Finite Group Databasebeta

← C103×#14364 #39919639

Subgroups — C103×#14364 #39919639

Order 26368.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C103C211yesmaximal, characteristic
2C2×#391×C103C211yesmaximal, characteristic, complemented
3C2×#388×C103C211yesmaximal, characteristic
4C2×#388×C103C211yesmaximal, characteristic
5C2×#381×C103C211yesmaximal, characteristic
6C103×#1446C211yesmaximal, characteristic, complemented
7C103×#1445C211yesmaximal, characteristic, complemented
8C103×#1441C211yesmaximal, characteristic, complemented
9C103×#1441C211yesmaximal, characteristic, complemented
10C103×#1440C211yesmaximal, characteristic
11C103×#1440C211yesmaximal, characteristic
12C103×#1436C211yesmaximal, characteristic, complemented
13C103×#1436C211yesmaximal, characteristic, complemented
14C103×C4⋊#95C211yesmaximal, characteristic, complemented
15C103×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C103C2211yescharacteristic
17C24×C4×C103C2211yescharacteristic
18C2×C22⋊Q8×C103—24no—
19C2×C22⋊Q8×C103—24no—
20C2×C22⋊Q8×C103C418yescomplemented
21C22×C4⋊C4×C103C2211yescharacteristic
22C22×C4⋊C4×C103C2211yescharacteristic
23C22×C4⋊C4×C103C2211yescharacteristic
24C22×C4⋊C4×C103C2211yescharacteristic
25C22×C4⋊C4×C103C2211yescharacteristic
26C22×C22⋊C4×C103C2211yescharacteristic
27C22×C22⋊C4×C103C2211yescharacteristic
28C22×C22⋊C4×C103C2211yescharacteristic
29C22×C22⋊C4×C103C2211yescharacteristic
30C22×C22⋊C4×C103C2211yescharacteristic
31C22×C22⋊C4×C103C2211yescharacteristic
32C22×C42×C103C2211yescharacteristic
33C22×C42×C103C2211yescharacteristic
34#391×C103—24no—
35#388×C103—24no—
36#388×C103—24no—
37#381×C103—24no—
38C2×#95×C103C2211yescharacteristic
39C2×#95×C103C2211yescharacteristic
40C2×#95×C103C2211yescharacteristic
41C2×#95×C103C2211yescharacteristic
42C2×#95×C103C2211yescharacteristic
43C2×#95×C103C2211yescharacteristic
44C2×#95×C103C2211yescharacteristic
45C2×#95×C103C2211yescharacteristic
46C2×#95×C103C2211yescharacteristic
47C2×#95×C103C2211yescharacteristic
48C2×#95×C103C2211yescharacteristic
49C2×#95×C103C2211yescharacteristic
50C2×#95×C103C2211yescharacteristic
51C2×#95×C103C2211yescharacteristic
52C2×#95×C103C2211yescharacteristic
53C2×#95×C103C2211yescharacteristic
54C2×#95×C103C2211yescharacteristic
55C2×#95×C103C2211yescharacteristic
56C2×#95×C103C2211yescharacteristic
57C2×#95×C103C2211yescharacteristic
58C25×C103C2311yescharacteristic
59C22×Q8×C103—22no—
60C22×Q8×C103—22no—
61C22×Q8×C103—22no—
62C22×Q8×C103—22no—
63C22×Q8×C103—41no—
64C22×Q8×C103—41no—
65C22×Q8×C103C2×C414yes—
66C23×C4×C103—22no—
67C23×C4×C103—22no—
68C23×C4×C103—22no—
69C23×C4×C103—22no—
70C23×C4×C103—41no—
71C23×C4×C103—41no—
72C23×C4×C103C2×C414yes—
73C23×C4×C103C2311yescharacteristic
74C23×C4×C103C2311yescharacteristic
75C23×C4×C103C2311yescharacteristic
76C23×C4×C103C2311yescharacteristic
77C23×C4×C103C2311yescharacteristic
78C23×C4×C103C2311yescharacteristic
79C23×C4×C103C2311yescharacteristic
80C23×C4×C103C2311yescharacteristic
81C23×C4×C103C2311yescharacteristic
82C23×C4×C103C2311yescharacteristic
83C23×C4×C103C2311yescharacteristic
84C23×C4×C103C2311yescharacteristic
85C23×C4×C103C2311yescharacteristic
86C23×C4×C103C2311yescharacteristic
87C22⋊Q8×C103—232no—
88C2×C4⋊C4×C103—22no—
89C2×C4⋊C4×C103—22no—
90C2×C4⋊C4×C103—22no—
91C2×C4⋊C4×C103—22no—
92C2×C4⋊C4×C103—22no—
93C2×C4⋊C4×C103—22no—
94C2×C4⋊C4×C103—22no—
95C2×C4⋊C4×C103—22no—
96C2×C4⋊C4×C103—22no—
97C2×C4⋊C4×C103—22no—
98C2×C4⋊C4×C103—41no—
99C2×C4⋊C4×C103—41no—
100C2×C4⋊C4×C103C2×C414yes—
101C2×C4⋊C4×C103C2×C414yes—
102C2×C4⋊C4×C103C2×C414yes—
103C2×C22⋊C4×C103—22no—
104C2×C22⋊C4×C103—22no—
105C2×C22⋊C4×C103—22no—
106C2×C22⋊C4×C103—22no—
107C2×C22⋊C4×C103—22no—
108C2×C22⋊C4×C103—22no—
109C2×C22⋊C4×C103—22no—
110C2×C22⋊C4×C103—22no—
111C2×C22⋊C4×C103—22no—
112C2×C22⋊C4×C103—22no—
113C2×C22⋊C4×C103—41no—
114C2×C22⋊C4×C103—41no—
115C2×C22⋊C4×C103—41no—
116C2×C22⋊C4×C103—41no—
117C2×C22⋊C4×C103C2×C414yes—
118C2×C22⋊C4×C103C2×C414yes—
119C2×C22⋊C4×C103D414yes—
120C2×C22⋊C4×C103D414yes—
121C2×C42×C103—22no—
122C2×C42×C103—22no—
123C2×C42×C103—22no—
124C2×C42×C103—22no—
125C2×C42×C103—41no—
126C2×C42×C103—41no—
127#95×C103—22no—
128#95×C103—22no—
129#95×C103—22no—
130#95×C103—22no—
131#95×C103—22no—
132#95×C103—22no—
133#95×C103—22no—
134#95×C103—22no—
135#95×C103—22no—
136#95×C103—22no—
137#95×C103—22no—
138#95×C103—22no—
139#95×C103—22no—
140#95×C103—41no—
141#95×C103—41no—
142#95×C103—41no—
143#95×C103—41no—
144#95×C103—41no—
145#95×C103—41no—
146#95×C103D414yes—
147C24×C103—21no—
148C24×C103—21no—
149C24×C103—21no—
150C24×C103—21no—
151C24×C103—21no—
152C24×C103—21no—
153C24×C103—21no—
154C24×C103—21no—
155C24×C103—21no—
156C24×C103—21no—
157C24×C103—21no—
158C24×C103—21no—
159C24×C103C22×C412yes—
160C24×C103C2×D412yes—
161C24×C103C2×D412yes—
162C24×C103C2411yescharacteristic
163C2×Q8×C103—28no—
164C2×Q8×C103—28no—
165C2×Q8×C103—44no—
166C2×Q8×C103—44no—
167C2×Q8×C103—44no—
168C2×Q8×C103—44no—
169C2×Q8×C103—44no—
170C22×C4×C103—21no—
171C22×C4×C103—21no—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—28no—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—21no—
191C22×C4×C103—21no—
192C22×C4×C103—21no—
193C22×C4×C103—21no—
194C22×C4×C103—21no—
195C22×C4×C103—21no—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—21no—
205C22×C4×C103—21no—
206C22×C4×C103—21no—
207C22×C4×C103—21no—
208C22×C4×C103—21no—
209C22×C4×C103—21no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—21no—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—21no—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—28no—
226C22×C4×C103—21no—
227C22×C4×C103—21no—
228C22×C4×C103—21no—
229C22×C4×C103—21no—
230C22×C4×C103—21no—
231C22×C4×C103—21no—
232C22×C4×C103—21no—
233C22×C4×C103—21no—
234C22×C4×C103—21no—
235C22×C4×C103—21no—
236C22×C4×C103—21no—
237C22×C4×C103—21no—
238C22×C4×C103—21no—
239C22×C4×C103—21no—
240C22×C4×C103—21no—
241C22×C4×C103—21no—
242C22×C4×C103—21no—
243C22×C4×C103—21no—
244C22×C4×C103—21no—
245C22×C4×C103—21no—
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—21no—
249C22×C4×C103—21no—
250C22×C4×C103—21no—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103—21no—
254C22×C4×C103—44no—
255C22×C4×C103—44no—
256C22×C4×C103—44no—
257C22×C4×C103—44no—
258C22×C4×C103—44no—
259C22×C4×C103C22×C412yes—
260C22×C4×C103C22×C412yes—
261C22×C4×C103C22×C412yes—
262C22×C4×C103C22×C412yes—
263C22×C4×C103C22×C412yes—
264C22×C4×C103C22×C412yes—
265C22×C4×C103C2×D412yes—
266C22×C4×C103C2×D412yes—
267C22×C4×C103C2×D412yes—
268C22×C4×C103C2×D412yes—
269C22×C4×C103C2×D412yes—
270C22×C4×C103C2×D412yes—
271C22×C4×C103C2×D412yes—
272C22×C4×C103#4112yes—
273C22×C4×C103#4112yes—
274C22×C4×C103#4112yes—
275C4⋊C4×C103—28no—
276C4⋊C4×C103—28no—
277C4⋊C4×C103—28no—
278C4⋊C4×C103—44no—
279C4⋊C4×C103—44no—
280C22⋊C4×C103—28no—
281C22⋊C4×C103—44no—
282C22⋊C4×C103—44no—
283C22⋊C4×C103—44no—
284C22⋊C4×C103—44no—
285C22⋊C4×C103C22⋊C4116yes—
286C42×C103—44no—
287C42×C103—44no—
288C23×C103—22no—
289C23×C103—22no—
290C23×C103—22no—
291C23×C103—22no—
292C23×C103—22no—
293C23×C103—22no—
294C23×C103—22no—
295C23×C103—22no—
296C23×C103—22no—
297C23×C103—22no—
298C23×C103—22no—
299C23×C103—22no—
300C23×C103—22no—
301C23×C103—22no—
302C23×C103—22no—
303C23×C103—22no—
304C23×C103—22no—
305C23×C103—22no—
306C23×C103—41no—
307C23×C103—41no—
308C23×C103—41no—
309C23×C103—41no—
310C23×C103—41no—
311C23×C103—41no—
312C23×C103—41no—
313C23×C103—41no—
314C23×C103—41no—
315C23×C103—41no—
316C23×C103—41no—
317C23×C103—41no—
318C23×C103—41no—
319C23×C103—41no—
320C23×C103—41no—
321C23×C103—41no—
322C23×C103C2×C22⋊C414yes—
323C23×C103C23×C411yescharacteristic
324C23×C103C22×D411yescharacteristic
325C23×C103C22×D411yescharacteristic
326C23×C103C22×D411yescharacteristic
327C23×C103C2×#4111yescharacteristic
328C23×C103C2×#4111yescharacteristic
329C23×C103C2×#4111yescharacteristic
330C23×C103H(5,𝔽2)11yescharacteristic
331C23×C103H(5,𝔽2)11yescharacteristic
332C23×C103H(5,𝔽2)11yescharacteristic
333C23×C1032−1+411yescharacteristic
334C23×C1032−1+411yescharacteristic
335C23×C1032−1+411yescharacteristic
336C23×C1032−1+411yescharacteristic
337C23×C1032−1+411yescharacteristic
338Q8×C103—416no—
339C2×C4×C103—22no—
340C2×C4×C103—22no—
341C2×C4×C103—22no—
342C2×C4×C103—22no—
343C2×C4×C103—22no—
344C2×C4×C103—22no—
345C2×C4×C103—22no—
346C2×C4×C103—22no—
347C2×C4×C103—22no—
348C2×C4×C103—22no—
349C2×C4×C103—22no—
350C2×C4×C103—22no—
351C2×C4×C103—22no—
352C2×C4×C103—22no—
353C2×C4×C103—22no—
354C2×C4×C103—22no—
355C2×C4×C103—22no—
356C2×C4×C103—22no—
357C2×C4×C103—22no—
358C2×C4×C103—22no—
359C2×C4×C103—22no—
360C2×C4×C103—22no—
361C2×C4×C103—22no—
362C2×C4×C103—22no—
363C2×C4×C103—22no—
364C2×C4×C103—22no—
365C2×C4×C103—22no—
366C2×C4×C103—22no—
367C2×C4×C103—22no—
368C2×C4×C103—22no—
369C2×C4×C103—22no—
370C2×C4×C103—22no—
371C2×C4×C103—22no—
372C2×C4×C103—22no—
373C2×C4×C103—22no—
374C2×C4×C103—22no—
375C2×C4×C103—22no—
376C2×C4×C103—22no—
377C2×C4×C103—22no—
378C2×C4×C103—416no—
379C2×C4×C103—41no—
380C2×C4×C103—41no—
381C2×C4×C103—41no—
382C2×C4×C103—41no—
383C2×C4×C103—41no—
384C2×C4×C103—41no—
385C2×C4×C103—41no—
386C2×C4×C103—41no—
387C2×C4×C103—41no—
388C2×C4×C103—41no—
389C2×C4×C103—41no—
390C2×C4×C103—41no—
391C2×C4×C103—41no—
392C2×C4×C103—41no—
393C2×C4×C103—41no—
394C2×C4×C103—41no—
395C2×C4×C103—41no—
396C2×C4×C103—41no—
397C2×C4×C103—41no—
398C2×C4×C103—41no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—41no—
402C2×C4×C103—41no—
403C2×C4×C103—41no—
404C2×C4×C103—41no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—41no—
408C2×C4×C103—41no—
409C2×C4×C103—41no—
410C2×C4×C103—41no—
411C2×C4×C103—41no—
412C2×C4×C103—41no—
413C2×C4×C103—41no—
414C2×C4×C103—41no—
415C2×C4×C103—41no—
416C2×C4×C103—41no—
417C2×C4×C103—41no—
418C2×C4×C103—41no—
419C2×C4×C103—41no—
420C2×C4×C103—41no—
421C2×C4×C103—41no—
422C2×C4×C103—41no—
423C2×C4×C103—41no—
424C2×C4×C103—41no—
425C2×C4×C103—41no—
426C2×C4×C103—41no—
427C2×C4×C103—41no—
428C2×C4×C103—41no—
429C2×C4×C103—41no—
430C2×C4×C103—41no—
431C2×C4×C103—41no—
432C2×C4×C103—41no—
433C2×C4×C103—41no—
434C2×C4×C103—41no—
435C2×C4×C103C2×C22⋊C414yes—
436C2×C4×C103C2×C22⋊C414yes—
437C2×C4×C103C4×D414yes—
438C22×C103—24no—
439C22×C103—24no—
440C22×C103—24no—
441C22×C103—42no—
442C22×C103—42no—
443C22×C103—42no—
444C22×C103—42no—
445C22×C103—42no—
446C22×C103—42no—
447C22×C103—42no—
448C22×C103—42no—
449C22×C103—42no—
450C22×C103—42no—
451C22×C103—42no—
452C22×C103—42no—
453C22×C103C22×C22⋊C411yescharacteristic
454C22×C103C2×C4×D411yescharacteristic
455C22×C103C4×#4111yescharacteristic
456C22×C103#51811yescharacteristic
457C22×C103#51911yescharacteristic
458C22×C103#51911yescharacteristic
459C22×C103#52011yescharacteristic
460C22×C103#53611yescharacteristic
461C22×C103#53611yescharacteristic
462C22×C103#53611yescharacteristic
463C22×C103#53611yescharacteristic
464C22×C103#53611yescharacteristic
465C22×C103#53711yescharacteristic
466C22×C103#53911yescharacteristic
467C22×C103#53911yescharacteristic
468C22×C103#54111yescharacteristic
469C22×C103#54211yescharacteristic
470C22×C103#54211yescharacteristic
471C22×C103#54211yescharacteristic
472C22×C103D4211yescharacteristic
473C22×C103D4211yescharacteristic
474C22×C103#54611yescharacteristic
475C22×C103#54611yescharacteristic
476C22×C103#54611yescharacteristic
477C22×C103#54611yescharacteristic
478C22×C103#54711yescharacteristic
479C22×C103#54711yescharacteristic
480C22×C103#54711yescharacteristic
481C22×C103#54811yescharacteristic
482C22×C103#55211yescharacteristic
483C22×C103#55611yescharacteristic
484C22×C103#56211yescharacteristic
485C22×C103#56211yescharacteristic
486C22×C103#56311yescharacteristic
487C22×C103#56311yescharacteristic
488C4×C103—24no—
489C4×C103—24no—
490C4×C103—24no—
491C4×C103—42no—
492C4×C103—42no—
493C4×C103—42no—
494C4×C103—42no—
495C4×C103—42no—
496C4×C103—42no—
497C4×C103—42no—
498C4×C103—81no—
499C4×C103—81no—
500C4×C103—81no—
501C4×C103—81no—
502#14364C10311yesmaximal, characteristic, direct product factor, Sylow
503C2×C103—44no—
504C2×C103#231011yescharacteristic
505C2×C103#232311yescharacteristic
506C2×C103#233211yescharacteristic
507C2×C103D4×C22⋊C411yescharacteristic
508C2×C103#233911yescharacteristic
509C2×C103#236211yescharacteristic
510C2×C103#237811yescharacteristic
511C2×C103#267211yescharacteristic
512C2×C103#267411yescharacteristic
513C2×C103#268011yescharacteristic
514C2×C103#268111yescharacteristic
515C2×C103#268711yescharacteristic
516C2×C103#268911yescharacteristic
517C2×C103#269811yescharacteristic
518C2×C103#270011yescharacteristic
519C22×C22⋊Q8C2×C10311yescharacteristic
520C2×#391C2×C10311yescharacteristic, complemented
521C2×#388C2×C10311yescharacteristic
522C2×#388C2×C10311yescharacteristic
523C2×#381C2×C10311yescharacteristic
524#1446C2×C10311yescharacteristic, complemented
525#1445C2×C10311yescharacteristic, complemented
526#1441C2×C10311yescharacteristic, complemented
527#1441C2×C10311yescharacteristic, complemented
528#1440C2×C10311yescharacteristic
529#1440C2×C10311yescharacteristic
530#1436C2×C10311yescharacteristic, complemented
531#1436C2×C10311yescharacteristic, complemented
532C4⋊#95C2×C10311yescharacteristic, complemented
533C22⋊#95C2×C10311yescharacteristic
534C103#1436411yescharacteristic, direct product factor, Sylow
535C23×Q8C22×C10311yescharacteristic
536C24×C4C22×C10311yescharacteristic
537C2×C22⋊Q8—24no—
538C2×C22⋊Q8—24no—
539C2×C22⋊Q8C4×C10318yescomplemented
540C22×C4⋊C4C22×C10311yescharacteristic
541C22×C4⋊C4C22×C10311yescharacteristic
542C22×C4⋊C4C22×C10311yescharacteristic
543C22×C4⋊C4C22×C10311yescharacteristic
544C22×C4⋊C4C22×C10311yescharacteristic
545C22×C22⋊C4C22×C10311yescharacteristic
546C22×C22⋊C4C22×C10311yescharacteristic
547C22×C22⋊C4C22×C10311yescharacteristic
548C22×C22⋊C4C22×C10311yescharacteristic
549C22×C22⋊C4C22×C10311yescharacteristic
550C22×C22⋊C4C22×C10311yescharacteristic
551C22×C42C22×C10311yescharacteristic
552C22×C42C22×C10311yescharacteristic
553#391—24no—
554#388—24no—
555#388—24no—
556#381—24no—
557C2×#95C22×C10311yescharacteristic
558C2×#95C22×C10311yescharacteristic
559C2×#95C22×C10311yescharacteristic
560C2×#95C22×C10311yescharacteristic
561C2×#95C22×C10311yescharacteristic
562C2×#95C22×C10311yescharacteristic
563C2×#95C22×C10311yescharacteristic
564C2×#95C22×C10311yescharacteristic
565C2×#95C22×C10311yescharacteristic
566C2×#95C22×C10311yescharacteristic
567C2×#95C22×C10311yescharacteristic
568C2×#95C22×C10311yescharacteristic
569C2×#95C22×C10311yescharacteristic
570C2×#95C22×C10311yescharacteristic
571C2×#95C22×C10311yescharacteristic
572C2×#95C22×C10311yescharacteristic
573C2×#95C22×C10311yescharacteristic
574C2×#95C22×C10311yescharacteristic
575C2×#95C22×C10311yescharacteristic
576C2×#95C22×C10311yescharacteristic
577C25C23×C10311yescharacteristic
578C22×Q8—22no—
579C22×Q8—22no—
580C22×Q8—22no—
581C22×Q8—22no—
582C22×Q8—41no—
583C22×Q8—41no—
584C22×Q8C2×C4×C10314yes—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—41no—
590C23×C4—41no—
591C23×C4C2×C4×C10314yes—
592C23×C4C23×C10311yescharacteristic
593C23×C4C23×C10311yescharacteristic
594C23×C4C23×C10311yescharacteristic
595C23×C4C23×C10311yescharacteristic
596C23×C4C23×C10311yescharacteristic
597C23×C4C23×C10311yescharacteristic
598C23×C4C23×C10311yescharacteristic
599C23×C4C23×C10311yescharacteristic
600C23×C4C23×C10311yescharacteristic
601C23×C4C23×C10311yescharacteristic
602C23×C4C23×C10311yescharacteristic
603C23×C4C23×C10311yescharacteristic
604C23×C4C23×C10311yescharacteristic
605C23×C4C23×C10311yescharacteristic
606C22⋊Q8—232no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4C2×C4×C10314yes—
620C2×C4⋊C4C2×C4×C10314yes—
621C2×C4⋊C4C2×C4×C10314yes—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—41no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4C2×C4×C10314yes—
637C2×C22⋊C4C2×C4×C10314yes—
638C2×C22⋊C4D4×C10314yes—
639C2×C22⋊C4D4×C10314yes—
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—41no—
645C2×C42—41no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—41no—
660#95—41no—
661#95—41no—
662#95—41no—
663#95—41no—
664#95—41no—
665#95D4×C10314yes—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24C22×C4×C10312yes—
679C24C2×D4×C10312yes—
680C24C2×D4×C10312yes—
681C24C24×C10311yescharacteristic
682C2×Q8—28no—
683C2×Q8—28no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—28no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—28no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4C22×C4×C10312yes—
779C22×C4C22×C4×C10312yes—
780C22×C4C22×C4×C10312yes—
781C22×C4C22×C4×C10312yes—
782C22×C4C22×C4×C10312yes—
783C22×C4C22×C4×C10312yes—
784C22×C4C2×D4×C10312yes—
785C22×C4C2×D4×C10312yes—
786C22×C4C2×D4×C10312yes—
787C22×C4C2×D4×C10312yes—
788C22×C4C2×D4×C10312yes—
789C22×C4C2×D4×C10312yes—
790C22×C4C2×D4×C10312yes—
791C22×C4#41×C10312yes—
792C22×C4#41×C10312yes—
793C22×C4#41×C10312yes—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C22⋊C4—28no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4C22⋊C4×C103116yes—
805C42—44no—
806C42—44no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×C22⋊C4×C10314yes—
842C23C23×C4×C10311yescharacteristic
843C23C22×D4×C10311yescharacteristic
844C23C22×D4×C10311yescharacteristic
845C23C22×D4×C10311yescharacteristic
846C23C2×#41×C10311yescharacteristic
847C23C2×#41×C10311yescharacteristic
848C23C2×#41×C10311yescharacteristic
849C23H(5,𝔽2)×C10311yescharacteristic
850C23H(5,𝔽2)×C10311yescharacteristic
851C23H(5,𝔽2)×C10311yescharacteristic
852C232−1+4×C10311yescharacteristic
853C232−1+4×C10311yescharacteristic
854C232−1+4×C10311yescharacteristic
855C232−1+4×C10311yescharacteristic
856C232−1+4×C10311yescharacteristic
857Q8—416no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—416no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4C2×C22⋊C4×C10314yes—
955C2×C4C2×C22⋊C4×C10314yes—
956C2×C4C4×D4×C10314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C22⋊C4×C10311yescharacteristic
973C22C2×C4×D4×C10311yescharacteristic
974C22C4×#41×C10311yescharacteristic
975C22#518×C10311yescharacteristic
976C22#519×C10311yescharacteristic
977C22#519×C10311yescharacteristic
978C22#520×C10311yescharacteristic
979C22#536×C10311yescharacteristic
980C22#536×C10311yescharacteristic
981C22#536×C10311yescharacteristic
982C22#536×C10311yescharacteristic
983C22#536×C10311yescharacteristic
984C22#537×C10311yescharacteristic
985C22#539×C10311yescharacteristic
986C22#539×C10311yescharacteristic
987C22#541×C10311yescharacteristic
988C22#542×C10311yescharacteristic
989C22#542×C10311yescharacteristic
990C22#542×C10311yescharacteristic
991C22D42×C10311yescharacteristic
992C22D42×C10311yescharacteristic
993C22#546×C10311yescharacteristic
994C22#546×C10311yescharacteristic
995C22#546×C10311yescharacteristic
996C22#546×C10311yescharacteristic
997C22#547×C10311yescharacteristic
998C22#547×C10311yescharacteristic
999C22#547×C10311yescharacteristic
1000C22#548×C10311yescharacteristic
1001C22#552×C10311yescharacteristic
1002C22#556×C10311yescharacteristic
1003C22#562×C10311yescharacteristic
1004C22#562×C10311yescharacteristic
1005C22#563×C10311yescharacteristic
1006C22#563×C10311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C103×#231011yescharacteristic
1023C2C103×#232311yescharacteristic
1024C2C103×#233211yescharacteristic
1025C2D4×C22⋊C4×C10311yescharacteristic
1026C2C103×#233911yescharacteristic
1027C2C103×#236211yescharacteristic
1028C2C103×#237811yescharacteristic
1029C2C103×#267211yescharacteristic
1030C2C103×#267411yescharacteristic
1031C2C103×#268011yescharacteristic
1032C2C103×#268111yescharacteristic
1033C2C103×#268711yescharacteristic
1034C2C103×#268911yescharacteristic
1035C2C103×#269811yescharacteristic
1036C2C103×#270011yescharacteristic
subgroupG/H
center, socleC24×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC24C24×C103
prime radicalC25×C103C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C103C2semidirect
6. C103×#1446C2semidirect
7. C103×#1445C2semidirect
8. C103×#1441C2semidirect
9. C103×#1441C2semidirect
12. C103×#1436C2semidirect
13. C103×#1436C2semidirect
14. C103×C4⋊#95C2semidirect
20. C2×C22⋊Q8×C103C4semidirect
502. #14364C103direct (N × H)
520. C2×#391C2×C103semidirect
524. #1446C2×C103semidirect
525. #1445C2×C103semidirect
526. #1441C2×C103semidirect
527. #1441C2×C103semidirect
530. #1436C2×C103semidirect
531. #1436C2×C103semidirect
532. C4⋊#95C2×C103semidirect
534. C103#14364direct (N × H)
539. C2×C22⋊Q8C4×C103semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1032
C2×#391×C1032
C2×#388×C1032
C2×#381×C1032
C103×#14462
C103×#14452
C103×#14412
C103×#14402
C103×#14362
C103×C4⋊#952
C103×C22⋊#952
#14364103