Finite Group Databasebeta

← C103×#9937 #39915212

Subgroups — C103×#9937 #39915212

Order 26368.

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

normal subgroups only

This group has 526 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×#3195C211yesmaximal, characteristic
2C103×#3095C211yesmaximal, characteristic
3C103×#2625C211yesmaximal, characteristic
4C103×#1996C211yesmaximal, characteristic
5C103×#1826C211yesmaximal, characteristic
6C103×#1508C211yesmaximal, characteristic
7C103×#1305C211yesmaximal, characteristic
8C2×C22⋊Q8×C103C2211yescharacteristic
9C2×C22⋊Q8×C103C2211yescharacteristic
10C2×#117×C103C2211yescharacteristic
11#485×C103—22no—
12#484×C103—21no—
13#483×C103—21no—
14#483×C103—21no—
15#483×C103—21no—
16#470×C103—22no—
17#451×C103—21no—
18#451×C103—21no—
19#428×C103—21no—
20#419×C103—21no—
21#407×C103C2211yescharacteristic
22#407×C103C2211yescharacteristic
23#400×C103—21no—
24#398×C103—21no—
25#397×C103—22no—
26#391×C103—21no—
27#389×C103—21no—
28#380×C103C2211yescharacteristic
29C4×C22⋊C4×C103C2211yescharacteristic
30#342×C103—22no—
31#339×C103—22no—
32#328×C103—22no—
33C22×Q8×C103D411yescharacteristic
34C22×Q8×C103D411yescharacteristic
35C23×C4×C103C2311yescharacteristic
36C2×Q16×C103—22no—
37C2×M16×C103—21no—
38C2×M16×C103D412yes—
39C22⋊Q8×C103—21no—
40C22⋊Q8×C103—21no—
41C22⋊Q8×C103—21no—
42C22⋊Q8×C103—21no—
43C22⋊Q8×C103—21no—
44C22⋊Q8×C103—21no—
45C22⋊Q8×C103—21no—
46C22⋊Q8×C103—21no—
47#117×C103—21no—
48#117×C103—21no—
49#117×C103—21no—
50#117×C103—21no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103—22no—
55C2×C4⋊C4×C103D411yescharacteristic
56C2×C4⋊C4×C103D411yescharacteristic
57C2×C4⋊C4×C103D411yescharacteristic
58C2×C4⋊C4×C103D411yescharacteristic
59C2×C22⋊C4×C103—21no—
60C2×C22⋊C4×C103—21no—
61C2×C22⋊C4×C103—21no—
62C2×C22⋊C4×C103—21no—
63C2×C22⋊C4×C103D412yes—
64C2×C42×C103—21no—
65C2×C42×C103—21no—
66#107×C103—22no—
67#106×C103—22no—
68#106×C103—22no—
69#103×C103—22no—
70#103×C103—22no—
71#103×C103—22no—
72#103×C103—22no—
73C22⋊C8×C103—21no—
74C22⋊C8×C103—21no—
75C22⋊C8×C103—21no—
76C22⋊C8×C103D412yes—
77#95×C103—22no—
78#95×C103—22no—
79#95×C103—22no—
80#95×C103—21no—
81#95×C103—21no—
82C24×C103C2×D411yescharacteristic
83C2×Q8×C103—21no—
84C2×Q8×C103—21no—
85C2×Q8×C103—21no—
86C2×Q8×C103—21no—
87C2×Q8×C103—42no—
88C2×Q8×C103—42no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—22no—
92C22×C4×C103—21no—
93C22×C4×C103—21no—
94C22×C4×C103—21no—
95C22×C4×C103—21no—
96C22×C4×C103—42no—
97C22×C4×C103—41no—
98C22×C4×C103C2×D411yescharacteristic
99C22×C4×C103C2×D411yescharacteristic
100C22×C4×C103C2×D411yescharacteristic
101C22×C4×C103C2×D411yescharacteristic
102C22×C4×C103C2×D411yescharacteristic
103C22×C4×C103#4111yescharacteristic
104Q16×C103—82no—
105M16×C103—42no—
106M16×C103—42no—
107C2×C8×C103—22no—
108C2×C8×C103—22no—
109C4⋊C4×C103—21no—
110C4⋊C4×C103—21no—
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103—21no—
116C4⋊C4×C103—21no—
117C4⋊C4×C103—42no—
118C4⋊C4×C103—41no—
119C4⋊C4×C103—41no—
120C4⋊C4×C103—41no—
121C4⋊C4×C103—41no—
122C4⋊C4×C103—82no—
123C22⋊C4×C103—22no—
124C22⋊C4×C103—41no—
125C22⋊C4×C103—41no—
126C22⋊C4×C103—41no—
127C22⋊C4×C103—41no—
128C22⋊C4×C103—41no—
129C22⋊C4×C103—41no—
130C22⋊C4×C103—41no—
131C22⋊C4×C103—42no—
132C42×C103—42no—
133C42×C103—41no—
134C42×C103—41no—
135C23×C103—21no—
136C23×C103—21no—
137C23×C103—41no—
138C23×C103—41no—
139C23×C103#12011yescharacteristic
140C23×C103#12111yescharacteristic
141C23×C103#12711yescharacteristic
142Q8×C103—42no—
143Q8×C103—42no—
144Q8×C103—42no—
145Q8×C103—81no—
146C2×C4×C103—22no—
147C2×C4×C103—22no—
148C2×C4×C103—22no—
149C2×C4×C103—41no—
150C2×C4×C103—41no—
151C2×C4×C103—41no—
152C2×C4×C103—42no—
153C2×C4×C103—42no—
154C2×C4×C103—42no—
155C2×C4×C103—42no—
156C2×C4×C103—42no—
157C2×C4×C103—41no—
158C2×C4×C103—41no—
159C2×C4×C103—41no—
160C2×C4×C103—41no—
161C2×C4×C103—41no—
162C2×C4×C103—41no—
163C2×C4×C103—42no—
164C2×C4×C103—41no—
165C2×C4×C103—41no—
166C2×C4×C103—41no—
167C2×C4×C103—41no—
168C2×C4×C103—81no—
169C2×C4×C103—81no—
170C2×C4×C103—81no—
171C2×C4×C103—81no—
172C2×C4×C103#12011yescharacteristic
173C2×C4×C103#12011yescharacteristic
174C2×C4×C103#12111yescharacteristic
175C2×C4×C103#12111yescharacteristic
176C8×C103—42no—
177C8×C103—42no—
178C22×C103—21no—
179C22×C103—21no—
180C22×C103—21no—
181C22×C103—21no—
182C22×C103—21no—
183C22×C103—21no—
184C22×C103—21no—
185C22×C103—21no—
186C22×C103—81no—
187C22×C103—81no—
188C22×C103#39211yescharacteristic
189C22×C103#45511yescharacteristic
190C22×C103#45611yescharacteristic
191C4×C103—21no—
192C4×C103—21no—
193C4×C103—21no—
194C4×C103—82no—
195C4×C103—82no—
196C4×C103—81no—
197C4×C103—81no—
198C4×C103—81no—
199C4×C103—81no—
200C4×C103—81no—
201C4×C103—81no—
202C4×C103#45812yes—
203#9937C10311yesmaximal, characteristic, direct product factor, Sylow
204C2×C103—21no—
205C2×C103—21no—
206C2×C103—41no—
207C2×C103—41no—
208C2×C103#200711yescharacteristic
209C2×C103#200911yescharacteristic
210C2×C103#202211yescharacteristic
211#3195C2×C10311yescharacteristic
212#3095C2×C10311yescharacteristic
213#2625C2×C10311yescharacteristic
214#1996C2×C10311yescharacteristic
215#1826C2×C10311yescharacteristic
216#1508C2×C10311yescharacteristic
217#1305C2×C10311yescharacteristic
218C103#993711yescharacteristic, direct product factor, Sylow
219C2×C22⋊Q8C22×C10311yescharacteristic
220C2×C22⋊Q8C22×C10311yescharacteristic
221C2×#117C22×C10311yescharacteristic
222#485—22no—
223#484—21no—
224#483—21no—
225#483—21no—
226#483—21no—
227#470—22no—
228#451—21no—
229#451—21no—
230#428—21no—
231#419—21no—
232#407C22×C10311yescharacteristic
233#407C22×C10311yescharacteristic
234#400—21no—
235#398—21no—
236#397—22no—
237#391—21no—
238#389—21no—
239#380C22×C10311yescharacteristic
240C4×C22⋊C4C22×C10311yescharacteristic
241#342—22no—
242#339—22no—
243#328—22no—
244C22×Q8D4×C10311yescharacteristic
245C22×Q8D4×C10311yescharacteristic
246C23×C4C23×C10311yescharacteristic
247C2×Q16—22no—
248C2×M16—21no—
249C2×M16D4×C10312yes—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117—21no—
261#117—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4D4×C10311yescharacteristic
267C2×C4⋊C4D4×C10311yescharacteristic
268C2×C4⋊C4D4×C10311yescharacteristic
269C2×C4⋊C4D4×C10311yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4D4×C10312yes—
275C2×C42—21no—
276C2×C42—21no—
277#107—22no—
278#106—22no—
279#106—22no—
280#103—22no—
281#103—22no—
282#103—22no—
283#103—22no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8D4×C10312yes—
288#95—22no—
289#95—22no—
290#95—22no—
291#95—21no—
292#95—21no—
293C24C2×D4×C10311yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—42no—
299C2×Q8—42no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4C2×D4×C10311yescharacteristic
310C22×C4C2×D4×C10311yescharacteristic
311C22×C4C2×D4×C10311yescharacteristic
312C22×C4C2×D4×C10311yescharacteristic
313C22×C4C2×D4×C10311yescharacteristic
314C22×C4#41×C10311yescharacteristic
315Q16—82no—
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—82no—
334C22⋊C4—22no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C42—42no—
344C42—41no—
345C42—41no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23#120×C10311yescharacteristic
351C23#121×C10311yescharacteristic
352C23#127×C10311yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—81no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4#120×C10311yescharacteristic
384C2×C4#120×C10311yescharacteristic
385C2×C4#121×C10311yescharacteristic
386C2×C4#121×C10311yescharacteristic
387C8—42no—
388C8—42no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—81no—
398C22—81no—
399C22#392×C10311yescharacteristic
400C22#455×C10311yescharacteristic
401C22#456×C10311yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—82no—
406C4—82no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4#458×C10312yes—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2C103×#200711yescharacteristic
419C2C103×#200911yescharacteristic
420C2C103×#202211yescharacteristic
subgroupG/H
center, socleC22×C103#392
commutator, Frattini, cosocleC23×C4C23×C103
prime radicalC24×C103C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
203. #9937C103direct (N × H)
218. C103#9937direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31952
C103×#30952
C103×#26252
C103×#19962
C103×#18262
C103×#15082
C103×#13052
#9937103