semidirect
13. C101×#1504C2semidirect
14. C2×#327×C101C2semidirect
15. C101×#1468C2semidirect
16. C22×#41×C101C22semidirect
40. #451×C101C22semidirect
41. #450×C101C22semidirect
46. #448×C101C22semidirect
47. #448×C101C22semidirect
49. #447×C101C22semidirect
50. #447×C101C22semidirect
53. #407×C101C22semidirect
54. C2×C22⋊C8×C101C22semidirect
55. #395×C101C22semidirect
56. #394×C101C22semidirect
57. #393×C101C22semidirect
58. #392×C101C22semidirect
62. C2×#95×C101C22semidirect
63. #328×C101C22semidirect
64. #328×C101C22semidirect
67. #327×C101C22semidirect
68. #327×C101C22semidirect
69. #327×C101C22semidirect
70. #327×C101C22semidirect
71. #324×C101C22semidirect
72. #324×C101C22semidirect
73. #323×C101C22semidirect
74. #323×C101C22semidirect
81. C2×#41×C101D4semidirect
89. C22×D4×C101D4semidirect
135. C22⋊Q8×C101D4semidirect
153. #121×C101D4semidirect
154. #121×C101D4semidirect
155. #121×C101D4semidirect
176. #117×C101D4semidirect
179. C2×C4⋊C4×C101D4semidirect
519. #18252C101direct (N × H)
532. #3534C2×C101semidirect
533. #3006C2×C101semidirect
534. #3002C2×C101semidirect
535. #2430C2×C101semidirect
536. #1606C2×C101semidirect
537. #1604C2×C101semidirect
538. #1603C2×C101semidirect
539. #1601C2×C101semidirect
540. #1600C2×C101semidirect
541. #1598C2×C101semidirect
542. #1597C2×C101semidirect
543. #1595C2×C101semidirect
544. #1504C2×C101semidirect
545. C2×#327C2×C101semidirect
546. #1468C2×C101semidirect
547. C101#18252direct (N × H)
548. C22×#41C22×C101semidirect
572. #451C22×C101semidirect
573. #450C22×C101semidirect
578. #448C22×C101semidirect
579. #448C22×C101semidirect
581. #447C22×C101semidirect
582. #447C22×C101semidirect
585. #407C22×C101semidirect
586. C2×C22⋊C8C22×C101semidirect
587. #395C22×C101semidirect
588. #394C22×C101semidirect
589. #393C22×C101semidirect
590. #392C22×C101semidirect
594. C2×#95C22×C101semidirect
595. #328C22×C101semidirect
596. #328C22×C101semidirect
599. #327C22×C101semidirect
600. #327C22×C101semidirect
601. #327C22×C101semidirect
602. #327C22×C101semidirect
603. #324C22×C101semidirect
604. #324C22×C101semidirect
605. #323C22×C101semidirect
606. #323C22×C101semidirect
613. C2×#41D4×C101semidirect
621. C22×D4D4×C101semidirect
667. C22⋊Q8D4×C101semidirect
685. #121D4×C101semidirect
686. #121D4×C101semidirect
687. #121D4×C101semidirect
708. #117D4×C101semidirect
711. C2×C4⋊C4D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#35342
C101×#30062
C101×#30022
C101×#24302
C101×#16062
C101×#16042
C101×#16032
C101×#16012
C101×#16002
C101×#15982
C101×#15972
C101×#15952
C101×#15042
C2×#327×C1012
C101×#14682
#18252101