Finite Group Databasebeta

← C101×#10008 #38792159

Subgroups — C101×#10008 #38792159

Order 25856.

654 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3215C211yesmaximal, characteristic, complemented
2C101×#3110C211yesmaximal, characteristic, complemented
3C101×#2540C211yesmaximal, characteristic
4C101×#1986C211yesmaximal, characteristic, complemented
5C101×#1527C211yesmaximal, characteristic, complemented
6C101×#1490C211yesmaximal, characteristic, complemented
7C101×#1285C211yesmaximal, characteristic, complemented
8#533×C101C2211yescharacteristic
9C2×#124×C101C2211yescharacteristic
10C2×C22⋊Q8×C101—21no—
11C2×#121×C101—21no—
12C2×C4×D4×C101C2211yescharacteristic
13#497×C101—21no—
14#489×C101—21no—
15#484×C101—21no—
16#474×C101—21no—
17#464×C101—22no—
18#461×C101—21no—
19#451×C101—21no—
20#450×C101—21no—
21#450×C101—21no—
22#440×C101—22no—
23#432×C101C2211yescharacteristic
24#432×C101C2211yescharacteristic
25C4×M16×C101C2211yescharacteristic
26#399×C101—21no—
27#392×C101—21no—
28#390×C101—22no—
29C4×C4⋊C4×C101C2211yescharacteristic
30#339×C101—22no—
31#329×C101—22no—
32D4⋊C8×C101—22no—
33C22×Q8×C101D411yescharacteristic
34C22×D4×C101—22no—
35C22×D4×C101D411yescharacteristic
36C22×D4×C101D411yescharacteristic
37C23×C4×C101—21no—
38C2×Q16×C101—22no—
39C2×SD16×C101—22no—
40C2×SD16×C101—22no—
41C2×M16×C101—21no—
42C4⋊Q8×C101D411yescharacteristic, complemented
43C4⋊Q8×C101D411yescharacteristic, complemented
44#125×C101—21no—
45#124×C101—21no—
46#124×C101—21no—
47#124×C101—21no—
48#124×C101—21no—
49C22⋊Q8×C101—21no—
50C22⋊Q8×C101—21no—
51C22⋊Q8×C101—44no—
52#121×C101—44no—
53C4×Q8×C101—21no—
54C4×Q8×C101—21no—
55C4×D4×C101—21no—
56C4×D4×C101—21no—
57C4×D4×C101—21no—
58C4×D4×C101—21no—
59#117×C101—21no—
60C2×C4⋊C4×C101—21no—
61C2×C4⋊C4×C101—22no—
62C2×C4⋊C4×C101D411yescharacteristic
63C2×C22⋊C4×C101—22no—
64C2×C22⋊C4×C101—22no—
65C2×C22⋊C4×C101—21no—
66C2×C22⋊C4×C101—21no—
67C2×C22⋊C4×C101—21no—
68C2×C42×C101D412yes—
69C2×C42×C101C2311yescharacteristic
70#107×C101—22no—
71C4⋊C8×C101—21no—
72C4⋊C8×C101D412yescomplemented
73#103×C101—22no—
74#103×C101—22no—
75#102×C101—22no—
76#102×C101—22no—
77C22⋊C8×C101—21no—
78C22⋊C8×C101—21no—
79#97×C101—21no—
80#97×C101—21no—
81#97×C101D412yescomplemented
82C4×C8×C101—21no—
83#95×C101—21no—
84C24×C101—21no—
85C24×C101—21no—
86C2×Q8×C101—21no—
87C2×Q8×C101—21no—
88C2×Q8×C101—21no—
89C2×Q8×C101—21no—
90C2×Q8×C101—42no—
91C2×D4×C101—21no—
92C2×D4×C101—21no—
93C2×D4×C101—21no—
94C2×D4×C101—21no—
95C2×D4×C101—42no—
96C2×D4×C101—44no—
97C2×D4×C101—42no—
98C2×D4×C101—44no—
99C2×D4×C101—82no—
100C22×C4×C101—22no—
101C22×C4×C101—21no—
102C22×C4×C101—21no—
103C22×C4×C101—42no—
104C22×C4×C101—42no—
105C22×C4×C101—41no—
106C22×C4×C101—41no—
107C22×C4×C101C2×D411yescharacteristic
108C22×C4×C101C2×D411yescharacteristic
109C22×C4×C101C2×D411yescharacteristic
110Q16×C101—82no—
111SD16×C101—44no—
112SD16×C101—82no—
113M16×C101—22no—
114M16×C101—41no—
115C2×C8×C101—22no—
116C2×C8×C101—22no—
117C2×C8×C101—41no—
118C4⋊C4×C101—24no—
119C4⋊C4×C101—21no—
120C4⋊C4×C101—21no—
121C4⋊C4×C101—21no—
122C4⋊C4×C101—21no—
123C4⋊C4×C101—21no—
124C4⋊C4×C101—21no—
125C4⋊C4×C101—44no—
126C4⋊C4×C101—41no—
127C4⋊C4×C101—41no—
128C22⋊C4×C101—44no—
129C22⋊C4×C101—44no—
130C22⋊C4×C101—41no—
131C22⋊C4×C101—41no—
132C22⋊C4×C101—41no—
133C22⋊C4×C101—41no—
134C22⋊C4×C101—41no—
135C22⋊C4×C101—41no—
136C22⋊C4×C101—41no—
137C42×C101—42no—
138C42×C101—41no—
139C42×C101C2×D411yescharacteristic
140C42×C101C2×D411yescharacteristic
141C42×C101C2×D411yescharacteristic
142C42×C101#4111yescharacteristic
143C23×C101—22no—
144C23×C101—41no—
145C23×C101—41no—
146C23×C101—41no—
147C23×C101—42no—
148C23×C101—42no—
149C23×C101—41no—
150C23×C101—41no—
151C23×C101—41no—
152C23×C101—41no—
153C23×C101—41no—
154C23×C101—41no—
155C23×C101#12011yescharacteristic
156Q8×C101—42no—
157Q8×C101—42no—
158Q8×C101—42no—
159Q8×C101—81no—
160D4×C101—22no—
161D4×C101—22no—
162D4×C101—41no—
163D4×C101—41no—
164D4×C101—42no—
165D4×C101—81no—
166D4×C101—88no—
167C2×C4×C101—21no—
168C2×C4×C101—21no—
169C2×C4×C101—22no—
170C2×C4×C101—24no—
171C2×C4×C101—41no—
172C2×C4×C101—42no—
173C2×C4×C101—42no—
174C2×C4×C101—41no—
175C2×C4×C101—42no—
176C2×C4×C101—41no—
177C2×C4×C101—41no—
178C2×C4×C101—41no—
179C2×C4×C101—41no—
180C2×C4×C101—41no—
181C2×C4×C101—82no—
182C2×C4×C101—82no—
183C2×C4×C101#12011yescharacteristic
184C2×C4×C101#12011yescharacteristic
185C2×C4×C101#12111yescharacteristic
186C2×C4×C101#12111yescharacteristic
187C2×C4×C101#12111yescharacteristic
188C2×C4×C101#12711yescharacteristic
189C8×C101—42no—
190C8×C101—42no—
191C8×C101—42no—
192C22×C101—21no—
193C22×C101—21no—
194C22×C101—42no—
195C22×C101—42no—
196C22×C101—42no—
197C22×C101—81no—
198C22×C101—81no—
199C22×C101—82no—
200C22×C101—82no—
201C22×C101—81no—
202C22×C101—81no—
203C22×C101—81no—
204C22×C101—81no—
205C22×C101—81no—
206C22×C101#39211yescharacteristic
207C22×C101#45511yescharacteristic
208C22×C101#45611yescharacteristic
209C4×C101—21no—
210C4×C101—21no—
211C4×C101—21no—
212C4×C101—21no—
213C4×C101—21no—
214C4×C101—44no—
215C4×C101—81no—
216C4×C101—81no—
217C4×C101—81no—
218C4×C101—81no—
219C4×C101#45312yes—
220#10008C10111yesmaximal, characteristic, direct product factor, Sylow
221C2×C101—21no—
222C2×C101—21no—
223C2×C101—82no—
224C2×C101—161no—
225C2×C101#200211yescharacteristic
226C2×C101#200711yescharacteristic
227C2×C101#201011yescharacteristic
228#3215C2×C10111yescharacteristic, complemented
229#3110C2×C10111yescharacteristic, complemented
230#2540C2×C10111yescharacteristic
231#1986C2×C10111yescharacteristic, complemented
232#1527C2×C10111yescharacteristic, complemented
233#1490C2×C10111yescharacteristic, complemented
234#1285C2×C10111yescharacteristic, complemented
235C101#1000811yescharacteristic, direct product factor, Sylow
236#533C22×C10111yescharacteristic
237C2×#124C22×C10111yescharacteristic
238C2×C22⋊Q8—21no—
239C2×#121—21no—
240C2×C4×D4C22×C10111yescharacteristic
241#497—21no—
242#489—21no—
243#484—21no—
244#474—21no—
245#464—22no—
246#461—21no—
247#451—21no—
248#450—21no—
249#450—21no—
250#440—22no—
251#432C22×C10111yescharacteristic
252#432C22×C10111yescharacteristic
253C4×M16C22×C10111yescharacteristic
254#399—21no—
255#392—21no—
256#390—22no—
257C4×C4⋊C4C22×C10111yescharacteristic
258#339—22no—
259#329—22no—
260D4⋊C8—22no—
261C22×Q8D4×C10111yescharacteristic
262C22×D4—22no—
263C22×D4D4×C10111yescharacteristic
264C22×D4D4×C10111yescharacteristic
265C23×C4—21no—
266C2×Q16—22no—
267C2×SD16—22no—
268C2×SD16—22no—
269C2×M16—21no—
270C4⋊Q8D4×C10111yescharacteristic, complemented
271C4⋊Q8D4×C10111yescharacteristic, complemented
272#125—21no—
273#124—21no—
274#124—21no—
275#124—21no—
276#124—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—44no—
280#121—44no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×D4—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4—21no—
287#117—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4D4×C10111yescharacteristic
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C42D4×C10112yes—
297C2×C42C23×C10111yescharacteristic
298#107—22no—
299C4⋊C8—21no—
300C4⋊C8D4×C10112yescomplemented
301#103—22no—
302#103—22no—
303#102—22no—
304#102—22no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307#97—21no—
308#97—21no—
309#97D4×C10112yescomplemented
310C4×C8—21no—
311#95—21no—
312C24—21no—
313C24—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—42no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—42no—
324C2×D4—44no—
325C2×D4—42no—
326C2×D4—44no—
327C2×D4—82no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4C2×D4×C10111yescharacteristic
336C22×C4C2×D4×C10111yescharacteristic
337C22×C4C2×D4×C10111yescharacteristic
338Q16—82no—
339SD16—44no—
340SD16—82no—
341M16—22no—
342M16—41no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—41no—
346C4⋊C4—24no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—44no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C42—42no—
366C42—41no—
367C42C2×D4×C10111yescharacteristic
368C42C2×D4×C10111yescharacteristic
369C42C2×D4×C10111yescharacteristic
370C42#41×C10111yescharacteristic
371C23—22no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23#120×C10111yescharacteristic
384Q8—42no—
385Q8—42no—
386Q8—42no—
387Q8—81no—
388D4—22no—
389D4—22no—
390D4—41no—
391D4—41no—
392D4—42no—
393D4—81no—
394D4—88no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4#120×C10111yescharacteristic
412C2×C4#120×C10111yescharacteristic
413C2×C4#121×C10111yescharacteristic
414C2×C4#121×C10111yescharacteristic
415C2×C4#121×C10111yescharacteristic
416C2×C4#127×C10111yescharacteristic
417C8—42no—
418C8—42no—
419C8—42no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22#392×C10111yescharacteristic
435C22#455×C10111yescharacteristic
436C22#456×C10111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—44no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4#453×C10112yes—
448C2—21no—
449C2—21no—
450C2—82no—
451C2—161no—
452C2C101×#200211yescharacteristic
453C2C101×#200711yescharacteristic
454C2C101×#201011yescharacteristic
subgroupG/H
center, socleC22×C101#392
commutator, Frattini, cosocleC2×C42C23×C101
prime radicalC101×#2540C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3215C2semidirect
2. C101×#3110C2semidirect
4. C101×#1986C2semidirect
5. C101×#1527C2semidirect
6. C101×#1490C2semidirect
7. C101×#1285C2semidirect
42. C4⋊Q8×C101D4semidirect
43. C4⋊Q8×C101D4semidirect
72. C4⋊C8×C101D4semidirect
81. #97×C101D4semidirect
220. #10008C101direct (N × H)
228. #3215C2×C101semidirect
229. #3110C2×C101semidirect
231. #1986C2×C101semidirect
232. #1527C2×C101semidirect
233. #1490C2×C101semidirect
234. #1285C2×C101semidirect
235. C101#10008direct (N × H)
270. C4⋊Q8D4×C101semidirect
271. C4⋊Q8D4×C101semidirect
300. C4⋊C8D4×C101semidirect
309. #97D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#32152
C101×#31102
C101×#25402
C101×#19862
C101×#15272
C101×#14902
C101×#12852
#10008101