Finite Group Databasebeta

← C103×#24124 #39929399

Subgroups — C103×#24124 #39929399

Order 26368.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C103C211yesmaximal, characteristic, complemented
2C2×#478×C103C211yesmaximal, characteristic, complemented
3C2×C4×D8×C103C211yesmaximal, characteristic, complemented
4C103×#2535C211yesmaximal, characteristic, complemented
5C103×#2034C211yesmaximal, characteristic, complemented
6C103×#2033C211yesmaximal, characteristic, complemented
7C103×#1999C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1991C211yesmaximal, characteristic, complemented
10C103×#1954C211yesmaximal, characteristic, complemented
11C103×#1875C211yesmaximal, characteristic, complemented
12C103×#1874C211yesmaximal, characteristic, complemented
13C103×#1854C211yesmaximal, characteristic, complemented
14C103×#1852C211yesmaximal, characteristic, complemented
15C103×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17#553×C103—24no—
18#553×C103—24no—
19C2×#126×C103—21no—
20C2×#125×C103C2211yescharacteristic
21C2×#123×C103—21no—
22C2×#121×C103—21no—
23C2×#121×C103C2211yescharacteristic
24C2×#121×C103C2211yescharacteristic
25C2×#121×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×C4×D4×C103—21no—
28C2×C4×D4×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C2×#117×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic
33#478×C103—24no—
34C4×D8×C103—24no—
35C2×#107×C103C2211yescharacteristic
36C2×#107×C103C2211yescharacteristic
37C2×#106×C103C2211yescharacteristic
38C2×C4⋊C8×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×C22⋊C8×C103C2211yescharacteristic
46C2×C22⋊C8×C103C2211yescharacteristic
47C2×C22⋊C8×C103C2211yescharacteristic
48C2×C22⋊C8×C103C2211yescharacteristic
49C2×C4×C8×C103C2211yescharacteristic
50#397×C103—21no—
51#392×C103—21no—
52#386×C103—21no—
53#386×C103—21no—
54#382×C103C2211yescharacteristic
55#380×C103C2211yescharacteristic
56#380×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic
62#340×C103C2211yescharacteristic
63C22×D4×C103—21no—
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103—21no—
67C22×D4×C103D411yescharacteristic
68C22×D4×C103C2311yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C23×C4×C103—21no—
71C23×C4×C103—21no—
72C23×C4×C103—21no—
73C23×C4×C103C2311yescharacteristic
74C23×C4×C103C2311yescharacteristic
75C2×D8×C103—22no—
76C2×D8×C103—22no—
77C2×D8×C103—22no—
78C22×C8×C103C2311yescharacteristic
79C22×C8×C103C2311yescharacteristic
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82#126×C103—28no—
83#125×C103—22no—
84#125×C103D414yescomplemented
85#123×C103—28no—
86#121×C103—28no—
87#121×C103—22no—
88#121×C103—22no—
89#121×C103—22no—
90#121×C103—22no—
91#121×C103—22no—
92#121×C103—22no—
93#121×C103—41no—
94#121×C103—41no—
95C4×D4×C103—28no—
96C4×D4×C103—22no—
97C4×D4×C103—22no—
98C4×D4×C103—22no—
99C4×D4×C103—22no—
100C4×D4×C103—22no—
101C4×D4×C103D414yescomplemented
102#117×C103—22no—
103#117×C103—22no—
104C2×C4⋊C4×C103—21no—
105C2×C4⋊C4×C103—21no—
106C2×C4⋊C4×C103—21no—
107C2×C4⋊C4×C103—22no—
108C2×C4⋊C4×C103—22no—
109C2×C4⋊C4×C103D411yescharacteristic
110C2×C4⋊C4×C103C2311yescharacteristic
111C2×C4⋊C4×C103C2311yescharacteristic
112C2×C4⋊C4×C103C2311yescharacteristic
113C2×C4⋊C4×C103C2311yescharacteristic
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C22⋊C4×C103—21no—
117C2×C22⋊C4×C103—21no—
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103D411yescharacteristic
126C2×C22⋊C4×C103D411yescharacteristic
127C2×C42×C103—21no—
128C2×C42×C103C2311yescharacteristic
129#107×C103—22no—
130#107×C103—22no—
131#106×C103—22no—
132C4⋊C8×C103—22no—
133#102×C103—22no—
134#102×C103—22no—
135#102×C103—22no—
136#102×C103—22no—
137#102×C103—41no—
138#102×C103—41no—
139C22⋊C8×C103—22no—
140C22⋊C8×C103—22no—
141C22⋊C8×C103—41no—
142C22⋊C8×C103—41no—
143C4×C8×C103—22no—
144#95×C103—21no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148C24×C103—21no—
149C24×C103—21no—
150C24×C103C2×D411yescharacteristic
151C24×C103C2×D411yescharacteristic
152C2×D4×C103—24no—
153C2×D4×C103—22no—
154C2×D4×C103—24no—
155C2×D4×C103—22no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
161C2×D4×C103—21no—
162C2×D4×C103—21no—
163C2×D4×C103—21no—
164C2×D4×C103—21no—
165C2×D4×C103—21no—
166C2×D4×C103—41no—
167C2×D4×C103—42no—
168C2×D4×C103—42no—
169C2×D4×C103—42no—
170C2×D4×C103—42no—
171C2×D4×C103—42no—
172C2×D4×C103—42no—
173C2×D4×C103—81no—
174C2×D4×C103—81no—
175C2×D4×C103—81no—
176C2×D4×C103—81no—
177C2×D4×C103C2×D412yes—
178C2×D4×C103#4112yes—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—24no—
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—24no—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—42no—
200C22×C4×C103—81no—
201C22×C4×C103—81no—
202C22×C4×C103—81no—
203C22×C4×C103—81no—
204C22×C4×C103—81no—
205C22×C4×C103—81no—
206C22×C4×C103C2×D411yescharacteristic
207C22×C4×C103C2×D411yescharacteristic
208C22×C4×C103C2×D411yescharacteristic
209C22×C4×C103C2×D411yescharacteristic
210C22×C4×C103C2411yescharacteristic
211D8×C103—28no—
212C2×C8×C103—21no—
213C2×C8×C103—21no—
214C2×C8×C103—21no—
215C2×C8×C103—21no—
216C2×C8×C103—21no—
217C2×C8×C103—21no—
218C2×C8×C103—21no—
219C2×C8×C103—21no—
220C2×C8×C103—21no—
221C2×C8×C103—21no—
222C2×C8×C103—21no—
223C2×C8×C103#4112yes—
224C4⋊C4×C103—24no—
225C4⋊C4×C103—24no—
226C4⋊C4×C103—24no—
227C4⋊C4×C103—22no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—21no—
233C4⋊C4×C103—21no—
234C4⋊C4×C103—21no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—21no—
237C4⋊C4×C103C2×D412yes—
238C4⋊C4×C103C2×D412yes—
239C4⋊C4×C103C2×D412yes—
240C22⋊C4×C103—24no—
241C22⋊C4×C103—24no—
242C22⋊C4×C103—24no—
243C22⋊C4×C103—24no—
244C22⋊C4×C103—22no—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—42no—
247C22⋊C4×C103—42no—
248C22⋊C4×C103—42no—
249C22⋊C4×C103—81no—
250C22⋊C4×C103—81no—
251C42×C103—24no—
252C42×C103C2×D412yes—
253C42×C103C2×D412yes—
254C23×C103—21no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—22no—
262C23×C103—22no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—21no—
269C23×C103—41no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103—41no—
273C23×C103—41no—
274C23×C103—41no—
275C23×C103—41no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103—41no—
279C23×C103—41no—
280C23×C103—41no—
281C23×C103#13512yes—
282C23×C103C22×D411yescharacteristic
283D4×C103—22no—
284D4×C103—22no—
285D4×C103—22no—
286D4×C103—22no—
287D4×C103—44no—
288D4×C103—48no—
289D4×C103—41no—
290D4×C103—41no—
291D4×C103—41no—
292D4×C103—41no—
293D4×C103—84no—
294D4×C103—84no—
295D4×C103—84no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—21no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—22no—
302C2×C4×C103—22no—
303C2×C4×C103—21no—
304C2×C4×C103—22no—
305C2×C4×C103—21no—
306C2×C4×C103—21no—
307C2×C4×C103—21no—
308C2×C4×C103—21no—
309C2×C4×C103—41no—
310C2×C4×C103—41no—
311C2×C4×C103—41no—
312C2×C4×C103—41no—
313C2×C4×C103—41no—
314C2×C4×C103—41no—
315C2×C4×C103—41no—
316C2×C4×C103—41no—
317C2×C4×C103—41no—
318C2×C4×C103—41no—
319C2×C4×C103—41no—
320C2×C4×C103—41no—
321C2×C4×C103—41no—
322C2×C4×C103—41no—
323C2×C4×C103—41no—
324C2×C4×C103—41no—
325C2×C4×C103—41no—
326C2×C4×C103—41no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—41no—
331C2×C4×C103—41no—
332C2×C4×C103—84no—
333C2×C4×C103—84no—
334C2×C4×C103—84no—
335C2×C4×C103#12012yes—
336C2×C4×C103#12012yes—
337C2×C4×C103C22×D411yescharacteristic
338C2×C4×C103C22×D411yescharacteristic
339C2×C4×C103C2×#4111yescharacteristic
340C2×C4×C103C2×#4111yescharacteristic
341C2×C4×C103H(5,𝔽2)11yescharacteristic
342C2×C4×C1032−1+411yescharacteristic
343C8×C103—22no—
344C8×C103—41no—
345C8×C103—41no—
346C8×C103—41no—
347C22×C103—22no—
348C22×C103—22no—
349C22×C103—22no—
350C22×C103—41no—
351C22×C103—41no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—41no—
356C22×C103—41no—
357C22×C103—42no—
358C22×C103—42no—
359C22×C103—41no—
360C22×C103—42no—
361C22×C103—42no—
362C22×C103—41no—
363C22×C103—42no—
364C22×C103—41no—
365C22×C103—41no—
366C22×C103—42no—
367C22×C103—81no—
368C22×C103—81no—
369C22×C103—81no—
370C22×C103—81no—
371C22×C103—81no—
372C22×C103—81no—
373C22×C103—81no—
374C22×C103—81no—
375C22×C103C2×#12011yescharacteristic
376C22×C103#54611yescharacteristic
377C22×C103#54711yescharacteristic
378C22×C103C2×#13511yescharacteristic
379C22×C103#57511yescharacteristic
380C22×C103#57611yescharacteristic
381C22×C103#57611yescharacteristic
382C4×C103—22no—
383C4×C103—22no—
384C4×C103—41no—
385C4×C103—41no—
386C4×C103—42no—
387C4×C103—42no—
388C4×C103—42no—
389C4×C103—81no—
390C4×C103—81no—
391C4×C103—81no—
392C4×C103#52511yescharacteristic
393C4×C103#53711yescharacteristic
394C4×C103#54811yescharacteristic
395C4×C103#55011yescharacteristic
396#24124C10311yesmaximal, characteristic, direct product factor, Sylow
397C2×C103—42no—
398C2×C103—81no—
399C2×C103—82no—
400C2×C103—82no—
401C2×C103#240711yescharacteristic
402C2×C103#300211yescharacteristic
403C2×C103#300811yescharacteristic
404C2×C103#329711yescharacteristic
405C2×C103#332211yescharacteristic
406C2×C103#333911yescharacteristic
407C2×C103#335511yescharacteristic
408C2×#553C2×C10311yescharacteristic, complemented
409C2×#478C2×C10311yescharacteristic, complemented
410C2×C4×D8C2×C10311yescharacteristic, complemented
411#2535C2×C10311yescharacteristic, complemented
412#2034C2×C10311yescharacteristic, complemented
413#2033C2×C10311yescharacteristic, complemented
414#1999C2×C10311yescharacteristic, complemented
415#1999C2×C10311yescharacteristic, complemented
416#1991C2×C10311yescharacteristic, complemented
417#1954C2×C10311yescharacteristic, complemented
418#1875C2×C10311yescharacteristic, complemented
419#1874C2×C10311yescharacteristic, complemented
420#1854C2×C10311yescharacteristic, complemented
421#1852C2×C10311yescharacteristic, complemented
422#1804C2×C10311yescharacteristic, complemented
423C103#2412411yescharacteristic, direct product factor, Sylow
424C22×D8C22×C10311yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C10311yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C10311yescharacteristic
432C2×#121C22×C10311yescharacteristic
433C2×#121C22×C10311yescharacteristic
434C2×#121C22×C10311yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C10311yescharacteristic
437C2×C4×D4C22×C10311yescharacteristic
438C2×C4×D4C22×C10311yescharacteristic
439C2×#117C22×C10311yescharacteristic
440C22×C4⋊C4C22×C10311yescharacteristic
441#478—24no—
442C4×D8—24no—
443C2×#107C22×C10311yescharacteristic
444C2×#107C22×C10311yescharacteristic
445C2×#106C22×C10311yescharacteristic
446C2×C4⋊C8C22×C10311yescharacteristic
447C2×#102C22×C10311yescharacteristic
448C2×#102C22×C10311yescharacteristic
449C2×#102C22×C10311yescharacteristic
450C2×#102C22×C10311yescharacteristic
451C2×#102C22×C10311yescharacteristic
452C2×#102C22×C10311yescharacteristic
453C2×C22⋊C8C22×C10311yescharacteristic
454C2×C22⋊C8C22×C10311yescharacteristic
455C2×C22⋊C8C22×C10311yescharacteristic
456C2×C22⋊C8C22×C10311yescharacteristic
457C2×C4×C8C22×C10311yescharacteristic
458#397—21no—
459#392—21no—
460#386—21no—
461#386—21no—
462#382C22×C10311yescharacteristic
463#380C22×C10311yescharacteristic
464#380C22×C10311yescharacteristic
465#340C22×C10311yescharacteristic
466#340C22×C10311yescharacteristic
467#340C22×C10311yescharacteristic
468#340C22×C10311yescharacteristic
469#340C22×C10311yescharacteristic
470#340C22×C10311yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C10311yescharacteristic
476C22×D4C23×C10311yescharacteristic
477C22×D4C23×C10311yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C10311yescharacteristic
482C23×C4C23×C10311yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C10311yescharacteristic
487C22×C8C23×C10311yescharacteristic
488C22×C8C23×C10311yescharacteristic
489C22×C8C23×C10311yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C10314yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C10314yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C10311yescharacteristic
518C2×C4⋊C4C23×C10311yescharacteristic
519C2×C4⋊C4C23×C10311yescharacteristic
520C2×C4⋊C4C23×C10311yescharacteristic
521C2×C4⋊C4C23×C10311yescharacteristic
522C2×C4⋊C4C23×C10311yescharacteristic
523C2×C4⋊C4C23×C10311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4D4×C10311yescharacteristic
534C2×C22⋊C4D4×C10311yescharacteristic
535C2×C42—21no—
536C2×C42C23×C10311yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C10311yescharacteristic
559C24C2×D4×C10311yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C10312yes—
586C2×D4#41×C10312yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C10311yescharacteristic
615C22×C4C2×D4×C10311yescharacteristic
616C22×C4C2×D4×C10311yescharacteristic
617C22×C4C2×D4×C10311yescharacteristic
618C22×C4C24×C10311yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C10312yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C10312yes—
646C4⋊C4C2×D4×C10312yes—
647C4⋊C4C2×D4×C10312yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C10312yes—
661C42C2×D4×C10312yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C10312yes—
690C23C22×D4×C10311yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C10312yes—
744C2×C4#120×C10312yes—
745C2×C4C22×D4×C10311yescharacteristic
746C2×C4C22×D4×C10311yescharacteristic
747C2×C4C2×#41×C10311yescharacteristic
748C2×C4C2×#41×C10311yescharacteristic
749C2×C4H(5,𝔽2)×C10311yescharacteristic
750C2×C42−1+4×C10311yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C10311yescharacteristic
784C22#546×C10311yescharacteristic
785C22#547×C10311yescharacteristic
786C22C2×#135×C10311yescharacteristic
787C22#575×C10311yescharacteristic
788C22#576×C10311yescharacteristic
789C22#576×C10311yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4#525×C10311yescharacteristic
801C4#537×C10311yescharacteristic
802C4#548×C10311yescharacteristic
803C4#550×C10311yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C103×#240711yescharacteristic
809C2C103×#300211yescharacteristic
810C2C103×#300811yescharacteristic
811C2C103×#329711yescharacteristic
812C2C103×#332211yescharacteristic
813C2C103×#333911yescharacteristic
814C2C103×#335511yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C103C2semidirect
2. C2×#478×C103C2semidirect
3. C2×C4×D8×C103C2semidirect
4. C103×#2535C2semidirect
5. C103×#2034C2semidirect
6. C103×#2033C2semidirect
7. C103×#1999C2semidirect
8. C103×#1999C2semidirect
9. C103×#1991C2semidirect
10. C103×#1954C2semidirect
11. C103×#1875C2semidirect
12. C103×#1874C2semidirect
13. C103×#1854C2semidirect
14. C103×#1852C2semidirect
15. C103×#1804C2semidirect
84. #125×C103D4semidirect
101. C4×D4×C103D4semidirect
396. #24124C103direct (N × H)
408. C2×#553C2×C103semidirect
409. C2×#478C2×C103semidirect
410. C2×C4×D8C2×C103semidirect
411. #2535C2×C103semidirect
412. #2034C2×C103semidirect
413. #2033C2×C103semidirect
414. #1999C2×C103semidirect
415. #1999C2×C103semidirect
416. #1991C2×C103semidirect
417. #1954C2×C103semidirect
418. #1875C2×C103semidirect
419. #1874C2×C103semidirect
420. #1854C2×C103semidirect
421. #1852C2×C103semidirect
422. #1804C2×C103semidirect
423. C103#24124direct (N × H)
492. #125D4×C103semidirect
509. C4×D4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1032
C2×#478×C1032
C2×C4×D8×C1032
C103×#25352
C103×#20342
C103×#20332
C103×#19992
C103×#19912
C103×#19542
C103×#18752
C103×#18742
C103×#18542
C103×#18522
C103×#18042
#24124103