Finite Group Databasebeta

← C103×#8974 #39914249

Subgroups — C103×#8974 #39914249

Order 26368.

516 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#477×C103C211yesmaximal, characteristic
2C103×#2355C211yesmaximal, characteristic
3C103×#1987C211yesmaximal, characteristic
4C103×#1956C211yesmaximal, characteristic
5C2×Q8⋊C8×C103C211yesmaximal, characteristic
6C103×#1296C211yesmaximal, characteristic
7C103×#1279C211yesmaximal, characteristic
8C2×C4⋊Q8×C103C2211yescharacteristic
9C2×C4×Q8×C103C2211yescharacteristic
10#477×C103—22no—
11#477×C103C414yescomplemented
12C2×#107×C103—21no—
13C2×C4⋊C8×C103C2211yescharacteristic
14C2×C4⋊C8×C103C2211yescharacteristic
15C2×#103×C103—21no—
16C2×#103×C103—22no—
17C2×C4×C8×C103C2211yescharacteristic
18#391×C103—21no—
19#387×C103—22no—
20#384×C103C2211yescharacteristic
21#382×C103—21no—
22C4×C4⋊C4×C103—21no—
23C4×C4⋊C4×C103—21no—
24C4×C4⋊C4×C103C2211yescharacteristic
25#340×C103—21no—
26#340×C103—21no—
27Q8⋊C8×C103—22no—
28C22×Q8×C103—21no—
29C22×Q8×C103D411yescharacteristic
30C22×C8×C103—21no—
31C22×C8×C103—21no—
32C22×C8×C103—21no—
33C4⋊Q8×C103—21no—
34C4⋊Q8×C103—21no—
35C4⋊Q8×C103—21no—
36C4⋊Q8×C103C2×C412yes—
37C4×Q8×C103—21no—
38C4×Q8×C103—21no—
39C4×Q8×C103C2×C412yes—
40C4×Q8×C103D412yes—
41C2×C4⋊C4×C103—21no—
42C2×C4⋊C4×C103—21no—
43C2×C4⋊C4×C103—21no—
44C2×C4⋊C4×C103—21no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103D411yescharacteristic
47C2×C4⋊C4×C103D411yescharacteristic
48C2×C4⋊C4×C103D411yescharacteristic
49C2×C4⋊C4×C103D412yes—
50C2×C42×C103—21no—
51C2×C42×C103—21no—
52C2×C42×C103—22no—
53C2×C42×C103C2311yescharacteristic
54#107×C103—24no—
55C4⋊C8×C103—21no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103C2×C412yes—
59#103×C103—24no—
60#103×C103—44no—
61C4×C8×C103—21no—
62C4×C8×C103—21no—
63#95×C103—22no—
64#95×C103—22no—
65#95×C103—22no—
66#95×C103—21no—
67C2×Q8×C103—21no—
68C2×Q8×C103—22no—
69C2×Q8×C103—21no—
70C2×Q8×C103—21no—
71C2×Q8×C103—21no—
72C2×Q8×C103—21no—
73C2×Q8×C103—42no—
74C2×Q8×C103—42no—
75C2×Q8×C103—41no—
76C2×Q8×C103C22⋊C412yes—
77C22×C4×C103—21no—
78C22×C4×C103—21no—
79C22×C4×C103—21no—
80C22×C4×C103—21no—
81C22×C4×C103—22no—
82C22×C4×C103—41no—
83C22×C4×C103C2×D411yescharacteristic
84C22×C4×C103C2×D411yescharacteristic
85C22×C4×C103C2×D411yescharacteristic
86C2×C8×C103—22no—
87C2×C8×C103—22no—
88C2×C8×C103—41no—
89C2×C8×C103—41no—
90C2×C8×C103—41no—
91C2×C8×C103—41no—
92C2×C8×C103—41no—
93C2×C8×C103—41no—
94C2×C8×C103—41no—
95C4⋊C4×C103—22no—
96C4⋊C4×C103—22no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—21no—
103C4⋊C4×C103—42no—
104C4⋊C4×C103—41no—
105C4⋊C4×C103—41no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103—41no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103C22⋊C412yes—
111C4⋊C4×C103Q1612yes—
112C42×C103—22no—
113C42×C103—22no—
114C42×C103—41no—
115C42×C103—41no—
116C42×C103—82no—
117C42×C103C22×C411yescharacteristic
118C42×C103C2×D411yescharacteristic
119C42×C103#4111yescharacteristic
120C42×C103#4111yescharacteristic
121C23×C103#12011yescharacteristic
122Q8×C103—22no—
123Q8×C103—22no—
124Q8×C103—44no—
125Q8×C103—41no—
126Q8×C103—41no—
127Q8×C103—82no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—41no—
134C2×C4×C103—41no—
135C2×C4×C103—41no—
136C2×C4×C103—41no—
137C2×C4×C103—41no—
138C2×C4×C103—41no—
139C2×C4×C103—42no—
140C2×C4×C103—41no—
141C2×C4×C103—41no—
142C2×C4×C103—42no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—41no—
146C2×C4×C103—81no—
147C2×C4×C103—81no—
148C2×C4×C103C2×C22⋊C411yescharacteristic
149C2×C4×C103C4×D411yescharacteristic
150C2×C4×C103C4×D411yescharacteristic
151C2×C4×C103#12111yescharacteristic
152C2×C4×C103#12111yescharacteristic
153C2×C4×C103#12311yescharacteristic
154C2×C4×C103C2×Q1611yescharacteristic
155C2×C4×C103#13511yescharacteristic
156C2×C4×C103#13511yescharacteristic
157C2×C4×C103#13511yescharacteristic
158C2×C4×C103#13711yescharacteristic
159C2×C4×C103#13711yescharacteristic
160C2×C4×C103#13711yescharacteristic
161C2×C4×C103#13711yescharacteristic
162C8×C103—42no—
163C8×C103—42no—
164C8×C103—81no—
165C22×C103#38611yescharacteristic
166C22×C103#45111yescharacteristic
167C22×C103#45211yescharacteristic
168C22×C103#45211yescharacteristic
169C22×C103#45211yescharacteristic
170C22×C103#45311yescharacteristic
171C22×C103#45411yescharacteristic
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—42no—
175C4×C103—42no—
176C4×C103—42no—
177C4×C103—82no—
178C4×C103—82no—
179C4×C103—81no—
180C4×C103#41611yescharacteristic
181C4×C103#41911yescharacteristic
182C4×C103C4×Q1611yescharacteristic
183C4×C103#44111yescharacteristic
184C4×C103#46211yescharacteristic
185C4×C103#46411yescharacteristic
186C4×C103#48511yescharacteristic
187C4×C103#48511yescharacteristic
188#8974C10311yesmaximal, characteristic, direct product factor, Sylow
189C2×C103#163011yescharacteristic
190C2×C103#163211yescharacteristic
191C2×C103#163611yescharacteristic
192C2×C103#163811yescharacteristic
193C2×C103#187311yescharacteristic
194C2×C103#187811yescharacteristic
195C2×C103#188311yescharacteristic
196C2×#477C2×C10311yescharacteristic
197#2355C2×C10311yescharacteristic
198#1987C2×C10311yescharacteristic
199#1956C2×C10311yescharacteristic
200C2×Q8⋊C8C2×C10311yescharacteristic
201#1296C2×C10311yescharacteristic
202#1279C2×C10311yescharacteristic
203C103#897411yescharacteristic, direct product factor, Sylow
204C2×C4⋊Q8C22×C10311yescharacteristic
205C2×C4×Q8C22×C10311yescharacteristic
206#477—22no—
207#477C4×C10314yescomplemented
208C2×#107—21no—
209C2×C4⋊C8C22×C10311yescharacteristic
210C2×C4⋊C8C22×C10311yescharacteristic
211C2×#103—21no—
212C2×#103—22no—
213C2×C4×C8C22×C10311yescharacteristic
214#391—21no—
215#387—22no—
216#384C22×C10311yescharacteristic
217#382—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4C22×C10311yescharacteristic
221#340—21no—
222#340—21no—
223Q8⋊C8—22no—
224C22×Q8—21no—
225C22×Q8D4×C10311yescharacteristic
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8C2×C4×C10312yes—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8C2×C4×C10312yes—
236C4×Q8D4×C10312yes—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4D4×C10311yescharacteristic
243C2×C4⋊C4D4×C10311yescharacteristic
244C2×C4⋊C4D4×C10311yescharacteristic
245C2×C4⋊C4D4×C10312yes—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—22no—
249C2×C42C23×C10311yescharacteristic
250#107—24no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8C2×C4×C10312yes—
255#103—24no—
256#103—44no—
257C4×C8—21no—
258C4×C8—21no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95—21no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—41no—
272C2×Q8C22⋊C4×C10312yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—41no—
279C22×C4C2×D4×C10311yescharacteristic
280C22×C4C2×D4×C10311yescharacteristic
281C22×C4C2×D4×C10311yescharacteristic
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C10312yes—
307C4⋊C4Q16×C10312yes—
308C42—22no—
309C42—22no—
310C42—41no—
311C42—41no—
312C42—82no—
313C42C22×C4×C10311yescharacteristic
314C42C2×D4×C10311yescharacteristic
315C42#41×C10311yescharacteristic
316C42#41×C10311yescharacteristic
317C23#120×C10311yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—44no—
321Q8—41no—
322Q8—41no—
323Q8—82no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4C2×C22⋊C4×C10311yescharacteristic
345C2×C4C4×D4×C10311yescharacteristic
346C2×C4C4×D4×C10311yescharacteristic
347C2×C4#121×C10311yescharacteristic
348C2×C4#121×C10311yescharacteristic
349C2×C4#123×C10311yescharacteristic
350C2×C4C2×Q16×C10311yescharacteristic
351C2×C4#135×C10311yescharacteristic
352C2×C4#135×C10311yescharacteristic
353C2×C4#135×C10311yescharacteristic
354C2×C4#137×C10311yescharacteristic
355C2×C4#137×C10311yescharacteristic
356C2×C4#137×C10311yescharacteristic
357C2×C4#137×C10311yescharacteristic
358C8—42no—
359C8—42no—
360C8—81no—
361C22#386×C10311yescharacteristic
362C22#451×C10311yescharacteristic
363C22#452×C10311yescharacteristic
364C22#452×C10311yescharacteristic
365C22#452×C10311yescharacteristic
366C22#453×C10311yescharacteristic
367C22#454×C10311yescharacteristic
368C4—21no—
369C4—21no—
370C4—42no—
371C4—42no—
372C4—42no—
373C4—82no—
374C4—82no—
375C4—81no—
376C4#416×C10311yescharacteristic
377C4#419×C10311yescharacteristic
378C4C4×Q16×C10311yescharacteristic
379C4#441×C10311yescharacteristic
380C4#462×C10311yescharacteristic
381C4#464×C10311yescharacteristic
382C4#485×C10311yescharacteristic
383C4#485×C10311yescharacteristic
384C2C103×#163011yescharacteristic
385C2C103×#163211yescharacteristic
386C2C103×#163611yescharacteristic
387C2C103×#163811yescharacteristic
388C2C103×#187311yescharacteristic
389C2C103×#187811yescharacteristic
390C2C103×#188311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
11. #477×C103C4semidirect
188. #8974C103direct (N × H)
203. C103#8974direct (N × H)
207. #477C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#477×C1032
C103×#23552
C103×#19872
C103×#19562
C2×Q8⋊C8×C1032
C103×#12962
C103×#12792
#8974103