Finite Group Databasebeta

← C103×#25378 #39930653

Subgroups — C103×#25378 #39930653

Order 26368.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C103C211yesmaximal, characteristic
2C2×#460×C103C211yesmaximal, characteristic, complemented
3C2×#463×C103C211yesmaximal, characteristic, complemented
4C2×#461×C103C211yesmaximal, characteristic, complemented
5C103×#2545C211yesmaximal, characteristic, complemented
6C103×#2366C211yesmaximal, characteristic, complemented
7C103×#2055C211yesmaximal, characteristic, complemented
8C103×#2054C211yesmaximal, characteristic, complemented
9C103×#2013C211yesmaximal, characteristic, complemented
10C103×#2012C211yesmaximal, characteristic, complemented
11C103×#1983C211yesmaximal, characteristic, complemented
12C103×#1940C211yesmaximal, characteristic, complemented
13C103×#1879C211yesmaximal, characteristic, complemented
14C103×#1877C211yesmaximal, characteristic, complemented
15C103×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18C22×SD16×C103C2211yescharacteristic
19C22×SD16×C103C2211yescharacteristic
20C22×D8×C103C2211yescharacteristic
21C22×D8×C103C2211yescharacteristic
22C2×C4⋊Q8×C103C2211yescharacteristic
23C2×#127×C103C2211yescharacteristic
24C2×#124×C103C2211yescharacteristic
25C2×#124×C103C2211yescharacteristic
26C2×C4×Q8×C103C2211yescharacteristic
27C2×C4×D4×C103—21no—
28C2×C4×D4×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30#496×C103—24no—
31#463×C103—24no—
32#461×C103—24no—
33#460×C103—24no—
34C2×C4⋊C8×C103C2211yescharacteristic
35C2×C4⋊C8×C103C2211yescharacteristic
36C2×C4⋊C8×C103C2211yescharacteristic
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#97×C103C2211yescharacteristic
46#396×C103—21no—
47#396×C103—21no—
48#391×C103C2211yescharacteristic
49#390×C103—21no—
50#390×C103C2211yescharacteristic
51#390×C103C2211yescharacteristic
52#390×C103C2211yescharacteristic
53#388×C103—21no—
54#388×C103—21no—
55#386×C103—21no—
56#386×C103—21no—
57C4×C4⋊C4×C103C2211yescharacteristic
58C4×C4⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
64C22×Q8×C103C2311yescharacteristic
65C22×D4×C103—21no—
66C22×D4×C103—21no—
67C22×D4×C103C2311yescharacteristic
68C22×D4×C103C2311yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C23×C4×C103—21no—
71C23×C4×C103—21no—
72C2×SD16×C103—22no—
73C2×SD16×C103—22no—
74C2×SD16×C103—22no—
75C2×SD16×C103—22no—
76C2×SD16×C103—22no—
77C2×SD16×C103—22no—
78C2×SD16×C103—22no—
79C2×SD16×C103—22no—
80C2×SD16×C103—41no—
81C2×SD16×C103—41no—
82C2×SD16×C103—41no—
83C2×SD16×C103—41no—
84C2×D8×C103—22no—
85C2×D8×C103—22no—
86C2×D8×C103—22no—
87C2×D8×C103—22no—
88C2×D8×C103—41no—
89C2×D8×C103—41no—
90C22×C8×C103C2311yescharacteristic
91C22×C8×C103C2311yescharacteristic
92C22×C8×C103C2311yescharacteristic
93C22×C8×C103C2311yescharacteristic
94C4⋊Q8×C103—22no—
95C4⋊Q8×C103—41no—
96#127×C103—22no—
97#127×C103D414yes—
98#124×C103—22no—
99#124×C103—22no—
100#124×C103—22no—
101#124×C103—41no—
102C4×Q8×C103—22no—
103C4×Q8×C103—22no—
104C4×D4×C103—22no—
105C4×D4×C103—22no—
106C4×D4×C103—41no—
107C4×D4×C103—41no—
108C4×D4×C103—44no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103D411yescharacteristic
113C2×C4⋊C4×C103D411yescharacteristic
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C42×C103—21no—
130C2×C42×C103—21no—
131C2×C42×C103C2311yescharacteristic
132C2×C42×C103C2311yescharacteristic
133C2×C42×C103C2311yescharacteristic
134C4⋊C8×C103—22no—
135C4⋊C8×C103—22no—
136C4⋊C8×C103—22no—
137#103×C103—22no—
138#103×C103—22no—
139#103×C103—41no—
140#103×C103D414yescomplemented
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—22no—
144#102×C103—41no—
145#97×C103—22no—
146#95×C103—21no—
147#95×C103—21no—
148#95×C103—21no—
149#95×C103D411yescharacteristic
150#95×C103D411yescharacteristic
151C24×C103—21no—
152C24×C103—21no—
153C24×C103—21no—
154C2×Q8×C103—21no—
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×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103C2×D412yes—
166C2×D4×C103—24no—
167C2×D4×C103—24no—
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—21no—
177C2×D4×C103—21no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×C103—21no—
181C2×D4×C103—21no—
182C2×D4×C103—21no—
183C2×D4×C103—21no—
184C2×D4×C103—42no—
185C2×D4×C103—42no—
186C2×D4×C103—81no—
187C2×D4×C103—81no—
188C2×D4×C103C2×D412yes—
189C2×D4×C103C2×D412yes—
190C22×C4×C103—21no—
191C22×C4×C103—21no—
192C22×C4×C103—21no—
193C22×C4×C103—21no—
194C22×C4×C103—21no—
195C22×C4×C103—42no—
196C22×C4×C103—42no—
197C22×C4×C103—42no—
198C22×C4×C103—42no—
199C22×C4×C103—81no—
200C22×C4×C103—81no—
201C22×C4×C103C2×D411yescharacteristic
202C22×C4×C103C2×D411yescharacteristic
203C22×C4×C103C2×D411yescharacteristic
204C22×C4×C103C2×D411yescharacteristic
205C22×C4×C103C2×D411yescharacteristic
206C22×C4×C103C2×D411yescharacteristic
207C22×C4×C103C2411yescharacteristic
208SD16×C103—44no—
209SD16×C103—44no—
210SD16×C103—44no—
211SD16×C103—44no—
212D8×C103—44no—
213D8×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×C103C2×D412yes—
225C2×C8×C103#4112yes—
226C4⋊C4×C103—22no—
227C4⋊C4×C103—21no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—41no—
233C4⋊C4×C103—42no—
234C4⋊C4×C103—42no—
235C4⋊C4×C103—42no—
236C4⋊C4×C103C2×D412yes—
237C22⋊C4×C103—42no—
238C22⋊C4×C103—42no—
239C22⋊C4×C103—42no—
240C22⋊C4×C103—42no—
241C22⋊C4×C103—42no—
242C22⋊C4×C103—42no—
243C22⋊C4×C103—42no—
244C22⋊C4×C103—42no—
245C22⋊C4×C103—42no—
246C22⋊C4×C103—42no—
247C22⋊C4×C103—81no—
248C22⋊C4×C103—81no—
249C42×C103—21no—
250C42×C103—21no—
251C42×C103—21no—
252C42×C103—21no—
253C42×C103—42no—
254C42×C103—42no—
255C42×C103C2×D412yes—
256C42×C103#4112yes—
257C23×C103—22no—
258C23×C103—22no—
259C23×C103—41no—
260C23×C103—41no—
261C23×C103—41no—
262C23×C103—41no—
263C23×C103—41no—
264C23×C103—41no—
265C23×C103—41no—
266C23×C103—41no—
267C23×C103—41no—
268C23×C103—41no—
269C23×C103—41no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103—41no—
273C23×C103—41no—
274C23×C103—41no—
275C23×C103—41no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103C22×D411yescharacteristic
279Q8×C103—22no—
280Q8×C103—22no—
281Q8×C103—41no—
282Q8×C103—41no—
283Q8×C103—41no—
284Q8×C103—41no—
285Q8×C103—41no—
286Q8×C103—41no—
287D4×C103—22no—
288D4×C103—22no—
289D4×C103—22no—
290D4×C103—22no—
291D4×C103—48no—
292D4×C103—41no—
293D4×C103—41no—
294D4×C103—41no—
295D4×C103—41no—
296D4×C103—41no—
297D4×C103—41no—
298D4×C103—41no—
299D4×C103—41no—
300D4×C103—84no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—21no—
305C2×C4×C103—21no—
306C2×C4×C103—21no—
307C2×C4×C103—21no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—22no—
311C2×C4×C103—22no—
312C2×C4×C103—21no—
313C2×C4×C103—21no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—41no—
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—84no—
332C2×C4×C103—84no—
333C2×C4×C103#12112yes—
334C2×C4×C103#12112yes—
335C2×C4×C103AGL(1,ℤ/8)12yes—
336C2×C4×C103C22×D411yescharacteristic
337C2×C4×C103C22×D411yescharacteristic
338C2×C4×C103C2×#4111yescharacteristic
339C2×C4×C103C2×#4111yescharacteristic
340C2×C4×C103H(5,𝔽2)11yescharacteristic
341C2×C4×C103H(5,𝔽2)11yescharacteristic
342C8×C103—22no—
343C8×C103—22no—
344C8×C103—41no—
345C8×C103—41no—
346C22×C103—42no—
347C22×C103—42no—
348C22×C103—42no—
349C22×C103—42no—
350C22×C103—42no—
351C22×C103—42no—
352C22×C103—81no—
353C22×C103—81no—
354C22×C103—81no—
355C22×C103—81no—
356C22×C103—81no—
357C22×C103—81no—
358C22×C103—81no—
359C22×C103—81no—
360C22×C103—81no—
361C22×C103—81no—
362C22×C103—81no—
363C22×C103—81no—
364C22×C103—81no—
365C22×C103—81no—
366C22×C103—81no—
367C22×C103C2×#12111yescharacteristic
368C22×C103D4211yescharacteristic
369C22×C103#55011yescharacteristic
370C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C103#57511yescharacteristic
372C22×C103#57711yescharacteristic
373C22×C103#57711yescharacteristic
374C4×C103—22no—
375C4×C103—22no—
376C4×C103—22no—
377C4×C103—42no—
378C4×C103—41no—
379C4×C103—42no—
380C4×C103—41no—
381C4×C103—41no—
382C4×C103—81no—
383C4×C103—81no—
384C4×C103—81no—
385C4×C103#53211yescharacteristic
386C4×C103#54011yescharacteristic
387C4×C103D4211yescharacteristic
388C4×C103#54611yescharacteristic
389#25378C10311yesmaximal, characteristic, direct product factor, Sylow
390C2×C103—82no—
391C2×C103—82no—
392C2×C103—161no—
393C2×C103#242811yescharacteristic
394C2×C103#303611yescharacteristic
395C2×C103#304211yescharacteristic
396C2×C103#326511yescharacteristic
397C2×C103#327111yescharacteristic
398C2×C103#339711yescharacteristic
399C2×C103#340111yescharacteristic
400C2×#496C2×C10311yescharacteristic
401C2×#460C2×C10311yescharacteristic, complemented
402C2×#463C2×C10311yescharacteristic, complemented
403C2×#461C2×C10311yescharacteristic, complemented
404#2545C2×C10311yescharacteristic, complemented
405#2366C2×C10311yescharacteristic, complemented
406#2055C2×C10311yescharacteristic, complemented
407#2054C2×C10311yescharacteristic, complemented
408#2013C2×C10311yescharacteristic, complemented
409#2012C2×C10311yescharacteristic, complemented
410#1983C2×C10311yescharacteristic, complemented
411#1940C2×C10311yescharacteristic, complemented
412#1879C2×C10311yescharacteristic, complemented
413#1877C2×C10311yescharacteristic, complemented
414#1763C2×C10311yescharacteristic, complemented
415C103#2537811yescharacteristic, direct product factor, Sylow
416C22×SD16C22×C10311yescharacteristic
417C22×SD16C22×C10311yescharacteristic
418C22×SD16C22×C10311yescharacteristic
419C22×SD16C22×C10311yescharacteristic
420C22×D8C22×C10311yescharacteristic
421C22×D8C22×C10311yescharacteristic
422C2×C4⋊Q8C22×C10311yescharacteristic
423C2×#127C22×C10311yescharacteristic
424C2×#124C22×C10311yescharacteristic
425C2×#124C22×C10311yescharacteristic
426C2×C4×Q8C22×C10311yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4C22×C10311yescharacteristic
429C2×C4×D4C22×C10311yescharacteristic
430#496—24no—
431#463—24no—
432#461—24no—
433#460—24no—
434C2×C4⋊C8C22×C10311yescharacteristic
435C2×C4⋊C8C22×C10311yescharacteristic
436C2×C4⋊C8C22×C10311yescharacteristic
437C2×#103C22×C10311yescharacteristic
438C2×#103C22×C10311yescharacteristic
439C2×#103C22×C10311yescharacteristic
440C2×#103C22×C10311yescharacteristic
441C2×#102C22×C10311yescharacteristic
442C2×#102C22×C10311yescharacteristic
443C2×#102C22×C10311yescharacteristic
444C2×#102C22×C10311yescharacteristic
445C2×#97C22×C10311yescharacteristic
446#396—21no—
447#396—21no—
448#391C22×C10311yescharacteristic
449#390—21no—
450#390C22×C10311yescharacteristic
451#390C22×C10311yescharacteristic
452#390C22×C10311yescharacteristic
453#388—21no—
454#388—21no—
455#386—21no—
456#386—21no—
457C4×C4⋊C4C22×C10311yescharacteristic
458C4×C4⋊C4C22×C10311yescharacteristic
459#340C22×C10311yescharacteristic
460#340C22×C10311yescharacteristic
461#336C22×C10311yescharacteristic
462#336C22×C10311yescharacteristic
463C22×Q8C23×C10311yescharacteristic
464C22×Q8C23×C10311yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C23×C10311yescharacteristic
468C22×D4C23×C10311yescharacteristic
469C22×D4C23×C10311yescharacteristic
470C23×C4—21no—
471C23×C4—21no—
472C2×SD16—22no—
473C2×SD16—22no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—22no—
478C2×SD16—22no—
479C2×SD16—22no—
480C2×SD16—41no—
481C2×SD16—41no—
482C2×SD16—41no—
483C2×SD16—41no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—41no—
489C2×D8—41no—
490C22×C8C23×C10311yescharacteristic
491C22×C8C23×C10311yescharacteristic
492C22×C8C23×C10311yescharacteristic
493C22×C8C23×C10311yescharacteristic
494C4⋊Q8—22no—
495C4⋊Q8—41no—
496#127—22no—
497#127D4×C10314yes—
498#124—22no—
499#124—22no—
500#124—22no—
501#124—41no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—41no—
507C4×D4—41no—
508C4×D4—44no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4D4×C10311yescharacteristic
513C2×C4⋊C4D4×C10311yescharacteristic
514C2×C4⋊C4C23×C10311yescharacteristic
515C2×C4⋊C4C23×C10311yescharacteristic
516C2×C4⋊C4C23×C10311yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42C23×C10311yescharacteristic
532C2×C42C23×C10311yescharacteristic
533C2×C42C23×C10311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—22no—
537#103—22no—
538#103—22no—
539#103—41no—
540#103D4×C10314yescomplemented
541#102—22no—
542#102—22no—
543#102—22no—
544#102—41no—
545#97—22no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95D4×C10311yescharacteristic
550#95D4×C10311yescharacteristic
551C24—21no—
552C24—21no—
553C24—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8C2×D4×C10312yes—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
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—21no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4C2×D4×C10312yes—
589C2×D4C2×D4×C10312yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4C2×D4×C10311yescharacteristic
602C22×C4C2×D4×C10311yescharacteristic
603C22×C4C2×D4×C10311yescharacteristic
604C22×C4C2×D4×C10311yescharacteristic
605C22×C4C2×D4×C10311yescharacteristic
606C22×C4C2×D4×C10311yescharacteristic
607C22×C4C24×C10311yescharacteristic
608SD16—44no—
609SD16—44no—
610SD16—44no—
611SD16—44no—
612D8—44no—
613D8—44no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8C2×D4×C10312yes—
625C2×C8#41×C10312yes—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—41no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C10312yes—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—42no—
654C42—42no—
655C42C2×D4×C10312yes—
656C42#41×C10312yes—
657C23—22no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23C22×D4×C10311yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687D4—22no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—48no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4#121×C10312yes—
734C2×C4#121×C10312yes—
735C2×C4AGL(1,ℤ/8)×C10312yes—
736C2×C4C22×D4×C10311yescharacteristic
737C2×C4C22×D4×C10311yescharacteristic
738C2×C4C2×#41×C10311yescharacteristic
739C2×C4C2×#41×C10311yescharacteristic
740C2×C4H(5,𝔽2)×C10311yescharacteristic
741C2×C4H(5,𝔽2)×C10311yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C10311yescharacteristic
768C22D42×C10311yescharacteristic
769C22#550×C10311yescharacteristic
770C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
771C22#575×C10311yescharacteristic
772C22#577×C10311yescharacteristic
773C22#577×C10311yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4#532×C10311yescharacteristic
786C4#540×C10311yescharacteristic
787C4D42×C10311yescharacteristic
788C4#546×C10311yescharacteristic
789C2—82no—
790C2—82no—
791C2—161no—
792C2C103×#242811yescharacteristic
793C2C103×#303611yescharacteristic
794C2C103×#304211yescharacteristic
795C2C103×#326511yescharacteristic
796C2C103×#327111yescharacteristic
797C2C103×#339711yescharacteristic
798C2C103×#340111yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#496×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
2. C2×#460×C103C2semidirect
3. C2×#463×C103C2semidirect
4. C2×#461×C103C2semidirect
5. C103×#2545C2semidirect
6. C103×#2366C2semidirect
7. C103×#2055C2semidirect
8. C103×#2054C2semidirect
9. C103×#2013C2semidirect
10. C103×#2012C2semidirect
11. C103×#1983C2semidirect
12. C103×#1940C2semidirect
13. C103×#1879C2semidirect
14. C103×#1877C2semidirect
15. C103×#1763C2semidirect
140. #103×C103D4semidirect
389. #25378C103direct (N × H)
401. C2×#460C2×C103semidirect
402. C2×#463C2×C103semidirect
403. C2×#461C2×C103semidirect
404. #2545C2×C103semidirect
405. #2366C2×C103semidirect
406. #2055C2×C103semidirect
407. #2054C2×C103semidirect
408. #2013C2×C103semidirect
409. #2012C2×C103semidirect
410. #1983C2×C103semidirect
411. #1940C2×C103semidirect
412. #1879C2×C103semidirect
413. #1877C2×C103semidirect
414. #1763C2×C103semidirect
415. C103#25378direct (N × H)
540. #103D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C1032
C2×#460×C1032
C2×#463×C1032
C2×#461×C1032
C103×#25452
C103×#23662
C103×#20552
C103×#20542
C103×#20132
C103×#20122
C103×#19832
C103×#19402
C103×#18792
C103×#18772
C103×#17632
#25378103