Finite Group Databasebeta

← C103×#10005 #39915280

Subgroups — C103×#10005 #39915280

Order 26368.

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

normal subgroups only

This group has 566 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
1C103×#3234C211yesmaximal, characteristic, complemented
2C103×#3109C211yesmaximal, characteristic
3C103×#2562C211yesmaximal, characteristic, complemented
4C103×#1980C211yesmaximal, characteristic, complemented
5C103×#1528C211yesmaximal, characteristic, complemented
6C103×#1490C211yesmaximal, characteristic, complemented
7C103×#1285C211yesmaximal, characteristic, complemented
8#532×C103C2211yescharacteristic
9C2×#125×C103C2211yescharacteristic
10C2×C4×D4×C103C2211yescharacteristic
11#501×C103—21no—
12#490×C103—21no—
13#481×C103—21no—
14#481×C103—21no—
15#480×C103—21no—
16#478×C103—22no—
17#476×C103—21no—
18#459×C103—21no—
19#447×C103—21no—
20#442×C103—22no—
21#432×C103C2211yescharacteristic
22#432×C103C2211yescharacteristic
23C2×#104×C103—22no—
24C4×M16×C103C2211yescharacteristic
25#400×C103—21no—
26#394×C103—21no—
27#388×C103—22no—
28#380×C103—21no—
29#380×C103—21no—
30C4×C4⋊C4×C103C2211yescharacteristic
31#330×C103—22no—
32D4⋊C8×C103—22no—
33C2×#41×C103—21no—
34C22×D4×C103D411yescharacteristic
35C23×C4×C103—21no—
36C2×D8×C103—22no—
37C2×M16×C103—21no—
38C4⋊Q8×C103D411yescharacteristic
39#127×C103D411yescharacteristic
40#125×C103—21no—
41#125×C103—21no—
42#125×C103—21no—
43#125×C103—21no—
44#124×C103—21no—
45#121×C103—21no—
46#121×C103—21no—
47C4×D4×C103—21no—
48C4×D4×C103—21no—
49C4×D4×C103—21no—
50C4×D4×C103—21no—
51C4×D4×C103—21no—
52C4×D4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103—21no—
55C2×C4⋊C4×C103—21no—
56C2×C4⋊C4×C103D411yescharacteristic
57C2×C4⋊C4×C103D411yescharacteristic
58C2×C4⋊C4×C103D411yescharacteristic
59C2×C22⋊C4×C103—22no—
60C2×C22⋊C4×C103—21no—
61C2×C22⋊C4×C103—22no—
62C2×C42×C103D412yes—
63C2×C42×C103C2311yescharacteristic
64#107×C103—22no—
65#106×C103—22no—
66#106×C103—22no—
67C4⋊C8×C103—21no—
68C4⋊C8×C103D412yes—
69#104×C103—44no—
70#102×C103—22no—
71#102×C103—22no—
72#102×C103—22no—
73#102×C103—22no—
74C22⋊C8×C103—21no—
75C22⋊C8×C103—21no—
76#97×C103—21no—
77#97×C103—21no—
78#97×C103D412yes—
79C4×C8×C103—21no—
80#95×C103—22no—
81#95×C103—22no—
82#95×C103—21no—
83C24×C103—21no—
84#41×C103—42no—
85#41×C103—42no—
86C2×Q8×C103—21no—
87C2×D4×C103—21no—
88C2×D4×C103—21no—
89C2×D4×C103—21no—
90C2×D4×C103—21no—
91C2×D4×C103—21no—
92C2×D4×C103—42no—
93C2×D4×C103—41no—
94C22×C4×C103—21no—
95C22×C4×C103—22no—
96C22×C4×C103—21no—
97C22×C4×C103—21no—
98C22×C4×C103—42no—
99C22×C4×C103—42no—
100C22×C4×C103—41no—
101C22×C4×C103—41no—
102C22×C4×C103—41no—
103C22×C4×C103C2×D411yescharacteristic
104C22×C4×C103C2×D411yescharacteristic
105C22×C4×C103C2×D411yescharacteristic
106D8×C103—44no—
107M16×C103—22no—
108M16×C103—41no—
109C2×C8×C103—22no—
110C2×C8×C103—22no—
111C2×C8×C103—41no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103—21no—
116C4⋊C4×C103—21no—
117C4⋊C4×C103—21no—
118C4⋊C4×C103—21no—
119C4⋊C4×C103—21no—
120C4⋊C4×C103—42no—
121C4⋊C4×C103—41no—
122C4⋊C4×C103—41no—
123C4⋊C4×C103—41no—
124C4⋊C4×C103—41no—
125C22⋊C4×C103—44no—
126C22⋊C4×C103—41no—
127C22⋊C4×C103—41no—
128C22⋊C4×C103—41no—
129C22⋊C4×C103—41no—
130C22⋊C4×C103—82no—
131C42×C103—42no—
132C42×C103C2×D411yescharacteristic
133C42×C103C2×D411yescharacteristic
134C42×C103C2×D411yescharacteristic
135C42×C103#4111yescharacteristic
136C23×C103—22no—
137C23×C103—41no—
138C23×C103—41no—
139C23×C103—41no—
140C23×C103—41no—
141C23×C103—41no—
142C23×C103—41no—
143C23×C103—41no—
144C23×C103#12011yescharacteristic
145Q8×C103—42no—
146D4×C103—22no—
147D4×C103—22no—
148D4×C103—41no—
149D4×C103—41no—
150D4×C103—42no—
151D4×C103—42no—
152D4×C103—42no—
153D4×C103—81no—
154D4×C103—81no—
155C2×C4×C103—21no—
156C2×C4×C103—21no—
157C2×C4×C103—22no—
158C2×C4×C103—41no—
159C2×C4×C103—42no—
160C2×C4×C103—42no—
161C2×C4×C103—42no—
162C2×C4×C103—41no—
163C2×C4×C103—41no—
164C2×C4×C103—41no—
165C2×C4×C103—41no—
166C2×C4×C103—41no—
167C2×C4×C103—41no—
168C2×C4×C103—42no—
169C2×C4×C103—41no—
170C2×C4×C103—41no—
171C2×C4×C103—82no—
172C2×C4×C103—82no—
173C2×C4×C103—82no—
174C2×C4×C103#12011yescharacteristic
175C2×C4×C103#12011yescharacteristic
176C2×C4×C103#12111yescharacteristic
177C2×C4×C103#12111yescharacteristic
178C2×C4×C103#12111yescharacteristic
179C2×C4×C103#12711yescharacteristic
180C8×C103—42no—
181C8×C103—42no—
182C8×C103—42no—
183C22×C103—21no—
184C22×C103—21no—
185C22×C103—42no—
186C22×C103—42no—
187C22×C103—42no—
188C22×C103—81no—
189C22×C103—81no—
190C22×C103—81no—
191C22×C103—81no—
192C22×C103—81no—
193C22×C103—81no—
194C22×C103—81no—
195C22×C103#39211yescharacteristic
196C22×C103#45311yescharacteristic
197C22×C103#45411yescharacteristic
198C4×C103—21no—
199C4×C103—21no—
200C4×C103—21no—
201C4×C103—21no—
202C4×C103—21no—
203C4×C103—82no—
204C4×C103—81no—
205C4×C103—81no—
206C4×C103—81no—
207C4×C103—81no—
208C4×C103#45412yes—
209#10005C10311yesmaximal, characteristic, direct product factor, Sylow
210C2×C103—21no—
211C2×C103—21no—
212C2×C103—82no—
213C2×C103—161no—
214C2×C103#200311yescharacteristic
215C2×C103#200611yescharacteristic
216C2×C103#201011yescharacteristic
217#3234C2×C10311yescharacteristic, complemented
218#3109C2×C10311yescharacteristic
219#2562C2×C10311yescharacteristic, complemented
220#1980C2×C10311yescharacteristic, complemented
221#1528C2×C10311yescharacteristic, complemented
222#1490C2×C10311yescharacteristic, complemented
223#1285C2×C10311yescharacteristic, complemented
224C103#1000511yescharacteristic, direct product factor, Sylow
225#532C22×C10311yescharacteristic
226C2×#125C22×C10311yescharacteristic
227C2×C4×D4C22×C10311yescharacteristic
228#501—21no—
229#490—21no—
230#481—21no—
231#481—21no—
232#480—21no—
233#478—22no—
234#476—21no—
235#459—21no—
236#447—21no—
237#442—22no—
238#432C22×C10311yescharacteristic
239#432C22×C10311yescharacteristic
240C2×#104—22no—
241C4×M16C22×C10311yescharacteristic
242#400—21no—
243#394—21no—
244#388—22no—
245#380—21no—
246#380—21no—
247C4×C4⋊C4C22×C10311yescharacteristic
248#330—22no—
249D4⋊C8—22no—
250C2×#41—21no—
251C22×D4D4×C10311yescharacteristic
252C23×C4—21no—
253C2×D8—22no—
254C2×M16—21no—
255C4⋊Q8D4×C10311yescharacteristic
256#127D4×C10311yescharacteristic
257#125—21no—
258#125—21no—
259#125—21no—
260#125—21no—
261#124—21no—
262#121—21no—
263#121—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4D4×C10311yescharacteristic
274C2×C4⋊C4D4×C10311yescharacteristic
275C2×C4⋊C4D4×C10311yescharacteristic
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—22no—
279C2×C42D4×C10312yes—
280C2×C42C23×C10311yescharacteristic
281#107—22no—
282#106—22no—
283#106—22no—
284C4⋊C8—21no—
285C4⋊C8D4×C10312yes—
286#104—44no—
287#102—22no—
288#102—22no—
289#102—22no—
290#102—22no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293#97—21no—
294#97—21no—
295#97D4×C10312yes—
296C4×C8—21no—
297#95—22no—
298#95—22no—
299#95—21no—
300C24—21no—
301#41—42no—
302#41—42no—
303C2×Q8—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—42no—
310C2×D4—41no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C10311yescharacteristic
321C22×C4C2×D4×C10311yescharacteristic
322C22×C4C2×D4×C10311yescharacteristic
323D8—44no—
324M16—22no—
325M16—41no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C22⋊C4—44no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—82no—
348C42—42no—
349C42C2×D4×C10311yescharacteristic
350C42C2×D4×C10311yescharacteristic
351C42C2×D4×C10311yescharacteristic
352C42#41×C10311yescharacteristic
353C23—22no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#120×C10311yescharacteristic
362Q8—42no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—81no—
371D4—81no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4#120×C10311yescharacteristic
392C2×C4#120×C10311yescharacteristic
393C2×C4#121×C10311yescharacteristic
394C2×C4#121×C10311yescharacteristic
395C2×C4#121×C10311yescharacteristic
396C2×C4#127×C10311yescharacteristic
397C8—42no—
398C8—42no—
399C8—42no—
400C22—21no—
401C22—21no—
402C22—42no—
403C22—42no—
404C22—42no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#392×C10311yescharacteristic
413C22#453×C10311yescharacteristic
414C22#454×C10311yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—81no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4#454×C10312yes—
426C2—21no—
427C2—21no—
428C2—82no—
429C2—161no—
430C2C103×#200311yescharacteristic
431C2C103×#200611yescharacteristic
432C2C103×#201011yescharacteristic
subgroupG/H
center, socleC22×C103#392
commutator, Frattini, cosocleC2×C42C23×C103
prime radicalC103×#3109C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3234C2semidirect
3. C103×#2562C2semidirect
4. C103×#1980C2semidirect
5. C103×#1528C2semidirect
6. C103×#1490C2semidirect
7. C103×#1285C2semidirect
209. #10005C103direct (N × H)
217. #3234C2×C103semidirect
219. #2562C2×C103semidirect
220. #1980C2×C103semidirect
221. #1528C2×C103semidirect
222. #1490C2×C103semidirect
223. #1285C2×C103semidirect
224. C103#10005direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32342
C103×#31092
C103×#25622
C103×#19802
C103×#15282
C103×#14902
C103×#12852
#10005103