Finite Group Databasebeta

← C103×#26977 #39932252

Subgroups — C103×#26977 #39932252

Order 26368.

1028 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C103C211yesmaximal, characteristic, complemented
2C2×#442×C103C211yesmaximal, characteristic, complemented
3C103×#2428C211yesmaximal, characteristic, complemented
4C103×#2420C211yesmaximal, characteristic, complemented
5C103×#2085C211yesmaximal, characteristic, complemented
6C103×#2034C211yesmaximal, characteristic, complemented
7C103×#2011C211yesmaximal, characteristic, complemented
8C103×#1999C211yesmaximal, characteristic, complemented
9C103×#1961C211yesmaximal, characteristic, complemented
10C103×#1936C211yesmaximal, characteristic, complemented
11C103×#1936C211yesmaximal, characteristic, complemented
12C103×#1893C211yesmaximal, characteristic, complemented
13C103×#1879C211yesmaximal, characteristic, complemented
14C103×#1862C211yesmaximal, characteristic, complemented
15C103×#1752C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C23×C8×C103C2211yescharacteristic
19C2×#127×C103C2211yescharacteristic
20C2×#121×C103—21no—
21C2×#121×C103C2211yescharacteristic
22C2×#121×C103C2211yescharacteristic
23C2×#121×C103C2211yescharacteristic
24C2×C4×D4×C103C2211yescharacteristic
25C2×C4×D4×C103C2211yescharacteristic
26#466×C103—24no—
27#442×C103—24no—
28C2×#107×C103C2211yescharacteristic
29C2×#106×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×#102×C103C2211yescharacteristic
35C2×#102×C103C2211yescharacteristic
36C2×#102×C103C2211yescharacteristic
37C2×#102×C103C2211yescharacteristic
38C2×C22⋊C8×C103C2211yescharacteristic
39C2×#97×C103C2211yescharacteristic
40C2×#97×C103C2211yescharacteristic
41#397×C103—21no—
42#394×C103—21no—
43#394×C103—21no—
44#392×C103—21no—
45#390×C103C2211yescharacteristic
46#390×C103C2211yescharacteristic
47#389×C103C2211yescharacteristic
48#389×C103C2211yescharacteristic
49#386×C103—21no—
50#386×C103—21no—
51#382×C103C2211yescharacteristic
52#381×C103—21no—
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—
78C22×C8×C103—22no—
79C22×C8×C103—22no—
80C22×C8×C103—41no—
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85#127×C103—22no—
86#127×C103—41no—
87#121×C103—22no—
88#121×C103—22no—
89#121×C103—22no—
90#121×C103—44no—
91#121×C103—41no—
92#121×C103—41no—
93#121×C103—41no—
94C4×D4×C103—22no—
95C4×D4×C103—22no—
96C4×D4×C103—41no—
97C4×D4×C103—41no—
98C2×C4⋊C4×C103—21no—
99C2×C4⋊C4×C103—21no—
100C2×C4⋊C4×C103C2311yescharacteristic
101C2×C4⋊C4×C103C2311yescharacteristic
102C2×C4⋊C4×C103C2311yescharacteristic
103C2×C4⋊C4×C103C2311yescharacteristic
104C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
115C2×C22⋊C4×C103D411yescharacteristic
116C2×C22⋊C4×C103D411yescharacteristic
117C2×C42×C103C2311yescharacteristic
118C2×C42×C103C2311yescharacteristic
119#107×C103—22no—
120#106×C103—22no—
121#102×C103—22no—
122#102×C103—22no—
123#102×C103—22no—
124#102×C103—22no—
125#102×C103—41no—
126#102×C103—41no—
127#102×C103—41no—
128#102×C103D414yescomplemented
129C22⋊C8×C103—22no—
130#97×C103—22no—
131#97×C103—41no—
132#95×C103—21no—
133#95×C103—21no—
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—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—21no—
154C2×D4×C103—21no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—42no—
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—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—28no—
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—44no—
211C2×C8×C103C2×D412yes—
212C2×C8×C103#4112yes—
213C2×C8×C103#4112yes—
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—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—42no—
224C4⋊C4×C103—81no—
225C4⋊C4×C103C2×D412yes—
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—81no—
235C22⋊C4×C103—81no—
236C22⋊C4×C103—81no—
237C22⋊C4×C103—81no—
238C42×C103—21no—
239C42×C103—21no—
240C42×C103—21no—
241C42×C103—21no—
242C23×C103—21no—
243C23×C103—21no—
244C23×C103—21no—
245C23×C103—21no—
246C23×C103—21no—
247C23×C103—21no—
248C23×C103—22no—
249C23×C103—22no—
250C23×C103—41no—
251C23×C103—41no—
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×C103AGL(1,ℤ/8)12yes—
270C23×C103C22×D411yescharacteristic
271D4×C103—22no—
272D4×C103—22no—
273D4×C103—22no—
274D4×C103—22no—
275D4×C103—41no—
276D4×C103—41no—
277D4×C103—41no—
278D4×C103—41no—
279D4×C103—41no—
280D4×C103—41no—
281D4×C103—41no—
282D4×C103—41no—
283D4×C103—84no—
284D4×C103—84no—
285D4×C103—84no—
286D4×C103—84no—
287D4×C103—84no—
288C2×C4×C103—21no—
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—21no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—21no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—41no—
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—84no—
323C2×C4×C103—84no—
324C2×C4×C103C22×D411yescharacteristic
325C2×C4×C103C2×#4111yescharacteristic
326C2×C4×C103C2×#4111yescharacteristic
327C2×C4×C103C2×#4111yescharacteristic
328C2×C4×C103H(5,𝔽2)11yescharacteristic
329C2×C4×C103H(5,𝔽2)11yescharacteristic
330C8×C103—22no—
331C8×C103—22no—
332C8×C103—22no—
333C8×C103—41no—
334C22×C103—22no—
335C22×C103—22no—
336C22×C103—22no—
337C22×C103—41no—
338C22×C103—41no—
339C22×C103—41no—
340C22×C103—41no—
341C22×C103—42no—
342C22×C103—42no—
343C22×C103—42no—
344C22×C103—42no—
345C22×C103—42no—
346C22×C103—42no—
347C22×C103—81no—
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#53211yescharacteristic
363C22×C103D4211yescharacteristic
364C22×C103#54611yescharacteristic
365C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C103#57511yescharacteristic
367C22×C103#57611yescharacteristic
368C22×C103#57611yescharacteristic
369C4×C103—41no—
370C4×C103—41no—
371C4×C103—42no—
372C4×C103—41no—
373C4×C103—41no—
374C4×C103—41no—
375C4×C103—81no—
376C4×C103—81no—
377C4×C103—81no—
378C4×C103—81no—
379C4×C103#52511yescharacteristic
380C4×C103#54011yescharacteristic
381C4×C103#54611yescharacteristic
382C4×C103#55311yescharacteristic
383#26977C10311yesmaximal, characteristic, direct product factor, Sylow
384C2×C103—42no—
385C2×C103—82no—
386C2×C103—82no—
387C2×C103—161no—
388C2×C103#246411yescharacteristic
389C2×C103#317611yescharacteristic
390C2×C103#318011yescharacteristic
391C2×C103#326411yescharacteristic
392C2×C103#326811yescharacteristic
393C2×C103#331811yescharacteristic
394C2×C103#331911yescharacteristic
395C2×#466C2×C10311yescharacteristic, complemented
396C2×#442C2×C10311yescharacteristic, complemented
397#2428C2×C10311yescharacteristic, complemented
398#2420C2×C10311yescharacteristic, complemented
399#2085C2×C10311yescharacteristic, complemented
400#2034C2×C10311yescharacteristic, complemented
401#2011C2×C10311yescharacteristic, complemented
402#1999C2×C10311yescharacteristic, complemented
403#1961C2×C10311yescharacteristic, complemented
404#1936C2×C10311yescharacteristic, complemented
405#1936C2×C10311yescharacteristic, complemented
406#1893C2×C10311yescharacteristic, complemented
407#1879C2×C10311yescharacteristic, complemented
408#1862C2×C10311yescharacteristic, complemented
409#1752C2×C10311yescharacteristic, complemented
410C103#2697711yescharacteristic, direct product factor, Sylow
411C22×D8C22×C10311yescharacteristic
412C22×D8C22×C10311yescharacteristic
413C23×C8C22×C10311yescharacteristic
414C2×#127C22×C10311yescharacteristic
415C2×#121—21no—
416C2×#121C22×C10311yescharacteristic
417C2×#121C22×C10311yescharacteristic
418C2×#121C22×C10311yescharacteristic
419C2×C4×D4C22×C10311yescharacteristic
420C2×C4×D4C22×C10311yescharacteristic
421#466—24no—
422#442—24no—
423C2×#107C22×C10311yescharacteristic
424C2×#106C22×C10311yescharacteristic
425C2×#102C22×C10311yescharacteristic
426C2×#102C22×C10311yescharacteristic
427C2×#102C22×C10311yescharacteristic
428C2×#102C22×C10311yescharacteristic
429C2×#102C22×C10311yescharacteristic
430C2×#102C22×C10311yescharacteristic
431C2×#102C22×C10311yescharacteristic
432C2×#102C22×C10311yescharacteristic
433C2×C22⋊C8C22×C10311yescharacteristic
434C2×#97C22×C10311yescharacteristic
435C2×#97C22×C10311yescharacteristic
436#397—21no—
437#394—21no—
438#394—21no—
439#392—21no—
440#390C22×C10311yescharacteristic
441#390C22×C10311yescharacteristic
442#389C22×C10311yescharacteristic
443#389C22×C10311yescharacteristic
444#386—21no—
445#386—21no—
446#382C22×C10311yescharacteristic
447#381—21no—
448#380C22×C10311yescharacteristic
449C4×C22⋊C4C22×C10311yescharacteristic
450#340C22×C10311yescharacteristic
451#340C22×C10311yescharacteristic
452#340C22×C10311yescharacteristic
453#340C22×C10311yescharacteristic
454#336C22×C10311yescharacteristic
455#336C22×C10311yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C23×C10311yescharacteristic
462C22×D4C23×C10311yescharacteristic
463C22×D4C23×C10311yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C23×C10311yescharacteristic
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8C23×C10311yescharacteristic
477C22×C8C23×C10311yescharacteristic
478C22×C8C23×C10311yescharacteristic
479C22×C8C23×C10311yescharacteristic
480#127—22no—
481#127—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—41no—
492C4×D4—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×C42C23×C10311yescharacteristic
513C2×C42C23×C10311yescharacteristic
514#107—22no—
515#106—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102D4×C10314yescomplemented
524C22⋊C8—22no—
525#97—22no—
526#97—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95D4×C10311yescharacteristic
533#95D4×C10311yescharacteristic
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C10311yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
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—42no—
555C2×D4—42no—
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×D4C2×D4×C10312yes—
570C2×D4#41×C10312yes—
571C22×C4—21no—
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—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×D4×C10311yescharacteristic
589C22×C4C2×D4×C10311yescharacteristic
590C22×C4C2×D4×C10311yescharacteristic
591C22×C4C2×D4×C10311yescharacteristic
592C22×C4C2×D4×C10311yescharacteristic
593C22×C4C24×C10311yescharacteristic
594D8—28no—
595D8—44no—
596C2×C8—21no—
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—44no—
606C2×C8C2×D4×C10312yes—
607C2×C8#41×C10312yes—
608C2×C8#41×C10312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4C2×D4×C10312yes—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
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—
664C23AGL(1,ℤ/8)×C10312yes—
665C23C22×D4×C10311yescharacteristic
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
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—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
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—84no—
718C2×C4—84no—
719C2×C4C22×D4×C10311yescharacteristic
720C2×C4C2×#41×C10311yescharacteristic
721C2×C4C2×#41×C10311yescharacteristic
722C2×C4C2×#41×C10311yescharacteristic
723C2×C4H(5,𝔽2)×C10311yescharacteristic
724C2×C4H(5,𝔽2)×C10311yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
743C22—81no—
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#532×C10311yescharacteristic
758C22D42×C10311yescharacteristic
759C22#546×C10311yescharacteristic
760C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
761C22#575×C10311yescharacteristic
762C22#576×C10311yescharacteristic
763C22#576×C10311yescharacteristic
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4#525×C10311yescharacteristic
775C4#540×C10311yescharacteristic
776C4#546×C10311yescharacteristic
777C4#553×C10311yescharacteristic
778C2—42no—
779C2—82no—
780C2—82no—
781C2—161no—
782C2C103×#246411yescharacteristic
783C2C103×#317611yescharacteristic
784C2C103×#318011yescharacteristic
785C2C103×#326411yescharacteristic
786C2C103×#326811yescharacteristic
787C2C103×#331811yescharacteristic
788C2C103×#331911yescharacteristic
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×#466×C103C2semidirect
2. C2×#442×C103C2semidirect
3. C103×#2428C2semidirect
4. C103×#2420C2semidirect
5. C103×#2085C2semidirect
6. C103×#2034C2semidirect
7. C103×#2011C2semidirect
8. C103×#1999C2semidirect
9. C103×#1961C2semidirect
10. C103×#1936C2semidirect
11. C103×#1936C2semidirect
12. C103×#1893C2semidirect
13. C103×#1879C2semidirect
14. C103×#1862C2semidirect
15. C103×#1752C2semidirect
128. #102×C103D4semidirect
383. #26977C103direct (N × H)
395. C2×#466C2×C103semidirect
396. C2×#442C2×C103semidirect
397. #2428C2×C103semidirect
398. #2420C2×C103semidirect
399. #2085C2×C103semidirect
400. #2034C2×C103semidirect
401. #2011C2×C103semidirect
402. #1999C2×C103semidirect
403. #1961C2×C103semidirect
404. #1936C2×C103semidirect
405. #1936C2×C103semidirect
406. #1893C2×C103semidirect
407. #1879C2×C103semidirect
408. #1862C2×C103semidirect
409. #1752C2×C103semidirect
410. C103#26977direct (N × H)
523. #102D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1032
C2×#442×C1032
C103×#24282
C103×#24202
C103×#20852
C103×#20342
C103×#20112
C103×#19992
C103×#19612
C103×#19362
C103×#18932
C103×#18792
C103×#18622
C103×#17522
#26977103