Finite Group Databasebeta

← C103×#25554 #39930829

Subgroups — C103×#25554 #39930829

Order 26368.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C103C211yesmaximal, characteristic, complemented
2C2×#482×C103C211yesmaximal, characteristic, complemented
3C2×#469×C103C211yesmaximal, characteristic, complemented
4C103×#2416C211yesmaximal, characteristic, complemented
5C103×#2058C211yesmaximal, characteristic, complemented
6C103×#2034C211yesmaximal, characteristic, complemented
7C103×#2023C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1879C211yesmaximal, characteristic, complemented
10C103×#1875C211yesmaximal, characteristic, complemented
11C103×#1874C211yesmaximal, characteristic, complemented
12C103×#1870C211yesmaximal, characteristic, complemented
13C103×#1862C211yesmaximal, characteristic, complemented
14C103×#1854C211yesmaximal, characteristic, complemented
15C103×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18#555×C103—24no—
19#555×C103—24no—
20C2×C4⋊Q8×C103C2211yescharacteristic
21C2×#124×C103—21no—
22C2×#124×C103—21no—
23C2×#121×C103—21no—
24C2×#121×C103—21no—
25C2×#121×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×#121×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30C2×C4×D4×C103C2211yescharacteristic
31C2×#117×C103—21no—
32C2×#117×C103C2211yescharacteristic
33C2×#117×C103C2211yescharacteristic
34C22×C4⋊C4×C103C2211yescharacteristic
35#482×C103—24no—
36#469×C103—24no—
37C2×#107×C103C2211yescharacteristic
38C2×#106×C103C2211yescharacteristic
39C2×#106×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
49#396×C103—21no—
50#394×C103—21no—
51#390×C103C2211yescharacteristic
52#389×C103C2211yescharacteristic
53#386×C103—21no—
54#380×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103—21no—
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103—21no—
67C22×D4×C103—21no—
68C22×D4×C103D411yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C22×D4×C103C2311yescharacteristic
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—41no—
78C2×M16×C103—22no—
79C2×M16×C103—22no—
80C2×M16×C103—41no—
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85C4⋊Q8×C103—22no—
86C4⋊Q8×C103—22no—
87#124×C103—28no—
88#124×C103—28no—
89#121×C103—28no—
90#121×C103—22no—
91#121×C103—22no—
92#121×C103—22no—
93#121×C103—22no—
94#121×C103—22no—
95#121×C103—22no—
96#121×C103—41no—
97#121×C103—44no—
98#121×C103D414yescomplemented
99C4×D4×C103—22no—
100C4×D4×C103—22no—
101C4×D4×C103—22no—
102C4×D4×C103—22no—
103#117×C103—28no—
104#117×C103—22no—
105#117×C103—22no—
106#117×C103—22no—
107#117×C103D414yescomplemented
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—22no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—41no—
113C2×C4⋊C4×C103D411yescharacteristic
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
117C2×C4⋊C4×C103C2311yescharacteristic
118C2×C4⋊C4×C103C2311yescharacteristic
119C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103D411yescharacteristic
131C2×C22⋊C4×C103D411yescharacteristic
132C2×C42×C103—21no—
133C2×C42×C103—21no—
134C2×C42×C103C2311yescharacteristic
135#107×C103—22no—
136#106×C103—22no—
137#106×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—41no—
144C22⋊C8×C103—22no—
145C22⋊C8×C103—22no—
146C22⋊C8×C103—41no—
147#95×C103—21no—
148#95×C103—21no—
149C24×C103—21no—
150C24×C103—21no—
151C24×C103C2×D411yescharacteristic
152C24×C103C2×D411yescharacteristic
153C2×Q8×C103—24no—
154C2×Q8×C103—81no—
155C2×Q8×C103—81no—
156C2×D4×C103—22no—
157C2×D4×C103—24no—
158C2×D4×C103—24no—
159C2×D4×C103—22no—
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—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—41no—
172C2×D4×C103—42no—
173C2×D4×C103—42no—
174C2×D4×C103—42no—
175C2×D4×C103—42no—
176C2×D4×C103—42no—
177C2×D4×C103—81no—
178C2×D4×C103—81no—
179C2×D4×C103—81no—
180C2×D4×C103—81no—
181C2×D4×C103—81no—
182C2×D4×C103C2×D412yes—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—24no—
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—42no—
201C22×C4×C103—42no—
202C22×C4×C103—42no—
203C22×C4×C103—42no—
204C22×C4×C103—81no—
205C22×C4×C103C2×D411yescharacteristic
206C22×C4×C103C2×D411yescharacteristic
207C22×C4×C103C2×D411yescharacteristic
208C22×C4×C103C2×D412yes—
209C22×C4×C103C2×D412yes—
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103C2411yescharacteristic
212D8×C103—44no—
213M16×C103—44no—
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—21no—
225C2×C8×C103#4112yes—
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—42no—
237C4⋊C4×C103—42no—
238C4⋊C4×C103C2×D412yes—
239C4⋊C4×C103C2×D412yes—
240C4⋊C4×C103C2×D412yes—
241C4⋊C4×C103#4112yes—
242C22⋊C4×C103—24no—
243C22⋊C4×C103—24no—
244C22⋊C4×C103—24no—
245C22⋊C4×C103—24no—
246C22⋊C4×C103—22no—
247C22⋊C4×C103—24no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—42no—
250C22⋊C4×C103—42no—
251C22⋊C4×C103—42no—
252C22⋊C4×C103—42no—
253C22⋊C4×C103—81no—
254C42×C103—24no—
255C42×C103—24no—
256C42×C103—21no—
257C42×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—21no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—21no—
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×C103—41no—
285C23×C103#12012yes—
286C23×C103C22×D411yescharacteristic
287Q8×C103—84no—
288D4×C103—22no—
289D4×C103—22no—
290D4×C103—44no—
291D4×C103—41no—
292D4×C103—41no—
293D4×C103—41no—
294D4×C103—41no—
295D4×C103—41no—
296D4×C103—41no—
297D4×C103—84no—
298D4×C103—84no—
299D4×C103—84no—
300D4×C103—84no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—21no—
305C2×C4×C103—22no—
306C2×C4×C103—22no—
307C2×C4×C103—22no—
308C2×C4×C103—22no—
309C2×C4×C103—21no—
310C2×C4×C103—22no—
311C2×C4×C103—21no—
312C2×C4×C103—22no—
313C2×C4×C103—22no—
314C2×C4×C103—21no—
315C2×C4×C103—22no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
319C2×C4×C103—48no—
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—41no—
336C2×C4×C103—41no—
337C2×C4×C103—41no—
338C2×C4×C103—84no—
339C2×C4×C103#12012yes—
340C2×C4×C103AGL(1,ℤ/8)12yes—
341C2×C4×C103C22×D411yescharacteristic
342C2×C4×C103C22×D411yescharacteristic
343C2×C4×C103C2×#4111yescharacteristic
344C2×C4×C103C2×#4111yescharacteristic
345C2×C4×C103H(5,𝔽2)11yescharacteristic
346C2×C4×C1032−1+411yescharacteristic
347C8×C103—22no—
348C8×C103—41no—
349C8×C103—41no—
350C8×C103—41no—
351C22×C103—22no—
352C22×C103—22no—
353C22×C103—22no—
354C22×C103—41no—
355C22×C103—41no—
356C22×C103—41no—
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—41no—
361C22×C103—42no—
362C22×C103—42no—
363C22×C103—41no—
364C22×C103—41no—
365C22×C103—42no—
366C22×C103—41no—
367C22×C103—41no—
368C22×C103—81no—
369C22×C103—81no—
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×C103—81no—
379C22×C103C2×#12011yescharacteristic
380C22×C103#54611yescharacteristic
381C22×C103#54711yescharacteristic
382C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C103#57511yescharacteristic
384C22×C103#57611yescharacteristic
385C22×C103#57711yescharacteristic
386C4×C103—22no—
387C4×C103—22no—
388C4×C103—41no—
389C4×C103—42no—
390C4×C103—41no—
391C4×C103—42no—
392C4×C103—42no—
393C4×C103—42no—
394C4×C103—81no—
395C4×C103—81no—
396C4×C103#53211yescharacteristic
397C4×C103#53711yescharacteristic
398C4×C103#54611yescharacteristic
399C4×C103#54711yescharacteristic
400#25554C10311yesmaximal, characteristic, direct product factor, Sylow
401C2×C103—42no—
402C2×C103—81no—
403C2×C103—82no—
404C2×C103—161no—
405C2×C103#243011yescharacteristic
406C2×C103#300611yescharacteristic
407C2×C103#301211yescharacteristic
408C2×C103#332111yescharacteristic
409C2×C103#332511yescharacteristic
410C2×C103#334711yescharacteristic
411C2×C103#335411yescharacteristic
412C2×#555C2×C10311yescharacteristic, complemented
413C2×#482C2×C10311yescharacteristic, complemented
414C2×#469C2×C10311yescharacteristic, complemented
415#2416C2×C10311yescharacteristic, complemented
416#2058C2×C10311yescharacteristic, complemented
417#2034C2×C10311yescharacteristic, complemented
418#2023C2×C10311yescharacteristic, complemented
419#1999C2×C10311yescharacteristic, complemented
420#1879C2×C10311yescharacteristic, complemented
421#1875C2×C10311yescharacteristic, complemented
422#1874C2×C10311yescharacteristic, complemented
423#1870C2×C10311yescharacteristic, complemented
424#1862C2×C10311yescharacteristic, complemented
425#1854C2×C10311yescharacteristic, complemented
426#1736C2×C10311yescharacteristic, complemented
427C103#2555411yescharacteristic, direct product factor, Sylow
428C22×D8C22×C10311yescharacteristic
429C22×M16C22×C10311yescharacteristic
430#555—24no—
431#555—24no—
432C2×C4⋊Q8C22×C10311yescharacteristic
433C2×#124—21no—
434C2×#124—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C10311yescharacteristic
438C2×#121C22×C10311yescharacteristic
439C2×#121C22×C10311yescharacteristic
440C2×#121C22×C10311yescharacteristic
441C2×C4×D4C22×C10311yescharacteristic
442C2×C4×D4C22×C10311yescharacteristic
443C2×#117—21no—
444C2×#117C22×C10311yescharacteristic
445C2×#117C22×C10311yescharacteristic
446C22×C4⋊C4C22×C10311yescharacteristic
447#482—24no—
448#469—24no—
449C2×#107C22×C10311yescharacteristic
450C2×#106C22×C10311yescharacteristic
451C2×#106C22×C10311yescharacteristic
452C2×#102C22×C10311yescharacteristic
453C2×#102C22×C10311yescharacteristic
454C2×#102C22×C10311yescharacteristic
455C2×#102C22×C10311yescharacteristic
456C2×#102C22×C10311yescharacteristic
457C2×#102C22×C10311yescharacteristic
458C2×C22⋊C8C22×C10311yescharacteristic
459C2×C22⋊C8C22×C10311yescharacteristic
460C2×C22⋊C8C22×C10311yescharacteristic
461#396—21no—
462#394—21no—
463#390C22×C10311yescharacteristic
464#389C22×C10311yescharacteristic
465#386—21no—
466#380C22×C10311yescharacteristic
467#340C22×C10311yescharacteristic
468#340C22×C10311yescharacteristic
469#340C22×C10311yescharacteristic
470#340C22×C10311yescharacteristic
471#340C22×C10311yescharacteristic
472#340C22×C10311yescharacteristic
473#336C22×C10311yescharacteristic
474#336C22×C10311yescharacteristic
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C10311yescharacteristic
481C22×D4C23×C10311yescharacteristic
482C22×D4C23×C10311yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C10311yescharacteristic
486C23×C4C23×C10311yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C10311yescharacteristic
494C22×C8C23×C10311yescharacteristic
495C22×C8C23×C10311yescharacteristic
496C22×C8C23×C10311yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C10314yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C10314yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C10311yescharacteristic
526C2×C4⋊C4C23×C10311yescharacteristic
527C2×C4⋊C4C23×C10311yescharacteristic
528C2×C4⋊C4C23×C10311yescharacteristic
529C2×C4⋊C4C23×C10311yescharacteristic
530C2×C4⋊C4C23×C10311yescharacteristic
531C2×C4⋊C4C23×C10311yescharacteristic
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⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C10311yescharacteristic
543C2×C22⋊C4D4×C10311yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C10311yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C10311yescharacteristic
564C24C2×D4×C10311yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C10312yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C10311yescharacteristic
618C22×C4C2×D4×C10311yescharacteristic
619C22×C4C2×D4×C10311yescharacteristic
620C22×C4C2×D4×C10312yes—
621C22×C4C2×D4×C10312yes—
622C22×C4C2×D4×C10311yescharacteristic
623C22×C4C24×C10311yescharacteristic
624D8—44no—
625M16—44no—
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—21no—
636C2×C8—21no—
637C2×C8#41×C10312yes—
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—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C10312yes—
651C4⋊C4C2×D4×C10312yes—
652C4⋊C4C2×D4×C10312yes—
653C4⋊C4#41×C10312yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#120×C10312yes—
698C23C22×D4×C10311yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
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—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4#120×C10312yes—
752C2×C4AGL(1,ℤ/8)×C10312yes—
753C2×C4C22×D4×C10311yescharacteristic
754C2×C4C22×D4×C10311yescharacteristic
755C2×C4C2×#41×C10311yescharacteristic
756C2×C4C2×#41×C10311yescharacteristic
757C2×C4H(5,𝔽2)×C10311yescharacteristic
758C2×C42−1+4×C10311yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C10311yescharacteristic
792C22#546×C10311yescharacteristic
793C22#547×C10311yescharacteristic
794C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
795C22#575×C10311yescharacteristic
796C22#576×C10311yescharacteristic
797C22#577×C10311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—41no—
806C4—81no—
807C4—81no—
808C4#532×C10311yescharacteristic
809C4#537×C10311yescharacteristic
810C4#546×C10311yescharacteristic
811C4#547×C10311yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2C103×#243011yescharacteristic
817C2C103×#300611yescharacteristic
818C2C103×#301211yescharacteristic
819C2C103×#332111yescharacteristic
820C2C103×#332511yescharacteristic
821C2C103×#334711yescharacteristic
822C2C103×#335411yescharacteristic
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×#555×C103C2semidirect
2. C2×#482×C103C2semidirect
3. C2×#469×C103C2semidirect
4. C103×#2416C2semidirect
5. C103×#2058C2semidirect
6. C103×#2034C2semidirect
7. C103×#2023C2semidirect
8. C103×#1999C2semidirect
9. C103×#1879C2semidirect
10. C103×#1875C2semidirect
11. C103×#1874C2semidirect
12. C103×#1870C2semidirect
13. C103×#1862C2semidirect
14. C103×#1854C2semidirect
15. C103×#1736C2semidirect
98. #121×C103D4semidirect
107. #117×C103D4semidirect
400. #25554C103direct (N × H)
412. C2×#555C2×C103semidirect
413. C2×#482C2×C103semidirect
414. C2×#469C2×C103semidirect
415. #2416C2×C103semidirect
416. #2058C2×C103semidirect
417. #2034C2×C103semidirect
418. #2023C2×C103semidirect
419. #1999C2×C103semidirect
420. #1879C2×C103semidirect
421. #1875C2×C103semidirect
422. #1874C2×C103semidirect
423. #1870C2×C103semidirect
424. #1862C2×C103semidirect
425. #1854C2×C103semidirect
426. #1736C2×C103semidirect
427. C103#25554direct (N × H)
510. #121D4×C103semidirect
519. #117D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1032
C2×#482×C1032
C2×#469×C1032
C103×#24162
C103×#20582
C103×#20342
C103×#20232
C103×#19992
C103×#18792
C103×#18752
C103×#18742
C103×#18702
C103×#18622
C103×#18542
C103×#17362
#25554103