Finite Group Databasebeta

← C103×#9219 #39914494

Subgroups — C103×#9219 #39914494

Order 26368.

594 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C103C211yesmaximal, characteristic
2C2×C8×D4×C103C211yesmaximal, characteristic
3C103×#1956C211yesmaximal, characteristic, complemented
4C103×#1802C211yesmaximal, characteristic
5C2×#332×C103C211yesmaximal, characteristic, complemented
6C103×#1296C211yesmaximal, characteristic, complemented
7C103×#1277C211yesmaximal, characteristic, complemented
8C23×C8×C103—21no—
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4×D4×C103C2211yescharacteristic
11#474×C103—22no—
12#474×C103C414yescomplemented
13C8×D4×C103—22no—
14C8×D4×C103—22no—
15C2×#107×C103—21no—
16C2×C4⋊C8×C103C2211yescharacteristic
17C2×C4⋊C8×C103C2211yescharacteristic
18C2×C4⋊C8×C103C2211yescharacteristic
19C2×#103×C103—21no—
20C2×#103×C103—21no—
21C2×#102×C103—21no—
22C2×#102×C103—21no—
23C2×C22⋊C8×C103—21no—
24C2×C4×C8×C103C2211yescharacteristic
25#384×C103C2211yescharacteristic
26#340×C103—21no—
27#332×C103—22no—
28C22×Q8×C103—21no—
29C22×D4×C103D411yescharacteristic
30C23×C4×C103—21no—
31C22×C8×C103—24no—
32C22×C8×C103—21no—
33C22×C8×C103—21no—
34C22×C8×C103—21no—
35C22×C8×C103—42no—
36C22×C8×C103—42no—
37C22×C8×C103D411yescharacteristic
38C22×C8×C103D411yescharacteristic
39C4⋊Q8×C103—21no—
40C4⋊Q8×C103—21no—
41C4⋊Q8×C103—21no—
42C4⋊Q8×C103C2×C412yes—
43C4×D4×C103—21no—
44C4×D4×C103—21no—
45C4×D4×C103C2×C412yes—
46C4×D4×C103D412yes—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103D411yescharacteristic
53C2×C22⋊C4×C103—21no—
54C2×C42×C103C2311yescharacteristic
55#107×C103—24no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103—21no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103C2×C412yes—
61C4⋊C8×C103D412yes—
62#103×C103—42no—
63#103×C103—42no—
64#102×C103—24no—
65#102×C103—42no—
66C22⋊C8×C103—24no—
67C4×C8×C103—21no—
68C4×C8×C103—21no—
69C24×C103—21no—
70C2×Q8×C103—22no—
71C2×Q8×C103—41no—
72C2×Q8×C103—41no—
73C2×Q8×C103—41no—
74C2×Q8×C103—41no—
75C2×Q8×C103—41no—
76C2×D4×C103—21no—
77C2×D4×C103—21no—
78C2×D4×C103—21no—
79C2×D4×C103C22⋊C412yes—
80C2×D4×C103SD1612yes—
81C2×D4×C103Q1612yes—
82C22×C4×C103—21no—
83C22×C4×C103—22no—
84C22×C4×C103—22no—
85C22×C4×C103—41no—
86C22×C4×C103—41no—
87C22×C4×C103—41no—
88C22×C4×C103—41no—
89C22×C4×C103—41no—
90C22×C4×C103—41no—
91C22×C4×C103C2×D411yescharacteristic
92C22×C4×C103C2×D411yescharacteristic
93C22×C4×C103#4111yescharacteristic
94C2×C8×C103—21no—
95C2×C8×C103—21no—
96C2×C8×C103—22no—
97C2×C8×C103—21no—
98C2×C8×C103—22no—
99C2×C8×C103—21no—
100C2×C8×C103—21no—
101C2×C8×C103—48no—
102C2×C8×C103—41no—
103C2×C8×C103—41no—
104C2×C8×C103—41no—
105C2×C8×C103—41no—
106C2×C8×C103—41no—
107C2×C8×C103—41no—
108C2×C8×C103—41no—
109C2×C8×C103D812yes—
110C4⋊C4×C103—21no—
111C4⋊C4×C103—22no—
112C4⋊C4×C103—22no—
113C4⋊C4×C103—41no—
114C4⋊C4×C103—41no—
115C4⋊C4×C103—41no—
116C4⋊C4×C103—41no—
117C4⋊C4×C103—41no—
118C4⋊C4×C103—41no—
119C4⋊C4×C103—81no—
120C4⋊C4×C103C22⋊C412yes—
121C22⋊C4×C103—22no—
122C22⋊C4×C103—22no—
123C42×C103C22×C411yescharacteristic
124C42×C103C2×D411yescharacteristic
125C42×C103C2×D411yescharacteristic
126C42×C103#4111yescharacteristic
127C23×C103—22no—
128C23×C103—22no—
129C23×C103—22no—
130C23×C103—41no—
131C23×C103—41no—
132C23×C103—41no—
133C23×C103—41no—
134C23×C103#12111yescharacteristic
135Q8×C103—42no—
136Q8×C103—42no—
137Q8×C103—81no—
138Q8×C103—81no—
139D4×C103—22no—
140D4×C103—22no—
141D4×C103—22no—
142D4×C103#10314yescomplemented
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—22no—
146C2×C4×C103—41no—
147C2×C4×C103—41no—
148C2×C4×C103—42no—
149C2×C4×C103—42no—
150C2×C4×C103—42no—
151C2×C4×C103—42no—
152C2×C4×C103—42no—
153C2×C4×C103—81no—
154C2×C4×C103—81no—
155C2×C4×C103—81no—
156C2×C4×C103—81no—
157C2×C4×C103—81no—
158C2×C4×C103C2×C22⋊C411yescharacteristic
159C2×C4×C103C4×D411yescharacteristic
160C2×C4×C103C4×D411yescharacteristic
161C2×C4×C103#12011yescharacteristic
162C2×C4×C103#12111yescharacteristic
163C2×C4×C103#12311yescharacteristic
164C2×C4×C103C2×D811yescharacteristic
165C2×C4×C103C2×SD1611yescharacteristic
166C2×C4×C103C2×Q1611yescharacteristic
167C2×C4×C103#13511yescharacteristic
168C2×C4×C103#13511yescharacteristic
169C2×C4×C103#13511yescharacteristic
170C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
172C8×C103—22no—
173C8×C103—42no—
174C8×C103—42no—
175C8×C103—41no—
176C8×C103—81no—
177C22×C103—24no—
178C22×C103—42no—
179C22×C103—42no—
180C22×C103—42no—
181C22×C103—42no—
182C22×C103—42no—
183C22×C103—42no—
184C22×C103#38611yescharacteristic
185C22×C103#45911yescharacteristic
186C22×C103#46311yescharacteristic
187C22×C103#46511yescharacteristic
188C22×C103#46711yescharacteristic
189C22×C103#47111yescharacteristic
190C22×C103#47311yescharacteristic
191C4×C103—21no—
192C4×C103—21no—
193C4×C103—42no—
194C4×C103—82no—
195C4×C103—161no—
196C4×C103C2×#10311yescharacteristic
197C4×C103#41611yescharacteristic
198C4×C103C4×D811yescharacteristic
199C4×C103#44211yescharacteristic
200C4×C103#44711yescharacteristic
201C4×C103#44911yescharacteristic
202C4×C103#46511yescharacteristic
203C4×C103#46711yescharacteristic
204#9219C10311yesmaximal, characteristic, direct product factor, Sylow
205C2×C103—44no—
206C2×C103#166511yescharacteristic
207C2×C103#166911yescharacteristic
208C2×C103#167911yescharacteristic
209C2×C103#168311yescharacteristic
210C2×C103#187911yescharacteristic
211C2×C103#189211yescharacteristic
212C2×C103#190811yescharacteristic
213C2×#474C2×C10311yescharacteristic
214C2×C8×D4C2×C10311yescharacteristic
215#1956C2×C10311yescharacteristic, complemented
216#1802C2×C10311yescharacteristic
217C2×#332C2×C10311yescharacteristic, complemented
218#1296C2×C10311yescharacteristic, complemented
219#1277C2×C10311yescharacteristic, complemented
220C103#921911yescharacteristic, direct product factor, Sylow
221C23×C8—21no—
222C2×C4⋊Q8C22×C10311yescharacteristic
223C2×C4×D4C22×C10311yescharacteristic
224#474—22no—
225#474C4×C10314yescomplemented
226C8×D4—22no—
227C8×D4—22no—
228C2×#107—21no—
229C2×C4⋊C8C22×C10311yescharacteristic
230C2×C4⋊C8C22×C10311yescharacteristic
231C2×C4⋊C8C22×C10311yescharacteristic
232C2×#103—21no—
233C2×#103—21no—
234C2×#102—21no—
235C2×#102—21no—
236C2×C22⋊C8—21no—
237C2×C4×C8C22×C10311yescharacteristic
238#384C22×C10311yescharacteristic
239#340—21no—
240#332—22no—
241C22×Q8—21no—
242C22×D4D4×C10311yescharacteristic
243C23×C4—21no—
244C22×C8—24no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—42no—
249C22×C8—42no—
250C22×C8D4×C10311yescharacteristic
251C22×C8D4×C10311yescharacteristic
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8C2×C4×C10312yes—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C2×C4×C10312yes—
259C4×D4D4×C10312yes—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C10311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C23×C10311yescharacteristic
268#107—24no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8C2×C4×C10312yes—
274C4⋊C8D4×C10312yes—
275#103—42no—
276#103—42no—
277#102—24no—
278#102—42no—
279C22⋊C8—24no—
280C4×C8—21no—
281C4×C8—21no—
282C24—21no—
283C2×Q8—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4C22⋊C4×C10312yes—
293C2×D4SD16×C10312yes—
294C2×D4Q16×C10312yes—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4C2×D4×C10311yescharacteristic
305C22×C4C2×D4×C10311yescharacteristic
306C22×C4#41×C10311yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—48no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8D8×C10312yes—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C10312yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C42C22×C4×C10311yescharacteristic
337C42C2×D4×C10311yescharacteristic
338C42C2×D4×C10311yescharacteristic
339C42#41×C10311yescharacteristic
340C23—22no—
341C23—22no—
342C23—22no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23#121×C10311yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352D4—22no—
353D4—22no—
354D4—22no—
355D4#103×C10314yescomplemented
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4C2×C22⋊C4×C10311yescharacteristic
372C2×C4C4×D4×C10311yescharacteristic
373C2×C4C4×D4×C10311yescharacteristic
374C2×C4#120×C10311yescharacteristic
375C2×C4#121×C10311yescharacteristic
376C2×C4#123×C10311yescharacteristic
377C2×C4C2×D8×C10311yescharacteristic
378C2×C4C2×SD16×C10311yescharacteristic
379C2×C4C2×Q16×C10311yescharacteristic
380C2×C4#135×C10311yescharacteristic
381C2×C4#135×C10311yescharacteristic
382C2×C4#135×C10311yescharacteristic
383C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
384C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
385C8—22no—
386C8—42no—
387C8—42no—
388C8—41no—
389C8—81no—
390C22—24no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22#386×C10311yescharacteristic
398C22#459×C10311yescharacteristic
399C22#463×C10311yescharacteristic
400C22#465×C10311yescharacteristic
401C22#467×C10311yescharacteristic
402C22#471×C10311yescharacteristic
403C22#473×C10311yescharacteristic
404C4—21no—
405C4—21no—
406C4—42no—
407C4—82no—
408C4—161no—
409C4C2×#103×C10311yescharacteristic
410C4#416×C10311yescharacteristic
411C4C4×D8×C10311yescharacteristic
412C4#442×C10311yescharacteristic
413C4#447×C10311yescharacteristic
414C4#449×C10311yescharacteristic
415C4#465×C10311yescharacteristic
416C4#467×C10311yescharacteristic
417C2—44no—
418C2C103×#166511yescharacteristic
419C2C103×#166911yescharacteristic
420C2C103×#167911yescharacteristic
421C2C103×#168311yescharacteristic
422C2C103×#187911yescharacteristic
423C2C103×#189211yescharacteristic
424C2C103×#190811yescharacteristic
subgroupG/H
center, socleC23×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC22×D4×C103D4
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
3. C103×#1956C2semidirect
5. C2×#332×C103C2semidirect
6. C103×#1296C2semidirect
7. C103×#1277C2semidirect
12. #474×C103C4semidirect
142. D4×C103#103semidirect
204. #9219C103direct (N × H)
215. #1956C2×C103semidirect
217. C2×#332C2×C103semidirect
218. #1296C2×C103semidirect
219. #1277C2×C103semidirect
220. C103#9219direct (N × H)
225. #474C4×C103semidirect
355. D4#103×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1032
C2×C8×D4×C1032
C103×#19562
C103×#18022
C2×#332×C1032
C103×#12962
C103×#12772
#9219103