Finite Group Databasebeta

← C103×#25587 #39930862

Subgroups — C103×#25587 #39930862

Order 26368.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3505C211yesmaximal, characteristic, complemented
2C103×#2561C211yesmaximal, characteristic, complemented
3C103×#2539C211yesmaximal, characteristic, complemented
4C103×#2534C211yesmaximal, characteristic, complemented
5C103×#2022C212yesmaximal, complemented
6C103×#2021C212yesmaximal, complemented
7C103×#1996C211yesmaximal, characteristic, complemented
8C103×#1964C211yesmaximal, characteristic, complemented
9C103×#1890C212yesmaximal, complemented
10C103×#1889C212yesmaximal, complemented
11C4×#99×C103C211yesmaximal, characteristic, complemented
12#553×C103—22no—
13#553×C103—21no—
14#552×C103—21no—
15#551×C103—22no—
16#548×C103—21no—
17#546×C103—21no—
18#539×C103—21no—
19#538×C103—21no—
20#534×C103C2212yes—
21#529×C103—21no—
22#525×C103—21no—
23C2×#123×C103C2212yes—
24C2×#123×C103C2211yescharacteristic
25C2×C22⋊Q8×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×#120×C103C2212yes—
28C2×#120×C103C2211yescharacteristic
29#518×C103C2212yes—
30C2×C4×D4×C103C2211yescharacteristic
31C22×C22⋊C4×C103C2211yescharacteristic
32C2×#99×C103C2212yes—
33C2×#99×C103C2212yes—
34C2×#99×C103C2212yes—
35#399×C103—21no—
36#397×C103—21no—
37#396×C103—21no—
38#394×C103—21no—
39#393×C103—21no—
40#392×C103—21no—
41#390×C103—22no—
42#388×C103—22no—
43#388×C103—21no—
44#386×C103—21no—
45#381×C103C2212yes—
46#381×C103C2211yescharacteristic
47#380×C103C2211yescharacteristic
48#379×C103C2212yes—
49#379×C103C2211yescharacteristic
50C4×C22⋊C4×C103C2211yescharacteristic
51C4×C22⋊C4×C103C2211yescharacteristic
52#342×C103C2212yes—
53#342×C103C2212yes—
54#342×C103C2212yes—
55C25×C103C2311yescharacteristic
56C2×#41×C103—21no—
57C22×Q8×C103D411yescharacteristic, complemented
58C22×D4×C103—21no—
59C22×D4×C103—22no—
60C22×D4×C103D411yescharacteristic, complemented
61C22×D4×C103C2311yescharacteristic
62C22×D4×C103C2312yes—
63C23×C4×C103D411yescharacteristic, complemented
64C23×C4×C103C2311yescharacteristic
65C23×C4×C103C2311yescharacteristic
66#126×C103—22no—
67#126×C103—22no—
68#126×C103—22no—
69#125×C103—21no—
70#125×C103—22no—
71#124×C103—21no—
72#124×C103—22no—
73#123×C103—22no—
74#123×C103—22no—
75#123×C103—22no—
76#123×C103—22no—
77#123×C103—22no—
78#123×C103—24no—
79#123×C103—42no—
80#123×C103—42no—
81C22⋊Q8×C103—21no—
82C22⋊Q8×C103—22no—
83C22⋊Q8×C103—21no—
84C22⋊Q8×C103—21no—
85C22⋊Q8×C103—21no—
86C22⋊Q8×C103—21no—
87#121×C103—21no—
88#121×C103—22no—
89#121×C103—21no—
90#121×C103—21no—
91#121×C103—21no—
92#121×C103—21no—
93#121×C103—22no—
94#121×C103—22no—
95#120×C103—22no—
96#120×C103—22no—
97#120×C103—24no—
98#120×C103—42no—
99#120×C103—42no—
100C4×Q8×C103—21no—
101C4×D4×C103—22no—
102C4×D4×C103—21no—
103C4×D4×C103—21no—
104C4×D4×C103—21no—
105C4×D4×C103—21no—
106C4×D4×C103—21no—
107C4×D4×C103—22no—
108C4×D4×C103—22no—
109C4×D4×C103—22no—
110C4×D4×C103—22no—
111#117×C103—21no—
112#117×C103—22no—
113#117×C103—22no—
114C2×C4⋊C4×C103—21no—
115C2×C4⋊C4×C103—22no—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103D412yescomplemented
118C2×C4⋊C4×C103D411yescharacteristic, complemented
119C2×C4⋊C4×C103D411yescharacteristic, complemented
120C2×C4⋊C4×C103D411yescharacteristic, complemented
121C2×C22⋊C4×C103—22no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—22no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—22no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103—22no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103—21no—
135C2×C22⋊C4×C103—22no—
136C2×C22⋊C4×C103D412yescomplemented
137C2×C22⋊C4×C103D411yescharacteristic, complemented
138C2×C22⋊C4×C103C2311yescharacteristic
139C2×C22⋊C4×C103C2311yescharacteristic
140C2×C22⋊C4×C103C2312yes—
141C2×C22⋊C4×C103C2311yescharacteristic
142C2×C22⋊C4×C103C2312yes—
143C2×C22⋊C4×C103C2312yes—
144C2×C42×C103—21no—
145C2×C42×C103—21no—
146C2×C42×C103D411yescharacteristic, complemented
147#99×C103—24no—
148#99×C103—42no—
149#99×C103—42no—
150#95×C103—21no—
151#95×C103—21no—
152#95×C103—21no—
153#95×C103—21no—
154#95×C103—22no—
155#95×C103—21no—
156#95×C103—22no—
157C24×C103—21no—
158C24×C103—21no—
159C24×C103—21no—
160C24×C103—22no—
161C24×C103—22no—
162C24×C103—42no—
163C24×C103—81no—
164C24×C103C2×D412yes—
165C24×C103C2×D411yescharacteristic
166C24×C103C2411yescharacteristic
167#41×C103—82no—
168C2×Q8×C103—21no—
169C2×Q8×C103—21no—
170C2×Q8×C103—81no—
171C2×D4×C103—21no—
172C2×D4×C103—22no—
173C2×D4×C103—21no—
174C2×D4×C103—22no—
175C2×D4×C103—22no—
176C2×D4×C103—22no—
177C2×D4×C103—22no—
178C2×D4×C103—22no—
179C2×D4×C103—22no—
180C2×D4×C103—22no—
181C2×D4×C103—22no—
182C2×D4×C103—22no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—44no—
186C2×D4×C103—42no—
187C2×D4×C103—44no—
188C2×D4×C103—42no—
189C2×D4×C103—81no—
190C2×D4×C103—82no—
191C2×D4×C103—81no—
192C22×C4×C103—22no—
193C22×C4×C103—22no—
194C22×C4×C103—22no—
195C22×C4×C103—21no—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—22no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—22no—
204C22×C4×C103—22no—
205C22×C4×C103—81no—
206C22×C4×C103—81no—
207C22×C4×C103C2×D411yescharacteristic
208C22×C4×C103C2×D412yes—
209C22×C4×C103C2×D411yescharacteristic
210C22×C4×C103C2×D412yes—
211C22×C4×C103C2×D411yescharacteristic
212C22×C4×C103C2×D412yes—
213C22×C4×C103C2×D411yescharacteristic
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2×D411yescharacteristic
217C22×C4×C103C2×D411yescharacteristic
218C22×C4×C103C2×D411yescharacteristic
219C4⋊C4×C103—22no—
220C4⋊C4×C103—22no—
221C4⋊C4×C103—22no—
222C4⋊C4×C103—22no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103—22no—
225C4⋊C4×C103—21no—
226C4⋊C4×C103—21no—
227C4⋊C4×C103—21no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—22no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—44no—
232C4⋊C4×C103—42no—
233C4⋊C4×C103—81no—
234C22⋊C4×C103—22no—
235C22⋊C4×C103—22no—
236C22⋊C4×C103—22no—
237C22⋊C4×C103—22no—
238C22⋊C4×C103—22no—
239C22⋊C4×C103—22no—
240C22⋊C4×C103—21no—
241C22⋊C4×C103—22no—
242C22⋊C4×C103—21no—
243C22⋊C4×C103—22no—
244C22⋊C4×C103—22no—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—21no—
247C22⋊C4×C103—21no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—22no—
250C22⋊C4×C103—22no—
251C22⋊C4×C103—22no—
252C22⋊C4×C103—22no—
253C22⋊C4×C103—44no—
254C22⋊C4×C103—44no—
255C22⋊C4×C103—42no—
256C22⋊C4×C103—44no—
257C22⋊C4×C103—42no—
258C22⋊C4×C103—42no—
259C22⋊C4×C103—41no—
260C22⋊C4×C103—41no—
261C22⋊C4×C103—41no—
262C22⋊C4×C103—41no—
263C22⋊C4×C103—81no—
264C22⋊C4×C103—82no—
265C22⋊C4×C103#4114yescomplemented
266C42×C103—22no—
267C42×C103—22no—
268C42×C103—21no—
269C42×C103—21no—
270C42×C103—81no—
271C42×C103—81no—
272C23×C103—22no—
273C23×C103—22no—
274C23×C103—22no—
275C23×C103—22no—
276C23×C103—21no—
277C23×C103—21no—
278C23×C103—21no—
279C23×C103—22no—
280C23×C103—22no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103—41no—
285C23×C103—42no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—42no—
289C23×C103—41no—
290C23×C103—41no—
291C23×C103—41no—
292C23×C103—42no—
293C23×C103—42no—
294C23×C103—41no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—42no—
298C23×C103—42no—
299C23×C103—84no—
300C23×C103—84no—
301C23×C103C22×D411yescharacteristic
302C23×C103C22×D411yescharacteristic
303C23×C103C22×D411yescharacteristic
304C23×C103C2×#4112yes—
305C23×C103H(5,𝔽2)12yes—
306Q8×C103—42no—
307Q8×C103—81no—
308D4×C103—42no—
309D4×C103—42no—
310D4×C103—42no—
311D4×C103—42no—
312D4×C103—42no—
313D4×C103—42no—
314D4×C103—42no—
315D4×C103—81no—
316D4×C103—82no—
317D4×C103—82no—
318D4×C103—88no—
319D4×C103—84no—
320C2×C4×C103—21no—
321C2×C4×C103—22no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
324C2×C4×C103—22no—
325C2×C4×C103—22no—
326C2×C4×C103—21no—
327C2×C4×C103—21no—
328C2×C4×C103—24no—
329C2×C4×C103—22no—
330C2×C4×C103—22no—
331C2×C4×C103—41no—
332C2×C4×C103—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—41no—
336C2×C4×C103—41no—
337C2×C4×C103—42no—
338C2×C4×C103—42no—
339C2×C4×C103—42no—
340C2×C4×C103—41no—
341C2×C4×C103—42no—
342C2×C4×C103—41no—
343C2×C4×C103—42no—
344C2×C4×C103—42no—
345C2×C4×C103—42no—
346C2×C4×C103—41no—
347C2×C4×C103—41no—
348C2×C4×C103—41no—
349C2×C4×C103—41no—
350C2×C4×C103—41no—
351C2×C4×C103—41no—
352C2×C4×C103—41no—
353C2×C4×C103—41no—
354C2×C4×C103—41no—
355C2×C4×C103—42no—
356C2×C4×C103—42no—
357C2×C4×C103—42no—
358C2×C4×C103—81no—
359C2×C4×C103—82no—
360C2×C4×C103—82no—
361C2×C4×C103#12011yescharacteristic
362C2×C4×C103#12011yescharacteristic
363C2×C4×C103#12011yescharacteristic
364C2×C4×C103#12011yescharacteristic
365C22×C103—21no—
366C22×C103—21no—
367C22×C103—21no—
368C22×C103—21no—
369C22×C103—21no—
370C22×C103—21no—
371C22×C103—42no—
372C22×C103—42no—
373C22×C103—42no—
374C22×C103—44no—
375C22×C103—42no—
376C22×C103—44no—
377C22×C103—42no—
378C22×C103—41no—
379C22×C103—42no—
380C22×C103—42no—
381C22×C103—41no—
382C22×C103—42no—
383C22×C103—41no—
384C22×C103—42no—
385C22×C103—82no—
386C22×C103—82no—
387C22×C103—81no—
388C22×C103—82no—
389C22×C103—81no—
390C22×C103—82no—
391C22×C103—81no—
392C22×C103—81no—
393C22×C103—81no—
394C22×C103C2×#12011yescharacteristic
395C22×C103#53211yescharacteristic
396C22×C103#53511yescharacteristic
397C22×C103#54612yes—
398C22×C103#55012yes—
399C4×C103—21no—
400C4×C103—21no—
401C4×C103—21no—
402C4×C103—21no—
403C4×C103—44no—
404C4×C103—41no—
405C4×C103—42no—
406C4×C103—41no—
407C4×C103—42no—
408C4×C103—41no—
409C4×C103—42no—
410C4×C103—81no—
411C4×C103—82no—
412C4×C103—81no—
413C4×C103—81no—
414#25587C10311yesmaximal, characteristic, direct product factor, Sylow
415C2×C103—22no—
416C2×C103—21no—
417C2×C103—22no—
418C2×C103—21no—
419C2×C103—82no—
420C2×C103—81no—
421C2×C103—82no—
422C2×C103#243111yescharacteristic
423C2×C103#302511yescharacteristic
424C2×C103#302611yescharacteristic
425#3505C2×C10311yescharacteristic, complemented
426#2561C2×C10311yescharacteristic, complemented
427#2539C2×C10311yescharacteristic, complemented
428#2534C2×C10311yescharacteristic, complemented
429#2022C2×C10312yescomplemented
430#2021C2×C10312yescomplemented
431#1996C2×C10311yescharacteristic, complemented
432#1964C2×C10311yescharacteristic, complemented
433#1890C2×C10312yescomplemented
434#1889C2×C10312yescomplemented
435C4×#99C2×C10311yescharacteristic, complemented
436C103#2558711yescharacteristic, direct product factor, Sylow
437#553—22no—
438#553—21no—
439#552—21no—
440#551—22no—
441#548—21no—
442#546—21no—
443#539—21no—
444#538—21no—
445#534C22×C10312yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C10312yes—
449C2×#123C22×C10311yescharacteristic
450C2×C22⋊Q8C22×C10311yescharacteristic
451C2×#121C22×C10311yescharacteristic
452C2×#120C22×C10312yes—
453C2×#120C22×C10311yescharacteristic
454#518C22×C10312yes—
455C2×C4×D4C22×C10311yescharacteristic
456C22×C22⋊C4C22×C10311yescharacteristic
457C2×#99C22×C10312yes—
458C2×#99C22×C10312yes—
459C2×#99C22×C10312yes—
460#399—21no—
461#397—21no—
462#396—21no—
463#394—21no—
464#393—21no—
465#392—21no—
466#390—22no—
467#388—22no—
468#388—21no—
469#386—21no—
470#381C22×C10312yes—
471#381C22×C10311yescharacteristic
472#380C22×C10311yescharacteristic
473#379C22×C10312yes—
474#379C22×C10311yescharacteristic
475C4×C22⋊C4C22×C10311yescharacteristic
476C4×C22⋊C4C22×C10311yescharacteristic
477#342C22×C10312yes—
478#342C22×C10312yes—
479#342C22×C10312yes—
480C25C23×C10311yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C10311yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C10311yescharacteristic, complemented
486C22×D4C23×C10311yescharacteristic
487C22×D4C23×C10312yes—
488C23×C4D4×C10311yescharacteristic, complemented
489C23×C4C23×C10311yescharacteristic
490C23×C4C23×C10311yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C10311yescharacteristic, complemented
543C2×C4⋊C4D4×C10311yescharacteristic, complemented
544C2×C4⋊C4D4×C10312yescomplemented
545C2×C4⋊C4D4×C10311yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C10311yescharacteristic, complemented
562C2×C22⋊C4D4×C10312yescomplemented
563C2×C22⋊C4C23×C10311yescharacteristic
564C2×C22⋊C4C23×C10311yescharacteristic
565C2×C22⋊C4C23×C10312yes—
566C2×C22⋊C4C23×C10311yescharacteristic
567C2×C22⋊C4C23×C10312yes—
568C2×C22⋊C4C23×C10312yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C10311yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C10312yes—
590C24C2×D4×C10311yescharacteristic
591C24C24×C10311yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C10311yescharacteristic
633C22×C4C2×D4×C10312yes—
634C22×C4C2×D4×C10311yescharacteristic
635C22×C4C2×D4×C10312yes—
636C22×C4C2×D4×C10311yescharacteristic
637C22×C4C2×D4×C10312yes—
638C22×C4C2×D4×C10311yescharacteristic
639C22×C4C2×D4×C10311yescharacteristic
640C22×C4C2×D4×C10311yescharacteristic
641C22×C4C2×D4×C10311yescharacteristic
642C22×C4C2×D4×C10311yescharacteristic
643C22×C4C2×D4×C10311yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C10314yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C10311yescharacteristic
727C23C22×D4×C10311yescharacteristic
728C23C22×D4×C10311yescharacteristic
729C23C2×#41×C10312yes—
730C23H(5,𝔽2)×C10312yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C10311yescharacteristic
787C2×C4#120×C10311yescharacteristic
788C2×C4#120×C10311yescharacteristic
789C2×C4#120×C10311yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C10311yescharacteristic
820C22#532×C10311yescharacteristic
821C22#535×C10311yescharacteristic
822C22#546×C10312yes—
823C22#550×C10312yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C103×#243111yescharacteristic
847C2C103×#302511yescharacteristic
848C2C103×#302611yescharacteristic
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×#2561C2semidirect
3. C103×#2539C2semidirect
4. C103×#2534C2semidirect
5. C103×#2022C2semidirect
6. C103×#2021C2semidirect
7. C103×#1996C2semidirect
8. C103×#1964C2semidirect
9. C103×#1890C2semidirect
10. C103×#1889C2semidirect
11. C4×#99×C103C2semidirect
57. C22×Q8×C103D4semidirect
60. C22×D4×C103D4semidirect
63. C23×C4×C103D4semidirect
117. C2×C4⋊C4×C103D4semidirect
118. C2×C4⋊C4×C103D4semidirect
119. C2×C4⋊C4×C103D4semidirect
120. C2×C4⋊C4×C103D4semidirect
136. C2×C22⋊C4×C103D4semidirect
137. C2×C22⋊C4×C103D4semidirect
146. C2×C42×C103D4semidirect
265. C22⋊C4×C103#41semidirect
414. #25587C103direct (N × H)
425. #3505C2×C103semidirect
426. #2561C2×C103semidirect
427. #2539C2×C103semidirect
428. #2534C2×C103semidirect
429. #2022C2×C103semidirect
430. #2021C2×C103semidirect
431. #1996C2×C103semidirect
432. #1964C2×C103semidirect
433. #1890C2×C103semidirect
434. #1889C2×C103semidirect
435. C4×#99C2×C103semidirect
436. C103#25587direct (N × H)
482. C22×Q8D4×C103semidirect
485. C22×D4D4×C103semidirect
488. C23×C4D4×C103semidirect
542. C2×C4⋊C4D4×C103semidirect
543. C2×C4⋊C4D4×C103semidirect
544. C2×C4⋊C4D4×C103semidirect
545. C2×C4⋊C4D4×C103semidirect
561. C2×C22⋊C4D4×C103semidirect
562. C2×C22⋊C4D4×C103semidirect
571. C2×C42D4×C103semidirect
690. 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×#25612
C103×#25392
C103×#25342
C103×#20222
C103×#20212
C103×#19962
C103×#19642
C103×#18902
C103×#18892
C4×#99×C1032
#25587103