Finite Group Databasebeta

← C101×#25162 #38807313

Subgroups — C101×#25162 #38807313

Order 25856.

1240 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C101C211yesmaximal, characteristic, complemented
2C2×#449×C101C211yesmaximal, characteristic, complemented
3C2×#449×C101C211yesmaximal, characteristic, complemented
4C2×C4×D8×C101C211yesmaximal, characteristic, complemented
5C101×#2428C211yesmaximal, characteristic, complemented
6C101×#2339C211yesmaximal, characteristic, complemented
7C101×#2068C211yesmaximal, characteristic, complemented
8C101×#2034C211yesmaximal, characteristic, complemented
9C101×#2033C211yesmaximal, characteristic, complemented
10C101×#2014C211yesmaximal, characteristic, complemented
11C101×#1968C211yesmaximal, characteristic, complemented
12C101×#1923C211yesmaximal, characteristic, complemented
13C101×#1879C211yesmaximal, characteristic, complemented
14C101×#1877C211yesmaximal, characteristic, complemented
15C101×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C101C2211yescharacteristic
17C22×SD16×C101C2211yescharacteristic
18C22×SD16×C101C2211yescharacteristic
19C22×D8×C101C2211yescharacteristic
20C22×D8×C101C2211yescharacteristic
21C2×#127×C101C2211yescharacteristic
22C2×#121×C101—21no—
23C2×#121×C101C2211yescharacteristic
24C2×#121×C101C2211yescharacteristic
25C2×C4×D4×C101C2211yescharacteristic
26C2×C4×D4×C101C2211yescharacteristic
27C2×C4×D4×C101C2211yescharacteristic
28#459×C101—24no—
29#449×C101—24no—
30#449×C101—24no—
31C4×D8×C101—24no—
32C2×#107×C101C2211yescharacteristic
33C2×#106×C101C2211yescharacteristic
34C2×C4⋊C8×C101C2211yescharacteristic
35C2×#103×C101C2211yescharacteristic
36C2×#103×C101C2211yescharacteristic
37C2×#102×C101C2211yescharacteristic
38C2×#102×C101C2211yescharacteristic
39C2×#102×C101C2211yescharacteristic
40C2×#102×C101C2211yescharacteristic
41C2×#102×C101C2211yescharacteristic
42C2×#102×C101C2211yescharacteristic
43C2×C22⋊C8×C101C2211yescharacteristic
44C2×C22⋊C8×C101C2211yescharacteristic
45C2×C4×C8×C101C2211yescharacteristic
46#394×C101—21no—
47#392×C101—21no—
48#391×C101C2211yescharacteristic
49#391×C101C2211yescharacteristic
50#390×C101C2211yescharacteristic
51#389×C101C2211yescharacteristic
52#386×C101—21no—
53#386×C101—21no—
54#386×C101—21no—
55#381×C101—21no—
56#380×C101C2211yescharacteristic
57C4×C22⋊C4×C101C2211yescharacteristic
58C2×#95×C101—21no—
59#340×C101C2211yescharacteristic
60#340×C101C2211yescharacteristic
61#336×C101C2211yescharacteristic
62#336×C101C2211yescharacteristic
63C2×#41×C101—22no—
64C2×#41×C101—22no—
65C2×#41×C101—22no—
66C2×#41×C101—22no—
67C2×#41×C101—41no—
68C2×#41×C101—41no—
69C22×Q8×C101C2311yescharacteristic
70C22×D4×C101—21no—
71C22×D4×C101—21no—
72C22×D4×C101—21no—
73C22×D4×C101—21no—
74C22×D4×C101—21no—
75C22×D4×C101C2311yescharacteristic
76C22×D4×C101C2311yescharacteristic
77C22×D4×C101C2311yescharacteristic
78C23×C4×C101—21no—
79C23×C4×C101—21no—
80C23×C4×C101—21no—
81C23×C4×C101—21no—
82C23×C4×C101C2311yescharacteristic
83C2×SD16×C101—22no—
84C2×SD16×C101—22no—
85C2×SD16×C101—22no—
86C2×SD16×C101—22no—
87C2×SD16×C101—41no—
88C2×SD16×C101—41no—
89C2×D8×C101—22no—
90C2×D8×C101—22no—
91C2×D8×C101—22no—
92C2×D8×C101—22no—
93C2×D8×C101—22no—
94C2×D8×C101D414yescomplemented
95C22×C8×C101C2311yescharacteristic
96C22×C8×C101C2311yescharacteristic
97C22×C8×C101C2311yescharacteristic
98C22×C8×C101C2311yescharacteristic
99#127×C101—22no—
100#127×C101—41no—
101#121×C101—22no—
102#121×C101—22no—
103#121×C101—44no—
104#121×C101—41no—
105#121×C101—41no—
106C4×D4×C101—22no—
107C4×D4×C101—22no—
108C4×D4×C101—22no—
109C4×D4×C101—41no—
110C4×D4×C101—41no—
111C4×D4×C101—41no—
112C2×C4⋊C4×C101—21no—
113C2×C4⋊C4×C101C2311yescharacteristic
114C2×C4⋊C4×C101C2311yescharacteristic
115C2×C4⋊C4×C101C2311yescharacteristic
116C2×C4⋊C4×C101C2311yescharacteristic
117C2×C22⋊C4×C101—21no—
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×C101D411yescharacteristic
126C2×C22⋊C4×C101D411yescharacteristic
127C2×C42×C101C2311yescharacteristic
128C2×C42×C101C2311yescharacteristic
129#107×C101—22no—
130#106×C101—41no—
131C4⋊C8×C101—22no—
132#103×C101—22no—
133#103×C101—22no—
134#102×C101—22no—
135#102×C101—22no—
136#102×C101—22no—
137#102×C101—22no—
138#102×C101—41no—
139#102×C101D414yescomplemented
140C22⋊C8×C101—22no—
141C22⋊C8×C101—22no—
142C4×C8×C101—22no—
143#95×C101—21no—
144#95×C101—21no—
145#95×C101—21no—
146#95×C101—21no—
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
155#41×C101—44no—
156#41×C101—44no—
157#41×C101—44no—
158#41×C101—44no—
159C2×Q8×C101—21no—
160C2×Q8×C101—21no—
161C2×Q8×C101—21no—
162C2×Q8×C101—21no—
163C2×Q8×C101—21no—
164C2×Q8×C101#4112yes—
165C2×D4×C101—24no—
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—21no—
179C2×D4×C101—21no—
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—42no—
189C2×D4×C101—42no—
190C2×D4×C101—81no—
191C2×D4×C101—81no—
192C2×D4×C101—81no—
193C2×D4×C101—81no—
194C2×D4×C101C2×D412yes—
195C2×D4×C101C2×D412yes—
196C2×D4×C101C2×D412yes—
197C2×D4×C101#4112yes—
198C22×C4×C101—24no—
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—21no—
206C22×C4×C101—21no—
207C22×C4×C101—21no—
208C22×C4×C101—21no—
209C22×C4×C101—21no—
210C22×C4×C101—42no—
211C22×C4×C101—42no—
212C22×C4×C101—42no—
213C22×C4×C101—42no—
214C22×C4×C101—42no—
215C22×C4×C101—42no—
216C22×C4×C101—42no—
217C22×C4×C101—42no—
218C22×C4×C101—81no—
219C22×C4×C101—81no—
220C22×C4×C101—81no—
221C22×C4×C101C2×D411yescharacteristic
222C22×C4×C101C2×D411yescharacteristic
223C22×C4×C101C2×D411yescharacteristic
224C22×C4×C101C2×D411yescharacteristic
225C22×C4×C101C2×D411yescharacteristic
226C22×C4×C101C2411yescharacteristic
227SD16×C101—44no—
228SD16×C101—44no—
229D8×C101—28no—
230D8×C101—44no—
231C2×C8×C101—21no—
232C2×C8×C101—21no—
233C2×C8×C101—21no—
234C2×C8×C101—21no—
235C2×C8×C101—21no—
236C2×C8×C101—21no—
237C2×C8×C101—21no—
238C2×C8×C101—21no—
239C2×C8×C101—21no—
240C2×C8×C101—21no—
241C2×C8×C101C2×D412yes—
242C2×C8×C101C2×D412yes—
243C4⋊C4×C101—21no—
244C4⋊C4×C101—21no—
245C4⋊C4×C101—21no—
246C4⋊C4×C101—21no—
247C4⋊C4×C101—21no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—42no—
251C4⋊C4×C101C2×D412yes—
252C22⋊C4×C101—22no—
253C22⋊C4×C101—22no—
254C22⋊C4×C101—42no—
255C22⋊C4×C101—42no—
256C22⋊C4×C101—42no—
257C22⋊C4×C101—42no—
258C22⋊C4×C101—42no—
259C22⋊C4×C101—42no—
260C22⋊C4×C101—81no—
261C22⋊C4×C101—81no—
262C42×C101—21no—
263C42×C101—21no—
264C42×C101—21no—
265C42×C101—21no—
266C23×C101—22no—
267C23×C101—22no—
268C23×C101—22no—
269C23×C101—21no—
270C23×C101—22no—
271C23×C101—21no—
272C23×C101—21no—
273C23×C101—21no—
274C23×C101—21no—
275C23×C101—21no—
276C23×C101—21no—
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×C101—41no—
289C23×C101—41no—
290C23×C101—41no—
291C23×C101—41no—
292C23×C101—41no—
293C23×C101—41no—
294C23×C101C22×D411yescharacteristic
295Q8×C101—22no—
296Q8×C101—22no—
297Q8×C101—41no—
298Q8×C101—41no—
299D4×C101—22no—
300D4×C101—22no—
301D4×C101—22no—
302D4×C101—22no—
303D4×C101—22no—
304D4×C101—48no—
305D4×C101—41no—
306D4×C101—41no—
307D4×C101—41no—
308D4×C101—41no—
309D4×C101—41no—
310D4×C101—41no—
311D4×C101—84no—
312D4×C101—84no—
313D4×C101—84no—
314D4×C101—84no—
315D4×C101#12114yescomplemented
316C2×C4×C101—21no—
317C2×C4×C101—21no—
318C2×C4×C101—21no—
319C2×C4×C101—21no—
320C2×C4×C101—21no—
321C2×C4×C101—22no—
322C2×C4×C101—21no—
323C2×C4×C101—21no—
324C2×C4×C101—22no—
325C2×C4×C101—21no—
326C2×C4×C101—21no—
327C2×C4×C101—21no—
328C2×C4×C101—21no—
329C2×C4×C101—21no—
330C2×C4×C101—21no—
331C2×C4×C101—48no—
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—41no—
346C2×C4×C101—41no—
347C2×C4×C101—41no—
348C2×C4×C101—41no—
349C2×C4×C101—84no—
350C2×C4×C101—84no—
351C2×C4×C101—84no—
352C2×C4×C101#13512yes—
353C2×C4×C101AGL(1,ℤ/8)12yes—
354C2×C4×C101C22×D411yescharacteristic
355C2×C4×C101C22×D411yescharacteristic
356C2×C4×C101C2×#4111yescharacteristic
357C2×C4×C101C2×#4111yescharacteristic
358C2×C4×C101H(5,𝔽2)11yescharacteristic
359C2×C4×C101H(5,𝔽2)11yescharacteristic
360C8×C101—22no—
361C8×C101—22no—
362C8×C101—41no—
363C8×C101—41no—
364C22×C101—24no—
365C22×C101—42no—
366C22×C101—42no—
367C22×C101—42no—
368C22×C101—42no—
369C22×C101—42no—
370C22×C101—42no—
371C22×C101—41no—
372C22×C101—41no—
373C22×C101—41no—
374C22×C101—42no—
375C22×C101—41no—
376C22×C101—41no—
377C22×C101—42no—
378C22×C101—42no—
379C22×C101—41no—
380C22×C101—41no—
381C22×C101—81no—
382C22×C101—81no—
383C22×C101—81no—
384C22×C101—81no—
385C22×C101—81no—
386C22×C101—81no—
387C22×C101—81no—
388C22×C101—81no—
389C22×C101—81no—
390C22×C101—81no—
391C22×C101—81no—
392C22×C101#52511yescharacteristic
393C22×C101D4211yescharacteristic
394C22×C101D4211yescharacteristic
395C22×C101C2×#13511yescharacteristic
396C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C101#57611yescharacteristic
398C22×C101#57711yescharacteristic
399C4×C101—22no—
400C4×C101—22no—
401C4×C101—41no—
402C4×C101—42no—
403C4×C101—42no—
404C4×C101—41no—
405C4×C101—41no—
406C4×C101—81no—
407C4×C101—81no—
408C4×C101—81no—
409C4×C101C2×#12111yescharacteristic
410C4×C101#53811yescharacteristic
411C4×C101#54611yescharacteristic
412C4×C101#54611yescharacteristic
413#25162C10111yesmaximal, characteristic, direct product factor, Sylow
414C2×C101—44no—
415C2×C101—81no—
416C2×C101—82no—
417C2×C101—161no—
418C2×C101#242411yescharacteristic
419C2×C101#310611yescharacteristic
420C2×C101#311911yescharacteristic
421C2×C101#326411yescharacteristic
422C2×C101#327211yescharacteristic
423C2×C101#328011yescharacteristic
424C2×C101#328411yescharacteristic
425C2×#459C2×C10111yescharacteristic, complemented
426C2×#449C2×C10111yescharacteristic, complemented
427C2×#449C2×C10111yescharacteristic, complemented
428C2×C4×D8C2×C10111yescharacteristic, complemented
429#2428C2×C10111yescharacteristic, complemented
430#2339C2×C10111yescharacteristic, complemented
431#2068C2×C10111yescharacteristic, complemented
432#2034C2×C10111yescharacteristic, complemented
433#2033C2×C10111yescharacteristic, complemented
434#2014C2×C10111yescharacteristic, complemented
435#1968C2×C10111yescharacteristic, complemented
436#1923C2×C10111yescharacteristic, complemented
437#1879C2×C10111yescharacteristic, complemented
438#1877C2×C10111yescharacteristic, complemented
439#1864C2×C10111yescharacteristic, complemented
440C101#2516211yescharacteristic, direct product factor, Sylow
441C22×#41C22×C10111yescharacteristic
442C22×SD16C22×C10111yescharacteristic
443C22×SD16C22×C10111yescharacteristic
444C22×D8C22×C10111yescharacteristic
445C22×D8C22×C10111yescharacteristic
446C2×#127C22×C10111yescharacteristic
447C2×#121—21no—
448C2×#121C22×C10111yescharacteristic
449C2×#121C22×C10111yescharacteristic
450C2×C4×D4C22×C10111yescharacteristic
451C2×C4×D4C22×C10111yescharacteristic
452C2×C4×D4C22×C10111yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456C4×D8—24no—
457C2×#107C22×C10111yescharacteristic
458C2×#106C22×C10111yescharacteristic
459C2×C4⋊C8C22×C10111yescharacteristic
460C2×#103C22×C10111yescharacteristic
461C2×#103C22×C10111yescharacteristic
462C2×#102C22×C10111yescharacteristic
463C2×#102C22×C10111yescharacteristic
464C2×#102C22×C10111yescharacteristic
465C2×#102C22×C10111yescharacteristic
466C2×#102C22×C10111yescharacteristic
467C2×#102C22×C10111yescharacteristic
468C2×C22⋊C8C22×C10111yescharacteristic
469C2×C22⋊C8C22×C10111yescharacteristic
470C2×C4×C8C22×C10111yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C10111yescharacteristic
474#391C22×C10111yescharacteristic
475#390C22×C10111yescharacteristic
476#389C22×C10111yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C10111yescharacteristic
482C4×C22⋊C4C22×C10111yescharacteristic
483C2×#95—21no—
484#340C22×C10111yescharacteristic
485#340C22×C10111yescharacteristic
486#336C22×C10111yescharacteristic
487#336C22×C10111yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C10111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C10111yescharacteristic
501C22×D4C23×C10111yescharacteristic
502C22×D4C23×C10111yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C10111yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C10114yescomplemented
520C22×C8C23×C10111yescharacteristic
521C22×C8C23×C10111yescharacteristic
522C22×C8C23×C10111yescharacteristic
523C22×C8C23×C10111yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C10111yescharacteristic
539C2×C4⋊C4C23×C10111yescharacteristic
540C2×C4⋊C4C23×C10111yescharacteristic
541C2×C4⋊C4C23×C10111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C10111yescharacteristic
551C2×C22⋊C4D4×C10111yescharacteristic
552C2×C42C23×C10111yescharacteristic
553C2×C42C23×C10111yescharacteristic
554#107—22no—
555#106—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C10114yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C10111yescharacteristic
575#95D4×C10111yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C10111yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C10112yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C10112yes—
620C2×D4C2×D4×C10112yes—
621C2×D4C2×D4×C10112yes—
622C2×D4#41×C10112yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C10111yescharacteristic
647C22×C4C2×D4×C10111yescharacteristic
648C22×C4C2×D4×C10111yescharacteristic
649C22×C4C2×D4×C10111yescharacteristic
650C22×C4C2×D4×C10111yescharacteristic
651C22×C4C24×C10111yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C10112yes—
667C2×C8C2×D4×C10112yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C10112yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C10111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C10114yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4#135×C10112yes—
778C2×C4AGL(1,ℤ/8)×C10112yes—
779C2×C4C22×D4×C10111yescharacteristic
780C2×C4C22×D4×C10111yescharacteristic
781C2×C4C2×#41×C10111yescharacteristic
782C2×C4C2×#41×C10111yescharacteristic
783C2×C4H(5,𝔽2)×C10111yescharacteristic
784C2×C4H(5,𝔽2)×C10111yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C10111yescharacteristic
818C22D42×C10111yescharacteristic
819C22D42×C10111yescharacteristic
820C22C2×#135×C10111yescharacteristic
821C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
822C22#576×C10111yescharacteristic
823C22#577×C10111yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—41no—
830C4—41no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C10111yescharacteristic
835C4#538×C10111yescharacteristic
836C4#546×C10111yescharacteristic
837C4#546×C10111yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C101×#242411yescharacteristic
843C2C101×#310611yescharacteristic
844C2C101×#311911yescharacteristic
845C2C101×#326411yescharacteristic
846C2C101×#327211yescharacteristic
847C2C101×#328011yescharacteristic
848C2C101×#328411yescharacteristic
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×#459×C101C2semidirect
2. C2×#449×C101C2semidirect
3. C2×#449×C101C2semidirect
4. C2×C4×D8×C101C2semidirect
5. C101×#2428C2semidirect
6. C101×#2339C2semidirect
7. C101×#2068C2semidirect
8. C101×#2034C2semidirect
9. C101×#2033C2semidirect
10. C101×#2014C2semidirect
11. C101×#1968C2semidirect
12. C101×#1923C2semidirect
13. C101×#1879C2semidirect
14. C101×#1877C2semidirect
15. C101×#1864C2semidirect
94. C2×D8×C101D4semidirect
139. #102×C101D4semidirect
315. D4×C101#121semidirect
413. #25162C101direct (N × H)
425. C2×#459C2×C101semidirect
426. C2×#449C2×C101semidirect
427. C2×#449C2×C101semidirect
428. C2×C4×D8C2×C101semidirect
429. #2428C2×C101semidirect
430. #2339C2×C101semidirect
431. #2068C2×C101semidirect
432. #2034C2×C101semidirect
433. #2033C2×C101semidirect
434. #2014C2×C101semidirect
435. #1968C2×C101semidirect
436. #1923C2×C101semidirect
437. #1879C2×C101semidirect
438. #1877C2×C101semidirect
439. #1864C2×C101semidirect
440. C101#25162direct (N × H)
519. C2×D8D4×C101semidirect
564. #102D4×C101semidirect
740. D4#121×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1012
C2×#449×C1012
C2×C4×D8×C1012
C101×#24282
C101×#23392
C101×#20682
C101×#20342
C101×#20332
C101×#20142
C101×#19682
C101×#19232
C101×#18792
C101×#18772
C101×#18642
#25162101