Finite Group Databasebeta

← C103×#24142 #39929417

Subgroups — C103×#24142 #39929417

Order 26368.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3505C211yesmaximal, characteristic, complemented
2C103×#2626C211yesmaximal, characteristic, complemented
3C103×#2617C211yesmaximal, characteristic, complemented
4C103×#2321C211yesmaximal, characteristic, complemented
5C103×#2044C212yesmaximal, complemented
6C103×#2021C212yesmaximal, complemented
7C103×#1996C211yesmaximal, characteristic, complemented
8C103×#1964C211yesmaximal, characteristic, complemented
9C103×#1889C212yesmaximal, complemented
10C103×#1867C212yesmaximal, complemented
11C103×#1799C211yesmaximal, 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×C22⋊Q8×C103C2211yescharacteristic
24C2×#121×C103C2211yescharacteristic
25C2×#120×C103C2211yescharacteristic
26C2×#120×C103C2212yes—
27#518×C103C2212yes—
28C2×C4×D4×C103C2211yescharacteristic
29C22×C22⋊C4×C103C2211yescharacteristic
30C2×#99×C103C2212yes—
31C2×#99×C103C2212yes—
32C2×#99×C103C2212yes—
33#399×C103—21no—
34#397×C103—21no—
35#396×C103—22no—
36#394×C103—22no—
37#393×C103—21no—
38#392×C103—21no—
39#390×C103—21no—
40#388×C103—21no—
41#388×C103—21no—
42#386×C103—21no—
43#386×C103C2211yescharacteristic
44#386×C103C2212yes—
45#385×C103C2212yes—
46#385×C103C2211yescharacteristic
47#380×C103C2211yescharacteristic
48#380×C103C2211yescharacteristic
49#379×C103C2212yes—
50#379×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—
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#120×C103—22no—
93#120×C103—22no—
94#120×C103—22no—
95#120×C103—22no—
96#120×C103—24no—
97#120×C103—42no—
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×C103—21no—
114C2×C4⋊C4×C103—21no—
115C2×C4⋊C4×C103—22no—
116C2×C4⋊C4×C103D411yescharacteristic, complemented
117C2×C4⋊C4×C103D412yescomplemented
118C2×C4⋊C4×C103D411yescharacteristic, complemented
119C2×C4⋊C4×C103D411yescharacteristic, complemented
120C2×C22⋊C4×C103—22no—
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—22no—
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—22no—
134C2×C22⋊C4×C103—22no—
135C2×C22⋊C4×C103D411yescharacteristic, complemented
136C2×C22⋊C4×C103D412yescomplemented
137C2×C22⋊C4×C103C2312yes—
138C2×C22⋊C4×C103C2311yescharacteristic
139C2×C22⋊C4×C103C2312yes—
140C2×C22⋊C4×C103C2311yescharacteristic
141C2×C22⋊C4×C103C2312yes—
142C2×C22⋊C4×C103C2311yescharacteristic
143C2×C42×C103—21no—
144C2×C42×C103D411yescharacteristic, complemented
145#99×C103—24no—
146#99×C103—42no—
147#99×C103—42no—
148#95×C103—21no—
149#95×C103—21no—
150#95×C103—21no—
151#95×C103—21no—
152#95×C103—22no—
153#95×C103—21no—
154#95×C103—22no—
155C24×C103—21no—
156C24×C103—21no—
157C24×C103—21no—
158C24×C103—21no—
159C24×C103—21no—
160C24×C103—21no—
161C24×C103—81no—
162C24×C103—81no—
163C24×C103C2×D412yes—
164C24×C103C2×D411yescharacteristic
165C24×C103#4112yescomplemented
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—21no—
177C2×D4×C103—21no—
178C2×D4×C103—22no—
179C2×D4×C103—21no—
180C2×D4×C103—22no—
181C2×D4×C103—21no—
182C2×D4×C103—22no—
183C2×D4×C103—22no—
184C2×D4×C103—22no—
185C2×D4×C103—24no—
186C2×D4×C103—21no—
187C2×D4×C103—21no—
188C2×D4×C103—44no—
189C2×D4×C103—81no—
190C2×D4×C103—81no—
191C2×D4×C103—81no—
192C2×D4×C103—82no—
193C2×D4×C103—82no—
194C22×C4×C103—21no—
195C22×C4×C103—22no—
196C22×C4×C103—22no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—22no—
203C22×C4×C103—22no—
204C22×C4×C103—21no—
205C22×C4×C103—81no—
206C22×C4×C103—81no—
207C22×C4×C103—81no—
208C22×C4×C103C2×D411yescharacteristic
209C22×C4×C103C2×D412yes—
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103C2×D412yes—
212C22×C4×C103C2×D411yescharacteristic
213C22×C4×C103C2×D412yes—
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2×D411yescharacteristic
217C22×C4×C103C2×D411yescharacteristic
218C22×C4×C103C2×D411yescharacteristic
219C22×C4×C103C2×D411yescharacteristic
220C4⋊C4×C103—22no—
221C4⋊C4×C103—22no—
222C4⋊C4×C103—22no—
223C4⋊C4×C103—22no—
224C4⋊C4×C103—21no—
225C4⋊C4×C103—22no—
226C4⋊C4×C103—21no—
227C4⋊C4×C103—21no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—22no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—81no—
233C4⋊C4×C103—81no—
234C4⋊C4×C103—81no—
235C4⋊C4×C103—82no—
236C22⋊C4×C103—22no—
237C22⋊C4×C103—22no—
238C22⋊C4×C103—24no—
239C22⋊C4×C103—22no—
240C22⋊C4×C103—22no—
241C22⋊C4×C103—22no—
242C22⋊C4×C103—22no—
243C22⋊C4×C103—21no—
244C22⋊C4×C103—22no—
245C22⋊C4×C103—21no—
246C22⋊C4×C103—22no—
247C22⋊C4×C103—21no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—21no—
250C22⋊C4×C103—21no—
251C22⋊C4×C103—22no—
252C22⋊C4×C103—22no—
253C22⋊C4×C103—22no—
254C22⋊C4×C103—21no—
255C22⋊C4×C103—22no—
256C22⋊C4×C103—22no—
257C22⋊C4×C103—21no—
258C22⋊C4×C103—44no—
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—81no—
266C22⋊C4×C103—82no—
267C22⋊C4×C103—81no—
268C22⋊C4×C103—82no—
269C22⋊C4×C103#4112yescomplemented
270C42×C103—22no—
271C42×C103—22no—
272C42×C103—21no—
273C42×C103—21no—
274C42×C103—81no—
275C23×C103—21no—
276C23×C103—22no—
277C23×C103—22no—
278C23×C103—21no—
279C23×C103—22no—
280C23×C103—22no—
281C23×C103—21no—
282C23×C103—22no—
283C23×C103—22no—
284C23×C103—41no—
285C23×C103—41no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—42no—
289C23×C103—41no—
290C23×C103—42no—
291C23×C103—41no—
292C23×C103—41no—
293C23×C103—42no—
294C23×C103—41no—
295C23×C103—42no—
296C23×C103—42no—
297C23×C103—42no—
298C23×C103—41no—
299C23×C103—41no—
300C23×C103—41no—
301C23×C103—41no—
302C23×C103—82no—
303C23×C103—82no—
304C23×C103—82no—
305C23×C103—82no—
306C23×C103C22×D411yescharacteristic
307C23×C103C22×D411yescharacteristic
308C23×C103C22×D411yescharacteristic
309C23×C103C2×#4111yescharacteristic
310C23×C103C2×#4111yescharacteristic
311C23×C103H(5,𝔽2)11yescharacteristic
312C23×C1032−1+411yescharacteristic
313Q8×C103—42no—
314Q8×C103—81no—
315D4×C103—42no—
316D4×C103—42no—
317D4×C103—42no—
318D4×C103—41no—
319D4×C103—41no—
320D4×C103—41no—
321D4×C103—42no—
322D4×C103—42no—
323D4×C103—41no—
324D4×C103—81no—
325D4×C103—82no—
326D4×C103—84no—
327D4×C103—82no—
328D4×C103—88no—
329C2×C4×C103—21no—
330C2×C4×C103—22no—
331C2×C4×C103—21no—
332C2×C4×C103—21no—
333C2×C4×C103—22no—
334C2×C4×C103—22no—
335C2×C4×C103—21no—
336C2×C4×C103—22no—
337C2×C4×C103—21no—
338C2×C4×C103—22no—
339C2×C4×C103—22no—
340C2×C4×C103—41no—
341C2×C4×C103—41no—
342C2×C4×C103—41no—
343C2×C4×C103—41no—
344C2×C4×C103—41no—
345C2×C4×C103—41no—
346C2×C4×C103—42no—
347C2×C4×C103—41no—
348C2×C4×C103—41no—
349C2×C4×C103—41no—
350C2×C4×C103—42no—
351C2×C4×C103—41no—
352C2×C4×C103—42no—
353C2×C4×C103—41no—
354C2×C4×C103—41no—
355C2×C4×C103—42no—
356C2×C4×C103—42no—
357C2×C4×C103—41no—
358C2×C4×C103—42no—
359C2×C4×C103—42no—
360C2×C4×C103—42no—
361C2×C4×C103—41no—
362C2×C4×C103—42no—
363C2×C4×C103—41no—
364C2×C4×C103—41no—
365C2×C4×C103—42no—
366C2×C4×C103—42no—
367C2×C4×C103—81no—
368C2×C4×C103—82no—
369C2×C4×C103—82no—
370C2×C4×C103#12011yescharacteristic
371C2×C4×C103#12011yescharacteristic
372C2×C4×C103#12011yescharacteristic
373C2×C4×C103#12011yescharacteristic
374C22×C103—21no—
375C22×C103—21no—
376C22×C103—21no—
377C22×C103—21no—
378C22×C103—21no—
379C22×C103—21no—
380C22×C103—41no—
381C22×C103—41no—
382C22×C103—41no—
383C22×C103—41no—
384C22×C103—42no—
385C22×C103—42no—
386C22×C103—44no—
387C22×C103—42no—
388C22×C103—44no—
389C22×C103—41no—
390C22×C103—42no—
391C22×C103—42no—
392C22×C103—41no—
393C22×C103—42no—
394C22×C103—42no—
395C22×C103—41no—
396C22×C103—82no—
397C22×C103—81no—
398C22×C103—82no—
399C22×C103—82no—
400C22×C103—81no—
401C22×C103—81no—
402C22×C103—82no—
403C22×C103—81no—
404C22×C103—81no—
405C22×C103C2×#12011yescharacteristic
406C22×C103#52511yescharacteristic
407C22×C103#53711yescharacteristic
408C22×C103#54611yescharacteristic
409C22×C103#54711yescharacteristic
410C22×C103#54811yescharacteristic
411C22×C103#55011yescharacteristic
412C4×C103—21no—
413C4×C103—21no—
414C4×C103—21no—
415C4×C103—21no—
416C4×C103—42no—
417C4×C103—41no—
418C4×C103—42no—
419C4×C103—41no—
420C4×C103—42no—
421C4×C103—41no—
422C4×C103—42no—
423C4×C103—82no—
424C4×C103—81no—
425C4×C103—82no—
426C4×C103—81no—
427#24142C10311yesmaximal, characteristic, direct product factor, Sylow
428C2×C103—21no—
429C2×C103—21no—
430C2×C103—21no—
431C2×C103—21no—
432C2×C103—21no—
433C2×C103—21no—
434C2×C103—82no—
435C2×C103—81no—
436C2×C103—82no—
437C2×C103#240711yescharacteristic
438C2×C103#302611yescharacteristic
439C2×C103#302711yescharacteristic
440#3505C2×C10311yescharacteristic, complemented
441#2626C2×C10311yescharacteristic, complemented
442#2617C2×C10311yescharacteristic, complemented
443#2321C2×C10311yescharacteristic, complemented
444#2044C2×C10312yescomplemented
445#2021C2×C10312yescomplemented
446#1996C2×C10311yescharacteristic, complemented
447#1964C2×C10311yescharacteristic, complemented
448#1889C2×C10312yescomplemented
449#1867C2×C10312yescomplemented
450#1799C2×C10311yescharacteristic, complemented
451C103#2414211yescharacteristic, direct product factor, Sylow
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C10312yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C10311yescharacteristic
464C2×#121C22×C10311yescharacteristic
465C2×#120C22×C10311yescharacteristic
466C2×#120C22×C10312yes—
467#518C22×C10312yes—
468C2×C4×D4C22×C10311yescharacteristic
469C22×C22⋊C4C22×C10311yescharacteristic
470C2×#99C22×C10312yes—
471C2×#99C22×C10312yes—
472C2×#99C22×C10312yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C10311yescharacteristic
484#386C22×C10312yes—
485#385C22×C10311yescharacteristic
486#385C22×C10312yes—
487#380C22×C10311yescharacteristic
488#380C22×C10311yescharacteristic
489#379C22×C10311yescharacteristic
490#379C22×C10312yes—
491C4×C22⋊C4C22×C10311yescharacteristic
492#342C22×C10312yes—
493#342C22×C10312yes—
494#342C22×C10312yes—
495C25C23×C10311yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C10311yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C10311yescharacteristic, complemented
501C22×D4C23×C10311yescharacteristic
502C22×D4C23×C10312yes—
503C23×C4D4×C10311yescharacteristic, complemented
504C23×C4C23×C10311yescharacteristic
505C23×C4C23×C10311yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C10311yescharacteristic, complemented
557C2×C4⋊C4D4×C10311yescharacteristic, complemented
558C2×C4⋊C4D4×C10312yescomplemented
559C2×C4⋊C4D4×C10311yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C10311yescharacteristic, complemented
576C2×C22⋊C4D4×C10312yescomplemented
577C2×C22⋊C4C23×C10312yes—
578C2×C22⋊C4C23×C10311yescharacteristic
579C2×C22⋊C4C23×C10312yes—
580C2×C22⋊C4C23×C10311yescharacteristic
581C2×C22⋊C4C23×C10312yes—
582C2×C22⋊C4C23×C10311yescharacteristic
583C2×C42—21no—
584C2×C42D4×C10311yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C10312yes—
604C24C2×D4×C10311yescharacteristic
605C24#41×C10312yescomplemented
606C24C24×C10311yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C10311yescharacteristic
649C22×C4C2×D4×C10312yes—
650C22×C4C2×D4×C10311yescharacteristic
651C22×C4C2×D4×C10312yes—
652C22×C4C2×D4×C10311yescharacteristic
653C22×C4C2×D4×C10312yes—
654C22×C4C2×D4×C10311yescharacteristic
655C22×C4C2×D4×C10311yescharacteristic
656C22×C4C2×D4×C10311yescharacteristic
657C22×C4C2×D4×C10311yescharacteristic
658C22×C4C2×D4×C10311yescharacteristic
659C22×C4C2×D4×C10311yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C10312yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C10311yescharacteristic
747C23C22×D4×C10311yescharacteristic
748C23C22×D4×C10311yescharacteristic
749C23C2×#41×C10311yescharacteristic
750C23C2×#41×C10311yescharacteristic
751C23H(5,𝔽2)×C10311yescharacteristic
752C232−1+4×C10311yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C10311yescharacteristic
811C2×C4#120×C10311yescharacteristic
812C2×C4#120×C10311yescharacteristic
813C2×C4#120×C10311yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C10311yescharacteristic
846C22#525×C10311yescharacteristic
847C22#537×C10311yescharacteristic
848C22#546×C10311yescharacteristic
849C22#547×C10311yescharacteristic
850C22#548×C10311yescharacteristic
851C22#550×C10311yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C103×#240711yescharacteristic
877C2C103×#302611yescharacteristic
878C2C103×#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×#2626C2semidirect
3. C103×#2617C2semidirect
4. C103×#2321C2semidirect
5. C103×#2044C2semidirect
6. C103×#2021C2semidirect
7. C103×#1996C2semidirect
8. C103×#1964C2semidirect
9. C103×#1889C2semidirect
10. C103×#1867C2semidirect
11. C103×#1799C2semidirect
57. C22×Q8×C103D4semidirect
60. C22×D4×C103D4semidirect
63. C23×C4×C103D4semidirect
116. C2×C4⋊C4×C103D4semidirect
117. C2×C4⋊C4×C103D4semidirect
118. C2×C4⋊C4×C103D4semidirect
119. C2×C4⋊C4×C103D4semidirect
135. C2×C22⋊C4×C103D4semidirect
136. C2×C22⋊C4×C103D4semidirect
144. C2×C42×C103D4semidirect
165. C24×C103#41semidirect
269. C22⋊C4×C103#41semidirect
427. #24142C103direct (N × H)
440. #3505C2×C103semidirect
441. #2626C2×C103semidirect
442. #2617C2×C103semidirect
443. #2321C2×C103semidirect
444. #2044C2×C103semidirect
445. #2021C2×C103semidirect
446. #1996C2×C103semidirect
447. #1964C2×C103semidirect
448. #1889C2×C103semidirect
449. #1867C2×C103semidirect
450. #1799C2×C103semidirect
451. C103#24142direct (N × H)
497. C22×Q8D4×C103semidirect
500. C22×D4D4×C103semidirect
503. C23×C4D4×C103semidirect
556. C2×C4⋊C4D4×C103semidirect
557. C2×C4⋊C4D4×C103semidirect
558. C2×C4⋊C4D4×C103semidirect
559. C2×C4⋊C4D4×C103semidirect
575. C2×C22⋊C4D4×C103semidirect
576. C2×C22⋊C4D4×C103semidirect
584. C2×C42D4×C103semidirect
605. C24#41×C103semidirect
709. 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×#26262
C103×#26172
C103×#23212
C103×#20442
C103×#20212
C103×#19962
C103×#19642
C103×#18892
C103×#18672
C103×#17992
#24142103