Finite Group Databasebeta

← C101×#9497 #38791648

Subgroups — C101×#9497 #38791648

Order 25856.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2403C211yesmaximal, characteristic
2C101×#2309C211yesmaximal, characteristic, complemented
3C101×#1781C211yesmaximal, characteristic, complemented
4C101×#1781C212yesmaximal, complemented
5C101×#1304C212yesmaximal, complemented
6C23×D4×C101C2211yescharacteristic
7C23×D4×C101C2211yescharacteristic
8C2×#120×C101—21no—
9C2×#120×C101C412yescomplemented
10C2×#117×C101—21no—
11C2×#99×C101—22no—
12C2×#99×C101—24no—
13#392×C101—22no—
14#390×C101—24no—
15#386×C101—21no—
16#386×C101C412yescomplemented
17#379×C101—21no—
18#379×C101C2212yes—
19#379×C101C2211yescharacteristic
20#379×C101C2212yes—
21C25×C101C2×C411yescharacteristic
22C25×C101D411yescharacteristic
23C25×C101C2311yescharacteristic
24C22×D4×C101—22no—
25C22×D4×C101—21no—
26C22×D4×C101—22no—
27C22×D4×C101—22no—
28C22×D4×C101—21no—
29C22×D4×C101—22no—
30C22×D4×C101—22no—
31C22×D4×C101—44no—
32C22×D4×C101—44no—
33C22×D4×C101C2×C412yes—
34C22×D4×C101D412yes—
35C23×C4×C101C2×C411yescharacteristic
36C23×C4×C101D411yescharacteristic
37#120×C101—44no—
38#120×C101—44no—
39#117×C101—44no—
40C2×C4⋊C4×C101—22no—
41C2×C22⋊C4×C101—22no—
42C2×C22⋊C4×C101—22no—
43C2×C22⋊C4×C101—21no—
44C2×C22⋊C4×C101—22no—
45C2×C22⋊C4×C101—22no—
46C2×C22⋊C4×C101—22no—
47C2×C22⋊C4×C101—22no—
48C2×C22⋊C4×C101—22no—
49C2×C22⋊C4×C101—22no—
50C2×C22⋊C4×C101—21no—
51C2×C22⋊C4×C101—22no—
52C2×C22⋊C4×C101C2×C412yes—
53C2×C22⋊C4×C101D414yescomplemented
54C2×C42×C101—22no—
55#99×C101—48no—
56#99×C101—44no—
57#95×C101—22no—
58C24×C101—21no—
59C24×C101—21no—
60C24×C101—22no—
61C24×C101—21no—
62C24×C101—42no—
63C24×C101—42no—
64C24×C101—42no—
65C24×C101—42no—
66C24×C101—42no—
67C24×C101—42no—
68C24×C101—81no—
69C24×C101—81no—
70C24×C101—81no—
71C24×C101C22⋊C412yes—
72C24×C101C22×C411yescharacteristic
73C24×C101C2×D411yescharacteristic
74C24×C101C2×D411yescharacteristic
75C24×C101C2×D412yes—
76C24×C101#4112yes—
77C2×D4×C101—28no—
78C2×D4×C101—24no—
79C2×D4×C101—24no—
80C2×D4×C101—24no—
81C2×D4×C101—24no—
82C2×D4×C101—24no—
83C2×D4×C101—42no—
84C2×D4×C101—42no—
85C2×D4×C101—44no—
86C2×D4×C101—44no—
87C2×D4×C101—48no—
88C2×D4×C101—42no—
89C2×D4×C101—44no—
90C2×D4×C101—42no—
91C2×D4×C101—44no—
92C2×D4×C101—42no—
93C2×D4×C101—44no—
94C2×D4×C101—41no—
95C2×D4×C101—42no—
96C2×D4×C101—41no—
97C2×D4×C101—44no—
98C2×D4×C101—44no—
99C2×D4×C101—82no—
100C22×C4×C101—21no—
101C22×C4×C101—21no—
102C22×C4×C101—24no—
103C22×C4×C101—21no—
104C22×C4×C101—22no—
105C22×C4×C101—22no—
106C22×C4×C101—24no—
107C22×C4×C101—42no—
108C22×C4×C101—42no—
109C22×C4×C101C22⋊C412yes—
110C4⋊C4×C101—44no—
111C22⋊C4×C101—44no—
112C22⋊C4×C101—44no—
113C22⋊C4×C101—42no—
114C22⋊C4×C101—44no—
115C22⋊C4×C101—44no—
116C22⋊C4×C101—42no—
117C22⋊C4×C101—44no—
118C22⋊C4×C101—44no—
119C22⋊C4×C101—82no—
120C22⋊C4×C101—82no—
121C22⋊C4×C101—81no—
122C22⋊C4×C101—82no—
123C22⋊C4×C101—82no—
124C42×C101—44no—
125C23×C101—22no—
126C23×C101—22no—
127C23×C101—22no—
128C23×C101—22no—
129C23×C101—24no—
130C23×C101—22no—
131C23×C101—24no—
132C23×C101—22no—
133C23×C101—22no—
134C23×C101—22no—
135C23×C101—41no—
136C23×C101—41no—
137C23×C101—41no—
138C23×C101—42no—
139C23×C101—41no—
140C23×C101—42no—
141C23×C101—41no—
142C23×C101—42no—
143C23×C101—42no—
144C23×C101—42no—
145C23×C101—42no—
146C23×C101—42no—
147C23×C101—42no—
148C23×C101—41no—
149C23×C101—42no—
150C23×C101—42no—
151C23×C101—42no—
152C23×C101—42no—
153C23×C101—41no—
154C23×C101—42no—
155C23×C101—42no—
156C23×C101—81no—
157C23×C101—81no—
158C23×C101—82no—
159C23×C101—82no—
160C23×C101—88no—
161C23×C101—88no—
162C23×C101—88no—
163C23×C101C2×C22⋊C411yescharacteristic
164C23×C101C4×D412yes—
165C23×C101#12011yescharacteristic
166C23×C101#12112yes—
167C23×C101#12311yescharacteristic
168D4×C101—48no—
169D4×C101—48no—
170D4×C101—48no—
171D4×C101—44no—
172D4×C101—44no—
173D4×C101—88no—
174C2×C4×C101—22no—
175C2×C4×C101—22no—
176C2×C4×C101—24no—
177C2×C4×C101—22no—
178C2×C4×C101—22no—
179C2×C4×C101—22no—
180C2×C4×C101—24no—
181C2×C4×C101—41no—
182C2×C4×C101—42no—
183C2×C4×C101—41no—
184C2×C4×C101—44no—
185C2×C4×C101—42no—
186C2×C4×C101—44no—
187C2×C4×C101—42no—
188C2×C4×C101—42no—
189C2×C4×C101—44no—
190C2×C4×C101—82no—
191C2×C4×C101—82no—
192C2×C4×C101—82no—
193C2×C4×C101#9914yescomplemented
194C22×C101—21no—
195C22×C101—21no—
196C22×C101—21no—
197C22×C101—21no—
198C22×C101—22no—
199C22×C101—22no—
200C22×C101—21no—
201C22×C101—21no—
202C22×C101—22no—
203C22×C101—22no—
204C22×C101—22no—
205C22×C101—22no—
206C22×C101—21no—
207C22×C101—44no—
208C22×C101—44no—
209C22×C101—44no—
210C22×C101—44no—
211C22×C101—42no—
212C22×C101—42no—
213C22×C101—42no—
214C22×C101—42no—
215C22×C101—84no—
216C22×C101—82no—
217C22×C101—82no—
218C22×C101—84no—
219C22×C101—82no—
220C22×C101—84no—
221C22×C101—84no—
222C22×C101—84no—
223C22×C101—84no—
224C22×C101—81no—
225C22×C101—81no—
226C22×C101#38611yescharacteristic
227C22×C101C2×#9912yes—
228C22×C101B(4,𝔽2)12yes—
229C4×C101—24no—
230C4×C101—42no—
231C4×C101—84no—
232C4×C101—82no—
233C4×C101—162no—
234#9497C10111yesmaximal, characteristic, direct product factor, Sylow
235C2×C101—22no—
236C2×C101—22no—
237C2×C101—42no—
238C2×C101—42no—
239C2×C101—41no—
240C2×C101—82no—
241C2×C101—82no—
242C2×C101#188911yescharacteristic
243C2×C101#189811yescharacteristic
244C2×C101#191311yescharacteristic
245#2403C2×C10111yescharacteristic
246#2309C2×C10111yescharacteristic, complemented
247#1781C2×C10112yescomplemented
248#1781C2×C10111yescharacteristic, complemented
249#1304C2×C10112yescomplemented
250C101#949711yescharacteristic, direct product factor, Sylow
251C23×D4C22×C10111yescharacteristic
252C23×D4C22×C10111yescharacteristic
253C2×#120—21no—
254C2×#120C4×C10112yescomplemented
255C2×#117—21no—
256C2×#99—22no—
257C2×#99—24no—
258#392—22no—
259#390—24no—
260#386—21no—
261#386C4×C10112yescomplemented
262#379—21no—
263#379C22×C10112yes—
264#379C22×C10111yescharacteristic
265#379C22×C10112yes—
266C25C2×C4×C10111yescharacteristic
267C25D4×C10111yescharacteristic
268C25C23×C10111yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C10112yes—
279C22×D4D4×C10112yes—
280C23×C4C2×C4×C10111yescharacteristic
281C23×C4D4×C10111yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C10112yes—
298C2×C22⋊C4D4×C10114yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C10112yes—
317C24C22×C4×C10111yescharacteristic
318C24C2×D4×C10111yescharacteristic
319C24C2×D4×C10111yescharacteristic
320C24C2×D4×C10112yes—
321C24#41×C10112yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C10112yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C10111yescharacteristic
409C23C4×D4×C10112yes—
410C23#120×C10111yescharacteristic
411C23#121×C10112yes—
412C23#123×C10111yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C10114yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#386×C10111yescharacteristic
472C22C2×#99×C10112yes—
473C22B(4,𝔽2)×C10112yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C101×#188911yescharacteristic
487C2C101×#189811yescharacteristic
488C2C101×#191311yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC24C22×C4×C101
Frattini, cosocleC25C23×C101
prime radicalC101×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2309C2semidirect
3. C101×#1781C2semidirect
4. C101×#1781C2semidirect
5. C101×#1304C2semidirect
9. C2×#120×C101C4semidirect
16. #386×C101C4semidirect
53. C2×C22⋊C4×C101D4semidirect
193. C2×C4×C101#99semidirect
234. #9497C101direct (N × H)
246. #2309C2×C101semidirect
247. #1781C2×C101semidirect
248. #1781C2×C101semidirect
249. #1304C2×C101semidirect
250. C101#9497direct (N × H)
254. C2×#120C4×C101semidirect
261. #386C4×C101semidirect
298. C2×C22⋊C4D4×C101semidirect
438. C2×C4#99×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#24032
C101×#23092
C101×#17812
C101×#13042
#9497101