Finite Group Databasebeta

← C103×#25354 #39930629

Subgroups — C103×#25354 #39930629

Order 26368.

924 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C103C211yesmaximal, characteristic, complemented
2C2×#435×C103C211yesmaximal, characteristic, complemented
3C103×#2547C211yesmaximal, characteristic, complemented
4C103×#2535C211yesmaximal, characteristic
5C103×#2077C211yesmaximal, characteristic, complemented
6C103×#2077C211yesmaximal, characteristic, complemented
7C103×#2034C211yesmaximal, characteristic, complemented
8C103×#2033C211yesmaximal, characteristic, complemented
9C103×#1993C211yesmaximal, characteristic, complemented
10C103×#1949C211yesmaximal, characteristic, complemented
11C103×#1895C211yesmaximal, characteristic, complemented
12C103×#1893C211yesmaximal, characteristic, complemented
13C103×#1809C211yesmaximal, characteristic, complemented
14C103×#1807C211yesmaximal, characteristic, complemented
15C103×#1762C211yesmaximal, characteristic, complemented
16C22×M16×C103C2211yescharacteristic
17C23×C8×C103C2211yescharacteristic
18C2×C4⋊Q8×C103C2211yescharacteristic
19C2×#124×C103—21no—
20C2×#121×C103C2211yescharacteristic
21C2×#121×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24#476×C103—24no—
25#435×C103—24no—
26C2×#107×C103C2211yescharacteristic
27C2×#106×C103C2211yescharacteristic
28C2×#106×C103C2211yescharacteristic
29C2×#106×C103C2211yescharacteristic
30C2×C4⋊C8×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×#102×C103C2211yescharacteristic
35C2×C22⋊C8×C103C2211yescharacteristic
36C2×C22⋊C8×C103C2211yescharacteristic
37C2×#97×C103C2211yescharacteristic
38#397×C103—21no—
39#397×C103—21no—
40#397×C103—21no—
41#392×C103—21no—
42#391×C103—21no—
43#386×C103—21no—
44#386×C103—21no—
45#382×C103C2211yescharacteristic
46#380×C103C2211yescharacteristic
47#380×C103C2211yescharacteristic
48#380×C103C2211yescharacteristic
49#380×C103C2211yescharacteristic
50#380×C103C2211yescharacteristic
51#380×C103C2211yescharacteristic
52C4×C4⋊C4×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61C22×Q8×C103—21no—
62C22×D4×C103—21no—
63C22×D4×C103—21no—
64C22×D4×C103D411yescharacteristic
65C22×D4×C103C2311yescharacteristic
66C23×C4×C103—21no—
67C23×C4×C103C2311yescharacteristic
68C23×C4×C103C2311yescharacteristic
69C2×M16×C103—22no—
70C2×M16×C103—22no—
71C2×M16×C103—41no—
72C22×C8×C103—22no—
73C22×C8×C103—22no—
74C22×C8×C103—41no—
75C22×C8×C103C2311yescharacteristic
76C22×C8×C103C2311yescharacteristic
77C22×C8×C103C2311yescharacteristic
78C22×C8×C103C2311yescharacteristic
79C4⋊Q8×C103—22no—
80C4⋊Q8×C103—22no—
81#124×C103—44no—
82#121×C103—22no—
83#121×C103—22no—
84#121×C103—41no—
85#121×C103—41no—
86C4×D4×C103—22no—
87C4×D4×C103—22no—
88C4×D4×C103—22no—
89C4×D4×C103—22no—
90C2×C4⋊C4×C103—21no—
91C2×C4⋊C4×C103D411yescharacteristic
92C2×C4⋊C4×C103C2311yescharacteristic
93C2×C4⋊C4×C103C2311yescharacteristic
94C2×C4⋊C4×C103C2311yescharacteristic
95C2×C4⋊C4×C103C2311yescharacteristic
96C2×C4⋊C4×C103C2311yescharacteristic
97C2×C4⋊C4×C103C2311yescharacteristic
98C2×C4⋊C4×C103C2311yescharacteristic
99C2×C22⋊C4×C103—21no—
100C2×C22⋊C4×C103—21no—
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×C103D411yescharacteristic
109C2×C22⋊C4×C103D411yescharacteristic
110C2×C42×C103—21no—
111C2×C42×C103C2311yescharacteristic
112#107×C103—41no—
113#106×C103—22no—
114#106×C103—22no—
115#106×C103—41no—
116C4⋊C8×C103D414yescomplemented
117#102×C103—22no—
118#102×C103—22no—
119#102×C103—22no—
120#102×C103—22no—
121C22⋊C8×C103—22no—
122C22⋊C8×C103—22no—
123#97×C103—22no—
124#95×C103—21no—
125#95×C103—21no—
126#95×C103—21no—
127#95×C103—21no—
128#95×C103—21no—
129#95×C103—21no—
130#95×C103—21no—
131#95×C103—21no—
132#95×C103—21no—
133C24×C103—21no—
134C24×C103C2×D411yescharacteristic
135C24×C103C2×D411yescharacteristic
136C2×Q8×C103—42no—
137C2×Q8×C103—42no—
138C2×Q8×C103—42no—
139C2×D4×C103—22no—
140C2×D4×C103—22no—
141C2×D4×C103—21no—
142C2×D4×C103—21no—
143C2×D4×C103—21no—
144C2×D4×C103—21no—
145C2×D4×C103—21no—
146C2×D4×C103—41no—
147C2×D4×C103—42no—
148C2×D4×C103—42no—
149C2×D4×C103—42no—
150C2×D4×C103—42no—
151C2×D4×C103—81no—
152C2×D4×C103—81no—
153C2×D4×C103#4112yes—
154C22×C4×C103—21no—
155C22×C4×C103—21no—
156C22×C4×C103—21no—
157C22×C4×C103—21no—
158C22×C4×C103—21no—
159C22×C4×C103—21no—
160C22×C4×C103—21no—
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—21no—
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—21no—
172C22×C4×C103—21no—
173C22×C4×C103—42no—
174C22×C4×C103—81no—
175C22×C4×C103—81no—
176C22×C4×C103C2×D411yescharacteristic
177C22×C4×C103C2×D411yescharacteristic
178C22×C4×C103C2×D411yescharacteristic
179C22×C4×C103C2×D411yescharacteristic
180C22×C4×C103C2411yescharacteristic
181M16×C103—44no—
182C2×C8×C103—21no—
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—44no—
192C2×C8×C103C2×D412yes—
193C2×C8×C103C2×D412yes—
194C2×C8×C103#4112yes—
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—21no—
206C4⋊C4×C103—21no—
207C4⋊C4×C103—21no—
208C4⋊C4×C103—21no—
209C4⋊C4×C103—21no—
210C4⋊C4×C103—42no—
211C22⋊C4×C103—22no—
212C22⋊C4×C103—22no—
213C22⋊C4×C103—42no—
214C22⋊C4×C103—42no—
215C22⋊C4×C103—42no—
216C22⋊C4×C103—42no—
217C22⋊C4×C103—42no—
218C22⋊C4×C103—42no—
219C22⋊C4×C103—42no—
220C22⋊C4×C103—81no—
221C22⋊C4×C103—81no—
222C42×C103—42no—
223C42×C103C2×D412yes—
224C42×C103#4112yes—
225C23×C103—21no—
226C23×C103—21no—
227C23×C103—21no—
228C23×C103—21no—
229C23×C103—21no—
230C23×C103—21no—
231C23×C103—21no—
232C23×C103—22no—
233C23×C103—21no—
234C23×C103—21no—
235C23×C103—21no—
236C23×C103—21no—
237C23×C103—21no—
238C23×C103—21no—
239C23×C103—41no—
240C23×C103—41no—
241C23×C103—41no—
242C23×C103—41no—
243C23×C103—41no—
244C23×C103—41no—
245C23×C103AGL(1,ℤ/8)12yes—
246C23×C103C22×D411yescharacteristic
247Q8×C103—84no—
248D4×C103—22no—
249D4×C103—22no—
250D4×C103—44no—
251D4×C103—41no—
252D4×C103—41no—
253D4×C103—84no—
254D4×C103—84no—
255C2×C4×C103—21no—
256C2×C4×C103—21no—
257C2×C4×C103—21no—
258C2×C4×C103—21no—
259C2×C4×C103—21no—
260C2×C4×C103—21no—
261C2×C4×C103—21no—
262C2×C4×C103—21no—
263C2×C4×C103—21no—
264C2×C4×C103—21no—
265C2×C4×C103—41no—
266C2×C4×C103—41no—
267C2×C4×C103—41no—
268C2×C4×C103—41no—
269C2×C4×C103—41no—
270C2×C4×C103—41no—
271C2×C4×C103—41no—
272C2×C4×C103—41no—
273C2×C4×C103—41no—
274C2×C4×C103—41no—
275C2×C4×C103—41no—
276C2×C4×C103—41no—
277C2×C4×C103—41no—
278C2×C4×C103—41no—
279C2×C4×C103—41no—
280C2×C4×C103—41no—
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—84no—
295C2×C4×C103#12112yes—
296C2×C4×C103#12112yes—
297C2×C4×C103C22×D411yescharacteristic
298C2×C4×C103C2×#4111yescharacteristic
299C2×C4×C103C2×#4111yescharacteristic
300C2×C4×C103C2×#4111yescharacteristic
301C2×C4×C103H(5,𝔽2)11yescharacteristic
302C2×C4×C1032−1+411yescharacteristic
303C8×C103—22no—
304C8×C103—22no—
305C8×C103—22no—
306C8×C103—41no—
307C22×C103—22no—
308C22×C103—22no—
309C22×C103—22no—
310C22×C103—41no—
311C22×C103—41no—
312C22×C103—41no—
313C22×C103—41no—
314C22×C103—41no—
315C22×C103—41no—
316C22×C103—41no—
317C22×C103—42no—
318C22×C103—42no—
319C22×C103—41no—
320C22×C103—41no—
321C22×C103—41no—
322C22×C103—42no—
323C22×C103—41no—
324C22×C103—81no—
325C22×C103—81no—
326C22×C103—81no—
327C22×C103—81no—
328C22×C103C2×#12111yescharacteristic
329C22×C103#54611yescharacteristic
330C22×C103#54711yescharacteristic
331C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C103#57511yescharacteristic
333C22×C103#57711yescharacteristic
334C22×C103#57711yescharacteristic
335C4×C103—22no—
336C4×C103—22no—
337C4×C103—41no—
338C4×C103—41no—
339C4×C103—81no—
340C4×C103—81no—
341C4×C103—81no—
342C4×C103—81no—
343C4×C103—81no—
344C4×C103—81no—
345C4×C103—81no—
346C4×C103#52911yescharacteristic
347C4×C103#54211yescharacteristic
348C4×C103#54611yescharacteristic
349C4×C103#54811yescharacteristic
350#25354C10311yesmaximal, characteristic, direct product factor, Sylow
351C2×C103—42no—
352C2×C103—81no—
353C2×C103—82no—
354C2×C103#242711yescharacteristic
355C2×C103#305511yescharacteristic
356C2×C103#305711yescharacteristic
357C2×C103#330611yescharacteristic
358C2×C103#331111yescharacteristic
359C2×C103#334511yescharacteristic
360C2×C103#335011yescharacteristic
361C2×#476C2×C10311yescharacteristic, complemented
362C2×#435C2×C10311yescharacteristic, complemented
363#2547C2×C10311yescharacteristic, complemented
364#2535C2×C10311yescharacteristic
365#2077C2×C10311yescharacteristic, complemented
366#2077C2×C10311yescharacteristic, complemented
367#2034C2×C10311yescharacteristic, complemented
368#2033C2×C10311yescharacteristic, complemented
369#1993C2×C10311yescharacteristic, complemented
370#1949C2×C10311yescharacteristic, complemented
371#1895C2×C10311yescharacteristic, complemented
372#1893C2×C10311yescharacteristic, complemented
373#1809C2×C10311yescharacteristic, complemented
374#1807C2×C10311yescharacteristic, complemented
375#1762C2×C10311yescharacteristic, complemented
376C103#2535411yescharacteristic, direct product factor, Sylow
377C22×M16C22×C10311yescharacteristic
378C23×C8C22×C10311yescharacteristic
379C2×C4⋊Q8C22×C10311yescharacteristic
380C2×#124—21no—
381C2×#121C22×C10311yescharacteristic
382C2×#121C22×C10311yescharacteristic
383C2×C4×D4C22×C10311yescharacteristic
384C2×C4×D4C22×C10311yescharacteristic
385#476—24no—
386#435—24no—
387C2×#107C22×C10311yescharacteristic
388C2×#106C22×C10311yescharacteristic
389C2×#106C22×C10311yescharacteristic
390C2×#106C22×C10311yescharacteristic
391C2×C4⋊C8C22×C10311yescharacteristic
392C2×#102C22×C10311yescharacteristic
393C2×#102C22×C10311yescharacteristic
394C2×#102C22×C10311yescharacteristic
395C2×#102C22×C10311yescharacteristic
396C2×C22⋊C8C22×C10311yescharacteristic
397C2×C22⋊C8C22×C10311yescharacteristic
398C2×#97C22×C10311yescharacteristic
399#397—21no—
400#397—21no—
401#397—21no—
402#392—21no—
403#391—21no—
404#386—21no—
405#386—21no—
406#382C22×C10311yescharacteristic
407#380C22×C10311yescharacteristic
408#380C22×C10311yescharacteristic
409#380C22×C10311yescharacteristic
410#380C22×C10311yescharacteristic
411#380C22×C10311yescharacteristic
412#380C22×C10311yescharacteristic
413C4×C4⋊C4C22×C10311yescharacteristic
414#340C22×C10311yescharacteristic
415#340C22×C10311yescharacteristic
416#340C22×C10311yescharacteristic
417#340C22×C10311yescharacteristic
418#340C22×C10311yescharacteristic
419#340C22×C10311yescharacteristic
420#340C22×C10311yescharacteristic
421#340C22×C10311yescharacteristic
422C22×Q8—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4D4×C10311yescharacteristic
426C22×D4C23×C10311yescharacteristic
427C23×C4—21no—
428C23×C4C23×C10311yescharacteristic
429C23×C4C23×C10311yescharacteristic
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C22×C8—22no—
434C22×C8—22no—
435C22×C8—41no—
436C22×C8C23×C10311yescharacteristic
437C22×C8C23×C10311yescharacteristic
438C22×C8C23×C10311yescharacteristic
439C22×C8C23×C10311yescharacteristic
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442#124—44no—
443#121—22no—
444#121—22no—
445#121—41no—
446#121—41no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4D4×C10311yescharacteristic
453C2×C4⋊C4C23×C10311yescharacteristic
454C2×C4⋊C4C23×C10311yescharacteristic
455C2×C4⋊C4C23×C10311yescharacteristic
456C2×C4⋊C4C23×C10311yescharacteristic
457C2×C4⋊C4C23×C10311yescharacteristic
458C2×C4⋊C4C23×C10311yescharacteristic
459C2×C4⋊C4C23×C10311yescharacteristic
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4D4×C10311yescharacteristic
470C2×C22⋊C4D4×C10311yescharacteristic
471C2×C42—21no—
472C2×C42C23×C10311yescharacteristic
473#107—41no—
474#106—22no—
475#106—22no—
476#106—41no—
477C4⋊C8D4×C10314yescomplemented
478#102—22no—
479#102—22no—
480#102—22no—
481#102—22no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484#97—22no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494C24—21no—
495C24C2×D4×C10311yescharacteristic
496C24C2×D4×C10311yescharacteristic
497C2×Q8—42no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—41no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4—81no—
514C2×D4#41×C10312yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4C2×D4×C10311yescharacteristic
538C22×C4C2×D4×C10311yescharacteristic
539C22×C4C2×D4×C10311yescharacteristic
540C22×C4C2×D4×C10311yescharacteristic
541C22×C4C24×C10311yescharacteristic
542M16—44no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—44no—
553C2×C8C2×D4×C10312yes—
554C2×C8C2×D4×C10312yes—
555C2×C8#41×C10312yes—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
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—21no—
571C4⋊C4—42no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C42—42no—
584C42C2×D4×C10312yes—
585C42#41×C10312yes—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23AGL(1,ℤ/8)×C10312yes—
607C23C22×D4×C10311yescharacteristic
608Q8—84no—
609D4—22no—
610D4—22no—
611D4—44no—
612D4—41no—
613D4—41no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
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—84no—
656C2×C4#121×C10312yes—
657C2×C4#121×C10312yes—
658C2×C4C22×D4×C10311yescharacteristic
659C2×C4C2×#41×C10311yescharacteristic
660C2×C4C2×#41×C10311yescharacteristic
661C2×C4C2×#41×C10311yescharacteristic
662C2×C4H(5,𝔽2)×C10311yescharacteristic
663C2×C42−1+4×C10311yescharacteristic
664C8—22no—
665C8—22no—
666C8—22no—
667C8—41no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—42no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—42no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#121×C10311yescharacteristic
690C22#546×C10311yescharacteristic
691C22#547×C10311yescharacteristic
692C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
693C22#575×C10311yescharacteristic
694C22#577×C10311yescharacteristic
695C22#577×C10311yescharacteristic
696C4—22no—
697C4—22no—
698C4—41no—
699C4—41no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4#529×C10311yescharacteristic
708C4#542×C10311yescharacteristic
709C4#546×C10311yescharacteristic
710C4#548×C10311yescharacteristic
711C2—42no—
712C2—81no—
713C2—82no—
714C2C103×#242711yescharacteristic
715C2C103×#305511yescharacteristic
716C2C103×#305711yescharacteristic
717C2C103×#330611yescharacteristic
718C2C103×#331111yescharacteristic
719C2C103×#334511yescharacteristic
720C2C103×#335011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#2535C2
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×#476×C103C2semidirect
2. C2×#435×C103C2semidirect
3. C103×#2547C2semidirect
5. C103×#2077C2semidirect
6. C103×#2077C2semidirect
7. C103×#2034C2semidirect
8. C103×#2033C2semidirect
9. C103×#1993C2semidirect
10. C103×#1949C2semidirect
11. C103×#1895C2semidirect
12. C103×#1893C2semidirect
13. C103×#1809C2semidirect
14. C103×#1807C2semidirect
15. C103×#1762C2semidirect
116. C4⋊C8×C103D4semidirect
350. #25354C103direct (N × H)
361. C2×#476C2×C103semidirect
362. C2×#435C2×C103semidirect
363. #2547C2×C103semidirect
365. #2077C2×C103semidirect
366. #2077C2×C103semidirect
367. #2034C2×C103semidirect
368. #2033C2×C103semidirect
369. #1993C2×C103semidirect
370. #1949C2×C103semidirect
371. #1895C2×C103semidirect
372. #1893C2×C103semidirect
373. #1809C2×C103semidirect
374. #1807C2×C103semidirect
375. #1762C2×C103semidirect
376. C103#25354direct (N × H)
477. C4⋊C8D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1032
C2×#435×C1032
C103×#25472
C103×#25352
C103×#20772
C103×#20342
C103×#20332
C103×#19932
C103×#19492
C103×#18952
C103×#18932
C103×#18092
C103×#18072
C103×#17622
#25354103