Finite Group Databasebeta

← C103×#25585 #39930860

Subgroups — C103×#25585 #39930860

Order 26368.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3505C211yesmaximal, characteristic, complemented
2C103×#2435C211yesmaximal, characteristic, complemented
3C103×#2433C211yesmaximal, characteristic, complemented
4C103×#2408C211yesmaximal, characteristic, complemented
5C103×#2021C214yesmaximal, complemented
6C103×#1996C211yesmaximal, characteristic, complemented
7C103×#1964C211yesmaximal, characteristic, complemented
8C103×#1889C214yesmaximal, complemented
9C4×#99×C103C211yesmaximal, characteristic, complemented
10C23×D4×C103C2211yescharacteristic
11#553×C103—21no—
12#553×C103—22no—
13#552×C103—21no—
14#551×C103—22no—
15#548×C103—21no—
16#546×C103—21no—
17#539×C103—21no—
18#538×C103—21no—
19#534×C103C2212yes—
20C2×#127×C103—21no—
21#529×C103—21no—
22C2×#124×C103—21no—
23#525×C103—21no—
24C2×C22⋊Q8×C103C2211yescharacteristic
25C2×#121×C103—21no—
26C2×#121×C103C2211yescharacteristic
27C2×#120×C103C2214yes—
28C2×#120×C103C2212yes—
29#518×C103C2212yes—
30C2×C4×D4×C103C2211yescharacteristic
31C2×#99×C103C2212yes—
32C2×#99×C103C2214yes—
33#394×C103—21no—
34#394×C103—22no—
35#392×C103—21no—
36#392×C103—22no—
37#390×C103—21no—
38#390×C103—21no—
39#390×C103—21no—
40#380×C103C2211yescharacteristic
41#379×C103C2214yes—
42#379×C103C2212yes—
43C4×C22⋊C4×C103C2211yescharacteristic
44C4×C22⋊C4×C103C2211yescharacteristic
45#342×C103C2214yes—
46#342×C103C2212yes—
47C25×C103C2312yes—
48C2×#41×C103—21no—
49C22×Q8×C103D411yescharacteristic, complemented
50C22×D4×C103—22no—
51C22×D4×C103—24no—
52C22×D4×C103—21no—
53C22×D4×C103—21no—
54C22×D4×C103—21no—
55C22×D4×C103—21no—
56C22×D4×C103—21no—
57C22×D4×C103—21no—
58C22×D4×C103—44no—
59C22×D4×C103D411yescharacteristic, complemented
60C22×D4×C103C2311yescharacteristic
61C22×D4×C103C2312yes—
62C23×C4×C103D411yescharacteristic, complemented
63C23×C4×C103C2311yescharacteristic
64#127×C103—44no—
65#126×C103—22no—
66#126×C103—22no—
67#126×C103—22no—
68#125×C103—21no—
69#125×C103—22no—
70#124×C103—21no—
71#124×C103—22no—
72#124×C103—44no—
73#123×C103—22no—
74#123×C103—22no—
75#123×C103—22no—
76#123×C103—22no—
77#123×C103—22no—
78C22⋊Q8×C103—21no—
79C22⋊Q8×C103—22no—
80C22⋊Q8×C103—21no—
81C22⋊Q8×C103—21no—
82C22⋊Q8×C103—21no—
83C22⋊Q8×C103—21no—
84#121×C103—21no—
85#121×C103—22no—
86#121×C103—21no—
87#121×C103—21no—
88#121×C103—21no—
89#121×C103—21no—
90#121×C103—22no—
91#121×C103—22no—
92#121×C103—44no—
93#120×C103—22no—
94#120×C103—22no—
95#120×C103—28no—
96#120×C103—44no—
97#120×C103—44no—
98C4×Q8×C103—21no—
99C4×D4×C103—22no—
100C4×D4×C103—21no—
101C4×D4×C103—21no—
102C4×D4×C103—21no—
103C4×D4×C103—21no—
104C4×D4×C103—21no—
105C4×D4×C103—22no—
106C4×D4×C103—22no—
107C4×D4×C103—22no—
108C4×D4×C103—22no—
109#117×C103—21no—
110#117×C103—22no—
111#117×C103—22no—
112C2×C4⋊C4×C103—21no—
113C2×C4⋊C4×C103D411yescharacteristic, complemented
114C2×C4⋊C4×C103D411yescharacteristic, complemented
115C2×C4⋊C4×C103D411yescharacteristic, complemented
116C2×C4⋊C4×C103D412yescomplemented
117C2×C22⋊C4×C103—22no—
118C2×C22⋊C4×C103—22no—
119C2×C22⋊C4×C103—24no—
120C2×C22⋊C4×C103—24no—
121C2×C22⋊C4×C103—22no—
122C2×C22⋊C4×C103—22no—
123C2×C22⋊C4×C103—24no—
124C2×C22⋊C4×C103D411yescharacteristic, complemented
125C2×C22⋊C4×C103D412yescomplemented
126C2×C22⋊C4×C103C2312yes—
127C2×C22⋊C4×C103C2312yes—
128C2×C22⋊C4×C103C2311yescharacteristic
129C2×C22⋊C4×C103C2312yes—
130C2×C22⋊C4×C103C2312yes—
131C2×C42×C103—21no—
132C2×C42×C103—21no—
133C2×C42×C103D411yescharacteristic, complemented
134#99×C103—24no—
135#99×C103—44no—
136#95×C103—21no—
137#95×C103—21no—
138#95×C103—21no—
139C24×C103—22no—
140C24×C103—22no—
141C24×C103—22no—
142C24×C103—24no—
143C24×C103—24no—
144C24×C103—44no—
145C24×C103—82no—
146C24×C103C2×D412yes—
147C24×C103C2×D411yescharacteristic
148C24×C103C2411yescharacteristic
149#41×C103—82no—
150C2×Q8×C103—21no—
151C2×Q8×C103—21no—
152C2×Q8×C103—42no—
153C2×D4×C103—24no—
154C2×D4×C103—24no—
155C2×D4×C103—24no—
156C2×D4×C103—21no—
157C2×D4×C103—22no—
158C2×D4×C103—21no—
159C2×D4×C103—22no—
160C2×D4×C103—22no—
161C2×D4×C103—24no—
162C2×D4×C103—24no—
163C2×D4×C103—22no—
164C2×D4×C103—22no—
165C2×D4×C103—22no—
166C2×D4×C103—21no—
167C2×D4×C103—21no—
168C2×D4×C103—42no—
169C2×D4×C103—42no—
170C2×D4×C103—42no—
171C2×D4×C103—42no—
172C2×D4×C103—48no—
173C2×D4×C103—44no—
174C2×D4×C103—44no—
175C2×D4×C103—44no—
176C2×D4×C103—44no—
177C2×D4×C103—44no—
178C2×D4×C103—48no—
179C2×D4×C103—41no—
180C2×D4×C103—41no—
181C2×D4×C103—41no—
182C2×D4×C103—41no—
183C2×D4×C103—84no—
184C2×D4×C103—82no—
185C22×C4×C103—22no—
186C22×C4×C103—22no—
187C22×C4×C103—22no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—22no—
191C22×C4×C103—22no—
192C22×C4×C103—42no—
193C22×C4×C103—42no—
194C22×C4×C103C2×D411yescharacteristic
195C22×C4×C103C2×D412yes—
196C22×C4×C103C2×D411yescharacteristic
197C22×C4×C103C2×D411yescharacteristic
198C22×C4×C103C2×D411yescharacteristic
199C22×C4×C103C2×D411yescharacteristic
200C22×C4×C103C2×D412yes—
201C22×C4×C103C2×D411yescharacteristic
202C22×C4×C103C2×D412yes—
203C22×C4×C103C2×D411yescharacteristic
204C22×C4×C103C2×D411yescharacteristic
205C22×C4×C103C2×D411yescharacteristic
206C4⋊C4×C103—22no—
207C4⋊C4×C103—22no—
208C4⋊C4×C103—22no—
209C4⋊C4×C103—22no—
210C4⋊C4×C103—21no—
211C4⋊C4×C103—22no—
212C4⋊C4×C103—21no—
213C4⋊C4×C103—21no—
214C4⋊C4×C103—21no—
215C4⋊C4×C103—21no—
216C4⋊C4×C103—22no—
217C4⋊C4×C103—21no—
218C4⋊C4×C103—42no—
219C22⋊C4×C103—22no—
220C22⋊C4×C103—22no—
221C22⋊C4×C103—22no—
222C22⋊C4×C103—22no—
223C22⋊C4×C103—22no—
224C22⋊C4×C103—22no—
225C22⋊C4×C103—21no—
226C22⋊C4×C103—22no—
227C22⋊C4×C103—21no—
228C22⋊C4×C103—22no—
229C22⋊C4×C103—22no—
230C22⋊C4×C103—22no—
231C22⋊C4×C103—21no—
232C22⋊C4×C103—21no—
233C22⋊C4×C103—22no—
234C22⋊C4×C103—22no—
235C22⋊C4×C103—22no—
236C22⋊C4×C103—24no—
237C22⋊C4×C103—48no—
238C22⋊C4×C103—44no—
239C22⋊C4×C103—44no—
240C22⋊C4×C103—48no—
241C22⋊C4×C103—84no—
242C22⋊C4×C103—82no—
243C22⋊C4×C103#4114yescomplemented
244C42×C103—22no—
245C42×C103—22no—
246C42×C103—21no—
247C42×C103—21no—
248C42×C103—42no—
249C42×C103—42no—
250C23×C103—24no—
251C23×C103—24no—
252C23×C103—24no—
253C23×C103—21no—
254C23×C103—22no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—24no—
258C23×C103—41no—
259C23×C103—41no—
260C23×C103—41no—
261C23×C103—41no—
262C23×C103—44no—
263C23×C103—42no—
264C23×C103—42no—
265C23×C103—42no—
266C23×C103—42no—
267C23×C103—42no—
268C23×C103—44no—
269C23×C103—42no—
270C23×C103—42no—
271C23×C103—42no—
272C23×C103—42no—
273C23×C103—42no—
274C23×C103—44no—
275C23×C103—44no—
276C23×C103—88no—
277C23×C103—88no—
278C23×C103C22×D411yescharacteristic
279C23×C103C22×D411yescharacteristic
280C23×C103C22×D411yescharacteristic
281C23×C103C2×#4112yes—
282C23×C103H(5,𝔽2)12yes—
283Q8×C103—42no—
284Q8×C103—81no—
285D4×C103—44no—
286D4×C103—44no—
287D4×C103—44no—
288D4×C103—42no—
289D4×C103—42no—
290D4×C103—42no—
291D4×C103—42no—
292D4×C103—44no—
293D4×C103—44no—
294D4×C103—42no—
295D4×C103—81no—
296D4×C103—82no—
297D4×C103—82no—
298D4×C103—816no—
299D4×C103—88no—
300C2×C4×C103—22no—
301C2×C4×C103—22no—
302C2×C4×C103—22no—
303C2×C4×C103—21no—
304C2×C4×C103—22no—
305C2×C4×C103—21no—
306C2×C4×C103—21no—
307C2×C4×C103—22no—
308C2×C4×C103—22no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
311C2×C4×C103—24no—
312C2×C4×C103—24no—
313C2×C4×C103—41no—
314C2×C4×C103—41no—
315C2×C4×C103—41no—
316C2×C4×C103—42no—
317C2×C4×C103—42no—
318C2×C4×C103—42no—
319C2×C4×C103—41no—
320C2×C4×C103—42no—
321C2×C4×C103—41no—
322C2×C4×C103—42no—
323C2×C4×C103—42no—
324C2×C4×C103—42no—
325C2×C4×C103—42no—
326C2×C4×C103—42no—
327C2×C4×C103—42no—
328C2×C4×C103—42no—
329C2×C4×C103—81no—
330C2×C4×C103—82no—
331C2×C4×C103—82no—
332C2×C4×C103#12011yescharacteristic
333C2×C4×C103#12011yescharacteristic
334C2×C4×C103#12011yescharacteristic
335C2×C4×C103#12011yescharacteristic
336C22×C103—21no—
337C22×C103—21no—
338C22×C103—21no—
339C22×C103—21no—
340C22×C103—21no—
341C22×C103—21no—
342C22×C103—42no—
343C22×C103—42no—
344C22×C103—42no—
345C22×C103—48no—
346C22×C103—44no—
347C22×C103—48no—
348C22×C103—44no—
349C22×C103—41no—
350C22×C103—42no—
351C22×C103—41no—
352C22×C103—42no—
353C22×C103—44no—
354C22×C103—42no—
355C22×C103—41no—
356C22×C103—84no—
357C22×C103—81no—
358C22×C103—84no—
359C22×C103—82no—
360C22×C103—84no—
361C22×C103—82no—
362C22×C103—82no—
363C22×C103—82no—
364C22×C103C2×#12011yescharacteristic
365C22×C103#53211yescharacteristic
366C22×C103#53511yescharacteristic
367C22×C103#54612yes—
368C22×C103#55012yes—
369C4×C103—21no—
370C4×C103—21no—
371C4×C103—21no—
372C4×C103—44no—
373C4×C103—41no—
374C4×C103—42no—
375C4×C103—41no—
376C4×C103—42no—
377C4×C103—41no—
378C4×C103—42no—
379C4×C103—82no—
380C4×C103—82no—
381C4×C103B(4,𝔽2)12yes—
382#25585C10311yesmaximal, characteristic, direct product factor, Sylow
383C2×C103—22no—
384C2×C103—21no—
385C2×C103—22no—
386C2×C103—21no—
387C2×C103—84no—
388C2×C103—81no—
389C2×C103—82no—
390C2×C103#243111yescharacteristic
391C2×C103C2×B(4,𝔽2)11yescharacteristic
392C2×C103#302711yescharacteristic
393#3505C2×C10311yescharacteristic, complemented
394#2435C2×C10311yescharacteristic, complemented
395#2433C2×C10311yescharacteristic, complemented
396#2408C2×C10311yescharacteristic, complemented
397#2021C2×C10314yescomplemented
398#1996C2×C10311yescharacteristic, complemented
399#1964C2×C10311yescharacteristic, complemented
400#1889C2×C10314yescomplemented
401C4×#99C2×C10311yescharacteristic, complemented
402C103#2558511yescharacteristic, direct product factor, Sylow
403C23×D4C22×C10311yescharacteristic
404#553—21no—
405#553—22no—
406#552—21no—
407#551—22no—
408#548—21no—
409#546—21no—
410#539—21no—
411#538—21no—
412#534C22×C10312yes—
413C2×#127—21no—
414#529—21no—
415C2×#124—21no—
416#525—21no—
417C2×C22⋊Q8C22×C10311yescharacteristic
418C2×#121—21no—
419C2×#121C22×C10311yescharacteristic
420C2×#120C22×C10314yes—
421C2×#120C22×C10312yes—
422#518C22×C10312yes—
423C2×C4×D4C22×C10311yescharacteristic
424C2×#99C22×C10312yes—
425C2×#99C22×C10314yes—
426#394—21no—
427#394—22no—
428#392—21no—
429#392—22no—
430#390—21no—
431#390—21no—
432#390—21no—
433#380C22×C10311yescharacteristic
434#379C22×C10312yes—
435#379C22×C10314yes—
436C4×C22⋊C4C22×C10311yescharacteristic
437C4×C22⋊C4C22×C10311yescharacteristic
438#342C22×C10312yes—
439#342C22×C10314yes—
440C25C23×C10312yes—
441C2×#41—21no—
442C22×Q8D4×C10311yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C10311yescharacteristic, complemented
453C22×D4C23×C10311yescharacteristic
454C22×D4C23×C10312yes—
455C23×C4D4×C10311yescharacteristic, complemented
456C23×C4C23×C10311yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C10311yescharacteristic, complemented
507C2×C4⋊C4D4×C10311yescharacteristic, complemented
508C2×C4⋊C4D4×C10311yescharacteristic, complemented
509C2×C4⋊C4D4×C10312yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C10311yescharacteristic, complemented
518C2×C22⋊C4D4×C10312yescomplemented
519C2×C22⋊C4C23×C10312yes—
520C2×C22⋊C4C23×C10312yes—
521C2×C22⋊C4C23×C10311yescharacteristic
522C2×C22⋊C4C23×C10312yes—
523C2×C22⋊C4C23×C10312yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C10311yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C10312yes—
540C24C2×D4×C10311yescharacteristic
541C24C24×C10311yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C10311yescharacteristic
588C22×C4C2×D4×C10312yes—
589C22×C4C2×D4×C10311yescharacteristic
590C22×C4C2×D4×C10311yescharacteristic
591C22×C4C2×D4×C10311yescharacteristic
592C22×C4C2×D4×C10311yescharacteristic
593C22×C4C2×D4×C10312yes—
594C22×C4C2×D4×C10311yescharacteristic
595C22×C4C2×D4×C10312yes—
596C22×C4C2×D4×C10311yescharacteristic
597C22×C4C2×D4×C10311yescharacteristic
598C22×C4C2×D4×C10311yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C10314yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C10311yescharacteristic
672C23C22×D4×C10311yescharacteristic
673C23C22×D4×C10311yescharacteristic
674C23C2×#41×C10312yes—
675C23H(5,𝔽2)×C10312yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C10311yescharacteristic
726C2×C4#120×C10311yescharacteristic
727C2×C4#120×C10311yescharacteristic
728C2×C4#120×C10311yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—44no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C10311yescharacteristic
758C22#532×C10311yescharacteristic
759C22#535×C10311yescharacteristic
760C22#546×C10312yes—
761C22#550×C10312yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4B(4,𝔽2)×C10312yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C103×#243111yescharacteristic
783C2C2×B(4,𝔽2)×C10311yescharacteristic
784C2C103×#302711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC24C24×C103
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3505C2semidirect
2. C103×#2435C2semidirect
3. C103×#2433C2semidirect
4. C103×#2408C2semidirect
5. C103×#2021C2semidirect
6. C103×#1996C2semidirect
7. C103×#1964C2semidirect
8. C103×#1889C2semidirect
9. C4×#99×C103C2semidirect
49. C22×Q8×C103D4semidirect
59. C22×D4×C103D4semidirect
62. C23×C4×C103D4semidirect
113. C2×C4⋊C4×C103D4semidirect
114. C2×C4⋊C4×C103D4semidirect
115. C2×C4⋊C4×C103D4semidirect
116. C2×C4⋊C4×C103D4semidirect
124. C2×C22⋊C4×C103D4semidirect
125. C2×C22⋊C4×C103D4semidirect
133. C2×C42×C103D4semidirect
243. C22⋊C4×C103#41semidirect
382. #25585C103direct (N × H)
393. #3505C2×C103semidirect
394. #2435C2×C103semidirect
395. #2433C2×C103semidirect
396. #2408C2×C103semidirect
397. #2021C2×C103semidirect
398. #1996C2×C103semidirect
399. #1964C2×C103semidirect
400. #1889C2×C103semidirect
401. C4×#99C2×C103semidirect
402. C103#25585direct (N × H)
442. C22×Q8D4×C103semidirect
452. C22×D4D4×C103semidirect
455. C23×C4D4×C103semidirect
506. C2×C4⋊C4D4×C103semidirect
507. C2×C4⋊C4D4×C103semidirect
508. C2×C4⋊C4D4×C103semidirect
509. C2×C4⋊C4D4×C103semidirect
517. C2×C22⋊C4D4×C103semidirect
518. C2×C22⋊C4D4×C103semidirect
526. C2×C42D4×C103semidirect
636. C22⋊C4#41×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35052
C103×#24352
C103×#24332
C103×#24082
C103×#20212
C103×#19962
C103×#19642
C103×#18892
C4×#99×C1032
#25585103