Finite Group Databasebeta

← C103×#25131 #39930406

Subgroups — C103×#25131 #39930406

Order 26368.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C103C211yesmaximal, characteristic, complemented
2C2×#449×C103C211yesmaximal, characteristic, complemented
3C2×#435×C103C211yesmaximal, characteristic, complemented
4C2×#416×C103C211yesmaximal, characteristic, complemented
5C103×#2414C211yesmaximal, characteristic, complemented
6C103×#2407C211yesmaximal, characteristic, complemented
7C103×#2067C211yesmaximal, characteristic, complemented
8C103×#2055C211yesmaximal, characteristic, complemented
9C103×#2035C211yesmaximal, characteristic, complemented
10C103×#1999C211yesmaximal, characteristic, complemented
11C103×#1972C211yesmaximal, characteristic, complemented
12C103×#1935C211yesmaximal, characteristic, complemented
13C103×#1895C211yesmaximal, characteristic, complemented
14C103×#1893C211yesmaximal, characteristic, complemented
15C103×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18C22×D8×C103C2211yescharacteristic
19C22×M16×C103C2211yescharacteristic
20C23×C8×C103C2211yescharacteristic
21C2×C22⋊Q8×C103C2211yescharacteristic
22C2×#121×C103C2211yescharacteristic
23C2×#121×C103C2211yescharacteristic
24C2×#121×C103C2211yescharacteristic
25C2×C4×D4×C103C2211yescharacteristic
26C2×#117×C103C2211yescharacteristic
27#468×C103—24no—
28#449×C103—24no—
29#435×C103—24no—
30C2×#107×C103C2211yescharacteristic
31C2×#106×C103C2211yescharacteristic
32C2×C4⋊C8×C103C2211yescharacteristic
33#416×C103—24no—
34C2×#103×C103C2211yescharacteristic
35C2×#103×C103C2211yescharacteristic
36C2×#103×C103C2211yescharacteristic
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×C22⋊C8×C103C2211yescharacteristic
43C2×C22⋊C8×C103C2211yescharacteristic
44C2×#97×C103C2211yescharacteristic
45#394×C103—21no—
46#394×C103—21no—
47#392×C103—21no—
48#392×C103—21no—
49#391×C103C2211yescharacteristic
50#390×C103—21no—
51#390×C103C2211yescharacteristic
52#390×C103C2211yescharacteristic
53#389×C103C2211yescharacteristic
54#388×C103—21no—
55#386×C103—21no—
56#385×C103—21no—
57#380×C103C2211yescharacteristic
58#380×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic
62#340×C103C2211yescharacteristic
63C2×#41×C103—22no—
64C2×#41×C103—22no—
65C2×#41×C103—22no—
66C2×#41×C103—22no—
67C2×#41×C103—41no—
68C2×#41×C103—41no—
69C22×Q8×C103C2311yescharacteristic
70C22×D4×C103—21no—
71C22×D4×C103—21no—
72C22×D4×C103—21no—
73C22×D4×C103—21no—
74C22×D4×C103D411yescharacteristic
75C22×D4×C103C2311yescharacteristic
76C22×D4×C103C2311yescharacteristic
77C23×C4×C103—21no—
78C23×C4×C103C2311yescharacteristic
79C23×C4×C103C2311yescharacteristic
80C2×SD16×C103—22no—
81C2×SD16×C103—22no—
82C2×SD16×C103—41no—
83C2×D8×C103—22no—
84C2×D8×C103—22no—
85C2×D8×C103—41no—
86C2×M16×C103—22no—
87C2×M16×C103—22no—
88C2×M16×C103—41no—
89C22×C8×C103—22no—
90C22×C8×C103—22no—
91C22×C8×C103—41no—
92C22×C8×C103C2311yescharacteristic
93C22×C8×C103C2311yescharacteristic
94C22×C8×C103C2311yescharacteristic
95C22×C8×C103C2311yescharacteristic
96C22⋊Q8×C103—22no—
97C22⋊Q8×C103—41no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103—22no—
101#121×C103—22no—
102#121×C103—41no—
103#121×C103—41no—
104C4×D4×C103—22no—
105C4×D4×C103—22no—
106#117×C103—22no—
107#117×C103—41no—
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103D411yescharacteristic
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×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103D411yescharacteristic
128C2×C22⋊C4×C103D411yescharacteristic
129C2×C42×C103—21no—
130C2×C42×C103C2311yescharacteristic
131#107×C103—22no—
132#106×C103—41no—
133C4⋊C8×C103—22no—
134#103×C103—22no—
135#103×C103—22no—
136#103×C103D414yescomplemented
137#102×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—41no—
142C22⋊C8×C103—22no—
143C22⋊C8×C103D414yescomplemented
144#97×C103—22no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148#95×C103—21no—
149#95×C103—21no—
150C24×C103—21no—
151C24×C103—21no—
152C24×C103C2×D411yescharacteristic
153C24×C103C2×D411yescharacteristic
154#41×C103—28no—
155#41×C103—44no—
156#41×C103—44no—
157#41×C103—44no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103C2×D412yes—
164C2×D4×C103—22no—
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—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—21no—
176C2×D4×C103—41no—
177C2×D4×C103—41no—
178C2×D4×C103—42no—
179C2×D4×C103—42no—
180C2×D4×C103—42no—
181C2×D4×C103—42no—
182C2×D4×C103—42no—
183C2×D4×C103—42no—
184C2×D4×C103—42no—
185C2×D4×C103—42no—
186C2×D4×C103—81no—
187C2×D4×C103—81no—
188C2×D4×C103—81no—
189C2×D4×C103—81no—
190C2×D4×C103#4112yes—
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—42no—
208C22×C4×C103—42no—
209C22×C4×C103—42no—
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103C2×D411yescharacteristic
212C22×C4×C103C2×D411yescharacteristic
213C22×C4×C103C2×D411yescharacteristic
214C22×C4×C103C2×D412yes—
215C22×C4×C103#4112yes—
216C22×C4×C103C2411yescharacteristic
217SD16×C103—44no—
218D8×C103—44no—
219M16×C103—44no—
220C2×C8×C103—21no—
221C2×C8×C103—21no—
222C2×C8×C103—21no—
223C2×C8×C103—21no—
224C2×C8×C103—21no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—44no—
230C2×C8×C103C2×D412yes—
231C2×C8×C103C2×D412yes—
232C2×C8×C103C2×D412yes—
233C4⋊C4×C103—22no—
234C4⋊C4×C103—21no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—21no—
237C4⋊C4×C103—21no—
238C4⋊C4×C103—21no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—21no—
241C4⋊C4×C103—21no—
242C4⋊C4×C103—21no—
243C4⋊C4×C103—42no—
244C4⋊C4×C103—81no—
245C4⋊C4×C103C2×D412yes—
246C22⋊C4×C103—22no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—42no—
249C22⋊C4×C103—42no—
250C22⋊C4×C103—42no—
251C22⋊C4×C103—42no—
252C22⋊C4×C103—42no—
253C22⋊C4×C103—42no—
254C22⋊C4×C103—42no—
255C22⋊C4×C103—81no—
256C22⋊C4×C103—81no—
257C22⋊C4×C103—81no—
258C22⋊C4×C103—81no—
259C42×C103—21no—
260C42×C103—21no—
261C42×C103—42no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—21no—
269C23×C103—21no—
270C23×C103—22no—
271C23×C103—21no—
272C23×C103—21no—
273C23×C103—21no—
274C23×C103—21no—
275C23×C103—21no—
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—41no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—41no—
289C23×C103#12112yes—
290C23×C103C22×D411yescharacteristic
291Q8×C103—22no—
292Q8×C103—22no—
293Q8×C103—41no—
294Q8×C103—41no—
295D4×C103—22no—
296D4×C103—22no—
297D4×C103—44no—
298D4×C103—48no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—41no—
304D4×C103—41no—
305D4×C103—84no—
306D4×C103—84no—
307D4×C103—84no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—22no—
311C2×C4×C103—22no—
312C2×C4×C103—22no—
313C2×C4×C103—22no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—22no—
318C2×C4×C103—21no—
319C2×C4×C103—22no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—48no—
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—41no—
339C2×C4×C103—41no—
340C2×C4×C103—41no—
341C2×C4×C103—41no—
342C2×C4×C103—41no—
343C2×C4×C103—41no—
344C2×C4×C103—41no—
345C2×C4×C103—41no—
346C2×C4×C103#12112yes—
347C2×C4×C103C22×D411yescharacteristic
348C2×C4×C103C22×D411yescharacteristic
349C2×C4×C103C2×#4111yescharacteristic
350C2×C4×C103C2×#4111yescharacteristic
351C2×C4×C103H(5,𝔽2)11yescharacteristic
352C2×C4×C103H(5,𝔽2)11yescharacteristic
353C8×C103—22no—
354C8×C103—22no—
355C8×C103—22no—
356C8×C103—41no—
357C22×C103—22no—
358C22×C103—22no—
359C22×C103—22no—
360C22×C103—41no—
361C22×C103—41no—
362C22×C103—41no—
363C22×C103—41no—
364C22×C103—42no—
365C22×C103—41no—
366C22×C103—41no—
367C22×C103—41no—
368C22×C103—41no—
369C22×C103—42no—
370C22×C103—41no—
371C22×C103—41no—
372C22×C103—41no—
373C22×C103—42no—
374C22×C103—81no—
375C22×C103—81no—
376C22×C103—81no—
377C22×C103—81no—
378C22×C103—81no—
379C22×C103—81no—
380C22×C103—81no—
381C22×C103—81no—
382C22×C103—81no—
383C22×C103—81no—
384C22×C103—81no—
385C22×C103C2×#12111yescharacteristic
386C22×C103D4211yescharacteristic
387C22×C103#54611yescharacteristic
388C22×C103#57511yescharacteristic
389C22×C103#57511yescharacteristic
390C22×C103#57611yescharacteristic
391C22×C103#57711yescharacteristic
392C4×C103—22no—
393C4×C103—41no—
394C4×C103—42no—
395C4×C103—42no—
396C4×C103—41no—
397C4×C103—41no—
398C4×C103—81no—
399C4×C103—81no—
400C4×C103—81no—
401C4×C103—81no—
402C4×C103#52511yescharacteristic
403C4×C103#53811yescharacteristic
404C4×C103D4211yescharacteristic
405C4×C103#54611yescharacteristic
406#25131C10311yesmaximal, characteristic, direct product factor, Sylow
407C2×C103—42no—
408C2×C103—81no—
409C2×C103—82no—
410C2×C103—161no—
411C2×C103#242411yescharacteristic
412C2×C103#305411yescharacteristic
413C2×C103#306211yescharacteristic
414C2×C103#326811yescharacteristic
415C2×C103#327111yescharacteristic
416C2×C103#330711yescharacteristic
417C2×C103#331911yescharacteristic
418C2×#468C2×C10311yescharacteristic, complemented
419C2×#449C2×C10311yescharacteristic, complemented
420C2×#435C2×C10311yescharacteristic, complemented
421C2×#416C2×C10311yescharacteristic, complemented
422#2414C2×C10311yescharacteristic, complemented
423#2407C2×C10311yescharacteristic, complemented
424#2067C2×C10311yescharacteristic, complemented
425#2055C2×C10311yescharacteristic, complemented
426#2035C2×C10311yescharacteristic, complemented
427#1999C2×C10311yescharacteristic, complemented
428#1972C2×C10311yescharacteristic, complemented
429#1935C2×C10311yescharacteristic, complemented
430#1895C2×C10311yescharacteristic, complemented
431#1893C2×C10311yescharacteristic, complemented
432#1854C2×C10311yescharacteristic, complemented
433C103#2513111yescharacteristic, direct product factor, Sylow
434C22×#41C22×C10311yescharacteristic
435C22×SD16C22×C10311yescharacteristic
436C22×D8C22×C10311yescharacteristic
437C22×M16C22×C10311yescharacteristic
438C23×C8C22×C10311yescharacteristic
439C2×C22⋊Q8C22×C10311yescharacteristic
440C2×#121C22×C10311yescharacteristic
441C2×#121C22×C10311yescharacteristic
442C2×#121C22×C10311yescharacteristic
443C2×C4×D4C22×C10311yescharacteristic
444C2×#117C22×C10311yescharacteristic
445#468—24no—
446#449—24no—
447#435—24no—
448C2×#107C22×C10311yescharacteristic
449C2×#106C22×C10311yescharacteristic
450C2×C4⋊C8C22×C10311yescharacteristic
451#416—24no—
452C2×#103C22×C10311yescharacteristic
453C2×#103C22×C10311yescharacteristic
454C2×#103C22×C10311yescharacteristic
455C2×#102C22×C10311yescharacteristic
456C2×#102C22×C10311yescharacteristic
457C2×#102C22×C10311yescharacteristic
458C2×#102C22×C10311yescharacteristic
459C2×#102C22×C10311yescharacteristic
460C2×C22⋊C8C22×C10311yescharacteristic
461C2×C22⋊C8C22×C10311yescharacteristic
462C2×#97C22×C10311yescharacteristic
463#394—21no—
464#394—21no—
465#392—21no—
466#392—21no—
467#391C22×C10311yescharacteristic
468#390—21no—
469#390C22×C10311yescharacteristic
470#390C22×C10311yescharacteristic
471#389C22×C10311yescharacteristic
472#388—21no—
473#386—21no—
474#385—21no—
475#380C22×C10311yescharacteristic
476#380C22×C10311yescharacteristic
477#340C22×C10311yescharacteristic
478#340C22×C10311yescharacteristic
479#340C22×C10311yescharacteristic
480#340C22×C10311yescharacteristic
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C10311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C10311yescharacteristic
493C22×D4C23×C10311yescharacteristic
494C22×D4C23×C10311yescharacteristic
495C23×C4—21no—
496C23×C4C23×C10311yescharacteristic
497C23×C4C23×C10311yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C10311yescharacteristic
511C22×C8C23×C10311yescharacteristic
512C22×C8C23×C10311yescharacteristic
513C22×C8C23×C10311yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C10311yescharacteristic
529C2×C4⋊C4C23×C10311yescharacteristic
530C2×C4⋊C4C23×C10311yescharacteristic
531C2×C4⋊C4C23×C10311yescharacteristic
532C2×C4⋊C4C23×C10311yescharacteristic
533C2×C4⋊C4C23×C10311yescharacteristic
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⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C10311yescharacteristic
546C2×C22⋊C4D4×C10311yescharacteristic
547C2×C42—21no—
548C2×C42C23×C10311yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C10314yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C10314yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C10311yescharacteristic
571C24C2×D4×C10311yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C10312yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C10312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C10311yescharacteristic
629C22×C4C2×D4×C10311yescharacteristic
630C22×C4C2×D4×C10311yescharacteristic
631C22×C4C2×D4×C10311yescharacteristic
632C22×C4C2×D4×C10312yes—
633C22×C4#41×C10312yes—
634C22×C4C24×C10311yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C10312yes—
649C2×C8C2×D4×C10312yes—
650C2×C8C2×D4×C10312yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C10312yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C10312yes—
708C23C22×D4×C10311yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C10312yes—
765C2×C4C22×D4×C10311yescharacteristic
766C2×C4C22×D4×C10311yescharacteristic
767C2×C4C2×#41×C10311yescharacteristic
768C2×C4C2×#41×C10311yescharacteristic
769C2×C4H(5,𝔽2)×C10311yescharacteristic
770C2×C4H(5,𝔽2)×C10311yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—42no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C10311yescharacteristic
804C22D42×C10311yescharacteristic
805C22#546×C10311yescharacteristic
806C22#575×C10311yescharacteristic
807C22#575×C10311yescharacteristic
808C22#576×C10311yescharacteristic
809C22#577×C10311yescharacteristic
810C4—22no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#525×C10311yescharacteristic
821C4#538×C10311yescharacteristic
822C4D42×C10311yescharacteristic
823C4#546×C10311yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C103×#242411yescharacteristic
829C2C103×#305411yescharacteristic
830C2C103×#306211yescharacteristic
831C2C103×#326811yescharacteristic
832C2C103×#327111yescharacteristic
833C2C103×#330711yescharacteristic
834C2C103×#331911yescharacteristic
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×#468×C103C2semidirect
2. C2×#449×C103C2semidirect
3. C2×#435×C103C2semidirect
4. C2×#416×C103C2semidirect
5. C103×#2414C2semidirect
6. C103×#2407C2semidirect
7. C103×#2067C2semidirect
8. C103×#2055C2semidirect
9. C103×#2035C2semidirect
10. C103×#1999C2semidirect
11. C103×#1972C2semidirect
12. C103×#1935C2semidirect
13. C103×#1895C2semidirect
14. C103×#1893C2semidirect
15. C103×#1854C2semidirect
136. #103×C103D4semidirect
143. C22⋊C8×C103D4semidirect
406. #25131C103direct (N × H)
418. C2×#468C2×C103semidirect
419. C2×#449C2×C103semidirect
420. C2×#435C2×C103semidirect
421. C2×#416C2×C103semidirect
422. #2414C2×C103semidirect
423. #2407C2×C103semidirect
424. #2067C2×C103semidirect
425. #2055C2×C103semidirect
426. #2035C2×C103semidirect
427. #1999C2×C103semidirect
428. #1972C2×C103semidirect
429. #1935C2×C103semidirect
430. #1895C2×C103semidirect
431. #1893C2×C103semidirect
432. #1854C2×C103semidirect
433. C103#25131direct (N × H)
554. #103D4×C103semidirect
561. C22⋊C8D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1032
C2×#449×C1032
C2×#435×C1032
C2×#416×C1032
C103×#24142
C103×#24072
C103×#20672
C103×#20552
C103×#20352
C103×#19992
C103×#19722
C103×#19352
C103×#18952
C103×#18932
C103×#18542
#25131103