Finite Group Databasebeta

← C103×#25330 #39930605

Subgroups — C103×#25330 #39930605

Order 26368.

964 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#490×C103C211yesmaximal, characteristic, complemented
2C2×#459×C103C211yesmaximal, characteristic
3C103×#2566C211yesmaximal, characteristic, complemented
4C103×#2366C211yesmaximal, characteristic, complemented
5C103×#2073C211yesmaximal, characteristic, complemented
6C103×#2071C211yesmaximal, characteristic, complemented
7C103×#2054C211yesmaximal, characteristic, complemented
8C103×#2054C211yesmaximal, characteristic, complemented
9C103×#1989C211yesmaximal, characteristic, complemented
10C103×#1940C211yesmaximal, characteristic, complemented
11C103×#1879C211yesmaximal, characteristic, complemented
12C103×#1879C211yesmaximal, characteristic, complemented
13C103×#1804C211yesmaximal, characteristic, complemented
14C103×#1802C211yesmaximal, characteristic, complemented
15C103×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C2×#127×C103C2211yescharacteristic
19C2×#125×C103C2211yescharacteristic
20C2×C4×D4×C103—21no—
21C2×C4×D4×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24#490×C103—24no—
25#459×C103—24no—
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×#102×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×#102×C103C2211yescharacteristic
35C2×#102×C103C2211yescharacteristic
36C2×#102×C103C2211yescharacteristic
37C2×#97×C103C2211yescharacteristic
38#396×C103—21no—
39#396×C103—21no—
40#390×C103—21no—
41#390×C103C2211yescharacteristic
42#390×C103C2211yescharacteristic
43#390×C103C2211yescharacteristic
44#390×C103C2211yescharacteristic
45#386×C103—21no—
46#386×C103—21no—
47#385×C103—21no—
48#385×C103—21no—
49#384×C103C2211yescharacteristic
50#382×C103C2211yescharacteristic
51C4×C4⋊C4×C103C2211yescharacteristic
52C4×C4⋊C4×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60#336×C103C2211yescharacteristic
61C22×D4×C103—21no—
62C22×D4×C103—21no—
63C22×D4×C103C2311yescharacteristic
64C22×D4×C103C2311yescharacteristic
65C22×D4×C103C2311yescharacteristic
66C23×C4×C103—21no—
67C23×C4×C103—21no—
68C23×C4×C103—21no—
69C2×D8×C103—22no—
70C2×D8×C103—22no—
71C2×D8×C103—22no—
72C2×D8×C103—22no—
73C2×D8×C103—41no—
74C2×D8×C103—41no—
75C22×C8×C103C2311yescharacteristic
76C22×C8×C103C2311yescharacteristic
77C22×C8×C103C2311yescharacteristic
78C22×C8×C103C2311yescharacteristic
79#127×C103—22no—
80#127×C103D414yes—
81#125×C103—22no—
82#125×C103—22no—
83C4×D4×C103—22no—
84C4×D4×C103—22no—
85C4×D4×C103—22no—
86C4×D4×C103—22no—
87C4×D4×C103—41no—
88C4×D4×C103—41no—
89C4×D4×C103—44no—
90C2×C4⋊C4×C103—21no—
91C2×C4⋊C4×C103—21no—
92C2×C4⋊C4×C103—21no—
93C2×C4⋊C4×C103—21no—
94C2×C4⋊C4×C103D411yescharacteristic
95C2×C4⋊C4×C103D411yescharacteristic
96C2×C4⋊C4×C103C2311yescharacteristic
97C2×C4⋊C4×C103C2311yescharacteristic
98C2×C4⋊C4×C103C2311yescharacteristic
99C2×C4⋊C4×C103C2311yescharacteristic
100C2×C4⋊C4×C103C2311yescharacteristic
101C2×C22⋊C4×C103—21no—
102C2×C22⋊C4×C103—21no—
103C2×C22⋊C4×C103—21no—
104C2×C22⋊C4×C103—21no—
105C2×C22⋊C4×C103—21no—
106C2×C22⋊C4×C103—21no—
107C2×C22⋊C4×C103—21no—
108C2×C22⋊C4×C103—21no—
109C2×C22⋊C4×C103—21no—
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103—21no—
112C2×C42×C103—21no—
113C2×C42×C103C2311yescharacteristic
114C2×C42×C103C2311yescharacteristic
115C2×C42×C103C2311yescharacteristic
116C4⋊C8×C103—22no—
117C4⋊C8×C103—41no—
118C4⋊C8×C103—41no—
119#102×C103—22no—
120#102×C103—22no—
121#102×C103—22no—
122#102×C103—22no—
123#102×C103—22no—
124#102×C103—22no—
125#102×C103—22no—
126#102×C103—22no—
127#97×C103—22no—
128#95×C103—21no—
129#95×C103—21no—
130#95×C103—21no—
131#95×C103D411yescharacteristic
132#95×C103D411yescharacteristic
133C24×C103—21no—
134C24×C103—21no—
135C24×C103—21no—
136C2×D4×C103—24no—
137C2×D4×C103—24no—
138C2×D4×C103—21no—
139C2×D4×C103—21no—
140C2×D4×C103—21no—
141C2×D4×C103—21no—
142C2×D4×C103—21no—
143C2×D4×C103—21no—
144C2×D4×C103—21no—
145C2×D4×C103—21no—
146C2×D4×C103—21no—
147C2×D4×C103—21no—
148C2×D4×C103—21no—
149C2×D4×C103—21no—
150C2×D4×C103—21no—
151C2×D4×C103—21no—
152C2×D4×C103—21no—
153C2×D4×C103—42no—
154C2×D4×C103—42no—
155C2×D4×C103—81no—
156C2×D4×C103—81no—
157C2×D4×C103C2×D412yes—
158C2×D4×C103C2×D412yes—
159C2×D4×C103#4112yes—
160C22×C4×C103—21no—
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—42no—
166C22×C4×C103—42no—
167C22×C4×C103—42no—
168C22×C4×C103—42no—
169C22×C4×C103—42no—
170C22×C4×C103—81no—
171C22×C4×C103—81no—
172C22×C4×C103—81no—
173C22×C4×C103—81no—
174C22×C4×C103C2×D411yescharacteristic
175C22×C4×C103C2×D411yescharacteristic
176C22×C4×C103C2×D411yescharacteristic
177C22×C4×C103C2×D411yescharacteristic
178C22×C4×C103C2×D411yescharacteristic
179C22×C4×C103C2×D411yescharacteristic
180C22×C4×C103C2411yescharacteristic
181D8×C103—44no—
182D8×C103—44no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C2×C8×C103—21no—
186C2×C8×C103—21no—
187C2×C8×C103—21no—
188C2×C8×C103—21no—
189C2×C8×C103—21no—
190C2×C8×C103—21no—
191C2×C8×C103—21no—
192C2×C8×C103—21no—
193C2×C8×C103—21no—
194C2×C8×C103—21no—
195C4⋊C4×C103—22no—
196C4⋊C4×C103—21no—
197C4⋊C4×C103—21no—
198C4⋊C4×C103—21no—
199C4⋊C4×C103—21no—
200C4⋊C4×C103—21no—
201C4⋊C4×C103—21no—
202C4⋊C4×C103—21no—
203C4⋊C4×C103—21no—
204C4⋊C4×C103—21no—
205C4⋊C4×C103—41no—
206C4⋊C4×C103—42no—
207C4⋊C4×C103—42no—
208C4⋊C4×C103—81no—
209C4⋊C4×C103—81no—
210C4⋊C4×C103#4112yes—
211C22⋊C4×C103—42no—
212C22⋊C4×C103—42no—
213C22⋊C4×C103—42no—
214C22⋊C4×C103—42no—
215C22⋊C4×C103—42no—
216C22⋊C4×C103—42no—
217C22⋊C4×C103—42no—
218C22⋊C4×C103—81no—
219C22⋊C4×C103—81no—
220C22⋊C4×C103—81no—
221C22⋊C4×C103—81no—
222C42×C103—21no—
223C42×C103—21no—
224C42×C103—21no—
225C42×C103—21no—
226C42×C103—42no—
227C42×C103C2×D412yes—
228C42×C103#4112yes—
229C23×C103—22no—
230C23×C103—22no—
231C23×C103—22no—
232C23×C103—41no—
233C23×C103—41no—
234C23×C103—41no—
235C23×C103—41no—
236C23×C103—41no—
237C23×C103—41no—
238C23×C103—41no—
239C23×C103—41no—
240C23×C103—41no—
241C23×C103—41no—
242C23×C103—41no—
243C23×C103—41no—
244C23×C103—41no—
245C23×C103—41no—
246C23×C103—41no—
247C23×C103—41no—
248C23×C103—41no—
249C23×C103—41no—
250C23×C103C22×D411yescharacteristic
251D4×C103—22no—
252D4×C103—22no—
253D4×C103—22no—
254D4×C103—22no—
255D4×C103—22no—
256D4×C103—22no—
257D4×C103—48no—
258D4×C103—41no—
259D4×C103—41no—
260D4×C103—41no—
261D4×C103—41no—
262D4×C103—41no—
263D4×C103—41no—
264D4×C103—84no—
265C2×C4×C103—21no—
266C2×C4×C103—21no—
267C2×C4×C103—21no—
268C2×C4×C103—21no—
269C2×C4×C103—21no—
270C2×C4×C103—21no—
271C2×C4×C103—21no—
272C2×C4×C103—21no—
273C2×C4×C103—21no—
274C2×C4×C103—22no—
275C2×C4×C103—21no—
276C2×C4×C103—21no—
277C2×C4×C103—21no—
278C2×C4×C103—21no—
279C2×C4×C103—21no—
280C2×C4×C103—21no—
281C2×C4×C103—41no—
282C2×C4×C103—41no—
283C2×C4×C103—41no—
284C2×C4×C103—41no—
285C2×C4×C103—41no—
286C2×C4×C103—41no—
287C2×C4×C103—41no—
288C2×C4×C103—41no—
289C2×C4×C103—41no—
290C2×C4×C103—41no—
291C2×C4×C103—41no—
292C2×C4×C103—41no—
293C2×C4×C103—41no—
294C2×C4×C103—41no—
295C2×C4×C103—84no—
296C2×C4×C103—84no—
297C2×C4×C103—84no—
298C2×C4×C103#12112yes—
299C2×C4×C103#12112yes—
300C2×C4×C103AGL(1,ℤ/8)12yes—
301C2×C4×C103C22×D411yescharacteristic
302C2×C4×C103C2×#4111yescharacteristic
303C2×C4×C103C2×#4111yescharacteristic
304C2×C4×C103C2×#4111yescharacteristic
305C2×C4×C103H(5,𝔽2)11yescharacteristic
306C2×C4×C1032−1+411yescharacteristic
307C8×C103—41no—
308C8×C103—41no—
309C8×C103—41no—
310C8×C103—41no—
311C22×C103—42no—
312C22×C103—42no—
313C22×C103—42no—
314C22×C103—42no—
315C22×C103—42no—
316C22×C103—42no—
317C22×C103—42no—
318C22×C103—42no—
319C22×C103—42no—
320C22×C103—81no—
321C22×C103—81no—
322C22×C103—81no—
323C22×C103—81no—
324C22×C103—81no—
325C22×C103—81no—
326C22×C103—81no—
327C22×C103—81no—
328C22×C103—81no—
329C22×C103—81no—
330C22×C103—81no—
331C22×C103—81no—
332C22×C103C2×#12111yescharacteristic
333C22×C103#54611yescharacteristic
334C22×C103#54811yescharacteristic
335C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C103#57511yescharacteristic
337C22×C103#57611yescharacteristic
338C22×C103#57611yescharacteristic
339C4×C103—22no—
340C4×C103—22no—
341C4×C103—22no—
342C4×C103—41no—
343C4×C103—41no—
344C4×C103—41no—
345C4×C103—42no—
346C4×C103—81no—
347C4×C103—81no—
348C4×C103—81no—
349C4×C103—81no—
350C4×C103#52911yescharacteristic
351C4×C103#54211yescharacteristic
352C4×C103#54611yescharacteristic
353C4×C103#54711yescharacteristic
354#25330C10311yesmaximal, characteristic, direct product factor, Sylow
355C2×C103—82no—
356C2×C103—82no—
357C2×C103—82no—
358C2×C103#242711yescharacteristic
359C2×C103#303611yescharacteristic
360C2×C103#304111yescharacteristic
361C2×C103#330911yescharacteristic
362C2×C103#331811yescharacteristic
363C2×C103#336611yescharacteristic
364C2×C103#337011yescharacteristic
365C2×#490C2×C10311yescharacteristic, complemented
366C2×#459C2×C10311yescharacteristic
367#2566C2×C10311yescharacteristic, complemented
368#2366C2×C10311yescharacteristic, complemented
369#2073C2×C10311yescharacteristic, complemented
370#2071C2×C10311yescharacteristic, complemented
371#2054C2×C10311yescharacteristic, complemented
372#2054C2×C10311yescharacteristic, complemented
373#1989C2×C10311yescharacteristic, complemented
374#1940C2×C10311yescharacteristic, complemented
375#1879C2×C10311yescharacteristic, complemented
376#1879C2×C10311yescharacteristic, complemented
377#1804C2×C10311yescharacteristic, complemented
378#1802C2×C10311yescharacteristic, complemented
379#1762C2×C10311yescharacteristic, complemented
380C103#2533011yescharacteristic, direct product factor, Sylow
381C22×D8C22×C10311yescharacteristic
382C22×D8C22×C10311yescharacteristic
383C2×#127C22×C10311yescharacteristic
384C2×#125C22×C10311yescharacteristic
385C2×C4×D4—21no—
386C2×C4×D4C22×C10311yescharacteristic
387C2×C4×D4C22×C10311yescharacteristic
388C2×C4×D4C22×C10311yescharacteristic
389#490—24no—
390#459—24no—
391C2×C4⋊C8C22×C10311yescharacteristic
392C2×C4⋊C8C22×C10311yescharacteristic
393C2×C4⋊C8C22×C10311yescharacteristic
394C2×#102C22×C10311yescharacteristic
395C2×#102C22×C10311yescharacteristic
396C2×#102C22×C10311yescharacteristic
397C2×#102C22×C10311yescharacteristic
398C2×#102C22×C10311yescharacteristic
399C2×#102C22×C10311yescharacteristic
400C2×#102C22×C10311yescharacteristic
401C2×#102C22×C10311yescharacteristic
402C2×#97C22×C10311yescharacteristic
403#396—21no—
404#396—21no—
405#390—21no—
406#390C22×C10311yescharacteristic
407#390C22×C10311yescharacteristic
408#390C22×C10311yescharacteristic
409#390C22×C10311yescharacteristic
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#384C22×C10311yescharacteristic
415#382C22×C10311yescharacteristic
416C4×C4⋊C4C22×C10311yescharacteristic
417C4×C4⋊C4C22×C10311yescharacteristic
418#340C22×C10311yescharacteristic
419#340C22×C10311yescharacteristic
420#340C22×C10311yescharacteristic
421#340C22×C10311yescharacteristic
422#340C22×C10311yescharacteristic
423#340C22×C10311yescharacteristic
424#336C22×C10311yescharacteristic
425#336C22×C10311yescharacteristic
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C23×C10311yescharacteristic
429C22×D4C23×C10311yescharacteristic
430C22×D4C23×C10311yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C2×D8—22no—
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—41no—
439C2×D8—41no—
440C22×C8C23×C10311yescharacteristic
441C22×C8C23×C10311yescharacteristic
442C22×C8C23×C10311yescharacteristic
443C22×C8C23×C10311yescharacteristic
444#127—22no—
445#127D4×C10314yes—
446#125—22no—
447#125—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—22no—
452C4×D4—41no—
453C4×D4—41no—
454C4×D4—44no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4D4×C10311yescharacteristic
460C2×C4⋊C4D4×C10311yescharacteristic
461C2×C4⋊C4C23×C10311yescharacteristic
462C2×C4⋊C4C23×C10311yescharacteristic
463C2×C4⋊C4C23×C10311yescharacteristic
464C2×C4⋊C4C23×C10311yescharacteristic
465C2×C4⋊C4C23×C10311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C42—21no—
478C2×C42C23×C10311yescharacteristic
479C2×C42C23×C10311yescharacteristic
480C2×C42C23×C10311yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—41no—
483C4⋊C8—41no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102—22no—
492#97—22no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95D4×C10311yescharacteristic
497#95D4×C10311yescharacteristic
498C24—21no—
499C24—21no—
500C24—21no—
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4C2×D4×C10312yes—
523C2×D4C2×D4×C10312yes—
524C2×D4#41×C10312yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4C2×D4×C10311yescharacteristic
540C22×C4C2×D4×C10311yescharacteristic
541C22×C4C2×D4×C10311yescharacteristic
542C22×C4C2×D4×C10311yescharacteristic
543C22×C4C2×D4×C10311yescharacteristic
544C22×C4C2×D4×C10311yescharacteristic
545C22×C4C24×C10311yescharacteristic
546D8—44no—
547D8—44no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—41no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C4⋊C4#41×C10312yes—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42C2×D4×C10312yes—
593C42#41×C10312yes—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23C22×D4×C10311yescharacteristic
616D4—22no—
617D4—22no—
618D4—22no—
619D4—22no—
620D4—22no—
621D4—22no—
622D4—48no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—84no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4—84no—
663C2×C4#121×C10312yes—
664C2×C4#121×C10312yes—
665C2×C4AGL(1,ℤ/8)×C10312yes—
666C2×C4C22×D4×C10311yescharacteristic
667C2×C4C2×#41×C10311yescharacteristic
668C2×C4C2×#41×C10311yescharacteristic
669C2×C4C2×#41×C10311yescharacteristic
670C2×C4H(5,𝔽2)×C10311yescharacteristic
671C2×C42−1+4×C10311yescharacteristic
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22C2×#121×C10311yescharacteristic
698C22#546×C10311yescharacteristic
699C22#548×C10311yescharacteristic
700C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
701C22#575×C10311yescharacteristic
702C22#576×C10311yescharacteristic
703C22#576×C10311yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—42no—
711C4—81no—
712C4—81no—
713C4—81no—
714C4—81no—
715C4#529×C10311yescharacteristic
716C4#542×C10311yescharacteristic
717C4#546×C10311yescharacteristic
718C4#547×C10311yescharacteristic
719C2—82no—
720C2—82no—
721C2—82no—
722C2C103×#242711yescharacteristic
723C2C103×#303611yescharacteristic
724C2C103×#304111yescharacteristic
725C2C103×#330911yescharacteristic
726C2C103×#331811yescharacteristic
727C2C103×#336611yescharacteristic
728C2C103×#337011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#459×C103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C4⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#490×C103C2semidirect
3. C103×#2566C2semidirect
4. C103×#2366C2semidirect
5. C103×#2073C2semidirect
6. C103×#2071C2semidirect
7. C103×#2054C2semidirect
8. C103×#2054C2semidirect
9. C103×#1989C2semidirect
10. C103×#1940C2semidirect
11. C103×#1879C2semidirect
12. C103×#1879C2semidirect
13. C103×#1804C2semidirect
14. C103×#1802C2semidirect
15. C103×#1762C2semidirect
354. #25330C103direct (N × H)
365. C2×#490C2×C103semidirect
367. #2566C2×C103semidirect
368. #2366C2×C103semidirect
369. #2073C2×C103semidirect
370. #2071C2×C103semidirect
371. #2054C2×C103semidirect
372. #2054C2×C103semidirect
373. #1989C2×C103semidirect
374. #1940C2×C103semidirect
375. #1879C2×C103semidirect
376. #1879C2×C103semidirect
377. #1804C2×C103semidirect
378. #1802C2×C103semidirect
379. #1762C2×C103semidirect
380. C103#25330direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#490×C1032
C2×#459×C1032
C103×#25662
C103×#23662
C103×#20732
C103×#20712
C103×#20542
C103×#19892
C103×#19402
C103×#18792
C103×#18042
C103×#18022
C103×#17622
#25330103