Finite Group Databasebeta

← C103×#13091 #39918366

Subgroups — C103×#13091 #39918366

Order 26368.

724 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#410×C103C211yesmaximal, characteristic
2C103×#2432C211yesmaximal, characteristic
3C2×#354×C103C212yesmaximal, complemented
4C103×#1782C211yesmaximal, characteristic
5C103×#1393C212yesmaximal, complemented
6C22×#41×C103C2211yescharacteristic
7C2×C4⋊Q8×C103C411yescharacteristic, complemented
8C2×#124×C103C2211yescharacteristic
9C2×C22⋊Q8×C103C411yescharacteristic, complemented
10C2×#117×C103—21no—
11#410×C103—24no—
12C2×#99×C103—21no—
13C2×#99×C103—21no—
14C2×#99×C103C2212yes—
15C2×#99×C103C2212yes—
16#394×C103—21no—
17#394×C103—21no—
18#391×C103C411yescharacteristic, complemented
19#390×C103C2211yescharacteristic
20#385×C103—21no—
21#385×C103—21no—
22#381×C103—21no—
23C4×C22⋊C4×C103C411yescharacteristic, complemented
24#354×C103—24no—
25C2×#41×C103—22no—
26C2×#41×C103—22no—
27C2×#41×C103—41no—
28C2×#41×C103—41no—
29C2×#41×C103—42no—
30C22×Q8×C103C2×C411yescharacteristic
31C22×Q8×C103C2×C411yescharacteristic
32C22×D4×C103D411yescharacteristic
33C22×D4×C103D411yescharacteristic
34C22×D4×C103C2311yescharacteristic
35C23×C4×C103C2×C411yescharacteristic
36C23×C4×C103D411yescharacteristic
37C23×C4×C103D411yescharacteristic
38C4⋊Q8×C103—42no—
39#124×C103—22no—
40#124×C103—22no—
41C22⋊Q8×C103—41no—
42C22⋊Q8×C103—41no—
43#117×C103—24no—
44#117×C103—42no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103—21no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103—41no—
49C2×C4⋊C4×C103C2×C411yescharacteristic
50C2×C22⋊C4×C103—22no—
51C2×C22⋊C4×C103—21no—
52C2×C22⋊C4×C103—21no—
53C2×C22⋊C4×C103—21no—
54C2×C22⋊C4×C103—21no—
55C2×C22⋊C4×C103—21no—
56C2×C22⋊C4×C103—21no—
57C2×C22⋊C4×C103—22no—
58C2×C42×C103—41no—
59C2×C42×C103C2×C411yescharacteristic
60C2×C42×C103C2×C411yescharacteristic
61#99×C103—24no—
62#99×C103—22no—
63#99×C103—22no—
64#99×C103—22no—
65#99×C103—42no—
66#99×C103D414yes—
67#95×C103—21no—
68#95×C103—21no—
69#95×C103—21no—
70#95×C103—41no—
71#95×C103—41no—
72C24×C103C22⋊C411yescharacteristic
73C24×C103C2×D411yescharacteristic
74C24×C103C2×D411yescharacteristic
75#41×C103—44no—
76#41×C103—44no—
77#41×C103—44no—
78#41×C103—44no—
79C2×Q8×C103—22no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103—41no—
83C2×Q8×C103—41no—
84C2×Q8×C103—41no—
85C2×D4×C103—21no—
86C2×D4×C103—22no—
87C2×D4×C103—21no—
88C2×D4×C103—22no—
89C2×D4×C103—41no—
90C2×D4×C103—41no—
91C2×D4×C103—41no—
92C2×D4×C103—41no—
93C2×D4×C103—41no—
94C2×D4×C103C2×D412yes—
95C2×D4×C103#4112yes—
96C22×C4×C103—21no—
97C22×C4×C103—21no—
98C22×C4×C103—21no—
99C22×C4×C103—21no—
100C22×C4×C103—22no—
101C22×C4×C103—21no—
102C22×C4×C103—22no—
103C22×C4×C103—21no—
104C22×C4×C103—21no—
105C22×C4×C103—21no—
106C22×C4×C103—21no—
107C22×C4×C103—22no—
108C22×C4×C103—21no—
109C22×C4×C103—21no—
110C22×C4×C103—21no—
111C22×C4×C103—41no—
112C22×C4×C103—41no—
113C22×C4×C103—42no—
114C22×C4×C103—42no—
115C22×C4×C103C22⋊C411yescharacteristic
116C22×C4×C103C22⋊C411yescharacteristic
117C22×C4×C103C22⋊C411yescharacteristic
118C22×C4×C103C22×C411yescharacteristic
119C4⋊C4×C103—41no—
120C4⋊C4×C103—42no—
121C4⋊C4×C103—44no—
122C4⋊C4×C103—41no—
123C4⋊C4×C103—41no—
124C4⋊C4×C103—42no—
125C22⋊C4×C103—24no—
126C22⋊C4×C103—42no—
127C22⋊C4×C103—42no—
128C22⋊C4×C103—42no—
129C22⋊C4×C103—42no—
130C22⋊C4×C103—42no—
131C22⋊C4×C103—41no—
132C22⋊C4×C103—42no—
133C22⋊C4×C103—41no—
134C22⋊C4×C103—42no—
135C22⋊C4×C103—42no—
136C42×C103—22no—
137C42×C103—41no—
138C42×C103—44no—
139C23×C103—21no—
140C23×C103—21no—
141C23×C103—21no—
142C23×C103—21no—
143C23×C103—21no—
144C23×C103—21no—
145C23×C103—21no—
146C23×C103—41no—
147C23×C103—41no—
148C23×C103—41no—
149C23×C103—41no—
150C23×C103—41no—
151C23×C103—41no—
152C23×C103C2×C22⋊C411yescharacteristic
153C23×C103#12011yescharacteristic
154C23×C103#12112yes—
155C23×C103#12311yescharacteristic
156Q8×C103—44no—
157Q8×C103—82no—
158D4×C103—42no—
159D4×C103—42no—
160D4×C103—44no—
161D4×C103—42no—
162D4×C103—42no—
163C2×C4×C103—22no—
164C2×C4×C103—22no—
165C2×C4×C103—22no—
166C2×C4×C103—22no—
167C2×C4×C103—21no—
168C2×C4×C103—21no—
169C2×C4×C103—21no—
170C2×C4×C103—21no—
171C2×C4×C103—21no—
172C2×C4×C103—21no—
173C2×C4×C103—22no—
174C2×C4×C103—21no—
175C2×C4×C103—21no—
176C2×C4×C103—21no—
177C2×C4×C103—42no—
178C2×C4×C103—42no—
179C2×C4×C103—42no—
180C2×C4×C103—42no—
181C2×C4×C103—41no—
182C2×C4×C103—41no—
183C2×C4×C103—44no—
184C2×C4×C103—41no—
185C2×C4×C103—41no—
186C2×C4×C103—41no—
187C2×C4×C103—41no—
188C2×C4×C103—41no—
189C2×C4×C103—41no—
190C2×C4×C103—41no—
191C2×C4×C103—41no—
192C2×C4×C103—41no—
193C2×C4×C103—82no—
194C2×C4×C103—82no—
195C2×C4×C103—82no—
196C2×C4×C103—82no—
197C2×C4×C103—82no—
198C2×C4×C103#9912yes—
199C2×C4×C103#9911yescharacteristic
200C2×C4×C103#9911yescharacteristic
201C2×C4×C103C4×D412yes—
202C22×C103—21no—
203C22×C103—21no—
204C22×C103—21no—
205C22×C103—21no—
206C22×C103—22no—
207C22×C103—41no—
208C22×C103—42no—
209C22×C103—41no—
210C22×C103—41no—
211C22×C103—41no—
212C22×C103—41no—
213C22×C103—41no—
214C22×C103—41no—
215C22×C103—41no—
216C22×C103—41no—
217C22×C103—81no—
218C22×C103—81no—
219C22×C103—81no—
220C22×C103—81no—
221C22×C103#38611yescharacteristic
222C22×C103C2×#9911yescharacteristic
223C22×C103C2×#9911yescharacteristic
224C4×C103—21no—
225C4×C103—21no—
226C4×C103—22no—
227C4×C103—22no—
228C4×C103—42no—
229C4×C103—41no—
230C4×C103—81no—
231C4×C103—84no—
232C4×C103—81no—
233C4×C103—81no—
234C4×C103—162no—
235#13091C10311yesmaximal, characteristic, direct product factor, Sylow
236C2×C103—21no—
237C2×C103—21no—
238C2×C103—41no—
239C2×C103—42no—
240C2×C103—41no—
241C2×C103—81no—
242C2×C103#189811yescharacteristic
243C2×C103#212611yescharacteristic
244C2×C103#212911yescharacteristic
245C2×#410C2×C10311yescharacteristic
246#2432C2×C10311yescharacteristic
247C2×#354C2×C10312yescomplemented
248#1782C2×C10311yescharacteristic
249#1393C2×C10312yescomplemented
250C103#1309111yescharacteristic, direct product factor, Sylow
251C22×#41C22×C10311yescharacteristic
252C2×C4⋊Q8C4×C10311yescharacteristic, complemented
253C2×#124C22×C10311yescharacteristic
254C2×C22⋊Q8C4×C10311yescharacteristic, complemented
255C2×#117—21no—
256#410—24no—
257C2×#99—21no—
258C2×#99—21no—
259C2×#99C22×C10312yes—
260C2×#99C22×C10312yes—
261#394—21no—
262#394—21no—
263#391C4×C10311yescharacteristic, complemented
264#390C22×C10311yescharacteristic
265#385—21no—
266#385—21no—
267#381—21no—
268C4×C22⋊C4C4×C10311yescharacteristic, complemented
269#354—24no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—41no—
273C2×#41—41no—
274C2×#41—42no—
275C22×Q8C2×C4×C10311yescharacteristic
276C22×Q8C2×C4×C10311yescharacteristic
277C22×D4D4×C10311yescharacteristic
278C22×D4D4×C10311yescharacteristic
279C22×D4C23×C10311yescharacteristic
280C23×C4C2×C4×C10311yescharacteristic
281C23×C4D4×C10311yescharacteristic
282C23×C4D4×C10311yescharacteristic
283C4⋊Q8—42no—
284#124—22no—
285#124—22no—
286C22⋊Q8—41no—
287C22⋊Q8—41no—
288#117—24no—
289#117—42no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4C2×C4×C10311yescharacteristic
295C2×C22⋊C4—22no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C42—41no—
304C2×C42C2×C4×C10311yescharacteristic
305C2×C42C2×C4×C10311yescharacteristic
306#99—24no—
307#99—22no—
308#99—22no—
309#99—22no—
310#99—42no—
311#99D4×C10314yes—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—41no—
316#95—41no—
317C24C22⋊C4×C10311yescharacteristic
318C24C2×D4×C10311yescharacteristic
319C24C2×D4×C10311yescharacteristic
320#41—44no—
321#41—44no—
322#41—44no—
323#41—44no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—41no—
328C2×Q8—41no—
329C2×Q8—41no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4C2×D4×C10312yes—
340C2×D4#41×C10312yes—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4C22⋊C4×C10311yescharacteristic
361C22×C4C22⋊C4×C10311yescharacteristic
362C22×C4C22⋊C4×C10311yescharacteristic
363C22×C4C22×C4×C10311yescharacteristic
364C4⋊C4—41no—
365C4⋊C4—42no—
366C4⋊C4—44no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—42no—
370C22⋊C4—24no—
371C22⋊C4—42no—
372C22⋊C4—42no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—41no—
377C22⋊C4—42no—
378C22⋊C4—41no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C42—22no—
382C42—41no—
383C42—44no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23C2×C22⋊C4×C10311yescharacteristic
398C23#120×C10311yescharacteristic
399C23#121×C10312yes—
400C23#123×C10311yescharacteristic
401Q8—44no—
402Q8—82no—
403D4—42no—
404D4—42no—
405D4—44no—
406D4—42no—
407D4—42no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4#99×C10311yescharacteristic
444C2×C4#99×C10311yescharacteristic
445C2×C4#99×C10312yes—
446C2×C4C4×D4×C10312yes—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—41no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22#386×C10311yescharacteristic
467C22C2×#99×C10311yescharacteristic
468C22C2×#99×C10311yescharacteristic
469C4—21no—
470C4—21no—
471C4—22no—
472C4—22no—
473C4—42no—
474C4—41no—
475C4—81no—
476C4—84no—
477C4—81no—
478C4—81no—
479C4—162no—
480C2—21no—
481C2—21no—
482C2—41no—
483C2—42no—
484C2—41no—
485C2—81no—
486C2C103×#189811yescharacteristic
487C2C103×#212611yescharacteristic
488C2C103×#212911yescharacteristic
subgroupG/H
center, socleC22×C103C2×#99
commutatorC22×C4C22×C4×C103
Frattini, cosocleC22×D4C23×C103
prime radicalC22×#41×C103C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C22×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#354×C103C2semidirect
5. C103×#1393C2semidirect
7. C2×C4⋊Q8×C103C4semidirect
9. C2×C22⋊Q8×C103C4semidirect
18. #391×C103C4semidirect
23. C4×C22⋊C4×C103C4semidirect
235. #13091C103direct (N × H)
247. C2×#354C2×C103semidirect
249. #1393C2×C103semidirect
250. C103#13091direct (N × H)
252. C2×C4⋊Q8C4×C103semidirect
254. C2×C22⋊Q8C4×C103semidirect
263. #391C4×C103semidirect
268. C4×C22⋊C4C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#410×C1032
C103×#24322
C2×#354×C1032
C103×#17822
C103×#13932
#13091103