Finite Group Databasebeta

← C103×#9497 #39914772

Subgroups — C103×#9497 #39914772

Order 26368.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2403C211yesmaximal, characteristic
2C103×#2309C211yesmaximal, characteristic, complemented
3C103×#1781C211yesmaximal, characteristic, complemented
4C103×#1781C212yesmaximal, complemented
5C103×#1304C212yesmaximal, complemented
6C23×D4×C103C2211yescharacteristic
7C23×D4×C103C2211yescharacteristic
8C2×#120×C103—21no—
9C2×#120×C103C412yescomplemented
10C2×#117×C103—21no—
11C2×#99×C103—22no—
12C2×#99×C103—24no—
13#392×C103—22no—
14#390×C103—24no—
15#386×C103—21no—
16#386×C103C412yescomplemented
17#379×C103—21no—
18#379×C103C2212yes—
19#379×C103C2211yescharacteristic
20#379×C103C2212yes—
21C25×C103C2×C411yescharacteristic
22C25×C103D411yescharacteristic
23C25×C103C2311yescharacteristic
24C22×D4×C103—21no—
25C22×D4×C103—22no—
26C22×D4×C103—22no—
27C22×D4×C103—22no—
28C22×D4×C103—21no—
29C22×D4×C103—22no—
30C22×D4×C103—22no—
31C22×D4×C103—44no—
32C22×D4×C103—44no—
33C22×D4×C103C2×C412yes—
34C22×D4×C103D412yes—
35C23×C4×C103C2×C411yescharacteristic
36C23×C4×C103D411yescharacteristic
37#120×C103—44no—
38#120×C103—44no—
39#117×C103—44no—
40C2×C4⋊C4×C103—22no—
41C2×C22⋊C4×C103—22no—
42C2×C22⋊C4×C103—22no—
43C2×C22⋊C4×C103—21no—
44C2×C22⋊C4×C103—22no—
45C2×C22⋊C4×C103—22no—
46C2×C22⋊C4×C103—22no—
47C2×C22⋊C4×C103—22no—
48C2×C22⋊C4×C103—22no—
49C2×C22⋊C4×C103—22no—
50C2×C22⋊C4×C103—21no—
51C2×C22⋊C4×C103—22no—
52C2×C22⋊C4×C103C2×C412yes—
53C2×C22⋊C4×C103D414yescomplemented
54C2×C42×C103—22no—
55#99×C103—48no—
56#99×C103—44no—
57#95×C103—22no—
58C24×C103—21no—
59C24×C103—21no—
60C24×C103—22no—
61C24×C103—21no—
62C24×C103—42no—
63C24×C103—42no—
64C24×C103—42no—
65C24×C103—42no—
66C24×C103—42no—
67C24×C103—42no—
68C24×C103—81no—
69C24×C103—81no—
70C24×C103—81no—
71C24×C103C22⋊C412yes—
72C24×C103C22×C411yescharacteristic
73C24×C103C2×D411yescharacteristic
74C24×C103C2×D411yescharacteristic
75C24×C103C2×D412yes—
76C24×C103#4112yes—
77C2×D4×C103—28no—
78C2×D4×C103—24no—
79C2×D4×C103—24no—
80C2×D4×C103—24no—
81C2×D4×C103—24no—
82C2×D4×C103—24no—
83C2×D4×C103—42no—
84C2×D4×C103—42no—
85C2×D4×C103—44no—
86C2×D4×C103—44no—
87C2×D4×C103—48no—
88C2×D4×C103—42no—
89C2×D4×C103—44no—
90C2×D4×C103—42no—
91C2×D4×C103—44no—
92C2×D4×C103—42no—
93C2×D4×C103—44no—
94C2×D4×C103—41no—
95C2×D4×C103—42no—
96C2×D4×C103—41no—
97C2×D4×C103—44no—
98C2×D4×C103—44no—
99C2×D4×C103—82no—
100C22×C4×C103—21no—
101C22×C4×C103—21no—
102C22×C4×C103—24no—
103C22×C4×C103—21no—
104C22×C4×C103—22no—
105C22×C4×C103—22no—
106C22×C4×C103—24no—
107C22×C4×C103—42no—
108C22×C4×C103—42no—
109C22×C4×C103C22⋊C412yes—
110C4⋊C4×C103—44no—
111C22⋊C4×C103—44no—
112C22⋊C4×C103—44no—
113C22⋊C4×C103—42no—
114C22⋊C4×C103—44no—
115C22⋊C4×C103—44no—
116C22⋊C4×C103—42no—
117C22⋊C4×C103—44no—
118C22⋊C4×C103—44no—
119C22⋊C4×C103—82no—
120C22⋊C4×C103—82no—
121C22⋊C4×C103—81no—
122C22⋊C4×C103—82no—
123C22⋊C4×C103—82no—
124C42×C103—44no—
125C23×C103—22no—
126C23×C103—22no—
127C23×C103—22no—
128C23×C103—22no—
129C23×C103—24no—
130C23×C103—22no—
131C23×C103—24no—
132C23×C103—22no—
133C23×C103—22no—
134C23×C103—22no—
135C23×C103—41no—
136C23×C103—41no—
137C23×C103—41no—
138C23×C103—42no—
139C23×C103—41no—
140C23×C103—42no—
141C23×C103—41no—
142C23×C103—42no—
143C23×C103—42no—
144C23×C103—42no—
145C23×C103—42no—
146C23×C103—42no—
147C23×C103—42no—
148C23×C103—41no—
149C23×C103—42no—
150C23×C103—42no—
151C23×C103—42no—
152C23×C103—42no—
153C23×C103—41no—
154C23×C103—42no—
155C23×C103—42no—
156C23×C103—81no—
157C23×C103—81no—
158C23×C103—82no—
159C23×C103—82no—
160C23×C103—88no—
161C23×C103—88no—
162C23×C103—88no—
163C23×C103C2×C22⋊C411yescharacteristic
164C23×C103C4×D412yes—
165C23×C103#12011yescharacteristic
166C23×C103#12112yes—
167C23×C103#12311yescharacteristic
168D4×C103—48no—
169D4×C103—48no—
170D4×C103—48no—
171D4×C103—44no—
172D4×C103—44no—
173D4×C103—88no—
174C2×C4×C103—22no—
175C2×C4×C103—22no—
176C2×C4×C103—24no—
177C2×C4×C103—22no—
178C2×C4×C103—22no—
179C2×C4×C103—22no—
180C2×C4×C103—24no—
181C2×C4×C103—41no—
182C2×C4×C103—42no—
183C2×C4×C103—41no—
184C2×C4×C103—44no—
185C2×C4×C103—42no—
186C2×C4×C103—44no—
187C2×C4×C103—42no—
188C2×C4×C103—42no—
189C2×C4×C103—44no—
190C2×C4×C103—82no—
191C2×C4×C103—82no—
192C2×C4×C103—82no—
193C2×C4×C103#9914yescomplemented
194C22×C103—21no—
195C22×C103—21no—
196C22×C103—21no—
197C22×C103—21no—
198C22×C103—22no—
199C22×C103—22no—
200C22×C103—21no—
201C22×C103—21no—
202C22×C103—22no—
203C22×C103—22no—
204C22×C103—22no—
205C22×C103—22no—
206C22×C103—21no—
207C22×C103—44no—
208C22×C103—44no—
209C22×C103—44no—
210C22×C103—44no—
211C22×C103—42no—
212C22×C103—42no—
213C22×C103—42no—
214C22×C103—42no—
215C22×C103—84no—
216C22×C103—82no—
217C22×C103—82no—
218C22×C103—84no—
219C22×C103—82no—
220C22×C103—84no—
221C22×C103—84no—
222C22×C103—84no—
223C22×C103—84no—
224C22×C103—81no—
225C22×C103—81no—
226C22×C103#38611yescharacteristic
227C22×C103C2×#9912yes—
228C22×C103B(4,𝔽2)12yes—
229C4×C103—24no—
230C4×C103—42no—
231C4×C103—84no—
232C4×C103—82no—
233C4×C103—162no—
234#9497C10311yesmaximal, characteristic, direct product factor, Sylow
235C2×C103—22no—
236C2×C103—22no—
237C2×C103—42no—
238C2×C103—42no—
239C2×C103—41no—
240C2×C103—82no—
241C2×C103—82no—
242C2×C103#188911yescharacteristic
243C2×C103#189811yescharacteristic
244C2×C103#191311yescharacteristic
245#2403C2×C10311yescharacteristic
246#2309C2×C10311yescharacteristic, complemented
247#1781C2×C10312yescomplemented
248#1781C2×C10311yescharacteristic, complemented
249#1304C2×C10312yescomplemented
250C103#949711yescharacteristic, direct product factor, Sylow
251C23×D4C22×C10311yescharacteristic
252C23×D4C22×C10311yescharacteristic
253C2×#120—21no—
254C2×#120C4×C10312yescomplemented
255C2×#117—21no—
256C2×#99—22no—
257C2×#99—24no—
258#392—22no—
259#390—24no—
260#386—21no—
261#386C4×C10312yescomplemented
262#379—21no—
263#379C22×C10312yes—
264#379C22×C10311yescharacteristic
265#379C22×C10312yes—
266C25C2×C4×C10311yescharacteristic
267C25D4×C10311yescharacteristic
268C25C23×C10311yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C10312yes—
279C22×D4D4×C10312yes—
280C23×C4C2×C4×C10311yescharacteristic
281C23×C4D4×C10311yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C10312yes—
298C2×C22⋊C4D4×C10314yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C10312yes—
317C24C22×C4×C10311yescharacteristic
318C24C2×D4×C10311yescharacteristic
319C24C2×D4×C10311yescharacteristic
320C24C2×D4×C10312yes—
321C24#41×C10312yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C10312yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C10311yescharacteristic
409C23C4×D4×C10312yes—
410C23#120×C10311yescharacteristic
411C23#121×C10312yes—
412C23#123×C10311yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C10314yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#386×C10311yescharacteristic
472C22C2×#99×C10312yes—
473C22B(4,𝔽2)×C10312yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C103×#188911yescharacteristic
487C2C103×#189811yescharacteristic
488C2C103×#191311yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC24C22×C4×C103
Frattini, cosocleC25C23×C103
prime radicalC103×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C25×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2309C2semidirect
3. C103×#1781C2semidirect
4. C103×#1781C2semidirect
5. C103×#1304C2semidirect
9. C2×#120×C103C4semidirect
16. #386×C103C4semidirect
53. C2×C22⋊C4×C103D4semidirect
193. C2×C4×C103#99semidirect
234. #9497C103direct (N × H)
246. #2309C2×C103semidirect
247. #1781C2×C103semidirect
248. #1781C2×C103semidirect
249. #1304C2×C103semidirect
250. C103#9497direct (N × H)
254. C2×#120C4×C103semidirect
261. #386C4×C103semidirect
298. C2×C22⋊C4D4×C103semidirect
438. C2×C4#99×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#24032
C103×#23092
C103×#17812
C103×#13042
#9497103