Finite Group Databasebeta

← C103×#8984 #39914259

Subgroups — C103×#8984 #39914259

Order 26368.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C103C211yesmaximal, characteristic
2C103×#2354C211yesmaximal, characteristic
3C103×#1990C211yesmaximal, characteristic, complemented
4C103×#1981C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C103C211yesmaximal, characteristic
6C103×#1296C211yesmaximal, characteristic, complemented
7C103×#1279C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C103C2211yescharacteristic
9C2×C4×D4×C103C2211yescharacteristic
10C2×#117×C103—21no—
11#474×C103—22no—
12#474×C103C414yescomplemented
13C2×#107×C103—21no—
14C2×C4⋊C8×C103C2211yescharacteristic
15C2×C4⋊C8×C103C2211yescharacteristic
16C2×#103×C103—21no—
17C2×#103×C103—21no—
18C2×#102×C103—21no—
19C2×C4×C8×C103C2211yescharacteristic
20#390×C103—21no—
21#388×C103—22no—
22#384×C103C2211yescharacteristic
23#380×C103—21no—
24C4×C4⋊C4×C103—21no—
25C4×C4⋊C4×C103C2211yescharacteristic
26#340×C103—22no—
27D4⋊C8×C103—22no—
28C22×Q8×C103—21no—
29C22×D4×C103D411yescharacteristic
30C23×C4×C103—21no—
31C22×C8×C103—21no—
32C22×C8×C103—21no—
33C22×C8×C103—21no—
34C4⋊Q8×C103—21no—
35C4⋊Q8×C103—21no—
36C4⋊Q8×C103—21no—
37C4⋊Q8×C103C2×C412yes—
38C4×D4×C103—21no—
39C4×D4×C103—21no—
40C4×D4×C103C2×C412yes—
41C4×D4×C103D412yes—
42#117×C103—42no—
43#117×C103—42no—
44C2×C4⋊C4×C103—21no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103—21no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103D411yescharacteristic
49C2×C4⋊C4×C103D411yescharacteristic
50C2×C4⋊C4×C103D411yescharacteristic
51C2×C4⋊C4×C103D412yes—
52C2×C22⋊C4×C103—21no—
53C2×C22⋊C4×C103—22no—
54C2×C22⋊C4×C103—22no—
55C2×C42×C103—22no—
56C2×C42×C103—21no—
57C2×C42×C103C2311yescharacteristic
58#107×C103—24no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103—21no—
61C4⋊C8×C103—21no—
62C4⋊C8×C103C2×C412yes—
63#103×C103—42no—
64#103×C103—42no—
65#102×C103—24no—
66C4×C8×C103—21no—
67C4×C8×C103—21no—
68#95×C103—22no—
69#95×C103—21no—
70C24×C103—21no—
71C2×Q8×C103—22no—
72C2×Q8×C103—41no—
73C2×Q8×C103—41no—
74C2×Q8×C103—41no—
75C2×Q8×C103—41no—
76C2×Q8×C103—41no—
77C2×D4×C103—21no—
78C2×D4×C103—21no—
79C2×D4×C103—21no—
80C2×D4×C103—21no—
81C2×D4×C103—21no—
82C2×D4×C103C22⋊C412yes—
83C22×C4×C103—21no—
84C22×C4×C103—21no—
85C22×C4×C103—22no—
86C22×C4×C103—22no—
87C22×C4×C103—21no—
88C22×C4×C103—22no—
89C22×C4×C103—41no—
90C22×C4×C103—41no—
91C22×C4×C103—41no—
92C22×C4×C103—41no—
93C22×C4×C103—41no—
94C22×C4×C103C2×D411yescharacteristic
95C22×C4×C103C2×D411yescharacteristic
96C22×C4×C103C2×D411yescharacteristic
97C2×C8×C103—22no—
98C2×C8×C103—22no—
99C2×C8×C103—41no—
100C2×C8×C103—41no—
101C2×C8×C103—41no—
102C2×C8×C103—41no—
103C2×C8×C103—41no—
104C2×C8×C103—41no—
105C2×C8×C103—41no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103—21no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—21no—
111C4⋊C4×C103—21no—
112C4⋊C4×C103—42no—
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×C103C22⋊C412yes—
120C4⋊C4×C103D812yes—
121C22⋊C4×C103—22no—
122C22⋊C4×C103—22no—
123C22⋊C4×C103—44no—
124C22⋊C4×C103—82no—
125C42×C103—44no—
126C42×C103—41no—
127C42×C103—41no—
128C42×C103C22×C411yescharacteristic
129C42×C103C2×D411yescharacteristic
130C42×C103#4111yescharacteristic
131C42×C103#4111yescharacteristic
132C23×C103—22no—
133C23×C103—41no—
134C23×C103—41no—
135C23×C103—41no—
136C23×C103—41no—
137C23×C103—41no—
138C23×C103—41no—
139C23×C103#12011yescharacteristic
140Q8×C103—42no—
141Q8×C103—42no—
142Q8×C103—81no—
143Q8×C103—81no—
144D4×C103—22no—
145D4×C103—22no—
146D4×C103—41no—
147D4×C103—41no—
148C2×C4×C103—21no—
149C2×C4×C103—21no—
150C2×C4×C103—22no—
151C2×C4×C103—22no—
152C2×C4×C103—41no—
153C2×C4×C103—41no—
154C2×C4×C103—41no—
155C2×C4×C103—41no—
156C2×C4×C103—42no—
157C2×C4×C103—42no—
158C2×C4×C103—42no—
159C2×C4×C103—42no—
160C2×C4×C103—42no—
161C2×C4×C103—42no—
162C2×C4×C103—41no—
163C2×C4×C103—41no—
164C2×C4×C103—42no—
165C2×C4×C103—41no—
166C2×C4×C103—42no—
167C2×C4×C103—81no—
168C2×C4×C103—81no—
169C2×C4×C103C2×C22⋊C411yescharacteristic
170C2×C4×C103C4×D411yescharacteristic
171C2×C4×C103C4×D411yescharacteristic
172C2×C4×C103#12111yescharacteristic
173C2×C4×C103#12111yescharacteristic
174C2×C4×C103#12311yescharacteristic
175C2×C4×C103C2×D811yescharacteristic
176C2×C4×C103#13511yescharacteristic
177C2×C4×C103#13511yescharacteristic
178C2×C4×C103#13511yescharacteristic
179C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C103#13711yescharacteristic
182C2×C4×C103#13711yescharacteristic
183C8×C103—42no—
184C8×C103—42no—
185C8×C103—81no—
186C22×C103—42no—
187C22×C103—42no—
188C22×C103—42no—
189C22×C103—81no—
190C22×C103—81no—
191C22×C103—81no—
192C22×C103—81no—
193C22×C103#38611yescharacteristic
194C22×C103#44711yescharacteristic
195C22×C103#44911yescharacteristic
196C22×C103#45211yescharacteristic
197C22×C103#45211yescharacteristic
198C22×C103#45511yescharacteristic
199C22×C103#45611yescharacteristic
200C4×C103—21no—
201C4×C103—21no—
202C4×C103—42no—
203C4×C103—42no—
204C4×C103—82no—
205C4×C103—82no—
206C4×C103—81no—
207C4×C103#41611yescharacteristic
208C4×C103#41911yescharacteristic
209C4×C103C4×D811yescharacteristic
210C4×C103#44211yescharacteristic
211C4×C103#45911yescharacteristic
212C4×C103#46311yescharacteristic
213C4×C103#48511yescharacteristic
214C4×C103#48511yescharacteristic
215#8984C10311yesmaximal, characteristic, direct product factor, Sylow
216C2×C103—82no—
217C2×C103#164111yescharacteristic
218C2×C103#164611yescharacteristic
219C2×C103#164711yescharacteristic
220C2×C103#165211yescharacteristic
221C2×C103#187311yescharacteristic
222C2×C103#187911yescharacteristic
223C2×C103#188211yescharacteristic
224C2×#474C2×C10311yescharacteristic
225#2354C2×C10311yescharacteristic
226#1990C2×C10311yescharacteristic, complemented
227#1981C2×C10311yescharacteristic, complemented
228C2×D4⋊C8C2×C10311yescharacteristic
229#1296C2×C10311yescharacteristic, complemented
230#1279C2×C10311yescharacteristic, complemented
231C103#898411yescharacteristic, direct product factor, Sylow
232C2×C4⋊Q8C22×C10311yescharacteristic
233C2×C4×D4C22×C10311yescharacteristic
234C2×#117—21no—
235#474—22no—
236#474C4×C10314yescomplemented
237C2×#107—21no—
238C2×C4⋊C8C22×C10311yescharacteristic
239C2×C4⋊C8C22×C10311yescharacteristic
240C2×#103—21no—
241C2×#103—21no—
242C2×#102—21no—
243C2×C4×C8C22×C10311yescharacteristic
244#390—21no—
245#388—22no—
246#384C22×C10311yescharacteristic
247#380—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4C22×C10311yescharacteristic
250#340—22no—
251D4⋊C8—22no—
252C22×Q8—21no—
253C22×D4D4×C10311yescharacteristic
254C23×C4—21no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—21no—
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8C2×C4×C10312yes—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4C2×C4×C10312yes—
265C4×D4D4×C10312yes—
266#117—42no—
267#117—42no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C10311yescharacteristic
273C2×C4⋊C4D4×C10311yescharacteristic
274C2×C4⋊C4D4×C10311yescharacteristic
275C2×C4⋊C4D4×C10312yes—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C42—22no—
280C2×C42—21no—
281C2×C42C23×C10311yescharacteristic
282#107—24no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8C2×C4×C10312yes—
287#103—42no—
288#103—42no—
289#102—24no—
290C4×C8—21no—
291C4×C8—21no—
292#95—22no—
293#95—21no—
294C24—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4C22⋊C4×C10312yes—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C10311yescharacteristic
319C22×C4C2×D4×C10311yescharacteristic
320C22×C4C2×D4×C10311yescharacteristic
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—42no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4C22⋊C4×C10312yes—
344C4⋊C4D8×C10312yes—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—44no—
348C22⋊C4—82no—
349C42—44no—
350C42—41no—
351C42—41no—
352C42C22×C4×C10311yescharacteristic
353C42C2×D4×C10311yescharacteristic
354C42#41×C10311yescharacteristic
355C42#41×C10311yescharacteristic
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23#120×C10311yescharacteristic
364Q8—42no—
365Q8—42no—
366Q8—81no—
367Q8—81no—
368D4—22no—
369D4—22no—
370D4—41no—
371D4—41no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4C2×C22⋊C4×C10311yescharacteristic
394C2×C4C4×D4×C10311yescharacteristic
395C2×C4C4×D4×C10311yescharacteristic
396C2×C4#121×C10311yescharacteristic
397C2×C4#121×C10311yescharacteristic
398C2×C4#123×C10311yescharacteristic
399C2×C4C2×D8×C10311yescharacteristic
400C2×C4#135×C10311yescharacteristic
401C2×C4#135×C10311yescharacteristic
402C2×C4#135×C10311yescharacteristic
403C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
404C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
405C2×C4#137×C10311yescharacteristic
406C2×C4#137×C10311yescharacteristic
407C8—42no—
408C8—42no—
409C8—81no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#386×C10311yescharacteristic
418C22#447×C10311yescharacteristic
419C22#449×C10311yescharacteristic
420C22#452×C10311yescharacteristic
421C22#452×C10311yescharacteristic
422C22#455×C10311yescharacteristic
423C22#456×C10311yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—82no—
429C4—82no—
430C4—81no—
431C4#416×C10311yescharacteristic
432C4#419×C10311yescharacteristic
433C4C4×D8×C10311yescharacteristic
434C4#442×C10311yescharacteristic
435C4#459×C10311yescharacteristic
436C4#463×C10311yescharacteristic
437C4#485×C10311yescharacteristic
438C4#485×C10311yescharacteristic
439C2—82no—
440C2C103×#164111yescharacteristic
441C2C103×#164611yescharacteristic
442C2C103×#164711yescharacteristic
443C2C103×#165211yescharacteristic
444C2C103×#187311yescharacteristic
445C2C103×#187911yescharacteristic
446C2C103×#188211yescharacteristic
subgroupG/H
center, socleC23×C103#120
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×#1990C2semidirect
4. C103×#1981C2semidirect
6. C103×#1296C2semidirect
7. C103×#1279C2semidirect
12. #474×C103C4semidirect
215. #8984C103direct (N × H)
226. #1990C2×C103semidirect
227. #1981C2×C103semidirect
229. #1296C2×C103semidirect
230. #1279C2×C103semidirect
231. C103#8984direct (N × H)
236. #474C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1032
C103×#23542
C103×#19902
C103×#19812
C2×D4⋊C8×C1032
C103×#12962
C103×#12792
#8984103