Finite Group Databasebeta

← C103×#26984 #39932259

Subgroups — C103×#26984 #39932259

Order 26368.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C103C211yesmaximal, characteristic, complemented
2C2×#442×C103C211yesmaximal, characteristic, complemented
3C103×#2428C211yesmaximal, characteristic, complemented
4C103×#2422C211yesmaximal, characteristic, complemented
5C103×#2084C211yesmaximal, characteristic, complemented
6C103×#2034C211yesmaximal, characteristic, complemented
7C103×#2011C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1957C211yesmaximal, characteristic, complemented
10C103×#1936C211yesmaximal, characteristic, complemented
11C103×#1934C211yesmaximal, characteristic, complemented
12C103×#1895C211yesmaximal, characteristic, complemented
13C103×#1879C211yesmaximal, characteristic, complemented
14C103×#1864C211yesmaximal, characteristic, complemented
15C103×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C2×#127×C103C2211yescharacteristic
20C2×#123×C103—21no—
21C2×#121×C103—21no—
22C2×#121×C103C2211yescharacteristic
23C2×#121×C103C2211yescharacteristic
24C2×#121×C103C2211yescharacteristic
25C2×C4×D4×C103C2211yescharacteristic
26C2×C4×D4×C103C2211yescharacteristic
27#469×C103—24no—
28#442×C103—24no—
29C2×#106×C103C2211yescharacteristic
30C2×#106×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×#102×C103C2211yescharacteristic
35C2×#102×C103C2211yescharacteristic
36C2×#102×C103C2211yescharacteristic
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×C22⋊C8×C103C2211yescharacteristic
40C2×#97×C103C2211yescharacteristic
41C2×C4×C8×C103C2211yescharacteristic
42#397×C103—21no—
43#394×C103—21no—
44#394×C103—21no—
45#392×C103—21no—
46#390×C103C2211yescharacteristic
47#390×C103C2211yescharacteristic
48#389×C103C2211yescharacteristic
49#389×C103C2211yescharacteristic
50#386×C103—21no—
51#385×C103—21no—
52#384×C103C2211yescharacteristic
53#380×C103C2211yescharacteristic
54C4×C22⋊C4×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×C103—21no—
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103C2311yescharacteristic
67C22×D4×C103C2311yescharacteristic
68C22×D4×C103C2311yescharacteristic
69C23×C4×C103—21no—
70C23×C4×C103—21no—
71C23×C4×C103C2311yescharacteristic
72C2×D8×C103—22no—
73C2×D8×C103—22no—
74C2×D8×C103—22no—
75C2×D8×C103—22no—
76C2×D8×C103—22no—
77C2×D8×C103—41no—
78C2×M16×C103—22no—
79C2×M16×C103—22no—
80C2×M16×C103—41no—
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85#127×C103—22no—
86#127×C103—41no—
87#123×C103—44no—
88#121×C103—22no—
89#121×C103—22no—
90#121×C103—22no—
91#121×C103—44no—
92#121×C103—41no—
93#121×C103—41no—
94#121×C103—41no—
95C4×D4×C103—22no—
96C4×D4×C103—22no—
97C4×D4×C103—41no—
98C4×D4×C103—41no—
99C2×C4⋊C4×C103—21no—
100C2×C4⋊C4×C103—21no—
101C2×C4⋊C4×C103—21no—
102C2×C4⋊C4×C103—21no—
103C2×C4⋊C4×C103C2311yescharacteristic
104C2×C4⋊C4×C103C2311yescharacteristic
105C2×C4⋊C4×C103C2311yescharacteristic
106C2×C4⋊C4×C103C2311yescharacteristic
107C2×C4⋊C4×C103C2311yescharacteristic
108C2×C22⋊C4×C103—21no—
109C2×C22⋊C4×C103—21no—
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103—21no—
112C2×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—21no—
116C2×C22⋊C4×C103—21no—
117C2×C22⋊C4×C103—21no—
118C2×C22⋊C4×C103D411yescharacteristic
119C2×C22⋊C4×C103D411yescharacteristic
120C2×C42×C103C2311yescharacteristic
121C2×C42×C103C2311yescharacteristic
122#106×C103—22no—
123#106×C103—22no—
124#102×C103—22no—
125#102×C103—22no—
126#102×C103—22no—
127#102×C103—22no—
128#102×C103—41no—
129#102×C103—41no—
130#102×C103—41no—
131#102×C103D414yescomplemented
132C22⋊C8×C103—22no—
133#97×C103—22no—
134C4×C8×C103—41no—
135#95×C103—21no—
136#95×C103—21no—
137#95×C103—21no—
138#95×C103D411yescharacteristic
139#95×C103D411yescharacteristic
140C24×C103—21no—
141C24×C103—21no—
142C24×C103—21no—
143C24×C103C2×D411yescharacteristic
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—21no—
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—42no—
161C2×D4×C103—42no—
162C2×D4×C103—42no—
163C2×D4×C103—42no—
164C2×D4×C103—42no—
165C2×D4×C103—42no—
166C2×D4×C103—42no—
167C2×D4×C103—42no—
168C2×D4×C103—42no—
169C2×D4×C103—42no—
170C2×D4×C103—81no—
171C2×D4×C103—81no—
172C2×D4×C103—81no—
173C2×D4×C103—81no—
174C2×D4×C103—81no—
175C2×D4×C103C2×D412yes—
176C2×D4×C103#4112yes—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—42no—
189C22×C4×C103—42no—
190C22×C4×C103—42no—
191C22×C4×C103—42no—
192C22×C4×C103—81no—
193C22×C4×C103—81no—
194C22×C4×C103C2×D411yescharacteristic
195C22×C4×C103C2×D411yescharacteristic
196C22×C4×C103C2×D411yescharacteristic
197C22×C4×C103C2×D411yescharacteristic
198C22×C4×C103C2×D411yescharacteristic
199C22×C4×C103C2411yescharacteristic
200D8×C103—28no—
201D8×C103—44no—
202M16×C103—44no—
203C2×C8×C103—21no—
204C2×C8×C103—21no—
205C2×C8×C103—21no—
206C2×C8×C103—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103C2×D412yes—
213C2×C8×C103#4112yes—
214C2×C8×C103#4112yes—
215C4⋊C4×C103—21no—
216C4⋊C4×C103—21no—
217C4⋊C4×C103—21no—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103—42no—
225C4⋊C4×C103—42no—
226C4⋊C4×C103—42no—
227C4⋊C4×C103—81no—
228C4⋊C4×C103C2×D412yes—
229C22⋊C4×C103—22no—
230C22⋊C4×C103—22no—
231C22⋊C4×C103—42no—
232C22⋊C4×C103—42no—
233C22⋊C4×C103—42no—
234C22⋊C4×C103—42no—
235C22⋊C4×C103—42no—
236C22⋊C4×C103—42no—
237C22⋊C4×C103—42no—
238C22⋊C4×C103—42no—
239C22⋊C4×C103—42no—
240C22⋊C4×C103—81no—
241C42×C103—21no—
242C42×C103—21no—
243C42×C103—21no—
244C42×C103—21no—
245C23×C103—21no—
246C23×C103—22no—
247C23×C103—21no—
248C23×C103—22no—
249C23×C103—21no—
250C23×C103—21no—
251C23×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103—41no—
255C23×C103—41no—
256C23×C103—41no—
257C23×C103—41no—
258C23×C103—41no—
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×C103C22×D411yescharacteristic
274D4×C103—22no—
275D4×C103—22no—
276D4×C103—22no—
277D4×C103—22no—
278D4×C103—41no—
279D4×C103—41no—
280D4×C103—41no—
281D4×C103—41no—
282D4×C103—41no—
283D4×C103—41no—
284D4×C103—41no—
285D4×C103—41no—
286D4×C103—84no—
287D4×C103—84no—
288D4×C103—84no—
289D4×C103—84no—
290D4×C103—84no—
291C2×C4×C103—21no—
292C2×C4×C103—21no—
293C2×C4×C103—21no—
294C2×C4×C103—21no—
295C2×C4×C103—21no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—21no—
299C2×C4×C103—22no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—21no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103—41no—
309C2×C4×C103—41no—
310C2×C4×C103—41no—
311C2×C4×C103—41no—
312C2×C4×C103—41no—
313C2×C4×C103—41no—
314C2×C4×C103—41no—
315C2×C4×C103—41no—
316C2×C4×C103—41no—
317C2×C4×C103—41no—
318C2×C4×C103—41no—
319C2×C4×C103—41no—
320C2×C4×C103—41no—
321C2×C4×C103—41no—
322C2×C4×C103—41no—
323C2×C4×C103—84no—
324C2×C4×C103—84no—
325C2×C4×C103AGL(1,ℤ/8)12yes—
326C2×C4×C103AGL(1,ℤ/8)12yes—
327C2×C4×C103C22×D411yescharacteristic
328C2×C4×C103C2×#4111yescharacteristic
329C2×C4×C103C2×#4111yescharacteristic
330C2×C4×C103C2×#4111yescharacteristic
331C2×C4×C103H(5,𝔽2)11yescharacteristic
332C2×C4×C103H(5,𝔽2)11yescharacteristic
333C8×C103—22no—
334C8×C103—22no—
335C8×C103—22no—
336C8×C103—41no—
337C22×C103—41no—
338C22×C103—41no—
339C22×C103—41no—
340C22×C103—42no—
341C22×C103—42no—
342C22×C103—41no—
343C22×C103—42no—
344C22×C103—42no—
345C22×C103—41no—
346C22×C103—42no—
347C22×C103—41no—
348C22×C103—41no—
349C22×C103—42no—
350C22×C103—81no—
351C22×C103—81no—
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#53211yescharacteristic
366C22×C103D4211yescharacteristic
367C22×C103#54611yescharacteristic
368C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C103#57611yescharacteristic
371C22×C103#57711yescharacteristic
372C4×C103—22no—
373C4×C103—22no—
374C4×C103—41no—
375C4×C103—41no—
376C4×C103—42no—
377C4×C103—41no—
378C4×C103—81no—
379C4×C103—81no—
380C4×C103—81no—
381C4×C103—81no—
382C4×C103#52511yescharacteristic
383C4×C103#54011yescharacteristic
384C4×C103#54611yescharacteristic
385C4×C103#55311yescharacteristic
386#26984C10311yesmaximal, characteristic, direct product factor, Sylow
387C2×C103—81no—
388C2×C103—82no—
389C2×C103—82no—
390C2×C103—161no—
391C2×C103#246411yescharacteristic
392C2×C103#317911yescharacteristic
393C2×C103#318411yescharacteristic
394C2×C103#327211yescharacteristic
395C2×C103#327411yescharacteristic
396C2×C103#330611yescharacteristic
397C2×C103#331811yescharacteristic
398C2×#469C2×C10311yescharacteristic, complemented
399C2×#442C2×C10311yescharacteristic, complemented
400#2428C2×C10311yescharacteristic, complemented
401#2422C2×C10311yescharacteristic, complemented
402#2084C2×C10311yescharacteristic, complemented
403#2034C2×C10311yescharacteristic, complemented
404#2011C2×C10311yescharacteristic, complemented
405#1999C2×C10311yescharacteristic, complemented
406#1957C2×C10311yescharacteristic, complemented
407#1936C2×C10311yescharacteristic, complemented
408#1934C2×C10311yescharacteristic, complemented
409#1895C2×C10311yescharacteristic, complemented
410#1879C2×C10311yescharacteristic, complemented
411#1864C2×C10311yescharacteristic, complemented
412#1753C2×C10311yescharacteristic, complemented
413C103#2698411yescharacteristic, direct product factor, Sylow
414C22×D8C22×C10311yescharacteristic
415C22×D8C22×C10311yescharacteristic
416C22×M16C22×C10311yescharacteristic
417C2×#127C22×C10311yescharacteristic
418C2×#123—21no—
419C2×#121—21no—
420C2×#121C22×C10311yescharacteristic
421C2×#121C22×C10311yescharacteristic
422C2×#121C22×C10311yescharacteristic
423C2×C4×D4C22×C10311yescharacteristic
424C2×C4×D4C22×C10311yescharacteristic
425#469—24no—
426#442—24no—
427C2×#106C22×C10311yescharacteristic
428C2×#106C22×C10311yescharacteristic
429C2×#102C22×C10311yescharacteristic
430C2×#102C22×C10311yescharacteristic
431C2×#102C22×C10311yescharacteristic
432C2×#102C22×C10311yescharacteristic
433C2×#102C22×C10311yescharacteristic
434C2×#102C22×C10311yescharacteristic
435C2×#102C22×C10311yescharacteristic
436C2×#102C22×C10311yescharacteristic
437C2×C22⋊C8C22×C10311yescharacteristic
438C2×#97C22×C10311yescharacteristic
439C2×C4×C8C22×C10311yescharacteristic
440#397—21no—
441#394—21no—
442#394—21no—
443#392—21no—
444#390C22×C10311yescharacteristic
445#390C22×C10311yescharacteristic
446#389C22×C10311yescharacteristic
447#389C22×C10311yescharacteristic
448#386—21no—
449#385—21no—
450#384C22×C10311yescharacteristic
451#380C22×C10311yescharacteristic
452C4×C22⋊C4C22×C10311yescharacteristic
453#340C22×C10311yescharacteristic
454#340C22×C10311yescharacteristic
455#340C22×C10311yescharacteristic
456#340C22×C10311yescharacteristic
457#336C22×C10311yescharacteristic
458#336C22×C10311yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C10311yescharacteristic
465C22×D4C23×C10311yescharacteristic
466C22×D4C23×C10311yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C10311yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C10311yescharacteristic
480C22×C8C23×C10311yescharacteristic
481C22×C8C23×C10311yescharacteristic
482C22×C8C23×C10311yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492#121—41no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C10311yescharacteristic
502C2×C4⋊C4C23×C10311yescharacteristic
503C2×C4⋊C4C23×C10311yescharacteristic
504C2×C4⋊C4C23×C10311yescharacteristic
505C2×C4⋊C4C23×C10311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C10311yescharacteristic
517C2×C22⋊C4D4×C10311yescharacteristic
518C2×C42C23×C10311yescharacteristic
519C2×C42C23×C10311yescharacteristic
520#106—22no—
521#106—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C10314yescomplemented
530C22⋊C8—22no—
531#97—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C10311yescharacteristic
537#95D4×C10311yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C10311yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C10312yes—
574C2×D4#41×C10312yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C10311yescharacteristic
593C22×C4C2×D4×C10311yescharacteristic
594C22×C4C2×D4×C10311yescharacteristic
595C22×C4C2×D4×C10311yescharacteristic
596C22×C4C2×D4×C10311yescharacteristic
597C22×C4C24×C10311yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C10312yes—
611C2×C8#41×C10312yes—
612C2×C8#41×C10312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C10312yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C10311yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4AGL(1,ℤ/8)×C10312yes—
724C2×C4AGL(1,ℤ/8)×C10312yes—
725C2×C4C22×D4×C10311yescharacteristic
726C2×C4C2×#41×C10311yescharacteristic
727C2×C4C2×#41×C10311yescharacteristic
728C2×C4C2×#41×C10311yescharacteristic
729C2×C4H(5,𝔽2)×C10311yescharacteristic
730C2×C4H(5,𝔽2)×C10311yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—41no—
739C22—42no—
740C22—42no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22#532×C10311yescharacteristic
764C22D42×C10311yescharacteristic
765C22#546×C10311yescharacteristic
766C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
767C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
768C22#576×C10311yescharacteristic
769C22#577×C10311yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4#525×C10311yescharacteristic
781C4#540×C10311yescharacteristic
782C4#546×C10311yescharacteristic
783C4#553×C10311yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C103×#246411yescharacteristic
789C2C103×#317911yescharacteristic
790C2C103×#318411yescharacteristic
791C2C103×#327211yescharacteristic
792C2C103×#327411yescharacteristic
793C2C103×#330611yescharacteristic
794C2C103×#331811yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#469×C103C2semidirect
2. C2×#442×C103C2semidirect
3. C103×#2428C2semidirect
4. C103×#2422C2semidirect
5. C103×#2084C2semidirect
6. C103×#2034C2semidirect
7. C103×#2011C2semidirect
8. C103×#1999C2semidirect
9. C103×#1957C2semidirect
10. C103×#1936C2semidirect
11. C103×#1934C2semidirect
12. C103×#1895C2semidirect
13. C103×#1879C2semidirect
14. C103×#1864C2semidirect
15. C103×#1753C2semidirect
131. #102×C103D4semidirect
386. #26984C103direct (N × H)
398. C2×#469C2×C103semidirect
399. C2×#442C2×C103semidirect
400. #2428C2×C103semidirect
401. #2422C2×C103semidirect
402. #2084C2×C103semidirect
403. #2034C2×C103semidirect
404. #2011C2×C103semidirect
405. #1999C2×C103semidirect
406. #1957C2×C103semidirect
407. #1936C2×C103semidirect
408. #1934C2×C103semidirect
409. #1895C2×C103semidirect
410. #1879C2×C103semidirect
411. #1864C2×C103semidirect
412. #1753C2×C103semidirect
413. C103#26984direct (N × H)
529. #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×#442×C1032
C103×#24282
C103×#24222
C103×#20842
C103×#20342
C103×#20112
C103×#19992
C103×#19572
C103×#19362
C103×#19342
C103×#18952
C103×#18792
C103×#18642
C103×#17532
#26984103