Finite Group Databasebeta

← C103×#14112 #39919387

Subgroups — C103×#14112 #39919387

Order 26368.

1846 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
1C2×#389×C103C211yesmaximal, characteristic, complemented
2C2×#388×C103C211yesmaximal, characteristic
3C2×#388×C103C211yesmaximal, characteristic
4C2×#385×C103C211yesmaximal, characteristic
5C2×#385×C103C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C103C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C103C211yesmaximal, characteristic
8C103×#1444C211yesmaximal, characteristic, complemented
9C103×#1441C211yesmaximal, characteristic, complemented
10C103×#1439C211yesmaximal, characteristic
11C103×#1439C211yesmaximal, characteristic
12C103×#1436C211yesmaximal, characteristic, complemented
13C103×#1436C211yesmaximal, characteristic, complemented
14C103×#1436C211yesmaximal, characteristic, complemented
15C103×C4⋊#95C211yesmaximal, characteristic, complemented
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×C4⋊C4×C103C2211yescharacteristic
24C22×C4⋊C4×C103C2211yescharacteristic
25C22×C22⋊C4×C103C2211yescharacteristic
26C22×C22⋊C4×C103C2211yescharacteristic
27C22×C22⋊C4×C103C2211yescharacteristic
28C22×C22⋊C4×C103C2211yescharacteristic
29C22×C22⋊C4×C103C2211yescharacteristic
30C22×C22⋊C4×C103C2211yescharacteristic
31C22×C42×C103C2211yescharacteristic
32C22×C42×C103C2211yescharacteristic
33C22×C42×C103C2211yescharacteristic
34C22×C42×C103C2211yescharacteristic
35#389×C103—24no—
36#388×C103—24no—
37#388×C103C418yescomplemented
38#385×C103—24no—
39#385×C103—24no—
40C4×C4⋊C4×C103—24no—
41C4×C22⋊C4×C103—24no—
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
59C23×C4×C103—22no—
60C23×C4×C103—22no—
61C23×C4×C103—22no—
62C23×C4×C103—22no—
63C23×C4×C103—22no—
64C23×C4×C103—41no—
65C23×C4×C103—41no—
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
78C23×C4×C103C2311yescharacteristic
79C23×C4×C103C2311yescharacteristic
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—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×C103—41no—
101C2×C4⋊C4×C103—41no—
102C2×C4⋊C4×C103C2×C414yescomplemented
103C2×C4⋊C4×C103D414yes—
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—22no—
114C2×C22⋊C4×C103—22no—
115C2×C22⋊C4×C103—41no—
116C2×C22⋊C4×C103—41no—
117C2×C22⋊C4×C103C2×C414yes—
118C2×C22⋊C4×C103C2×C414yes—
119C2×C22⋊C4×C103C2×C414yes—
120C2×C22⋊C4×C103D414yes—
121C2×C22⋊C4×C103Q814yes—
122C2×C42×C103—22no—
123C2×C42×C103—22no—
124C2×C42×C103—22no—
125C2×C42×C103—22no—
126C2×C42×C103—22no—
127C2×C42×C103—22no—
128C2×C42×C103—22no—
129C2×C42×C103—22no—
130C2×C42×C103—41no—
131C2×C42×C103—41no—
132C2×C42×C103—41no—
133C2×C42×C103C2×C414yescomplemented
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—22no—
141#95×C103—22no—
142#95×C103—22no—
143#95×C103—22no—
144#95×C103—22no—
145#95×C103—22no—
146#95×C103—41no—
147#95×C103C2×C414yescomplemented
148#95×C103C2×C414yescomplemented
149#95×C103D414yes—
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×C103—21no—
160C24×C103—21no—
161C24×C103—21no—
162C24×C103C22×C412yes—
163C24×C103C2×D412yes—
164C24×C103C2×Q812yes—
165C24×C103C2411yescharacteristic
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—21no—
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—28no—
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—21no—
240C22×C4×C103—21no—
241C22×C4×C103—21no—
242C22×C4×C103—21no—
243C22×C4×C103—44no—
244C22×C4×C103—44no—
245C22×C4×C103—44no—
246C22×C4×C103—44no—
247C22×C4×C103—44no—
248C22×C4×C103—44no—
249C22×C4×C103C22×C412yes—
250C22×C4×C103C22×C412yes—
251C22×C4×C103C22×C412yes—
252C22×C4×C103C22×C412yes—
253C22×C4×C103C22×C412yes—
254C22×C4×C103C22×C412yes—
255C22×C4×C103C2×D412yes—
256C22×C4×C103C2×D412yes—
257C22×C4×C103C2×D412yes—
258C22×C4×C103C2×D412yes—
259C22×C4×C103C2×D412yes—
260C22×C4×C103C2×D412yes—
261C22×C4×C103C2×D412yes—
262C22×C4×C103C2×D412yes—
263C22×C4×C103C2×Q812yes—
264C22×C4×C103C2×Q812yes—
265C22×C4×C103#4112yes—
266C22×C4×C103#4112yes—
267C22×C4×C103#4112yes—
268C22×C4×C103#4112yes—
269C22×C4×C103#4112yes—
270C22×C4×C103#4112yes—
271C4⋊C4×C103—28no—
272C4⋊C4×C103—28no—
273C4⋊C4×C103—28no—
274C4⋊C4×C103—44no—
275C4⋊C4×C103—44no—
276C4⋊C4×C103—44no—
277C4⋊C4×C103—44no—
278C4⋊C4×C103—44no—
279C22⋊C4×C103—28no—
280C22⋊C4×C103—28no—
281C22⋊C4×C103—28no—
282C22⋊C4×C103—44no—
283C22⋊C4×C103—44no—
284C22⋊C4×C103C4⋊C4116yescomplemented
285C42×C103—28no—
286C42×C103—44no—
287C42×C103—44no—
288C42×C103—44no—
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—22no—
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×C103—41no—
323C23×C103C2×C4⋊C414yes—
324C23×C103C23×C411yescharacteristic
325C23×C103C22×D411yescharacteristic
326C23×C103C22×D411yescharacteristic
327C23×C103C22×D411yescharacteristic
328C23×C103C22×Q811yescharacteristic
329C23×C103C2×#4111yescharacteristic
330C23×C103C2×#4111yescharacteristic
331C23×C103C2×#4111yescharacteristic
332C23×C103C2×#4111yescharacteristic
333C23×C103C2×#4111yescharacteristic
334C23×C103C2×#4111yescharacteristic
335C23×C103H(5,𝔽2)11yescharacteristic
336C23×C103H(5,𝔽2)11yescharacteristic
337C23×C1032−1+411yescharacteristic
338C23×C1032−1+411yescharacteristic
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—22no—
380C2×C4×C103—22no—
381C2×C4×C103—22no—
382C2×C4×C103—22no—
383C2×C4×C103—22no—
384C2×C4×C103—22no—
385C2×C4×C103—22no—
386C2×C4×C103—22no—
387C2×C4×C103—22no—
388C2×C4×C103—22no—
389C2×C4×C103—22no—
390C2×C4×C103—416no—
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×C103C2×C4⋊C414yes—
434C2×C4×C103C2×C4⋊C414yes—
435C2×C4×C103C4×D414yes—
436C2×C4×C103C4×D414yes—
437C2×C4×C103#12114yes—
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×C4⋊C411yescharacteristic
454C22×C103C2×C4×D411yescharacteristic
455C22×C103C2×C4×D411yescharacteristic
456C22×C103C4×#4111yescharacteristic
457C22×C103C4×#4111yescharacteristic
458C22×C103#52011yescharacteristic
459C22×C103#52011yescharacteristic
460C22×C103C2×#12111yescharacteristic
461C22×C103#52511yescharacteristic
462C22×C103#52511yescharacteristic
463C22×C103#52511yescharacteristic
464C22×C103#52911yescharacteristic
465C22×C103#53211yescharacteristic
466C22×C103#53311yescharacteristic
467C22×C103#53311yescharacteristic
468C22×C103#53811yescharacteristic
469C22×C103#53911yescharacteristic
470C22×C103#54111yescharacteristic
471C22×C103#54211yescharacteristic
472C22×C103D4211yescharacteristic
473C22×C103D4211yescharacteristic
474C22×C103#54611yescharacteristic
475C22×C103#54611yescharacteristic
476C22×C103#54711yescharacteristic
477C22×C103#54711yescharacteristic
478C22×C103#54711yescharacteristic
479C22×C103#54811yescharacteristic
480C22×C103D4×Q811yescharacteristic
481C22×C103D4×Q811yescharacteristic
482C22×C103#55111yescharacteristic
483C22×C103#55211yescharacteristic
484C22×C103#55411yescharacteristic
485C22×C103#55411yescharacteristic
486C22×C103#55611yescharacteristic
487C22×C103#55911yescharacteristic
488C4×C103—24no—
489C4×C103—24no—
490C4×C103—24no—
491C4×C103—24no—
492C4×C103—24no—
493C4×C103—42no—
494C4×C103—42no—
495C4×C103—42no—
496C4×C103—42no—
497C4×C103—42no—
498C4×C103—42no—
499C4×C103—42no—
500C4×C103—81no—
501C4×C103—81no—
502#14112C10311yesmaximal, characteristic, direct product factor, Sylow
503C2×C103—44no—
504C2×C103#229611yescharacteristic
505C2×C103C4×#12111yescharacteristic
506C2×C103#233411yescharacteristic
507C2×C103D4×C4⋊C411yescharacteristic
508C2×C103D4×C4⋊C411yescharacteristic
509C2×C103#235911yescharacteristic
510C2×C103#236711yescharacteristic
511C2×C103#242411yescharacteristic
512C2×C103#242911yescharacteristic
513C2×C103#245511yescharacteristic
514C2×C103#246111yescharacteristic
515C2×C103#246511yescharacteristic
516C2×C103#247811yescharacteristic
517C2×C103#255611yescharacteristic
518C2×C103#258911yescharacteristic
519C2×#389C2×C10311yescharacteristic, complemented
520C2×#388C2×C10311yescharacteristic
521C2×#388C2×C10311yescharacteristic
522C2×#385C2×C10311yescharacteristic
523C2×#385C2×C10311yescharacteristic
524C2×C4×C4⋊C4C2×C10311yescharacteristic, complemented
525C2×C4×C22⋊C4C2×C10311yescharacteristic
526#1444C2×C10311yescharacteristic, complemented
527#1441C2×C10311yescharacteristic, complemented
528#1439C2×C10311yescharacteristic
529#1439C2×C10311yescharacteristic
530#1436C2×C10311yescharacteristic, complemented
531#1436C2×C10311yescharacteristic, complemented
532#1436C2×C10311yescharacteristic, complemented
533C4⋊#95C2×C10311yescharacteristic, complemented
534C103#1411211yescharacteristic, direct product factor, Sylow
535C24×C4C22×C10311yescharacteristic
536C22×C4⋊C4C22×C10311yescharacteristic
537C22×C4⋊C4C22×C10311yescharacteristic
538C22×C4⋊C4C22×C10311yescharacteristic
539C22×C4⋊C4C22×C10311yescharacteristic
540C22×C4⋊C4C22×C10311yescharacteristic
541C22×C4⋊C4C22×C10311yescharacteristic
542C22×C4⋊C4C22×C10311yescharacteristic
543C22×C4⋊C4C22×C10311yescharacteristic
544C22×C22⋊C4C22×C10311yescharacteristic
545C22×C22⋊C4C22×C10311yescharacteristic
546C22×C22⋊C4C22×C10311yescharacteristic
547C22×C22⋊C4C22×C10311yescharacteristic
548C22×C22⋊C4C22×C10311yescharacteristic
549C22×C22⋊C4C22×C10311yescharacteristic
550C22×C42C22×C10311yescharacteristic
551C22×C42C22×C10311yescharacteristic
552C22×C42C22×C10311yescharacteristic
553C22×C42C22×C10311yescharacteristic
554#389—24no—
555#388—24no—
556#388C4×C10318yescomplemented
557#385—24no—
558#385—24no—
559C4×C4⋊C4—24no—
560C4×C22⋊C4—24no—
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
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C10311yescharacteristic
586C23×C4C23×C10311yescharacteristic
587C23×C4C23×C10311yescharacteristic
588C23×C4C23×C10311yescharacteristic
589C23×C4C23×C10311yescharacteristic
590C23×C4C23×C10311yescharacteristic
591C23×C4C23×C10311yescharacteristic
592C23×C4C23×C10311yescharacteristic
593C23×C4C23×C10311yescharacteristic
594C23×C4C23×C10311yescharacteristic
595C23×C4C23×C10311yescharacteristic
596C23×C4C23×C10311yescharacteristic
597C23×C4C23×C10311yescharacteristic
598C23×C4C23×C10311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
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⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4C2×C4×C10314yescomplemented
622C2×C4⋊C4D4×C10314yes—
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—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4—41no—
636C2×C22⋊C4C2×C4×C10314yes—
637C2×C22⋊C4C2×C4×C10314yes—
638C2×C22⋊C4C2×C4×C10314yes—
639C2×C22⋊C4D4×C10314yes—
640C2×C22⋊C4Q8×C10314yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—41no—
650C2×C42—41no—
651C2×C42—41no—
652C2×C42C2×C4×C10314yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—41no—
666#95C2×C4×C10314yescomplemented
667#95C2×C4×C10314yescomplemented
668#95D4×C10314yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C10312yes—
682C24C2×D4×C10312yes—
683C24C2×Q8×C10312yes—
684C24C24×C10311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
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—28no—
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—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—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4C22×C4×C10312yes—
769C22×C4C22×C4×C10312yes—
770C22×C4C22×C4×C10312yes—
771C22×C4C22×C4×C10312yes—
772C22×C4C22×C4×C10312yes—
773C22×C4C22×C4×C10312yes—
774C22×C4C2×D4×C10312yes—
775C22×C4C2×D4×C10312yes—
776C22×C4C2×D4×C10312yes—
777C22×C4C2×D4×C10312yes—
778C22×C4C2×D4×C10312yes—
779C22×C4C2×D4×C10312yes—
780C22×C4C2×D4×C10312yes—
781C22×C4C2×D4×C10312yes—
782C22×C4C2×Q8×C10312yes—
783C22×C4C2×Q8×C10312yes—
784C22×C4#41×C10312yes—
785C22×C4#41×C10312yes—
786C22×C4#41×C10312yes—
787C22×C4#41×C10312yes—
788C22×C4#41×C10312yes—
789C22×C4#41×C10312yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C4⋊C4×C103116yescomplemented
804C42—28no—
805C42—44no—
806C42—44no—
807C42—44no—
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—22no—
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—
841C23—41no—
842C23C2×C4⋊C4×C10314yes—
843C23C23×C4×C10311yescharacteristic
844C23C22×D4×C10311yescharacteristic
845C23C22×D4×C10311yescharacteristic
846C23C22×D4×C10311yescharacteristic
847C23C22×Q8×C10311yescharacteristic
848C23C2×#41×C10311yescharacteristic
849C23C2×#41×C10311yescharacteristic
850C23C2×#41×C10311yescharacteristic
851C23C2×#41×C10311yescharacteristic
852C23C2×#41×C10311yescharacteristic
853C23C2×#41×C10311yescharacteristic
854C23H(5,𝔽2)×C10311yescharacteristic
855C23H(5,𝔽2)×C10311yescharacteristic
856C232−1+4×C10311yescharacteristic
857C232−1+4×C10311yescharacteristic
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—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—416no—
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×C4C2×C4⋊C4×C10314yes—
953C2×C4C2×C4⋊C4×C10314yes—
954C2×C4C4×D4×C10314yes—
955C2×C4C4×D4×C10314yes—
956C2×C4#121×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×C4⋊C4×C10311yescharacteristic
973C22C2×C4×D4×C10311yescharacteristic
974C22C2×C4×D4×C10311yescharacteristic
975C22C4×#41×C10311yescharacteristic
976C22C4×#41×C10311yescharacteristic
977C22#520×C10311yescharacteristic
978C22#520×C10311yescharacteristic
979C22C2×#121×C10311yescharacteristic
980C22#525×C10311yescharacteristic
981C22#525×C10311yescharacteristic
982C22#525×C10311yescharacteristic
983C22#529×C10311yescharacteristic
984C22#532×C10311yescharacteristic
985C22#533×C10311yescharacteristic
986C22#533×C10311yescharacteristic
987C22#538×C10311yescharacteristic
988C22#539×C10311yescharacteristic
989C22#541×C10311yescharacteristic
990C22#542×C10311yescharacteristic
991C22D42×C10311yescharacteristic
992C22D42×C10311yescharacteristic
993C22#546×C10311yescharacteristic
994C22#546×C10311yescharacteristic
995C22#547×C10311yescharacteristic
996C22#547×C10311yescharacteristic
997C22#547×C10311yescharacteristic
998C22#548×C10311yescharacteristic
999C22D4×Q8×C10311yescharacteristic
1000C22D4×Q8×C10311yescharacteristic
1001C22#551×C10311yescharacteristic
1002C22#552×C10311yescharacteristic
1003C22#554×C10311yescharacteristic
1004C22#554×C10311yescharacteristic
1005C22#556×C10311yescharacteristic
1006C22#559×C10311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C103×#229611yescharacteristic
1023C2C4×#121×C10311yescharacteristic
1024C2C103×#233411yescharacteristic
1025C2D4×C4⋊C4×C10311yescharacteristic
1026C2D4×C4⋊C4×C10311yescharacteristic
1027C2C103×#235911yescharacteristic
1028C2C103×#236711yescharacteristic
1029C2C103×#242411yescharacteristic
1030C2C103×#242911yescharacteristic
1031C2C103×#245511yescharacteristic
1032C2C103×#246111yescharacteristic
1033C2C103×#246511yescharacteristic
1034C2C103×#247811yescharacteristic
1035C2C103×#255611yescharacteristic
1036C2C103×#258911yescharacteristic
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
1. C2×#389×C103C2semidirect
6. C2×C4×C4⋊C4×C103C2semidirect
8. C103×#1444C2semidirect
9. C103×#1441C2semidirect
12. C103×#1436C2semidirect
13. C103×#1436C2semidirect
14. C103×#1436C2semidirect
15. C103×C4⋊#95C2semidirect
37. #388×C103C4semidirect
102. C2×C4⋊C4×C103C2×C4semidirect
133. C2×C42×C103C2×C4semidirect
147. #95×C103C2×C4semidirect
148. #95×C103C2×C4semidirect
284. C22⋊C4×C103C4⋊C4semidirect
502. #14112C103direct (N × H)
519. C2×#389C2×C103semidirect
524. C2×C4×C4⋊C4C2×C103semidirect
526. #1444C2×C103semidirect
527. #1441C2×C103semidirect
530. #1436C2×C103semidirect
531. #1436C2×C103semidirect
532. #1436C2×C103semidirect
533. C4⋊#95C2×C103semidirect
534. C103#14112direct (N × H)
556. #388C4×C103semidirect
621. C2×C4⋊C4C2×C4×C103semidirect
652. C2×C42C2×C4×C103semidirect
666. #95C2×C4×C103semidirect
667. #95C2×C4×C103semidirect
803. 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×#389×C1032
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
#14112103