Finite Group Databasebeta

← C103×#14118 #39919393

Subgroups — C103×#14118 #39919393

Order 26368.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C103C211yesmaximal, characteristic
2C2×#388×C103C211yesmaximal, characteristic
3C2×#385×C103C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C103C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C103C211yesmaximal, characteristic
6C103×#1444C211yesmaximal, characteristic, complemented
7C103×#1441C211yesmaximal, characteristic, complemented
8C103×#1439C211yesmaximal, characteristic
9C103×#1439C211yesmaximal, characteristic
10C103×#1436C211yesmaximal, characteristic, complemented
11C103×#1436C211yesmaximal, characteristic, complemented
12C103×#1436C211yesmaximal, characteristic, complemented
13C103×C4⋊#95C211yesmaximal, characteristic, complemented
14C103×#1434C211yesmaximal, characteristic, complemented
15C103×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C103C2211yescharacteristic
17C22×C4⋊C4×C103C2211yescharacteristic
18C22×C4⋊C4×C103C2211yescharacteristic
19C22×C4⋊C4×C103C2211yescharacteristic
20C22×C4⋊C4×C103C2211yescharacteristic
21C22×C4⋊C4×C103C2211yescharacteristic
22C22×C4⋊C4×C103C2211yescharacteristic
23C22×C22⋊C4×C103C2211yescharacteristic
24C22×C22⋊C4×C103C2211yescharacteristic
25C22×C22⋊C4×C103C2211yescharacteristic
26C22×C22⋊C4×C103C2211yescharacteristic
27C22×C22⋊C4×C103C2211yescharacteristic
28C22×C22⋊C4×C103C2211yescharacteristic
29C22×C42×C103C2211yescharacteristic
30C22×C42×C103C2211yescharacteristic
31C22×C42×C103C2211yescharacteristic
32C22×C42×C103C2211yescharacteristic
33#388×C103—24no—
34#388×C103C418yescomplemented
35#385×C103—24no—
36C4×C4⋊C4×C103—24no—
37C4×C22⋊C4×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
56C25×C103C2311yescharacteristic
57C23×C4×C103—22no—
58C23×C4×C103—22no—
59C23×C4×C103—22no—
60C23×C4×C103—22no—
61C23×C4×C103—22no—
62C23×C4×C103—41no—
63C23×C4×C103—41no—
64C23×C4×C103C2311yescharacteristic
65C23×C4×C103C2311yescharacteristic
66C23×C4×C103C2311yescharacteristic
67C23×C4×C103C2311yescharacteristic
68C23×C4×C103C2311yescharacteristic
69C23×C4×C103C2311yescharacteristic
70C23×C4×C103C2311yescharacteristic
71C23×C4×C103C2311yescharacteristic
72C23×C4×C103C2311yescharacteristic
73C23×C4×C103C2311yescharacteristic
74C23×C4×C103C2311yescharacteristic
75C23×C4×C103C2311yescharacteristic
76C23×C4×C103C2311yescharacteristic
77C23×C4×C103C2311yescharacteristic
78C2×C4⋊C4×C103—22no—
79C2×C4⋊C4×C103—22no—
80C2×C4⋊C4×C103—22no—
81C2×C4⋊C4×C103—22no—
82C2×C4⋊C4×C103—22no—
83C2×C4⋊C4×C103—22no—
84C2×C4⋊C4×C103—22no—
85C2×C4⋊C4×C103—22no—
86C2×C4⋊C4×C103—22no—
87C2×C4⋊C4×C103—22no—
88C2×C4⋊C4×C103—41no—
89C2×C4⋊C4×C103—41no—
90C2×C4⋊C4×C103—41no—
91C2×C4⋊C4×C103—41no—
92C2×C4⋊C4×C103—41no—
93C2×C4⋊C4×C103—41no—
94C2×C4⋊C4×C103C2×C414yescomplemented
95C2×C4⋊C4×C103D414yes—
96C2×C22⋊C4×C103—22no—
97C2×C22⋊C4×C103—22no—
98C2×C22⋊C4×C103—22no—
99C2×C22⋊C4×C103—22no—
100C2×C22⋊C4×C103—22no—
101C2×C22⋊C4×C103—22no—
102C2×C22⋊C4×C103—22no—
103C2×C22⋊C4×C103—22no—
104C2×C22⋊C4×C103—22no—
105C2×C22⋊C4×C103—41no—
106C2×C22⋊C4×C103—41no—
107C2×C22⋊C4×C103—41no—
108C2×C22⋊C4×C103—41no—
109C2×C22⋊C4×C103C2×C414yes—
110C2×C22⋊C4×C103C2×C414yes—
111C2×C22⋊C4×C103C2×C414yes—
112C2×C22⋊C4×C103D414yes—
113C2×C22⋊C4×C103Q814yes—
114C2×C42×C103—22no—
115C2×C42×C103—22no—
116C2×C42×C103—22no—
117C2×C42×C103—22no—
118C2×C42×C103—22no—
119C2×C42×C103—22no—
120C2×C42×C103—22no—
121C2×C42×C103—22no—
122C2×C42×C103—41no—
123C2×C42×C103—41no—
124C2×C42×C103—41no—
125C2×C42×C103C2×C414yescomplemented
126#95×C103—22no—
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—41no—
140#95×C103—41no—
141#95×C103—41no—
142#95×C103C2×C414yescomplemented
143#95×C103C2×C414yescomplemented
144C24×C103—21no—
145C24×C103—21no—
146C24×C103—21no—
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×C103C22×C412yes—
157C24×C103C2×D412yes—
158C24×C103C2×Q812yes—
159C24×C103C2411yescharacteristic
160C22×C4×C103—21no—
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—21no—
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
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—28no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
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—21no—
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—44no—
240C22×C4×C103—44no—
241C22×C4×C103—44no—
242C22×C4×C103—44no—
243C22×C4×C103—44no—
244C22×C4×C103—44no—
245C22×C4×C103C22×C412yes—
246C22×C4×C103C22×C412yes—
247C22×C4×C103C22×C412yes—
248C22×C4×C103C22×C412yes—
249C22×C4×C103C22×C412yes—
250C22×C4×C103C22×C412yes—
251C22×C4×C103C2×D412yes—
252C22×C4×C103C2×D412yes—
253C22×C4×C103C2×D412yes—
254C22×C4×C103C2×D412yes—
255C22×C4×C103C2×D412yes—
256C22×C4×C103C2×Q812yes—
257C22×C4×C103C2×Q812yes—
258C22×C4×C103#4112yes—
259C22×C4×C103#4112yes—
260C22×C4×C103#4112yes—
261C22×C4×C103#4112yes—
262C22×C4×C103#4112yes—
263C22×C4×C103#4112yes—
264C22×C4×C103#4112yes—
265C4⋊C4×C103—28no—
266C4⋊C4×C103—28no—
267C4⋊C4×C103—44no—
268C4⋊C4×C103—44no—
269C4⋊C4×C103—44no—
270C4⋊C4×C103—44no—
271C22⋊C4×C103—28no—
272C22⋊C4×C103—28no—
273C22⋊C4×C103—44no—
274C22⋊C4×C103—44no—
275C22⋊C4×C103—44no—
276C22⋊C4×C103C4⋊C4116yescomplemented
277C42×C103—28no—
278C42×C103—44no—
279C42×C103—44no—
280C42×C103—44no—
281C23×C103—22no—
282C23×C103—22no—
283C23×C103—22no—
284C23×C103—22no—
285C23×C103—22no—
286C23×C103—22no—
287C23×C103—22no—
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—41no—
300C23×C103—41no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103—41no—
305C23×C103—41no—
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×C103C2×C4⋊C414yes—
316C23×C103C23×C411yescharacteristic
317C23×C103C22×D411yescharacteristic
318C23×C103C22×D411yescharacteristic
319C23×C103C22×Q811yescharacteristic
320C23×C103C2×#4111yescharacteristic
321C23×C103C2×#4111yescharacteristic
322C23×C103C2×#4111yescharacteristic
323C23×C103C2×#4111yescharacteristic
324C23×C103C2×#4111yescharacteristic
325C23×C103C2×#4111yescharacteristic
326C23×C103C2×#4111yescharacteristic
327C23×C103H(5,𝔽2)11yescharacteristic
328C23×C103H(5,𝔽2)11yescharacteristic
329C23×C103H(5,𝔽2)11yescharacteristic
330C23×C1032−1+411yescharacteristic
331C2×C4×C103—22no—
332C2×C4×C103—22no—
333C2×C4×C103—22no—
334C2×C4×C103—22no—
335C2×C4×C103—22no—
336C2×C4×C103—22no—
337C2×C4×C103—22no—
338C2×C4×C103—22no—
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—22no—
379C2×C4×C103—416no—
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×C103C2×C4⋊C414yes—
427C2×C4×C103C2×C4⋊C414yes—
428C2×C4×C103C4×D414yes—
429C2×C4×C103#12314yes—
430C22×C103—24no—
431C22×C103—24no—
432C22×C103—24no—
433C22×C103—42no—
434C22×C103—42no—
435C22×C103—42no—
436C22×C103—42no—
437C22×C103—42no—
438C22×C103—42no—
439C22×C103—42no—
440C22×C103—42no—
441C22×C103—42no—
442C22×C103—42no—
443C22×C103—42no—
444C22×C103—42no—
445C22×C103C22×C4⋊C411yescharacteristic
446C22×C103C2×C4×D411yescharacteristic
447C22×C103C4×#4111yescharacteristic
448C22×C103C4×#4111yescharacteristic
449C22×C103C4×#4111yescharacteristic
450C22×C103#51811yescharacteristic
451C22×C103#52011yescharacteristic
452C22×C103C2×#12311yescharacteristic
453C22×C103#52511yescharacteristic
454C22×C103#52511yescharacteristic
455C22×C103#52511yescharacteristic
456C22×C103#52911yescharacteristic
457C22×C103#52911yescharacteristic
458C22×C103#53311yescharacteristic
459C22×C103#53311yescharacteristic
460C22×C103#53811yescharacteristic
461C22×C103#53811yescharacteristic
462C22×C103#54211yescharacteristic
463C22×C103#54211yescharacteristic
464C22×C103D4211yescharacteristic
465C22×C103#54611yescharacteristic
466C22×C103#54611yescharacteristic
467C22×C103#54611yescharacteristic
468C22×C103#54711yescharacteristic
469C22×C103D4×Q811yescharacteristic
470C22×C103#55011yescharacteristic
471C22×C103#55111yescharacteristic
472C22×C103#55211yescharacteristic
473C22×C103#55311yescharacteristic
474C22×C103#55311yescharacteristic
475C22×C103#55411yescharacteristic
476C22×C103#55411yescharacteristic
477C22×C103#55411yescharacteristic
478C22×C103#55511yescharacteristic
479C22×C103#55611yescharacteristic
480C4×C103—24no—
481C4×C103—24no—
482C4×C103—24no—
483C4×C103—24no—
484C4×C103—42no—
485C4×C103—42no—
486C4×C103—42no—
487C4×C103—42no—
488C4×C103—42no—
489C4×C103—42no—
490C4×C103—42no—
491C4×C103—42no—
492C4×C103—81no—
493C4×C103—81no—
494#14118C10311yesmaximal, characteristic, direct product factor, Sylow
495C2×C103—44no—
496C2×C103#229611yescharacteristic
497C2×C103C4×#12311yescharacteristic
498C2×C103#233711yescharacteristic
499C2×C103D4×C4⋊C411yescharacteristic
500C2×C103#234911yescharacteristic
501C2×C103#236311yescharacteristic
502C2×C103#237311yescharacteristic
503C2×C103#241811yescharacteristic
504C2×C103#242311yescharacteristic
505C2×C103#245611yescharacteristic
506C2×C103#246511yescharacteristic
507C2×C103#246811yescharacteristic
508C2×C103#247411yescharacteristic
509C2×C103#257411yescharacteristic
510C2×C103#258711yescharacteristic
511C2×#388C2×C10311yescharacteristic
512C2×#388C2×C10311yescharacteristic
513C2×#385C2×C10311yescharacteristic
514C2×C4×C4⋊C4C2×C10311yescharacteristic, complemented
515C2×C4×C22⋊C4C2×C10311yescharacteristic
516#1444C2×C10311yescharacteristic, complemented
517#1441C2×C10311yescharacteristic, complemented
518#1439C2×C10311yescharacteristic
519#1439C2×C10311yescharacteristic
520#1436C2×C10311yescharacteristic, complemented
521#1436C2×C10311yescharacteristic, complemented
522#1436C2×C10311yescharacteristic, complemented
523C4⋊#95C2×C10311yescharacteristic, complemented
524#1434C2×C10311yescharacteristic, complemented
525C22⋊#95C2×C10311yescharacteristic
526C103#1411811yescharacteristic, direct product factor, Sylow
527C24×C4C22×C10311yescharacteristic
528C22×C4⋊C4C22×C10311yescharacteristic
529C22×C4⋊C4C22×C10311yescharacteristic
530C22×C4⋊C4C22×C10311yescharacteristic
531C22×C4⋊C4C22×C10311yescharacteristic
532C22×C4⋊C4C22×C10311yescharacteristic
533C22×C4⋊C4C22×C10311yescharacteristic
534C22×C22⋊C4C22×C10311yescharacteristic
535C22×C22⋊C4C22×C10311yescharacteristic
536C22×C22⋊C4C22×C10311yescharacteristic
537C22×C22⋊C4C22×C10311yescharacteristic
538C22×C22⋊C4C22×C10311yescharacteristic
539C22×C22⋊C4C22×C10311yescharacteristic
540C22×C42C22×C10311yescharacteristic
541C22×C42C22×C10311yescharacteristic
542C22×C42C22×C10311yescharacteristic
543C22×C42C22×C10311yescharacteristic
544#388—24no—
545#388C4×C10318yescomplemented
546#385—24no—
547C4×C4⋊C4—24no—
548C4×C22⋊C4—24no—
549C2×#95C22×C10311yescharacteristic
550C2×#95C22×C10311yescharacteristic
551C2×#95C22×C10311yescharacteristic
552C2×#95C22×C10311yescharacteristic
553C2×#95C22×C10311yescharacteristic
554C2×#95C22×C10311yescharacteristic
555C2×#95C22×C10311yescharacteristic
556C2×#95C22×C10311yescharacteristic
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
567C25C23×C10311yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C10311yescharacteristic
576C23×C4C23×C10311yescharacteristic
577C23×C4C23×C10311yescharacteristic
578C23×C4C23×C10311yescharacteristic
579C23×C4C23×C10311yescharacteristic
580C23×C4C23×C10311yescharacteristic
581C23×C4C23×C10311yescharacteristic
582C23×C4C23×C10311yescharacteristic
583C23×C4C23×C10311yescharacteristic
584C23×C4C23×C10311yescharacteristic
585C23×C4C23×C10311yescharacteristic
586C23×C4C23×C10311yescharacteristic
587C23×C4C23×C10311yescharacteristic
588C23×C4C23×C10311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4C2×C4×C10314yescomplemented
606C2×C4⋊C4D4×C10314yes—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4C2×C4×C10314yes—
621C2×C22⋊C4C2×C4×C10314yes—
622C2×C22⋊C4C2×C4×C10314yes—
623C2×C22⋊C4D4×C10314yes—
624C2×C22⋊C4Q8×C10314yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C10314yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95C2×C4×C10314yescomplemented
654#95C2×C4×C10314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C10312yes—
668C24C2×D4×C10312yes—
669C24C2×Q8×C10312yes—
670C24C24×C10311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—28no—
688C22×C4—21no—
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—21no—
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—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4C22×C4×C10312yes—
757C22×C4C22×C4×C10312yes—
758C22×C4C22×C4×C10312yes—
759C22×C4C22×C4×C10312yes—
760C22×C4C22×C4×C10312yes—
761C22×C4C22×C4×C10312yes—
762C22×C4C2×D4×C10312yes—
763C22×C4C2×D4×C10312yes—
764C22×C4C2×D4×C10312yes—
765C22×C4C2×D4×C10312yes—
766C22×C4C2×D4×C10312yes—
767C22×C4C2×Q8×C10312yes—
768C22×C4C2×Q8×C10312yes—
769C22×C4#41×C10312yes—
770C22×C4#41×C10312yes—
771C22×C4#41×C10312yes—
772C22×C4#41×C10312yes—
773C22×C4#41×C10312yes—
774C22×C4#41×C10312yes—
775C22×C4#41×C10312yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4C4⋊C4×C103116yescomplemented
788C42—28no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C10314yes—
827C23C23×C4×C10311yescharacteristic
828C23C22×D4×C10311yescharacteristic
829C23C22×D4×C10311yescharacteristic
830C23C22×Q8×C10311yescharacteristic
831C23C2×#41×C10311yescharacteristic
832C23C2×#41×C10311yescharacteristic
833C23C2×#41×C10311yescharacteristic
834C23C2×#41×C10311yescharacteristic
835C23C2×#41×C10311yescharacteristic
836C23C2×#41×C10311yescharacteristic
837C23C2×#41×C10311yescharacteristic
838C23H(5,𝔽2)×C10311yescharacteristic
839C23H(5,𝔽2)×C10311yescharacteristic
840C23H(5,𝔽2)×C10311yescharacteristic
841C232−1+4×C10311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
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×C4C2×C4⋊C4×C10314yes—
938C2×C4C2×C4⋊C4×C10314yes—
939C2×C4C4×D4×C10314yes—
940C2×C4#123×C10314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C10311yescharacteristic
957C22C2×C4×D4×C10311yescharacteristic
958C22C4×#41×C10311yescharacteristic
959C22C4×#41×C10311yescharacteristic
960C22C4×#41×C10311yescharacteristic
961C22#518×C10311yescharacteristic
962C22#520×C10311yescharacteristic
963C22C2×#123×C10311yescharacteristic
964C22#525×C10311yescharacteristic
965C22#525×C10311yescharacteristic
966C22#525×C10311yescharacteristic
967C22#529×C10311yescharacteristic
968C22#529×C10311yescharacteristic
969C22#533×C10311yescharacteristic
970C22#533×C10311yescharacteristic
971C22#538×C10311yescharacteristic
972C22#538×C10311yescharacteristic
973C22#542×C10311yescharacteristic
974C22#542×C10311yescharacteristic
975C22D42×C10311yescharacteristic
976C22#546×C10311yescharacteristic
977C22#546×C10311yescharacteristic
978C22#546×C10311yescharacteristic
979C22#547×C10311yescharacteristic
980C22D4×Q8×C10311yescharacteristic
981C22#550×C10311yescharacteristic
982C22#551×C10311yescharacteristic
983C22#552×C10311yescharacteristic
984C22#553×C10311yescharacteristic
985C22#553×C10311yescharacteristic
986C22#554×C10311yescharacteristic
987C22#554×C10311yescharacteristic
988C22#554×C10311yescharacteristic
989C22#555×C10311yescharacteristic
990C22#556×C10311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C103×#229611yescharacteristic
1007C2C4×#123×C10311yescharacteristic
1008C2C103×#233711yescharacteristic
1009C2D4×C4⋊C4×C10311yescharacteristic
1010C2C103×#234911yescharacteristic
1011C2C103×#236311yescharacteristic
1012C2C103×#237311yescharacteristic
1013C2C103×#241811yescharacteristic
1014C2C103×#242311yescharacteristic
1015C2C103×#245611yescharacteristic
1016C2C103×#246511yescharacteristic
1017C2C103×#246811yescharacteristic
1018C2C103×#247411yescharacteristic
1019C2C103×#257411yescharacteristic
1020C2C103×#258711yescharacteristic
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
4. C2×C4×C4⋊C4×C103C2semidirect
6. C103×#1444C2semidirect
7. C103×#1441C2semidirect
10. C103×#1436C2semidirect
11. C103×#1436C2semidirect
12. C103×#1436C2semidirect
13. C103×C4⋊#95C2semidirect
14. C103×#1434C2semidirect
34. #388×C103C4semidirect
94. C2×C4⋊C4×C103C2×C4semidirect
125. C2×C42×C103C2×C4semidirect
142. #95×C103C2×C4semidirect
143. #95×C103C2×C4semidirect
276. C22⋊C4×C103C4⋊C4semidirect
494. #14118C103direct (N × H)
514. C2×C4×C4⋊C4C2×C103semidirect
516. #1444C2×C103semidirect
517. #1441C2×C103semidirect
520. #1436C2×C103semidirect
521. #1436C2×C103semidirect
522. #1436C2×C103semidirect
523. C4⋊#95C2×C103semidirect
524. #1434C2×C103semidirect
526. C103#14118direct (N × H)
545. #388C4×C103semidirect
605. C2×C4⋊C4C2×C4×C103semidirect
636. C2×C42C2×C4×C103semidirect
653. #95C2×C4×C103semidirect
654. #95C2×C4×C103semidirect
787. C22⋊C4C4⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1032
C2×#385×C1032
C2×C4×C4⋊C4×C1032
C2×C4×C22⋊C4×C1032
C103×#14442
C103×#14412
C103×#14392
C103×#14362
C103×C4⋊#952
C103×#14342
C103×C22⋊#952
#14118103