Finite Group Databasebeta

← C103×#25401 #39930676

Subgroups — C103×#25401 #39930676

Order 26368.

1118 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C103C211yesmaximal, characteristic, complemented
2C2×#465×C103C211yesmaximal, characteristic, complemented
3C2×#463×C103C211yesmaximal, characteristic, complemented
4C2×#435×C103C211yesmaximal, characteristic, complemented
5C103×#2540C211yesmaximal, characteristic, complemented
6C103×#2537C211yesmaximal, characteristic, complemented
7C103×#2035C211yesmaximal, characteristic, complemented
8C103×#2034C211yesmaximal, characteristic, complemented
9C103×#2000C211yesmaximal, characteristic, complemented
10C103×#1999C211yesmaximal, characteristic, complemented
11C103×#1959C211yesmaximal, characteristic, complemented
12C103×#1948C211yesmaximal, characteristic, complemented
13C103×#1894C211yesmaximal, characteristic, complemented
14C103×#1893C211yesmaximal, characteristic, complemented
15C103×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20C2×#124×C103C2211yescharacteristic
21C2×C22⋊Q8×C103C2211yescharacteristic
22C2×C22⋊Q8×C103C2211yescharacteristic
23C2×#121×C103—21no—
24C2×#121×C103C2211yescharacteristic
25C2×#121×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×C4×D4×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30#469×C103—24no—
31#465×C103—24no—
32#463×C103—24no—
33#435×C103—24no—
34C2×#106×C103C2211yescharacteristic
35C2×#106×C103C2211yescharacteristic
36C2×C4⋊C8×C103C2211yescharacteristic
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×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×#97×C103C2211yescharacteristic
48#399×C103—21no—
49#394×C103—21no—
50#394×C103—21no—
51#392×C103—21no—
52#390×C103—21no—
53#390×C103—21no—
54#384×C103C2211yescharacteristic
55#380×C103—21no—
56#380×C103C2211yescharacteristic
57#380×C103C2211yescharacteristic
58C4×C4⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic
62#340×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
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×C103C2311yescharacteristic
73C23×C4×C103C2311yescharacteristic
74C2×SD16×C103—22no—
75C2×SD16×C103—22no—
76C2×SD16×C103—41no—
77C2×D8×C103—22no—
78C2×D8×C103—22no—
79C2×D8×C103—41no—
80C2×M16×C103—22no—
81C2×M16×C103—22no—
82C2×M16×C103—41no—
83C22×C8×C103—22no—
84C22×C8×C103—22no—
85C22×C8×C103—41no—
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90#124×C103—22no—
91#124×C103—22no—
92C22⋊Q8×C103—22no—
93C22⋊Q8×C103—22no—
94C22⋊Q8×C103—41no—
95C22⋊Q8×C103—41no—
96#121×C103—22no—
97#121×C103—22no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103—41no—
101#121×C103—41no—
102#121×C103—41no—
103#121×C103—41no—
104#121×C103—44no—
105C4×D4×C103—22no—
106C4×D4×C103—22no—
107C4×D4×C103—22no—
108C4×D4×C103—22no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—21no—
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×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×C103—21no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103D411yescharacteristic
131C2×C22⋊C4×C103D411yescharacteristic
132C2×C42×C103—21no—
133C2×C42×C103C2311yescharacteristic
134#106×C103—22no—
135#106×C103—22no—
136C4⋊C8×C103D414yescomplemented
137#103×C103—22no—
138#103×C103—22no—
139#103×C103—41no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—41no—
144#102×C103D414yescomplemented
145C22⋊C8×C103—22no—
146C22⋊C8×C103—22no—
147#97×C103—22no—
148#95×C103—21no—
149#95×C103—21no—
150#95×C103—21no—
151C24×C103—21no—
152C24×C103—21no—
153C24×C103C2×D411yescharacteristic
154C24×C103C2×D411yescharacteristic
155C2×Q8×C103—21no—
156C2×Q8×C103—21no—
157C2×Q8×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×D4×C103—22no—
162C2×D4×C103—22no—
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—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—41no—
175C2×D4×C103—42no—
176C2×D4×C103—42no—
177C2×D4×C103—42no—
178C2×D4×C103—42no—
179C2×D4×C103—42no—
180C2×D4×C103—42no—
181C2×D4×C103—42no—
182C2×D4×C103—42no—
183C2×D4×C103—81no—
184C2×D4×C103—81no—
185C2×D4×C103—81no—
186C2×D4×C103—81no—
187C2×D4×C103C2×D412yes—
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—42no—
207C22×C4×C103—42no—
208C22×C4×C103—42no—
209C22×C4×C103C2×D411yescharacteristic
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103C2×D411yescharacteristic
212C22×C4×C103C2×D411yescharacteristic
213C22×C4×C103C2411yescharacteristic
214SD16×C103—44no—
215D8×C103—44no—
216M16×C103—44no—
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—21no—
226C2×C8×C103—44no—
227C2×C8×C103C2×D412yes—
228C2×C8×C103C2×D412yes—
229C2×C8×C103C2×D412yes—
230C4⋊C4×C103—22no—
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—21no—
239C4⋊C4×C103—42no—
240C4⋊C4×C103—42no—
241C4⋊C4×C103—42no—
242C4⋊C4×C103—81no—
243C4⋊C4×C103C2×D412yes—
244C4⋊C4×C103#4112yes—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—22no—
247C22⋊C4×C103—42no—
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—42no—
256C22⋊C4×C103—42no—
257C22⋊C4×C103—42no—
258C42×C103—81no—
259C42×C103C2×D412yes—
260C42×C103#4112yes—
261C23×C103—21no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—22no—
269C23×C103—21no—
270C23×C103—21no—
271C23×C103—21no—
272C23×C103—21no—
273C23×C103—21no—
274C23×C103—21no—
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—41no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103AGL(1,ℤ/8)12yes—
289C23×C103C22×D411yescharacteristic
290Q8×C103—41no—
291Q8×C103—41no—
292Q8×C103—41no—
293Q8×C103—41no—
294D4×C103—22no—
295D4×C103—22no—
296D4×C103—44no—
297D4×C103—41no—
298D4×C103—41no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—84no—
304D4×C103—84no—
305D4×C103—84no—
306D4×C103—84no—
307C2×C4×C103—21no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
311C2×C4×C103—21no—
312C2×C4×C103—21no—
313C2×C4×C103—21no—
314C2×C4×C103—22no—
315C2×C4×C103—21no—
316C2×C4×C103—22no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
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—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—84no—
344C2×C4×C103#12112yes—
345C2×C4×C103#12112yes—
346C2×C4×C103C22×D411yescharacteristic
347C2×C4×C103C22×D411yescharacteristic
348C2×C4×C103C2×#4111yescharacteristic
349C2×C4×C103C2×#4111yescharacteristic
350C2×C4×C103H(5,𝔽2)11yescharacteristic
351C2×C4×C103H(5,𝔽2)11yescharacteristic
352C8×C103—22no—
353C8×C103—22no—
354C8×C103—22no—
355C8×C103—41no—
356C22×C103—22no—
357C22×C103—22no—
358C22×C103—22no—
359C22×C103—41no—
360C22×C103—41no—
361C22×C103—41no—
362C22×C103—41no—
363C22×C103—41no—
364C22×C103—42no—
365C22×C103—41no—
366C22×C103—42no—
367C22×C103—41no—
368C22×C103—42no—
369C22×C103—41no—
370C22×C103—41no—
371C22×C103—41no—
372C22×C103—41no—
373C22×C103—81no—
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×C103C2×#12111yescharacteristic
385C22×C103D4211yescharacteristic
386C22×C103#54611yescharacteristic
387C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C103#57511yescharacteristic
389C22×C103#57711yescharacteristic
390C22×C103#57711yescharacteristic
391C4×C103—22no—
392C4×C103—22no—
393C4×C103—41no—
394C4×C103—41no—
395C4×C103—42no—
396C4×C103—42no—
397C4×C103—81no—
398C4×C103—81no—
399C4×C103—81no—
400C4×C103—81no—
401C4×C103#53211yescharacteristic
402C4×C103#54011yescharacteristic
403C4×C103D4211yescharacteristic
404C4×C103#55011yescharacteristic
405#25401C10311yesmaximal, characteristic, direct product factor, Sylow
406C2×C103—42no—
407C2×C103—81no—
408C2×C103—82no—
409C2×C103—161no—
410C2×C103#242811yescharacteristic
411C2×C103#305511yescharacteristic
412C2×C103#306011yescharacteristic
413C2×C103#326511yescharacteristic
414C2×C103#326711yescharacteristic
415C2×C103#330611yescharacteristic
416C2×C103#332111yescharacteristic
417C2×#469C2×C10311yescharacteristic, complemented
418C2×#465C2×C10311yescharacteristic, complemented
419C2×#463C2×C10311yescharacteristic, complemented
420C2×#435C2×C10311yescharacteristic, complemented
421#2540C2×C10311yescharacteristic, complemented
422#2537C2×C10311yescharacteristic, complemented
423#2035C2×C10311yescharacteristic, complemented
424#2034C2×C10311yescharacteristic, complemented
425#2000C2×C10311yescharacteristic, complemented
426#1999C2×C10311yescharacteristic, complemented
427#1959C2×C10311yescharacteristic, complemented
428#1948C2×C10311yescharacteristic, complemented
429#1894C2×C10311yescharacteristic, complemented
430#1893C2×C10311yescharacteristic, complemented
431#1762C2×C10311yescharacteristic, complemented
432C103#2540111yescharacteristic, direct product factor, Sylow
433C22×SD16C22×C10311yescharacteristic
434C22×D8C22×C10311yescharacteristic
435C22×M16C22×C10311yescharacteristic
436C23×C8C22×C10311yescharacteristic
437C2×#124C22×C10311yescharacteristic
438C2×C22⋊Q8C22×C10311yescharacteristic
439C2×C22⋊Q8C22×C10311yescharacteristic
440C2×#121—21no—
441C2×#121C22×C10311yescharacteristic
442C2×#121C22×C10311yescharacteristic
443C2×#121C22×C10311yescharacteristic
444C2×#121C22×C10311yescharacteristic
445C2×C4×D4C22×C10311yescharacteristic
446C2×C4×D4C22×C10311yescharacteristic
447#469—24no—
448#465—24no—
449#463—24no—
450#435—24no—
451C2×#106C22×C10311yescharacteristic
452C2×#106C22×C10311yescharacteristic
453C2×C4⋊C8C22×C10311yescharacteristic
454C2×#103C22×C10311yescharacteristic
455C2×#103C22×C10311yescharacteristic
456C2×#103C22×C10311yescharacteristic
457C2×#102C22×C10311yescharacteristic
458C2×#102C22×C10311yescharacteristic
459C2×#102C22×C10311yescharacteristic
460C2×#102C22×C10311yescharacteristic
461C2×#102C22×C10311yescharacteristic
462C2×C22⋊C8C22×C10311yescharacteristic
463C2×C22⋊C8C22×C10311yescharacteristic
464C2×#97C22×C10311yescharacteristic
465#399—21no—
466#394—21no—
467#394—21no—
468#392—21no—
469#390—21no—
470#390—21no—
471#384C22×C10311yescharacteristic
472#380—21no—
473#380C22×C10311yescharacteristic
474#380C22×C10311yescharacteristic
475C4×C4⋊C4C22×C10311yescharacteristic
476#340C22×C10311yescharacteristic
477#340C22×C10311yescharacteristic
478#340C22×C10311yescharacteristic
479#340C22×C10311yescharacteristic
480C22×Q8C23×C10311yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C10311yescharacteristic
486C22×D4C23×C10311yescharacteristic
487C22×D4C23×C10311yescharacteristic
488C23×C4—21no—
489C23×C4C23×C10311yescharacteristic
490C23×C4C23×C10311yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—41no—
494C2×D8—22no—
495C2×D8—22no—
496C2×D8—41no—
497C2×M16—22no—
498C2×M16—22no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—41no—
503C22×C8C23×C10311yescharacteristic
504C22×C8C23×C10311yescharacteristic
505C22×C8C23×C10311yescharacteristic
506C22×C8C23×C10311yescharacteristic
507#124—22no—
508#124—22no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—41no—
512C22⋊Q8—41no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—41no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—44no—
522C4×D4—22no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4D4×C10311yescharacteristic
531C2×C4⋊C4C23×C10311yescharacteristic
532C2×C4⋊C4C23×C10311yescharacteristic
533C2×C4⋊C4C23×C10311yescharacteristic
534C2×C4⋊C4C23×C10311yescharacteristic
535C2×C4⋊C4C23×C10311yescharacteristic
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⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4D4×C10311yescharacteristic
548C2×C22⋊C4D4×C10311yescharacteristic
549C2×C42—21no—
550C2×C42C23×C10311yescharacteristic
551#106—22no—
552#106—22no—
553C4⋊C8D4×C10314yescomplemented
554#103—22no—
555#103—22no—
556#103—41no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—41no—
561#102D4×C10314yescomplemented
562C22⋊C8—22no—
563C22⋊C8—22no—
564#97—22no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C10311yescharacteristic
571C24C2×D4×C10311yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
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—41no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4C2×D4×C10312yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
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—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4C2×D4×C10311yescharacteristic
627C22×C4C2×D4×C10311yescharacteristic
628C22×C4C2×D4×C10311yescharacteristic
629C22×C4C2×D4×C10311yescharacteristic
630C22×C4C24×C10311yescharacteristic
631SD16—44no—
632D8—44no—
633M16—44no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—44no—
644C2×C8C2×D4×C10312yes—
645C2×C8C2×D4×C10312yes—
646C2×C8C2×D4×C10312yes—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—81no—
660C4⋊C4C2×D4×C10312yes—
661C4⋊C4#41×C10312yes—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—81no—
676C42C2×D4×C10312yes—
677C42#41×C10312yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23AGL(1,ℤ/8)×C10312yes—
706C23C22×D4×C10311yescharacteristic
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—44no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723D4—84no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
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—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—84no—
761C2×C4#121×C10312yes—
762C2×C4#121×C10312yes—
763C2×C4C22×D4×C10311yescharacteristic
764C2×C4C22×D4×C10311yescharacteristic
765C2×C4C2×#41×C10311yescharacteristic
766C2×C4C2×#41×C10311yescharacteristic
767C2×C4H(5,𝔽2)×C10311yescharacteristic
768C2×C4H(5,𝔽2)×C10311yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—41no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22C2×#121×C10311yescharacteristic
802C22D42×C10311yescharacteristic
803C22#546×C10311yescharacteristic
804C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
805C22#575×C10311yescharacteristic
806C22#577×C10311yescharacteristic
807C22#577×C10311yescharacteristic
808C4—22no—
809C4—22no—
810C4—42no—
811C4—42no—
812C4—41no—
813C4—41no—
814C4—81no—
815C4—81no—
816C4—81no—
817C4—81no—
818C4#532×C10311yescharacteristic
819C4#540×C10311yescharacteristic
820C4D42×C10311yescharacteristic
821C4#550×C10311yescharacteristic
822C2—42no—
823C2—81no—
824C2—82no—
825C2—161no—
826C2C103×#242811yescharacteristic
827C2C103×#305511yescharacteristic
828C2C103×#306011yescharacteristic
829C2C103×#326511yescharacteristic
830C2C103×#326711yescharacteristic
831C2C103×#330611yescharacteristic
832C2C103×#332111yescharacteristic
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×#469×C103C2semidirect
2. C2×#465×C103C2semidirect
3. C2×#463×C103C2semidirect
4. C2×#435×C103C2semidirect
5. C103×#2540C2semidirect
6. C103×#2537C2semidirect
7. C103×#2035C2semidirect
8. C103×#2034C2semidirect
9. C103×#2000C2semidirect
10. C103×#1999C2semidirect
11. C103×#1959C2semidirect
12. C103×#1948C2semidirect
13. C103×#1894C2semidirect
14. C103×#1893C2semidirect
15. C103×#1762C2semidirect
136. C4⋊C8×C103D4semidirect
144. #102×C103D4semidirect
405. #25401C103direct (N × H)
417. C2×#469C2×C103semidirect
418. C2×#465C2×C103semidirect
419. C2×#463C2×C103semidirect
420. C2×#435C2×C103semidirect
421. #2540C2×C103semidirect
422. #2537C2×C103semidirect
423. #2035C2×C103semidirect
424. #2034C2×C103semidirect
425. #2000C2×C103semidirect
426. #1999C2×C103semidirect
427. #1959C2×C103semidirect
428. #1948C2×C103semidirect
429. #1894C2×C103semidirect
430. #1893C2×C103semidirect
431. #1762C2×C103semidirect
432. C103#25401direct (N × H)
553. C4⋊C8D4×C103semidirect
561. #102D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1032
C2×#465×C1032
C2×#463×C1032
C2×#435×C1032
C103×#25402
C103×#25372
C103×#20352
C103×#20342
C103×#20002
C103×#19992
C103×#19592
C103×#19482
C103×#18942
C103×#18932
C103×#17622
#25401103