Finite Group Databasebeta

← C103×#25988 #39931263

Subgroups — C103×#25988 #39931263

Order 26368.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2440C211yesmaximal, characteristic
2C103×#2344C211yesmaximal, characteristic
3C103×#2099C211yesmaximal, characteristic, complemented
4C103×#2086C211yesmaximal, characteristic, complemented
5C103×#2086C211yesmaximal, characteristic, complemented
6C103×#2057C211yesmaximal, characteristic, complemented
7C103×#1988C211yesmaximal, characteristic, complemented
8C103×#1947C211yesmaximal, characteristic, complemented
9C103×#1918C211yesmaximal, characteristic, complemented
10C103×#1918C211yesmaximal, characteristic, complemented
11C103×#1852C211yesmaximal, characteristic
12C103×#1850C211yesmaximal, characteristic
13C103×#1823C211yesmaximal, characteristic
14C103×#1808C211yesmaximal, characteristic
15C2×#340×C103C211yesmaximal, characteristic
16C23×C8×C103C2211yescharacteristic
17C2×C4⋊Q8×C103C2211yescharacteristic
18C2×C22⋊Q8×C103—21no—
19C2×#117×C103—21no—
20C22×C4⋊C4×C103C2211yescharacteristic
21C22×C4⋊C4×C103C2211yescharacteristic
22C2×#107×C103C2211yescharacteristic
23C2×#107×C103C2211yescharacteristic
24C2×#107×C103C2211yescharacteristic
25C2×#107×C103C2211yescharacteristic
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C22⋊C8×C103C2211yescharacteristic
29#398×C103—21no—
30#395×C103—21no—
31#389×C103C2211yescharacteristic
32#389×C103C2211yescharacteristic
33#389×C103C2211yescharacteristic
34#389×C103C2211yescharacteristic
35#387×C103—21no—
36#387×C103—21no—
37#385×C103—21no—
38#384×C103C2211yescharacteristic
39#381×C103—21no—
40#380×C103C2211yescharacteristic
41#380×C103C2211yescharacteristic
42C4×C4⋊C4×C103C2211yescharacteristic
43C4×C4⋊C4×C103C2211yescharacteristic
44C4×C22⋊C4×C103C2211yescharacteristic
45#340×C103C2211yescharacteristic
46#340×C103C2211yescharacteristic
47#340×C103C2211yescharacteristic
48#340×C103C2211yescharacteristic
49#340×C103C2211yescharacteristic
50#340×C103C2211yescharacteristic
51#340×C103C2211yescharacteristic
52#340×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×Q8×C103—21no—
60C23×C4×C103—21no—
61C23×C4×C103—21no—
62C23×C4×C103C2311yescharacteristic
63C22×C8×C103—22no—
64C22×C8×C103—22no—
65C22×C8×C103—41no—
66C22×C8×C103C2311yescharacteristic
67C22×C8×C103C2311yescharacteristic
68C22×C8×C103C2311yescharacteristic
69C22×C8×C103C2311yescharacteristic
70C4⋊Q8×C103—22no—
71C4⋊Q8×C103—41no—
72C22⋊Q8×C103—44no—
73#117×C103—44no—
74C2×C4⋊C4×C103—21no—
75C2×C4⋊C4×C103—22no—
76C2×C4⋊C4×C103—22no—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103—21no—
82C2×C4⋊C4×C103—21no—
83C2×C4⋊C4×C103—21no—
84C2×C4⋊C4×C103—21no—
85C2×C4⋊C4×C103—41no—
86C2×C4⋊C4×C103Q814yescomplemented
87C2×C4⋊C4×C103C2311yescharacteristic
88C2×C4⋊C4×C103C2311yescharacteristic
89C2×C4⋊C4×C103C2311yescharacteristic
90C2×C4⋊C4×C103C2311yescharacteristic
91C2×C4⋊C4×C103C2311yescharacteristic
92C2×C4⋊C4×C103C2311yescharacteristic
93C2×C4⋊C4×C103C2311yescharacteristic
94C2×C4⋊C4×C103C2311yescharacteristic
95C2×C22⋊C4×C103—21no—
96C2×C22⋊C4×C103—21no—
97C2×C22⋊C4×C103D411yescharacteristic
98C2×C22⋊C4×C103D411yescharacteristic
99C2×C42×C103—21no—
100C2×C42×C103—21no—
101C2×C42×C103C2311yescharacteristic
102C2×C42×C103C2311yescharacteristic
103#107×C103—22no—
104#107×C103—22no—
105#107×C103—41no—
106#107×C103—41no—
107C4⋊C8×C103—22no—
108C4⋊C8×C103—41no—
109C22⋊C8×C103—22no—
110#95×C103—21no—
111#95×C103—21no—
112#95×C103—21no—
113#95×C103—21no—
114#95×C103—21no—
115#95×C103—21no—
116#95×C103—21no—
117#95×C103—21no—
118#95×C103D411yescharacteristic
119#95×C103D411yescharacteristic
120C24×C103C2×D411yescharacteristic
121C2×Q8×C103—42no—
122C2×Q8×C103—42no—
123C2×Q8×C103—81no—
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—21no—
127C22×C4×C103—21no—
128C22×C4×C103—24no—
129C22×C4×C103—21no—
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—42no—
138C22×C4×C103—42no—
139C22×C4×C103—42no—
140C22×C4×C103—42no—
141C22×C4×C103—81no—
142C22×C4×C103C2×D411yescharacteristic
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103C2×D411yescharacteristic
147C22×C4×C103C2×Q812yes—
148C22×C4×C103#4112yes—
149C22×C4×C103C2411yescharacteristic
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C2×C8×C103—21no—
154C2×C8×C103—21no—
155C2×C8×C103—21no—
156C2×C8×C103—21no—
157C2×C8×C103—21no—
158C2×C8×C103—21no—
159C2×C8×C103—21no—
160C2×C8×C103—21no—
161C2×C8×C103—44no—
162C2×C8×C103#4112yes—
163C4⋊C4×C103—24no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—21no—
166C4⋊C4×C103—21no—
167C4⋊C4×C103—21no—
168C4⋊C4×C103—21no—
169C4⋊C4×C103—21no—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—21no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—42no—
178C4⋊C4×C103—42no—
179C4⋊C4×C103—42no—
180C4⋊C4×C103—42no—
181C4⋊C4×C103—42no—
182C4⋊C4×C103—42no—
183C4⋊C4×C103—42no—
184C4⋊C4×C103—81no—
185C4⋊C4×C103C2×Q812yes—
186C4⋊C4×C103C2×Q812yes—
187C4⋊C4×C103#4112yes—
188C22⋊C4×C103—22no—
189C22⋊C4×C103—42no—
190C22⋊C4×C103—42no—
191C22⋊C4×C103D814yes—
192C42×C103—21no—
193C42×C103—21no—
194C42×C103—21no—
195C42×C103—21no—
196C42×C103—42no—
197C42×C103—42no—
198C23×C103—21no—
199C23×C103—21no—
200C23×C103—21no—
201C23×C103—21no—
202C23×C103C22⋊Q812yes—
203C23×C103C2×D812yes—
204C23×C103#13712yes—
205C23×C103C22×D411yescharacteristic
206Q8×C103—84no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—21no—
210C2×C4×C103—21no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—22no—
214C2×C4×C103—22no—
215C2×C4×C103—22no—
216C2×C4×C103—22no—
217C2×C4×C103—22no—
218C2×C4×C103—22no—
219C2×C4×C103—21no—
220C2×C4×C103—22no—
221C2×C4×C103—21no—
222C2×C4×C103—21no—
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—41no—
227C2×C4×C103—41no—
228C2×C4×C103—41no—
229C2×C4×C103—41no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—48no—
233C2×C4×C103—41no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—84no—
249C2×C4×C103C22⋊Q812yes—
250C2×C4×C103C2×D812yes—
251C2×C4×C103C2×D812yes—
252C2×C4×C103C22×Q811yescharacteristic
253C2×C4×C103C2×#4111yescharacteristic
254C2×C4×C103C2×#4111yescharacteristic
255C2×C4×C103C2×#4111yescharacteristic
256C2×C4×C103H(5,𝔽2)11yescharacteristic
257C2×C4×C1032−1+411yescharacteristic
258C8×C103—22no—
259C8×C103—41no—
260C8×C103—41no—
261C8×C103—41no—
262C22×C103—22no—
263C22×C103—22no—
264C22×C103—22no—
265C22×C103—22no—
266C22×C103—22no—
267C22×C103—22no—
268C22×C103#47414yes—
269C22×C103C2×C22⋊Q811yescharacteristic
270C22×C103#54611yescharacteristic
271C22×C103#54711yescharacteristic
272C22×C103C22×D811yescharacteristic
273C22×C103C2×#13711yescharacteristic
274C22×C103#57711yescharacteristic
275C22×C103#57811yescharacteristic
276C4×C103—22no—
277C4×C103—22no—
278C4×C103—22no—
279C4×C103—41no—
280C4×C103—42no—
281C4×C103—41no—
282C4×C103—42no—
283C4×C103—42no—
284C4×C103—81no—
285C4×C103—81no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103#53311yescharacteristic
290C4×C103#54411yescharacteristic
291C4×C103#55111yescharacteristic
292C4×C103#55211yescharacteristic
293#25988C10311yesmaximal, characteristic, direct product factor, Sylow
294C2×C103—24no—
295C2×C103#243811yescharacteristic
296C2×C103C2×#47411yescharacteristic
297C2×C103#308211yescharacteristic
298C2×C103#329411yescharacteristic
299C2×C103#331211yescharacteristic
300C2×C103#333411yescharacteristic
301C2×C103#334411yescharacteristic
302#2440C2×C10311yescharacteristic
303#2344C2×C10311yescharacteristic
304#2099C2×C10311yescharacteristic, complemented
305#2086C2×C10311yescharacteristic, complemented
306#2086C2×C10311yescharacteristic, complemented
307#2057C2×C10311yescharacteristic, complemented
308#1988C2×C10311yescharacteristic, complemented
309#1947C2×C10311yescharacteristic, complemented
310#1918C2×C10311yescharacteristic, complemented
311#1918C2×C10311yescharacteristic, complemented
312#1852C2×C10311yescharacteristic
313#1850C2×C10311yescharacteristic
314#1823C2×C10311yescharacteristic
315#1808C2×C10311yescharacteristic
316C2×#340C2×C10311yescharacteristic
317C103#2598811yescharacteristic, direct product factor, Sylow
318C23×C8C22×C10311yescharacteristic
319C2×C4⋊Q8C22×C10311yescharacteristic
320C2×C22⋊Q8—21no—
321C2×#117—21no—
322C22×C4⋊C4C22×C10311yescharacteristic
323C22×C4⋊C4C22×C10311yescharacteristic
324C2×#107C22×C10311yescharacteristic
325C2×#107C22×C10311yescharacteristic
326C2×#107C22×C10311yescharacteristic
327C2×#107C22×C10311yescharacteristic
328C2×C4⋊C8C22×C10311yescharacteristic
329C2×C4⋊C8C22×C10311yescharacteristic
330C2×C22⋊C8C22×C10311yescharacteristic
331#398—21no—
332#395—21no—
333#389C22×C10311yescharacteristic
334#389C22×C10311yescharacteristic
335#389C22×C10311yescharacteristic
336#389C22×C10311yescharacteristic
337#387—21no—
338#387—21no—
339#385—21no—
340#384C22×C10311yescharacteristic
341#381—21no—
342#380C22×C10311yescharacteristic
343#380C22×C10311yescharacteristic
344C4×C4⋊C4C22×C10311yescharacteristic
345C4×C4⋊C4C22×C10311yescharacteristic
346C4×C22⋊C4C22×C10311yescharacteristic
347#340C22×C10311yescharacteristic
348#340C22×C10311yescharacteristic
349#340C22×C10311yescharacteristic
350#340C22×C10311yescharacteristic
351#340C22×C10311yescharacteristic
352#340C22×C10311yescharacteristic
353#340C22×C10311yescharacteristic
354#340C22×C10311yescharacteristic
355#340C22×C10311yescharacteristic
356#340C22×C10311yescharacteristic
357#340C22×C10311yescharacteristic
358#340C22×C10311yescharacteristic
359#336C22×C10311yescharacteristic
360#336C22×C10311yescharacteristic
361C22×Q8—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C23×C10311yescharacteristic
365C22×C8—22no—
366C22×C8—22no—
367C22×C8—41no—
368C22×C8C23×C10311yescharacteristic
369C22×C8C23×C10311yescharacteristic
370C22×C8C23×C10311yescharacteristic
371C22×C8C23×C10311yescharacteristic
372C4⋊Q8—22no—
373C4⋊Q8—41no—
374C22⋊Q8—44no—
375#117—44no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4Q8×C10314yescomplemented
389C2×C4⋊C4C23×C10311yescharacteristic
390C2×C4⋊C4C23×C10311yescharacteristic
391C2×C4⋊C4C23×C10311yescharacteristic
392C2×C4⋊C4C23×C10311yescharacteristic
393C2×C4⋊C4C23×C10311yescharacteristic
394C2×C4⋊C4C23×C10311yescharacteristic
395C2×C4⋊C4C23×C10311yescharacteristic
396C2×C4⋊C4C23×C10311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4D4×C10311yescharacteristic
400C2×C22⋊C4D4×C10311yescharacteristic
401C2×C42—21no—
402C2×C42—21no—
403C2×C42C23×C10311yescharacteristic
404C2×C42C23×C10311yescharacteristic
405#107—22no—
406#107—22no—
407#107—41no—
408#107—41no—
409C4⋊C8—22no—
410C4⋊C8—41no—
411C22⋊C8—22no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95D4×C10311yescharacteristic
421#95D4×C10311yescharacteristic
422C24C2×D4×C10311yescharacteristic
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—81no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4C2×D4×C10311yescharacteristic
445C22×C4C2×D4×C10311yescharacteristic
446C22×C4C2×D4×C10311yescharacteristic
447C22×C4C2×D4×C10311yescharacteristic
448C22×C4C2×D4×C10311yescharacteristic
449C22×C4C2×Q8×C10312yes—
450C22×C4#41×C10312yes—
451C22×C4C24×C10311yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—44no—
464C2×C8#41×C10312yes—
465C4⋊C4—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—81no—
487C4⋊C4C2×Q8×C10312yes—
488C4⋊C4C2×Q8×C10312yes—
489C4⋊C4#41×C10312yes—
490C22⋊C4—22no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4D8×C10314yes—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—42no—
499C42—42no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23—21no—
504C23C22⋊Q8×C10312yes—
505C23C2×D8×C10312yes—
506C23#137×C10312yes—
507C23C22×D4×C10311yescharacteristic
508Q8—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—48no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—84no—
551C2×C4C22⋊Q8×C10312yes—
552C2×C4C2×D8×C10312yes—
553C2×C4C2×D8×C10312yes—
554C2×C4C22×Q8×C10311yescharacteristic
555C2×C4C2×#41×C10311yescharacteristic
556C2×C4C2×#41×C10311yescharacteristic
557C2×C4C2×#41×C10311yescharacteristic
558C2×C4H(5,𝔽2)×C10311yescharacteristic
559C2×C42−1+4×C10311yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#474×C10314yes—
571C22C2×C22⋊Q8×C10311yescharacteristic
572C22#546×C10311yescharacteristic
573C22#547×C10311yescharacteristic
574C22C22×D8×C10311yescharacteristic
575C22C2×#137×C10311yescharacteristic
576C22#577×C10311yescharacteristic
577C22#578×C10311yescharacteristic
578C4—22no—
579C4—22no—
580C4—22no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4#533×C10311yescharacteristic
592C4#544×C10311yescharacteristic
593C4#551×C10311yescharacteristic
594C4#552×C10311yescharacteristic
595C2—24no—
596C2C103×#243811yescharacteristic
597C2C2×#474×C10311yescharacteristic
598C2C103×#308211yescharacteristic
599C2C103×#329411yescharacteristic
600C2C103×#331211yescharacteristic
601C2C103×#333411yescharacteristic
602C2C103×#334411yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2099C2semidirect
4. C103×#2086C2semidirect
5. C103×#2086C2semidirect
6. C103×#2057C2semidirect
7. C103×#1988C2semidirect
8. C103×#1947C2semidirect
9. C103×#1918C2semidirect
10. C103×#1918C2semidirect
86. C2×C4⋊C4×C103Q8semidirect
293. #25988C103direct (N × H)
304. #2099C2×C103semidirect
305. #2086C2×C103semidirect
306. #2086C2×C103semidirect
307. #2057C2×C103semidirect
308. #1988C2×C103semidirect
309. #1947C2×C103semidirect
310. #1918C2×C103semidirect
311. #1918C2×C103semidirect
317. C103#25988direct (N × H)
388. C2×C4⋊C4Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#24402
C103×#23442
C103×#20992
C103×#20862
C103×#20572
C103×#19882
C103×#19472
C103×#19182
C103×#18522
C103×#18502
C103×#18232
C103×#18082
C2×#340×C1032
#25988103