Finite Group Databasebeta

← C103×#24136 #39929411

Subgroups — C103×#24136 #39929411

Order 26368.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 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×#442×C103C211yesmaximal, characteristic, complemented
4C103×#2537C211yesmaximal, characteristic, complemented
5C103×#2034C211yesmaximal, characteristic, complemented
6C103×#2033C211yesmaximal, characteristic, complemented
7C103×#1999C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1992C211yesmaximal, characteristic, complemented
10C103×#1955C211yesmaximal, characteristic, complemented
11C103×#1875C211yesmaximal, characteristic, complemented
12C103×#1874C211yesmaximal, characteristic, complemented
13C103×#1854C211yesmaximal, characteristic, complemented
14C103×#1853C211yesmaximal, characteristic, complemented
15C103×#1802C211yesmaximal, 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×C103—21no—
24C2×#121×C103C2211yescharacteristic
25C2×#121×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×C4×D4×C103—21no—
29C2×C4×D4×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C2×C4×D4×C103C2211yescharacteristic
32C2×#117×C103C2211yescharacteristic
33C22×C4⋊C4×C103C2211yescharacteristic
34#478×C103—24no—
35#442×C103—24no—
36C2×#107×C103C2211yescharacteristic
37C2×#106×C103C2211yescharacteristic
38C2×#106×C103C2211yescharacteristic
39C2×C4⋊C8×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×C22⋊C8×C103C2211yescharacteristic
47C2×C22⋊C8×C103C2211yescharacteristic
48C2×C22⋊C8×C103C2211yescharacteristic
49C2×C22⋊C8×C103C2211yescharacteristic
50C2×#97×C103C2211yescharacteristic
51#394×C103—21no—
52#394×C103—21no—
53#384×C103C2211yescharacteristic
54#380×C103—21no—
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—
95#121×C103—44no—
96C4×D4×C103—28no—
97C4×D4×C103—22no—
98C4×D4×C103—22no—
99C4×D4×C103—22no—
100C4×D4×C103—22no—
101C4×D4×C103—22no—
102C4×D4×C103D414yescomplemented
103#117×C103—22no—
104#117×C103—22no—
105C2×C4⋊C4×C103—21no—
106C2×C4⋊C4×C103—21no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103—22no—
109C2×C4⋊C4×C103—22no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103D411yescharacteristic
113C2×C4⋊C4×C103C2311yescharacteristic
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
117C2×C4⋊C4×C103C2311yescharacteristic
118C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103D411yescharacteristic
129C2×C22⋊C4×C103D411yescharacteristic
130C2×C42×C103—21no—
131C2×C42×C103C2311yescharacteristic
132#107×C103—22no—
133#106×C103—22no—
134#106×C103—22no—
135C4⋊C8×C103—22no—
136#102×C103—22no—
137#102×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—41no—
141#102×C103—41no—
142C22⋊C8×C103—22no—
143C22⋊C8×C103—22no—
144C22⋊C8×C103—41no—
145C22⋊C8×C103—41no—
146#97×C103—22no—
147#95×C103—21no—
148#95×C103—21no—
149C24×C103—21no—
150C24×C103—21no—
151C24×C103C2×D411yescharacteristic
152C24×C103C2×D411yescharacteristic
153C2×D4×C103—24no—
154C2×D4×C103—22no—
155C2×D4×C103—24no—
156C2×D4×C103—22no—
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—21no—
167C2×D4×C103—41no—
168C2×D4×C103—42no—
169C2×D4×C103—42no—
170C2×D4×C103—42no—
171C2×D4×C103—42no—
172C2×D4×C103—42no—
173C2×D4×C103—42no—
174C2×D4×C103—81no—
175C2×D4×C103—81no—
176C2×D4×C103—81no—
177C2×D4×C103—81no—
178C2×D4×C103C2×D412yes—
179C2×D4×C103#4112yes—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
183C22×C4×C103—24no—
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—24no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—42no—
201C22×C4×C103—42no—
202C22×C4×C103—42no—
203C22×C4×C103—81no—
204C22×C4×C103—81no—
205C22×C4×C103—81no—
206C22×C4×C103—81no—
207C22×C4×C103C2×D411yescharacteristic
208C22×C4×C103C2×D411yescharacteristic
209C22×C4×C103C2×D411yescharacteristic
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103C2411yescharacteristic
212D8×C103—28no—
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—21no—
224C2×C8×C103#4112yes—
225C4⋊C4×C103—24no—
226C4⋊C4×C103—24no—
227C4⋊C4×C103—24no—
228C4⋊C4×C103—22no—
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×C103—21no—
238C4⋊C4×C103—42no—
239C4⋊C4×C103—81no—
240C4⋊C4×C103C2×D412yes—
241C4⋊C4×C103C2×D412yes—
242C4⋊C4×C103C2×D412yes—
243C22⋊C4×C103—24no—
244C22⋊C4×C103—24no—
245C22⋊C4×C103—24no—
246C22⋊C4×C103—24no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—42no—
250C22⋊C4×C103—42no—
251C22⋊C4×C103—42no—
252C22⋊C4×C103—42no—
253C22⋊C4×C103—42no—
254C42×C103—24no—
255C42×C103C2×D412yes—
256C42×C103C2×D412yes—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—21no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—22no—
265C23×C103—22no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—21no—
269C23×C103—21no—
270C23×C103—21no—
271C23×C103—21no—
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—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103AGL(1,ℤ/8)12yes—
285C23×C103C22×D411yescharacteristic
286D4×C103—22no—
287D4×C103—22no—
288D4×C103—22no—
289D4×C103—22no—
290D4×C103—44no—
291D4×C103—48no—
292D4×C103—41no—
293D4×C103—41no—
294D4×C103—41no—
295D4×C103—41no—
296D4×C103—84no—
297D4×C103—84no—
298D4×C103—84no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—22no—
305C2×C4×C103—22no—
306C2×C4×C103—21no—
307C2×C4×C103—22no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
311C2×C4×C103—21no—
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—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—84no—
336C2×C4×C103—84no—
337C2×C4×C103—84no—
338C2×C4×C103#12012yes—
339C2×C4×C103#12012yes—
340C2×C4×C103C22×D411yescharacteristic
341C2×C4×C103C22×D411yescharacteristic
342C2×C4×C103C2×#4111yescharacteristic
343C2×C4×C103C2×#4111yescharacteristic
344C2×C4×C103H(5,𝔽2)11yescharacteristic
345C2×C4×C1032−1+411yescharacteristic
346C8×C103—22no—
347C8×C103—41no—
348C8×C103—41no—
349C8×C103—41no—
350C22×C103—22no—
351C22×C103—22no—
352C22×C103—22no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—41no—
356C22×C103—41no—
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—42no—
361C22×C103—42no—
362C22×C103—41no—
363C22×C103—42no—
364C22×C103—42no—
365C22×C103—41no—
366C22×C103—41no—
367C22×C103—42no—
368C22×C103—41no—
369C22×C103—42no—
370C22×C103—81no—
371C22×C103—81no—
372C22×C103—81no—
373C22×C103—81no—
374C22×C103—81no—
375C22×C103—81no—
376C22×C103—81no—
377C22×C103—81no—
378C22×C103C2×#12011yescharacteristic
379C22×C103#54611yescharacteristic
380C22×C103#54711yescharacteristic
381C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C103#57511yescharacteristic
383C22×C103#57611yescharacteristic
384C22×C103#57711yescharacteristic
385C4×C103—22no—
386C4×C103—22no—
387C4×C103—41no—
388C4×C103—41no—
389C4×C103—42no—
390C4×C103—42no—
391C4×C103—42no—
392C4×C103—81no—
393C4×C103—81no—
394C4×C103—81no—
395C4×C103#52511yescharacteristic
396C4×C103#53711yescharacteristic
397C4×C103#54811yescharacteristic
398C4×C103#55011yescharacteristic
399#24136C10311yesmaximal, characteristic, direct product factor, Sylow
400C2×C103—42no—
401C2×C103—81no—
402C2×C103—82no—
403C2×C103—82no—
404C2×C103#240711yescharacteristic
405C2×C103#300611yescharacteristic
406C2×C103#301211yescharacteristic
407C2×C103#330711yescharacteristic
408C2×C103#331811yescharacteristic
409C2×C103#334511yescharacteristic
410C2×C103#334711yescharacteristic
411C2×#553C2×C10311yescharacteristic, complemented
412C2×#478C2×C10311yescharacteristic, complemented
413C2×#442C2×C10311yescharacteristic, complemented
414#2537C2×C10311yescharacteristic, complemented
415#2034C2×C10311yescharacteristic, complemented
416#2033C2×C10311yescharacteristic, complemented
417#1999C2×C10311yescharacteristic, complemented
418#1999C2×C10311yescharacteristic, complemented
419#1992C2×C10311yescharacteristic, complemented
420#1955C2×C10311yescharacteristic, complemented
421#1875C2×C10311yescharacteristic, complemented
422#1874C2×C10311yescharacteristic, complemented
423#1854C2×C10311yescharacteristic, complemented
424#1853C2×C10311yescharacteristic, complemented
425#1802C2×C10311yescharacteristic, complemented
426C103#2413611yescharacteristic, direct product factor, Sylow
427C22×D8C22×C10311yescharacteristic
428#553—24no—
429#553—24no—
430C2×#126—21no—
431C2×#125C22×C10311yescharacteristic
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C10311yescharacteristic
436C2×#121C22×C10311yescharacteristic
437C2×#121C22×C10311yescharacteristic
438C2×#121C22×C10311yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C10311yescharacteristic
441C2×C4×D4C22×C10311yescharacteristic
442C2×C4×D4C22×C10311yescharacteristic
443C2×#117C22×C10311yescharacteristic
444C22×C4⋊C4C22×C10311yescharacteristic
445#478—24no—
446#442—24no—
447C2×#107C22×C10311yescharacteristic
448C2×#106C22×C10311yescharacteristic
449C2×#106C22×C10311yescharacteristic
450C2×C4⋊C8C22×C10311yescharacteristic
451C2×#102C22×C10311yescharacteristic
452C2×#102C22×C10311yescharacteristic
453C2×#102C22×C10311yescharacteristic
454C2×#102C22×C10311yescharacteristic
455C2×#102C22×C10311yescharacteristic
456C2×#102C22×C10311yescharacteristic
457C2×C22⋊C8C22×C10311yescharacteristic
458C2×C22⋊C8C22×C10311yescharacteristic
459C2×C22⋊C8C22×C10311yescharacteristic
460C2×C22⋊C8C22×C10311yescharacteristic
461C2×#97C22×C10311yescharacteristic
462#394—21no—
463#394—21no—
464#384C22×C10311yescharacteristic
465#380—21no—
466#380C22×C10311yescharacteristic
467#380C22×C10311yescharacteristic
468#340C22×C10311yescharacteristic
469#340C22×C10311yescharacteristic
470#340C22×C10311yescharacteristic
471#340C22×C10311yescharacteristic
472#340C22×C10311yescharacteristic
473#340C22×C10311yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4D4×C10311yescharacteristic
479C22×D4C23×C10311yescharacteristic
480C22×D4C23×C10311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C10311yescharacteristic
485C23×C4C23×C10311yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C22×C8C23×C10311yescharacteristic
490C22×C8C23×C10311yescharacteristic
491C22×C8C23×C10311yescharacteristic
492C22×C8C23×C10311yescharacteristic
493#126—28no—
494#125—22no—
495#125D4×C10314yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—22no—
504#121—41no—
505#121—41no—
506#121—44no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C10314yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C10311yescharacteristic
524C2×C4⋊C4C23×C10311yescharacteristic
525C2×C4⋊C4C23×C10311yescharacteristic
526C2×C4⋊C4C23×C10311yescharacteristic
527C2×C4⋊C4C23×C10311yescharacteristic
528C2×C4⋊C4C23×C10311yescharacteristic
529C2×C4⋊C4C23×C10311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4D4×C10311yescharacteristic
540C2×C22⋊C4D4×C10311yescharacteristic
541C2×C42—21no—
542C2×C42C23×C10311yescharacteristic
543#107—22no—
544#106—22no—
545#106—22no—
546C4⋊C8—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102—41no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557#97—22no—
558#95—21no—
559#95—21no—
560C24—21no—
561C24—21no—
562C24C2×D4×C10311yescharacteristic
563C24C2×D4×C10311yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4C2×D4×C10312yes—
590C2×D4#41×C10312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
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—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×D4×C10311yescharacteristic
619C22×C4C2×D4×C10311yescharacteristic
620C22×C4C2×D4×C10311yescharacteristic
621C22×C4C2×D4×C10311yescharacteristic
622C22×C4C24×C10311yescharacteristic
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8#41×C10312yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—81no—
651C4⋊C4C2×D4×C10312yes—
652C4⋊C4C2×D4×C10312yes—
653C4⋊C4C2×D4×C10312yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42C2×D4×C10312yes—
667C42C2×D4×C10312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23AGL(1,ℤ/8)×C10312yes—
696C23C22×D4×C10311yescharacteristic
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—44no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
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—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4#120×C10312yes—
750C2×C4#120×C10312yes—
751C2×C4C22×D4×C10311yescharacteristic
752C2×C4C22×D4×C10311yescharacteristic
753C2×C4C2×#41×C10311yescharacteristic
754C2×C4C2×#41×C10311yescharacteristic
755C2×C4H(5,𝔽2)×C10311yescharacteristic
756C2×C42−1+4×C10311yescharacteristic
757C8—22no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22C2×#120×C10311yescharacteristic
790C22#546×C10311yescharacteristic
791C22#547×C10311yescharacteristic
792C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
793C22#575×C10311yescharacteristic
794C22#576×C10311yescharacteristic
795C22#577×C10311yescharacteristic
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4#525×C10311yescharacteristic
807C4#537×C10311yescharacteristic
808C4#548×C10311yescharacteristic
809C4#550×C10311yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—82no—
814C2C103×#240711yescharacteristic
815C2C103×#300611yescharacteristic
816C2C103×#301211yescharacteristic
817C2C103×#330711yescharacteristic
818C2C103×#331811yescharacteristic
819C2C103×#334511yescharacteristic
820C2C103×#334711yescharacteristic
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×#442×C103C2semidirect
4. C103×#2537C2semidirect
5. C103×#2034C2semidirect
6. C103×#2033C2semidirect
7. C103×#1999C2semidirect
8. C103×#1999C2semidirect
9. C103×#1992C2semidirect
10. C103×#1955C2semidirect
11. C103×#1875C2semidirect
12. C103×#1874C2semidirect
13. C103×#1854C2semidirect
14. C103×#1853C2semidirect
15. C103×#1802C2semidirect
84. #125×C103D4semidirect
102. C4×D4×C103D4semidirect
399. #24136C103direct (N × H)
411. C2×#553C2×C103semidirect
412. C2×#478C2×C103semidirect
413. C2×#442C2×C103semidirect
414. #2537C2×C103semidirect
415. #2034C2×C103semidirect
416. #2033C2×C103semidirect
417. #1999C2×C103semidirect
418. #1999C2×C103semidirect
419. #1992C2×C103semidirect
420. #1955C2×C103semidirect
421. #1875C2×C103semidirect
422. #1874C2×C103semidirect
423. #1854C2×C103semidirect
424. #1853C2×C103semidirect
425. #1802C2×C103semidirect
426. C103#24136direct (N × H)
495. #125D4×C103semidirect
513. 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×#442×C1032
C103×#25372
C103×#20342
C103×#20332
C103×#19992
C103×#19922
C103×#19552
C103×#18752
C103×#18742
C103×#18542
C103×#18532
C103×#18022
#24136103