Finite Group Databasebeta

← C103×#26954 #39932229

Subgroups — C103×#26954 #39932229

Order 26368.

1026 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C103C211yesmaximal, characteristic, complemented
2C2×#459×C103C211yesmaximal, characteristic, complemented
3C103×#2428C211yesmaximal, characteristic, complemented
4C103×#2363C211yesmaximal, characteristic, complemented
5C103×#2088C211yesmaximal, characteristic, complemented
6C103×#2041C211yesmaximal, characteristic, complemented
7C103×#1999C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1972C211yesmaximal, characteristic, complemented
10C103×#1925C211yesmaximal, characteristic, complemented
11C103×#1924C211yesmaximal, characteristic, complemented
12C103×#1879C211yesmaximal, characteristic, complemented
13C103×#1875C211yesmaximal, characteristic, complemented
14C103×#1862C211yesmaximal, characteristic, complemented
15C103×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C2×#127×C103C2211yescharacteristic
19C2×#121×C103—21no—
20C2×#121×C103C2211yescharacteristic
21C2×#121×C103C2211yescharacteristic
22C2×#121×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24C2×C4×D4×C103C2211yescharacteristic
25C2×#117×C103C2211yescharacteristic
26#482×C103—24no—
27#459×C103—24no—
28C2×#107×C103C2211yescharacteristic
29C2×#106×C103C2211yescharacteristic
30C2×C4⋊C8×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×C22⋊C8×C103C2211yescharacteristic
41C2×#97×C103C2211yescharacteristic
42#394×C103—21no—
43#392×C103—21no—
44#390×C103—21no—
45#390×C103C2211yescharacteristic
46#390×C103C2211yescharacteristic
47#389×C103C2211yescharacteristic
48#389×C103C2211yescharacteristic
49#388×C103—21no—
50#386×C103—21no—
51#386×C103—21no—
52C4×C4⋊C4×C103C2211yescharacteristic
53C4×C22⋊C4×C103—21no—
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—41no—
77C2×D8×C103—41no—
78C22×C8×C103C2311yescharacteristic
79C22×C8×C103C2311yescharacteristic
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82#127×C103—22no—
83#127×C103—41no—
84#121×C103—22no—
85#121×C103—22no—
86#121×C103—22no—
87#121×C103—22no—
88#121×C103—44no—
89#121×C103—41no—
90#121×C103—41no—
91C4×D4×C103—22no—
92C4×D4×C103—22no—
93C4×D4×C103—41no—
94C4×D4×C103—41no—
95#117×C103—22no—
96#117×C103—41no—
97C2×C4⋊C4×C103—21no—
98C2×C4⋊C4×C103—21no—
99C2×C4⋊C4×C103C2311yescharacteristic
100C2×C4⋊C4×C103C2311yescharacteristic
101C2×C4⋊C4×C103C2311yescharacteristic
102C2×C4⋊C4×C103C2311yescharacteristic
103C2×C4⋊C4×C103C2311yescharacteristic
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×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C22⋊C4×C103D411yescharacteristic
115C2×C22⋊C4×C103D411yescharacteristic
116C2×C42×C103—21no—
117C2×C42×C103—21no—
118C2×C42×C103C2311yescharacteristic
119C2×C42×C103C2311yescharacteristic
120#107×C103—22no—
121#106×C103—22no—
122C4⋊C8×C103—22no—
123#102×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×C103D414yescomplemented
131C22⋊C8×C103—22no—
132C22⋊C8×C103—41no—
133#97×C103—41no—
134#95×C103—21no—
135#95×C103—21no—
136#95×C103—21no—
137#95×C103D411yescharacteristic
138#95×C103D411yescharacteristic
139C24×C103—21no—
140C24×C103—21no—
141C24×C103—21no—
142C24×C103C2×D411yescharacteristic
143C2×D4×C103—24no—
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—81no—
169C2×D4×C103—81no—
170C2×D4×C103—81no—
171C2×D4×C103—81no—
172C2×D4×C103—81no—
173C2×D4×C103—81no—
174C2×D4×C103C2×D412yes—
175C2×D4×C103#4112yes—
176C22×C4×C103—21no—
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—42no—
188C22×C4×C103—42no—
189C22×C4×C103—42no—
190C22×C4×C103—42no—
191C22×C4×C103—81no—
192C22×C4×C103—81no—
193C22×C4×C103C2×D411yescharacteristic
194C22×C4×C103C2×D411yescharacteristic
195C22×C4×C103C2×D411yescharacteristic
196C22×C4×C103C2×D411yescharacteristic
197C22×C4×C103C2×D411yescharacteristic
198C22×C4×C103C2411yescharacteristic
199D8×C103—44no—
200D8×C103—44no—
201C2×C8×C103—21no—
202C2×C8×C103—21no—
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—
213C4⋊C4×C103—21no—
214C4⋊C4×C103—21no—
215C4⋊C4×C103—21no—
216C4⋊C4×C103—21no—
217C4⋊C4×C103—21no—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—42no—
221C4⋊C4×C103—81no—
222C4⋊C4×C103C2×D412yes—
223C4⋊C4×C103#4112yes—
224C4⋊C4×C103#4112yes—
225C22⋊C4×C103—24no—
226C22⋊C4×C103—22no—
227C22⋊C4×C103—41no—
228C22⋊C4×C103—42no—
229C22⋊C4×C103—42no—
230C22⋊C4×C103—42no—
231C22⋊C4×C103—42no—
232C22⋊C4×C103—42no—
233C22⋊C4×C103—42no—
234C22⋊C4×C103—42no—
235C22⋊C4×C103—81no—
236C22⋊C4×C103—81no—
237C42×C103—21no—
238C42×C103—21no—
239C42×C103—21no—
240C42×C103—21no—
241C42×C103—42no—
242C42×C103—81no—
243C23×C103—22no—
244C23×C103—21no—
245C23×C103—21no—
246C23×C103—22no—
247C23×C103—21no—
248C23×C103—21no—
249C23×C103—21no—
250C23×C103—21no—
251C23×C103—21no—
252C23×C103—41no—
253C23×C103—41no—
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×C103C22×D411yescharacteristic
272D4×C103—22no—
273D4×C103—22no—
274D4×C103—22no—
275D4×C103—22no—
276D4×C103—41no—
277D4×C103—41no—
278D4×C103—41no—
279D4×C103—41no—
280D4×C103—41no—
281D4×C103—41no—
282D4×C103—41no—
283D4×C103—41no—
284D4×C103—84no—
285D4×C103—84no—
286D4×C103—84no—
287D4×C103—84no—
288D4×C103—84no—
289C2×C4×C103—21no—
290C2×C4×C103—21no—
291C2×C4×C103—21no—
292C2×C4×C103—22no—
293C2×C4×C103—21no—
294C2×C4×C103—21no—
295C2×C4×C103—22no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—22no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—21no—
305C2×C4×C103—21no—
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—84no—
323C2×C4×C103—84no—
324C2×C4×C103AGL(1,ℤ/8)12yes—
325C2×C4×C103C22×D411yescharacteristic
326C2×C4×C103C2×#4111yescharacteristic
327C2×C4×C103C2×#4111yescharacteristic
328C2×C4×C103C2×#4111yescharacteristic
329C2×C4×C103H(5,𝔽2)11yescharacteristic
330C2×C4×C103H(5,𝔽2)11yescharacteristic
331C8×C103—22no—
332C8×C103—41no—
333C8×C103—41no—
334C8×C103—41no—
335C22×C103—41no—
336C22×C103—42no—
337C22×C103—41no—
338C22×C103—42no—
339C22×C103—41no—
340C22×C103—42no—
341C22×C103—42no—
342C22×C103—41no—
343C22×C103—42no—
344C22×C103—42no—
345C22×C103—41no—
346C22×C103—41no—
347C22×C103—41no—
348C22×C103—81no—
349C22×C103—81no—
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#52511yescharacteristic
364C22×C103D4211yescharacteristic
365C22×C103#54611yescharacteristic
366C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C103#57511yescharacteristic
368C22×C103#57611yescharacteristic
369C22×C103#57611yescharacteristic
370C4×C103—22no—
371C4×C103—42no—
372C4×C103—41no—
373C4×C103—42no—
374C4×C103—41no—
375C4×C103—41no—
376C4×C103—41no—
377C4×C103—42no—
378C4×C103—81no—
379C4×C103—81no—
380C4×C103#53211yescharacteristic
381C4×C103#54011yescharacteristic
382C4×C103#54611yescharacteristic
383C4×C103#55311yescharacteristic
384#26954C10311yesmaximal, characteristic, direct product factor, Sylow
385C2×C103—81no—
386C2×C103—82no—
387C2×C103—82no—
388C2×C103—161no—
389C2×C103#246411yescharacteristic
390C2×C103#311511yescharacteristic
391C2×C103#312211yescharacteristic
392C2×C103#326411yescharacteristic
393C2×C103#326811yescharacteristic
394C2×C103#330911yescharacteristic
395C2×C103#332511yescharacteristic
396C2×#482C2×C10311yescharacteristic, complemented
397C2×#459C2×C10311yescharacteristic, complemented
398#2428C2×C10311yescharacteristic, complemented
399#2363C2×C10311yescharacteristic, complemented
400#2088C2×C10311yescharacteristic, complemented
401#2041C2×C10311yescharacteristic, complemented
402#1999C2×C10311yescharacteristic, complemented
403#1999C2×C10311yescharacteristic, complemented
404#1972C2×C10311yescharacteristic, complemented
405#1925C2×C10311yescharacteristic, complemented
406#1924C2×C10311yescharacteristic, complemented
407#1879C2×C10311yescharacteristic, complemented
408#1875C2×C10311yescharacteristic, complemented
409#1862C2×C10311yescharacteristic, complemented
410#1762C2×C10311yescharacteristic, complemented
411C103#2695411yescharacteristic, direct product factor, Sylow
412C22×D8C22×C10311yescharacteristic
413C22×D8C22×C10311yescharacteristic
414C2×#127C22×C10311yescharacteristic
415C2×#121—21no—
416C2×#121C22×C10311yescharacteristic
417C2×#121C22×C10311yescharacteristic
418C2×#121C22×C10311yescharacteristic
419C2×C4×D4C22×C10311yescharacteristic
420C2×C4×D4C22×C10311yescharacteristic
421C2×#117C22×C10311yescharacteristic
422#482—24no—
423#459—24no—
424C2×#107C22×C10311yescharacteristic
425C2×#106C22×C10311yescharacteristic
426C2×C4⋊C8C22×C10311yescharacteristic
427C2×#102C22×C10311yescharacteristic
428C2×#102C22×C10311yescharacteristic
429C2×#102C22×C10311yescharacteristic
430C2×#102C22×C10311yescharacteristic
431C2×#102C22×C10311yescharacteristic
432C2×#102C22×C10311yescharacteristic
433C2×#102C22×C10311yescharacteristic
434C2×#102C22×C10311yescharacteristic
435C2×C22⋊C8C22×C10311yescharacteristic
436C2×C22⋊C8C22×C10311yescharacteristic
437C2×#97C22×C10311yescharacteristic
438#394—21no—
439#392—21no—
440#390—21no—
441#390C22×C10311yescharacteristic
442#390C22×C10311yescharacteristic
443#389C22×C10311yescharacteristic
444#389C22×C10311yescharacteristic
445#388—21no—
446#386—21no—
447#386—21no—
448C4×C4⋊C4C22×C10311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C10311yescharacteristic
451#340C22×C10311yescharacteristic
452#340C22×C10311yescharacteristic
453#340C22×C10311yescharacteristic
454#340C22×C10311yescharacteristic
455#336C22×C10311yescharacteristic
456#336C22×C10311yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C10311yescharacteristic
463C22×D4C23×C10311yescharacteristic
464C22×D4C23×C10311yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C10311yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C10311yescharacteristic
475C22×C8C23×C10311yescharacteristic
476C22×C8C23×C10311yescharacteristic
477C22×C8C23×C10311yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C10311yescharacteristic
496C2×C4⋊C4C23×C10311yescharacteristic
497C2×C4⋊C4C23×C10311yescharacteristic
498C2×C4⋊C4C23×C10311yescharacteristic
499C2×C4⋊C4C23×C10311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C10311yescharacteristic
511C2×C22⋊C4D4×C10311yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C23×C10311yescharacteristic
515C2×C42C23×C10311yescharacteristic
516#107—22no—
517#106—22no—
518C4⋊C8—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—41no—
525#102—41no—
526#102D4×C10314yescomplemented
527C22⋊C8—22no—
528C22⋊C8—41no—
529#97—41no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C10311yescharacteristic
534#95D4×C10311yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C10311yescharacteristic
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
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—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4C2×D4×C10312yes—
571C2×D4#41×C10312yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
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—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C10311yescharacteristic
590C22×C4C2×D4×C10311yescharacteristic
591C22×C4C2×D4×C10311yescharacteristic
592C22×C4C2×D4×C10311yescharacteristic
593C22×C4C2×D4×C10311yescharacteristic
594C22×C4C24×C10311yescharacteristic
595D8—44no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8C2×D4×C10312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C10312yes—
619C4⋊C4#41×C10312yes—
620C4⋊C4#41×C10312yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
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—
667C23C22×D4×C10311yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
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—84no—
719C2×C4—84no—
720C2×C4AGL(1,ℤ/8)×C10312yes—
721C2×C4C22×D4×C10311yescharacteristic
722C2×C4C2×#41×C10311yescharacteristic
723C2×C4C2×#41×C10311yescharacteristic
724C2×C4C2×#41×C10311yescharacteristic
725C2×C4H(5,𝔽2)×C10311yescharacteristic
726C2×C4H(5,𝔽2)×C10311yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22#525×C10311yescharacteristic
760C22D42×C10311yescharacteristic
761C22#546×C10311yescharacteristic
762C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
763C22#575×C10311yescharacteristic
764C22#576×C10311yescharacteristic
765C22#576×C10311yescharacteristic
766C4—22no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—42no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4#532×C10311yescharacteristic
777C4#540×C10311yescharacteristic
778C4#546×C10311yescharacteristic
779C4#553×C10311yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C103×#246411yescharacteristic
785C2C103×#311511yescharacteristic
786C2C103×#312211yescharacteristic
787C2C103×#326411yescharacteristic
788C2C103×#326811yescharacteristic
789C2C103×#330911yescharacteristic
790C2C103×#332511yescharacteristic
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×#482×C103C2semidirect
2. C2×#459×C103C2semidirect
3. C103×#2428C2semidirect
4. C103×#2363C2semidirect
5. C103×#2088C2semidirect
6. C103×#2041C2semidirect
7. C103×#1999C2semidirect
8. C103×#1999C2semidirect
9. C103×#1972C2semidirect
10. C103×#1925C2semidirect
11. C103×#1924C2semidirect
12. C103×#1879C2semidirect
13. C103×#1875C2semidirect
14. C103×#1862C2semidirect
15. C103×#1762C2semidirect
130. #102×C103D4semidirect
384. #26954C103direct (N × H)
396. C2×#482C2×C103semidirect
397. C2×#459C2×C103semidirect
398. #2428C2×C103semidirect
399. #2363C2×C103semidirect
400. #2088C2×C103semidirect
401. #2041C2×C103semidirect
402. #1999C2×C103semidirect
403. #1999C2×C103semidirect
404. #1972C2×C103semidirect
405. #1925C2×C103semidirect
406. #1924C2×C103semidirect
407. #1879C2×C103semidirect
408. #1875C2×C103semidirect
409. #1862C2×C103semidirect
410. #1762C2×C103semidirect
411. C103#26954direct (N × H)
526. #102D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1032
C2×#459×C1032
C103×#24282
C103×#23632
C103×#20882
C103×#20412
C103×#19992
C103×#19722
C103×#19252
C103×#19242
C103×#18792
C103×#18752
C103×#18622
C103×#17622
#26954103