Finite Group Databasebeta

← C101×#17609 #38799760

Subgroups — C101×#17609 #38799760

Order 25856.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3495C211yesmaximal, characteristic
2C101×#2924C211yesmaximal, characteristic, complemented
3C101×#2343C211yesmaximal, characteristic, complemented
4C101×#1521C211yesmaximal, characteristic, complemented
5C101×#1518C211yesmaximal, characteristic, complemented
6C101×#1516C211yesmaximal, characteristic
7C101×#1515C211yesmaximal, characteristic, complemented
8C101×#1512C211yesmaximal, characteristic, complemented
9C101×#1511C211yesmaximal, characteristic, complemented
10C101×#1509C211yesmaximal, characteristic, complemented
11C101×#1506C211yesmaximal, characteristic, complemented
12C101×#1504C211yesmaximal, characteristic
13C101×#1503C211yesmaximal, characteristic, complemented
14C101×#1500C211yesmaximal, characteristic, complemented
15C2×#328×C101C211yesmaximal, characteristic, complemented
16#556×C101—21no—
17#554×C101—21no—
18#552×C101—21no—
19#552×C101—21no—
20#552×C101—21no—
21#552×C101—21no—
22#551×C101—21no—
23#551×C101—21no—
24#544×C101C411yescharacteristic, complemented
25#542×C101C411yescharacteristic, complemented
26#542×C101C411yescharacteristic, complemented
27#541×C101C411yescharacteristic, complemented
28#541×C101C411yescharacteristic, complemented
29#536×C101C411yescharacteristic, complemented
30#533×C101C2211yescharacteristic
31#533×C101C2211yescharacteristic
32#529×C101C2211yescharacteristic
33#529×C101C2211yescharacteristic
34#525×C101C2211yescharacteristic
35C2×C22⋊Q8×C101C2211yescharacteristic
36#520×C101C411yescharacteristic, complemented
37#519×C101C411yescharacteristic, complemented
38C2×#117×C101C2211yescharacteristic
39#433×C101—21no—
40#433×C101—21no—
41#432×C101C2211yescharacteristic
42#432×C101C2211yescharacteristic
43#431×C101C2211yescharacteristic
44#431×C101C2211yescharacteristic
45#424×C101—21no—
46#407×C101C2211yescharacteristic
47C2×C22⋊C8×C101C2211yescharacteristic
48#405×C101—21no—
49#387×C101—21no—
50#387×C101—21no—
51#385×C101—21no—
52#383×C101C2211yescharacteristic
53#382×C101C2211yescharacteristic
54#381×C101C2211yescharacteristic
55C4×C4⋊C4×C101C2211yescharacteristic
56C4×C22⋊C4×C101—21no—
57#376×C101C2211yescharacteristic
58C2×#95×C101C2211yescharacteristic
59#328×C101C2211yescharacteristic
60#328×C101C2211yescharacteristic
61#328×C101C2211yescharacteristic
62#328×C101C2211yescharacteristic
63#328×C101C2211yescharacteristic
64#328×C101C2211yescharacteristic
65#328×C101C2211yescharacteristic
66#328×C101C2211yescharacteristic
67#328×C101C2211yescharacteristic
68#328×C101C2211yescharacteristic
69#328×C101C2211yescharacteristic
70#328×C101C2211yescharacteristic
71#327×C101C2211yescharacteristic
72#327×C101C2211yescharacteristic
73#327×C101C2211yescharacteristic
74#327×C101C2211yescharacteristic
75C2×#41×C101C2×C411yescharacteristic
76C22×Q8×C101C2×C411yescharacteristic
77C23×C4×C101—21no—
78C23×C4×C101C2311yescharacteristic
79C2×M16×C101—21no—
80C22×C8×C101—21no—
81C4⋊Q8×C101—21no—
82C4⋊Q8×C101C2×C411yescharacteristic, complemented
83C4⋊Q8×C101C2×C411yescharacteristic, complemented
84C4⋊Q8×C101C2×C411yescharacteristic, complemented
85C4⋊Q8×C101C2×C411yescharacteristic, complemented
86#126×C101—21no—
87#126×C101—21no—
88#126×C101—21no—
89#126×C101—21no—
90#126×C101—21no—
91#126×C101—21no—
92#126×C101—21no—
93#126×C101—21no—
94#125×C101—21no—
95#125×C101—21no—
96#125×C101—21no—
97#125×C101—21no—
98#125×C101—21no—
99#125×C101—21no—
100#125×C101—21no—
101#125×C101C2×C411yescharacteristic, complemented
102#125×C101C2×C411yescharacteristic, complemented
103#124×C101—21no—
104#124×C101—21no—
105#124×C101C2×C411yescharacteristic, complemented
106#124×C101C2×C411yescharacteristic, complemented
107#123×C101—21no—
108#123×C101—21no—
109#123×C101—21no—
110#123×C101—21no—
111#123×C101—21no—
112#123×C101—21no—
113#123×C101—21no—
114C22⋊Q8×C101—21no—
115C22⋊Q8×C101—21no—
116C22⋊Q8×C101—21no—
117C22⋊Q8×C101—21no—
118C22⋊Q8×C101—21no—
119C22⋊Q8×C101—21no—
120C22⋊Q8×C101—21no—
121C22⋊Q8×C101—21no—
122C22⋊Q8×C101—21no—
123C22⋊Q8×C101—21no—
124C22⋊Q8×C101C2×C411yescharacteristic
125C22⋊Q8×C101C2×C411yescharacteristic
126C22⋊Q8×C101C2×C411yescharacteristic
127C22⋊Q8×C101C2311yescharacteristic
128C22⋊Q8×C101C2311yescharacteristic
129C22⋊Q8×C101C2311yescharacteristic
130#121×C101C2×C411yescharacteristic
131#121×C101C2311yescharacteristic
132#120×C101—21no—
133C4×Q8×C101—21no—
134C4×Q8×C101—21no—
135C4×Q8×C101—21no—
136C4×Q8×C101—21no—
137C4×Q8×C101C2×C411yescharacteristic, complemented
138C4×Q8×C101C2×C411yescharacteristic, complemented
139C4×Q8×C101C2×C411yescharacteristic, complemented
140C4×Q8×C101C2×C411yescharacteristic, complemented
141C4×Q8×C101C2×C411yescharacteristic, complemented
142C4×Q8×C101C2×C411yescharacteristic, complemented
143C4×D4×C101—21no—
144C4×D4×C101—21no—
145C4×D4×C101—21no—
146C4×D4×C101—21no—
147C4×D4×C101—21no—
148C4×D4×C101—21no—
149C4×D4×C101C2×C411yescharacteristic, complemented
150C4×D4×C101C2×C411yescharacteristic, complemented
151#117×C101—21no—
152#117×C101—21no—
153#117×C101—21no—
154#117×C101—21no—
155#117×C101—21no—
156#117×C101—21no—
157#117×C101—21no—
158#117×C101C2×C411yescharacteristic
159#117×C101C2×C411yescharacteristic
160#117×C101C2×C411yescharacteristic
161#117×C101C2×C411yescharacteristic
162#117×C101C2×C411yescharacteristic
163#117×C101D411yescharacteristic
164#117×C101D411yescharacteristic
165#117×C101D411yescharacteristic
166#117×C101D411yescharacteristic
167C2×C4⋊C4×C101—21no—
168C2×C4⋊C4×C101—21no—
169C2×C4⋊C4×C101—21no—
170C2×C4⋊C4×C101—21no—
171C2×C4⋊C4×C101C2×C411yescharacteristic
172C2×C4⋊C4×C101D411yescharacteristic
173C2×C4⋊C4×C101D411yescharacteristic
174C2×C22⋊C4×C101—21no—
175C2×C22⋊C4×C101—21no—
176C2×C22⋊C4×C101D411yescharacteristic
177C2×C22⋊C4×C101D411yescharacteristic
178C2×C42×C101—21no—
179C2×C42×C101—21no—
180C2×C42×C101C2311yescharacteristic
181C2×C42×C101C2311yescharacteristic
182C4⋊C8×C101—21no—
183C4⋊C8×C101—21no—
184C4⋊C8×C101—21no—
185C4⋊C8×C101—21no—
186C22⋊C8×C101—21no—
187C22⋊C8×C101—21no—
188C22⋊C8×C101C2311yescharacteristic
189C22⋊C8×C101C2311yescharacteristic
190C22⋊C8×C101C2311yescharacteristic
191C22⋊C8×C101C2311yescharacteristic
192#97×C101—21no—
193#97×C101—21no—
194C4×C8×C101—21no—
195C4×C8×C101—21no—
196#95×C101—21no—
197#95×C101—21no—
198#95×C101—21no—
199#95×C101—21no—
200#95×C101—21no—
201#95×C101—21no—
202#95×C101C2311yescharacteristic
203#95×C101C2311yescharacteristic
204#95×C101C2311yescharacteristic
205#95×C101C2311yescharacteristic
206C24×C101C2×D411yescharacteristic
207#41×C101—42no—
208C2×Q8×C101—21no—
209C2×Q8×C101—21no—
210C2×Q8×C101—21no—
211C2×Q8×C101—42no—
212C2×Q8×C101C22×C411yescharacteristic
213C2×Q8×C101C22×C411yescharacteristic
214C2×Q8×C101C22×C411yescharacteristic
215C2×D4×C101—21no—
216C2×D4×C101—21no—
217C2×D4×C101—21no—
218C2×D4×C101C22×C411yescharacteristic
219C22×C4×C101—21no—
220C22×C4×C101—21no—
221C22×C4×C101—21no—
222C22×C4×C101—21no—
223C22×C4×C101—21no—
224C22×C4×C101—21no—
225C22×C4×C101—21no—
226C22×C4×C101—21no—
227C22×C4×C101—21no—
228C22×C4×C101—42no—
229C22×C4×C101—42no—
230C22×C4×C101—42no—
231C22×C4×C101—81no—
232C22×C4×C101C22×C411yescharacteristic
233C22×C4×C101C22×C411yescharacteristic
234C22×C4×C101C2×D411yescharacteristic
235C22×C4×C101C2×D411yescharacteristic
236C22×C4×C101C2×D411yescharacteristic
237C22×C4×C101C2×D411yescharacteristic
238C22×C4×C101C2×D411yescharacteristic
239C22×C4×C101C2×D411yescharacteristic
240C22×C4×C101C2×D411yescharacteristic
241C22×C4×C101C2411yescharacteristic
242M16×C101—42no—
243C2×C8×C101—21no—
244C2×C8×C101—21no—
245C2×C8×C101—21no—
246C2×C8×C101—21no—
247C2×C8×C101—42no—
248C4⋊C4×C101—21no—
249C4⋊C4×C101—21no—
250C4⋊C4×C101—21no—
251C4⋊C4×C101—21no—
252C4⋊C4×C101—21no—
253C4⋊C4×C101—21no—
254C4⋊C4×C101—21no—
255C4⋊C4×C101—21no—
256C4⋊C4×C101—21no—
257C4⋊C4×C101—21no—
258C4⋊C4×C101—21no—
259C4⋊C4×C101—21no—
260C4⋊C4×C101—21no—
261C4⋊C4×C101—21no—
262C4⋊C4×C101—21no—
263C4⋊C4×C101—21no—
264C4⋊C4×C101—21no—
265C4⋊C4×C101—21no—
266C4⋊C4×C101—21no—
267C4⋊C4×C101—21no—
268C4⋊C4×C101—21no—
269C4⋊C4×C101—21no—
270C4⋊C4×C101—21no—
271C4⋊C4×C101—42no—
272C4⋊C4×C101—81no—
273C4⋊C4×C101C22⋊C411yescharacteristic
274C4⋊C4×C101C22⋊C411yescharacteristic
275C4⋊C4×C101C22⋊C411yescharacteristic
276C4⋊C4×C101C22⋊C411yescharacteristic
277C4⋊C4×C101C22⋊C411yescharacteristic
278C4⋊C4×C101C22⋊C411yescharacteristic
279C4⋊C4×C101C22⋊C411yescharacteristic
280C4⋊C4×C101C22⋊C411yescharacteristic
281C4⋊C4×C101C22×C411yescharacteristic
282C4⋊C4×C101C22×C411yescharacteristic
283C4⋊C4×C101C22×C411yescharacteristic
284C4⋊C4×C101C22×C411yescharacteristic
285C22⋊C4×C101—21no—
286C22⋊C4×C101—21no—
287C22⋊C4×C101—21no—
288C22⋊C4×C101—21no—
289C22⋊C4×C101—21no—
290C22⋊C4×C101—21no—
291C22⋊C4×C101—21no—
292C22⋊C4×C101—21no—
293C22⋊C4×C101—21no—
294C22⋊C4×C101—21no—
295C22⋊C4×C101—21no—
296C22⋊C4×C101—21no—
297C22⋊C4×C101—21no—
298C22⋊C4×C101—21no—
299C22⋊C4×C101—21no—
300C22⋊C4×C101—42no—
301C22⋊C4×C101C22⋊C411yescharacteristic
302C22⋊C4×C101C22⋊C411yescharacteristic
303C22⋊C4×C101C22⋊C411yescharacteristic
304C22⋊C4×C101C22⋊C411yescharacteristic
305C22⋊C4×C101C22⋊C411yescharacteristic
306C22⋊C4×C101C22⋊C411yescharacteristic
307C22⋊C4×C101C22⋊C411yescharacteristic
308C22⋊C4×C101C22⋊C411yescharacteristic
309C42×C101—21no—
310C42×C101—21no—
311C42×C101—21no—
312C42×C101—21no—
313C42×C101—21no—
314C42×C101—21no—
315C42×C101—21no—
316C42×C101—42no—
317C42×C101—81no—
318C42×C101C22×C411yescharacteristic
319C42×C101C22×C411yescharacteristic
320C42×C101C22×C411yescharacteristic
321C42×C101C22×C411yescharacteristic
322C42×C101C2×D411yescharacteristic
323C42×C101C2×D411yescharacteristic
324C42×C101C2×D411yescharacteristic
325C42×C101C2×D411yescharacteristic
326C23×C101—21no—
327C23×C101—21no—
328C23×C101—22no—
329C23×C101—21no—
330C23×C101—41no—
331C23×C101C2×C22⋊C411yescharacteristic
332C23×C101C2×C22⋊C411yescharacteristic
333C23×C101C22×D411yescharacteristic
334Q8×C101—41no—
335Q8×C101—41no—
336Q8×C101—41no—
337Q8×C101—42no—
338Q8×C101—81no—
339Q8×C101—81no—
340D4×C101—41no—
341D4×C101—41no—
342D4×C101—41no—
343D4×C101—42no—
344D4×C101—81no—
345C2×C4×C101—21no—
346C2×C4×C101—21no—
347C2×C4×C101—21no—
348C2×C4×C101—21no—
349C2×C4×C101—22no—
350C2×C4×C101—22no—
351C2×C4×C101—22no—
352C2×C4×C101—21no—
353C2×C4×C101—21no—
354C2×C4×C101—21no—
355C2×C4×C101—21no—
356C2×C4×C101—21no—
357C2×C4×C101—21no—
358C2×C4×C101—21no—
359C2×C4×C101—41no—
360C2×C4×C101—41no—
361C2×C4×C101—41no—
362C2×C4×C101—41no—
363C2×C4×C101—41no—
364C2×C4×C101—41no—
365C2×C4×C101—42no—
366C2×C4×C101—41no—
367C2×C4×C101—41no—
368C2×C4×C101—42no—
369C2×C4×C101—41no—
370C2×C4×C101—41no—
371C2×C4×C101—41no—
372C2×C4×C101—41no—
373C2×C4×C101—41no—
374C2×C4×C101—41no—
375C2×C4×C101—41no—
376C2×C4×C101—41no—
377C2×C4×C101—41no—
378C2×C4×C101—81no—
379C2×C4×C101—81no—
380C2×C4×C101—81no—
381C2×C4×C101—84no—
382C2×C4×C101C2×C22⋊C411yescharacteristic
383C2×C4×C101C2×C22⋊C411yescharacteristic
384C2×C4×C101C2×C22⋊C411yescharacteristic
385C2×C4×C101C2×C22⋊C411yescharacteristic
386C2×C4×C101C2×C22⋊C411yescharacteristic
387C2×C4×C101C2×C22⋊C411yescharacteristic
388C2×C4×C101C2×C22⋊C411yescharacteristic
389C2×C4×C101C2×C22⋊C411yescharacteristic
390C2×C4×C101C2×C22⋊C411yescharacteristic
391C2×C4×C101C2×C22⋊C411yescharacteristic
392C2×C4×C101C23×C411yescharacteristic
393C2×C4×C101C22×D411yescharacteristic
394C8×C101—41no—
395C8×C101—41no—
396C8×C101—41no—
397C8×C101—41no—
398C22×C101—21no—
399C22×C101—21no—
400C22×C101—21no—
401C22×C101—21no—
402C22×C101—21no—
403C22×C101—21no—
404C22×C101—21no—
405C22×C101—42no—
406C22×C101—42no—
407C22×C101—41no—
408C22×C101—41no—
409C22×C101—41no—
410C22×C101#41012yes—
411C22×C101C22×C22⋊C411yescharacteristic
412C22×C101#57711yescharacteristic
413C22×C101#57811yescharacteristic
414C4×C101—21no—
415C4×C101—21no—
416C4×C101—21no—
417C4×C101—21no—
418C4×C101—21no—
419C4×C101—21no—
420C4×C101—21no—
421C4×C101—21no—
422C4×C101—21no—
423C4×C101—21no—
424C4×C101—21no—
425C4×C101—21no—
426C4×C101—42no—
427C4×C101—41no—
428C4×C101—41no—
429C4×C101—41no—
430C4×C101—41no—
431C4×C101—41no—
432C4×C101—41no—
433C4×C101—41no—
434C4×C101—81no—
435C4×C101—81no—
436C4×C101—81no—
437#17609C10111yesmaximal, characteristic, direct product factor, Sylow
438C2×C101—21no—
439C2×C101—21no—
440C2×C101—22no—
441C2×C101—41no—
442C2×C101—81no—
443C2×C101C2×#41011yescharacteristic
444C2×C101#289811yescharacteristic
445C2×C101#290111yescharacteristic
446#3495C2×C10111yescharacteristic
447#2924C2×C10111yescharacteristic, complemented
448#2343C2×C10111yescharacteristic, complemented
449#1521C2×C10111yescharacteristic, complemented
450#1518C2×C10111yescharacteristic, complemented
451#1516C2×C10111yescharacteristic
452#1515C2×C10111yescharacteristic, complemented
453#1512C2×C10111yescharacteristic, complemented
454#1511C2×C10111yescharacteristic, complemented
455#1509C2×C10111yescharacteristic, complemented
456#1506C2×C10111yescharacteristic, complemented
457#1504C2×C10111yescharacteristic
458#1503C2×C10111yescharacteristic, complemented
459#1500C2×C10111yescharacteristic, complemented
460C2×#328C2×C10111yescharacteristic, complemented
461C101#1760911yescharacteristic, direct product factor, Sylow
462#556—21no—
463#554—21no—
464#552—21no—
465#552—21no—
466#552—21no—
467#552—21no—
468#551—21no—
469#551—21no—
470#544C4×C10111yescharacteristic, complemented
471#542C4×C10111yescharacteristic, complemented
472#542C4×C10111yescharacteristic, complemented
473#541C4×C10111yescharacteristic, complemented
474#541C4×C10111yescharacteristic, complemented
475#536C4×C10111yescharacteristic, complemented
476#533C22×C10111yescharacteristic
477#533C22×C10111yescharacteristic
478#529C22×C10111yescharacteristic
479#529C22×C10111yescharacteristic
480#525C22×C10111yescharacteristic
481C2×C22⋊Q8C22×C10111yescharacteristic
482#520C4×C10111yescharacteristic, complemented
483#519C4×C10111yescharacteristic, complemented
484C2×#117C22×C10111yescharacteristic
485#433—21no—
486#433—21no—
487#432C22×C10111yescharacteristic
488#432C22×C10111yescharacteristic
489#431C22×C10111yescharacteristic
490#431C22×C10111yescharacteristic
491#424—21no—
492#407C22×C10111yescharacteristic
493C2×C22⋊C8C22×C10111yescharacteristic
494#405—21no—
495#387—21no—
496#387—21no—
497#385—21no—
498#383C22×C10111yescharacteristic
499#382C22×C10111yescharacteristic
500#381C22×C10111yescharacteristic
501C4×C4⋊C4C22×C10111yescharacteristic
502C4×C22⋊C4—21no—
503#376C22×C10111yescharacteristic
504C2×#95C22×C10111yescharacteristic
505#328C22×C10111yescharacteristic
506#328C22×C10111yescharacteristic
507#328C22×C10111yescharacteristic
508#328C22×C10111yescharacteristic
509#328C22×C10111yescharacteristic
510#328C22×C10111yescharacteristic
511#328C22×C10111yescharacteristic
512#328C22×C10111yescharacteristic
513#328C22×C10111yescharacteristic
514#328C22×C10111yescharacteristic
515#328C22×C10111yescharacteristic
516#328C22×C10111yescharacteristic
517#327C22×C10111yescharacteristic
518#327C22×C10111yescharacteristic
519#327C22×C10111yescharacteristic
520#327C22×C10111yescharacteristic
521C2×#41C2×C4×C10111yescharacteristic
522C22×Q8C2×C4×C10111yescharacteristic
523C23×C4—21no—
524C23×C4C23×C10111yescharacteristic
525C2×M16—21no—
526C22×C8—21no—
527C4⋊Q8—21no—
528C4⋊Q8C2×C4×C10111yescharacteristic, complemented
529C4⋊Q8C2×C4×C10111yescharacteristic, complemented
530C4⋊Q8C2×C4×C10111yescharacteristic, complemented
531C4⋊Q8C2×C4×C10111yescharacteristic, complemented
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—21no—
537#126—21no—
538#126—21no—
539#126—21no—
540#125—21no—
541#125—21no—
542#125—21no—
543#125—21no—
544#125—21no—
545#125—21no—
546#125—21no—
547#125C2×C4×C10111yescharacteristic, complemented
548#125C2×C4×C10111yescharacteristic, complemented
549#124—21no—
550#124—21no—
551#124C2×C4×C10111yescharacteristic, complemented
552#124C2×C4×C10111yescharacteristic, complemented
553#123—21no—
554#123—21no—
555#123—21no—
556#123—21no—
557#123—21no—
558#123—21no—
559#123—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8C2×C4×C10111yescharacteristic
571C22⋊Q8C2×C4×C10111yescharacteristic
572C22⋊Q8C2×C4×C10111yescharacteristic
573C22⋊Q8C23×C10111yescharacteristic
574C22⋊Q8C23×C10111yescharacteristic
575C22⋊Q8C23×C10111yescharacteristic
576#121C2×C4×C10111yescharacteristic
577#121C23×C10111yescharacteristic
578#120—21no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—21no—
582C4×Q8—21no—
583C4×Q8C2×C4×C10111yescharacteristic, complemented
584C4×Q8C2×C4×C10111yescharacteristic, complemented
585C4×Q8C2×C4×C10111yescharacteristic, complemented
586C4×Q8C2×C4×C10111yescharacteristic, complemented
587C4×Q8C2×C4×C10111yescharacteristic, complemented
588C4×Q8C2×C4×C10111yescharacteristic, complemented
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4C2×C4×C10111yescharacteristic, complemented
596C4×D4C2×C4×C10111yescharacteristic, complemented
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117C2×C4×C10111yescharacteristic
605#117C2×C4×C10111yescharacteristic
606#117C2×C4×C10111yescharacteristic
607#117C2×C4×C10111yescharacteristic
608#117C2×C4×C10111yescharacteristic
609#117D4×C10111yescharacteristic
610#117D4×C10111yescharacteristic
611#117D4×C10111yescharacteristic
612#117D4×C10111yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4C2×C4×C10111yescharacteristic
618C2×C4⋊C4D4×C10111yescharacteristic
619C2×C4⋊C4D4×C10111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C10111yescharacteristic
623C2×C22⋊C4D4×C10111yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42C23×C10111yescharacteristic
627C2×C42C23×C10111yescharacteristic
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8C23×C10111yescharacteristic
635C22⋊C8C23×C10111yescharacteristic
636C22⋊C8C23×C10111yescharacteristic
637C22⋊C8C23×C10111yescharacteristic
638#97—21no—
639#97—21no—
640C4×C8—21no—
641C4×C8—21no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646#95—21no—
647#95—21no—
648#95C23×C10111yescharacteristic
649#95C23×C10111yescharacteristic
650#95C23×C10111yescharacteristic
651#95C23×C10111yescharacteristic
652C24C2×D4×C10111yescharacteristic
653#41—42no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—42no—
658C2×Q8C22×C4×C10111yescharacteristic
659C2×Q8C22×C4×C10111yescharacteristic
660C2×Q8C22×C4×C10111yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22×C4×C10111yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—81no—
678C22×C4C22×C4×C10111yescharacteristic
679C22×C4C22×C4×C10111yescharacteristic
680C22×C4C2×D4×C10111yescharacteristic
681C22×C4C2×D4×C10111yescharacteristic
682C22×C4C2×D4×C10111yescharacteristic
683C22×C4C2×D4×C10111yescharacteristic
684C22×C4C2×D4×C10111yescharacteristic
685C22×C4C2×D4×C10111yescharacteristic
686C22×C4C2×D4×C10111yescharacteristic
687C22×C4C24×C10111yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—81no—
719C4⋊C4C22⋊C4×C10111yescharacteristic
720C4⋊C4C22⋊C4×C10111yescharacteristic
721C4⋊C4C22⋊C4×C10111yescharacteristic
722C4⋊C4C22⋊C4×C10111yescharacteristic
723C4⋊C4C22⋊C4×C10111yescharacteristic
724C4⋊C4C22⋊C4×C10111yescharacteristic
725C4⋊C4C22⋊C4×C10111yescharacteristic
726C4⋊C4C22⋊C4×C10111yescharacteristic
727C4⋊C4C22×C4×C10111yescharacteristic
728C4⋊C4C22×C4×C10111yescharacteristic
729C4⋊C4C22×C4×C10111yescharacteristic
730C4⋊C4C22×C4×C10111yescharacteristic
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—42no—
747C22⋊C4C22⋊C4×C10111yescharacteristic
748C22⋊C4C22⋊C4×C10111yescharacteristic
749C22⋊C4C22⋊C4×C10111yescharacteristic
750C22⋊C4C22⋊C4×C10111yescharacteristic
751C22⋊C4C22⋊C4×C10111yescharacteristic
752C22⋊C4C22⋊C4×C10111yescharacteristic
753C22⋊C4C22⋊C4×C10111yescharacteristic
754C22⋊C4C22⋊C4×C10111yescharacteristic
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—42no—
763C42—81no—
764C42C22×C4×C10111yescharacteristic
765C42C22×C4×C10111yescharacteristic
766C42C22×C4×C10111yescharacteristic
767C42C22×C4×C10111yescharacteristic
768C42C2×D4×C10111yescharacteristic
769C42C2×D4×C10111yescharacteristic
770C42C2×D4×C10111yescharacteristic
771C42C2×D4×C10111yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—41no—
777C23C2×C22⋊C4×C10111yescharacteristic
778C23C2×C22⋊C4×C10111yescharacteristic
779C23C22×D4×C10111yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—42no—
784Q8—81no—
785Q8—81no—
786D4—41no—
787D4—42no—
788D4—41no—
789D4—41no—
790D4—81no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C10111yescharacteristic
829C2×C4C2×C22⋊C4×C10111yescharacteristic
830C2×C4C2×C22⋊C4×C10111yescharacteristic
831C2×C4C2×C22⋊C4×C10111yescharacteristic
832C2×C4C2×C22⋊C4×C10111yescharacteristic
833C2×C4C2×C22⋊C4×C10111yescharacteristic
834C2×C4C2×C22⋊C4×C10111yescharacteristic
835C2×C4C2×C22⋊C4×C10111yescharacteristic
836C2×C4C2×C22⋊C4×C10111yescharacteristic
837C2×C4C2×C22⋊C4×C10111yescharacteristic
838C2×C4C23×C4×C10111yescharacteristic
839C2×C4C22×D4×C10111yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22#410×C10112yes—
857C22C22×C22⋊C4×C10111yescharacteristic
858C22#577×C10111yescharacteristic
859C22#578×C10111yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—81no—
881C4—81no—
882C4—81no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×#410×C10111yescharacteristic
889C2C101×#289811yescharacteristic
890C2C101×#290111yescharacteristic
subgroupG/H
center, socleC22×C101C22×C22⋊C4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radical#525×C101C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×#117×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2924C2semidirect
3. C101×#2343C2semidirect
4. C101×#1521C2semidirect
5. C101×#1518C2semidirect
7. C101×#1515C2semidirect
8. C101×#1512C2semidirect
9. C101×#1511C2semidirect
10. C101×#1509C2semidirect
11. C101×#1506C2semidirect
13. C101×#1503C2semidirect
14. C101×#1500C2semidirect
15. C2×#328×C101C2semidirect
24. #544×C101C4semidirect
25. #542×C101C4semidirect
26. #542×C101C4semidirect
27. #541×C101C4semidirect
28. #541×C101C4semidirect
29. #536×C101C4semidirect
36. #520×C101C4semidirect
37. #519×C101C4semidirect
82. C4⋊Q8×C101C2×C4semidirect
83. C4⋊Q8×C101C2×C4semidirect
84. C4⋊Q8×C101C2×C4semidirect
85. C4⋊Q8×C101C2×C4semidirect
101. #125×C101C2×C4semidirect
102. #125×C101C2×C4semidirect
105. #124×C101C2×C4semidirect
106. #124×C101C2×C4semidirect
137. C4×Q8×C101C2×C4semidirect
138. C4×Q8×C101C2×C4semidirect
139. C4×Q8×C101C2×C4semidirect
140. C4×Q8×C101C2×C4semidirect
141. C4×Q8×C101C2×C4semidirect
142. C4×Q8×C101C2×C4semidirect
149. C4×D4×C101C2×C4semidirect
150. C4×D4×C101C2×C4semidirect
437. #17609C101direct (N × H)
447. #2924C2×C101semidirect
448. #2343C2×C101semidirect
449. #1521C2×C101semidirect
450. #1518C2×C101semidirect
452. #1515C2×C101semidirect
453. #1512C2×C101semidirect
454. #1511C2×C101semidirect
455. #1509C2×C101semidirect
456. #1506C2×C101semidirect
458. #1503C2×C101semidirect
459. #1500C2×C101semidirect
460. C2×#328C2×C101semidirect
461. C101#17609direct (N × H)
470. #544C4×C101semidirect
471. #542C4×C101semidirect
472. #542C4×C101semidirect
473. #541C4×C101semidirect
474. #541C4×C101semidirect
475. #536C4×C101semidirect
482. #520C4×C101semidirect
483. #519C4×C101semidirect
528. C4⋊Q8C2×C4×C101semidirect
529. C4⋊Q8C2×C4×C101semidirect
530. C4⋊Q8C2×C4×C101semidirect
531. C4⋊Q8C2×C4×C101semidirect
547. #125C2×C4×C101semidirect
548. #125C2×C4×C101semidirect
551. #124C2×C4×C101semidirect
552. #124C2×C4×C101semidirect
583. C4×Q8C2×C4×C101semidirect
584. C4×Q8C2×C4×C101semidirect
585. C4×Q8C2×C4×C101semidirect
586. C4×Q8C2×C4×C101semidirect
587. C4×Q8C2×C4×C101semidirect
588. C4×Q8C2×C4×C101semidirect
595. C4×D4C2×C4×C101semidirect
596. C4×D4C2×C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34952
C101×#29242
C101×#23432
C101×#15212
C101×#15182
C101×#15162
C101×#15152
C101×#15122
C101×#15112
C101×#15092
C101×#15062
C101×#15042
C101×#15032
C101×#15002
C2×#328×C1012
#17609101