Finite Group Databasebeta

← C103×#23857 #39929132

Subgroups — C103×#23857 #39929132

Order 26368.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C103C211yesmaximal, characteristic, complemented
2C2×#550×C103C211yesmaximal, characteristic, complemented
3C2×#452×C103C211yesmaximal, characteristic, complemented
4C2×#449×C103C211yesmaximal, characteristic, complemented
5C2×#449×C103C211yesmaximal, characteristic, complemented
6C103×#2407C211yesmaximal, characteristic, complemented
7C103×#2014C211yesmaximal, characteristic, complemented
8C103×#2011C211yesmaximal, characteristic, complemented
9C103×#2000C211yesmaximal, characteristic, complemented
10C103×#1999C211yesmaximal, characteristic, complemented
11C103×#1893C211yesmaximal, characteristic, complemented
12C103×#1880C211yesmaximal, characteristic, complemented
13C103×#1878C211yesmaximal, characteristic, complemented
14C103×#1869C211yesmaximal, characteristic, complemented
15C103×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C22×#41×C103C2211yescharacteristic
19C2×#135×C103—24no—
20C2×#135×C103—24no—
21C2×#135×C103—24no—
22C22×Q16×C103C2211yescharacteristic
23C22×SD16×C103C2211yescharacteristic
24C22×SD16×C103C2211yescharacteristic
25C22×SD16×C103C2211yescharacteristic
26C22×D8×C103C2211yescharacteristic
27C22×D8×C103C2211yescharacteristic
28C23×C8×C103C2211yescharacteristic
29#550×C103—24no—
30#550×C103—24no—
31C2×#127×C103—21no—
32C2×#127×C103C2211yescharacteristic
33C2×C22⋊Q8×C103C2211yescharacteristic
34C2×#121×C103—21no—
35C2×#121×C103—21no—
36C2×#121×C103C2211yescharacteristic
37C2×#121×C103C2211yescharacteristic
38C2×#121×C103C2211yescharacteristic
39C2×C4×Q8×C103C2211yescharacteristic
40C2×C4×D4×C103—21no—
41C2×C4×D4×C103C2211yescharacteristic
42#452×C103—24no—
43#449×C103—24no—
44#449×C103—24no—
45C2×#103×C103C2211yescharacteristic
46C2×#103×C103C2211yescharacteristic
47C2×#103×C103C2211yescharacteristic
48C2×#102×C103C2211yescharacteristic
49C2×#102×C103C2211yescharacteristic
50C2×#102×C103C2211yescharacteristic
51C2×#102×C103C2211yescharacteristic
52C2×#102×C103C2211yescharacteristic
53C2×C22⋊C8×C103C2211yescharacteristic
54C2×C22⋊C8×C103C2211yescharacteristic
55C2×C22⋊C8×C103C2211yescharacteristic
56#394×C103—21no—
57#392×C103—21no—
58#391×C103C2211yescharacteristic
59#390×C103C2211yescharacteristic
60#386×C103—21no—
61#385×C103—21no—
62#380×C103C2211yescharacteristic
63#340×C103C2211yescharacteristic
64#340×C103C2211yescharacteristic
65#336×C103C2211yescharacteristic
66#336×C103C2211yescharacteristic
67C2×#41×C103—22no—
68C2×#41×C103—22no—
69C2×#41×C103—22no—
70C2×#41×C103—22no—
71C2×#41×C103—22no—
72C2×#41×C103—22no—
73C2×#41×C103—22no—
74C2×#41×C103—22no—
75C2×#41×C103—22no—
76C2×#41×C103—22no—
77C2×#41×C103—22no—
78C2×#41×C103—41no—
79C2×#41×C103—41no—
80C2×#41×C103—41no—
81C2×#41×C103—41no—
82C2×#41×C103—41no—
83C2×#41×C103—41no—
84C2×#41×C103D414yescomplemented
85C22×Q8×C103C2311yescharacteristic
86C22×Q8×C103C2311yescharacteristic
87C22×D4×C103—21no—
88C22×D4×C103—21no—
89C22×D4×C103—21no—
90C22×D4×C103—21no—
91C22×D4×C103—21no—
92C22×D4×C103—21no—
93C22×D4×C103—21no—
94C22×D4×C103—21no—
95C22×D4×C103D411yescharacteristic
96C22×D4×C103C2311yescharacteristic
97C22×D4×C103C2311yescharacteristic
98C22×D4×C103C2311yescharacteristic
99C23×C4×C103—21no—
100C23×C4×C103—21no—
101C23×C4×C103—21no—
102C23×C4×C103C2311yescharacteristic
103C23×C4×C103C2311yescharacteristic
104#135×C103—232no—
105C2×Q16×C103—22no—
106C2×Q16×C103—22no—
107C2×Q16×C103D414yescomplemented
108C2×SD16×C103—22no—
109C2×SD16×C103—22no—
110C2×SD16×C103—22no—
111C2×SD16×C103—22no—
112C2×SD16×C103—22no—
113C2×SD16×C103—22no—
114C2×SD16×C103—22no—
115C2×SD16×C103—41no—
116C2×SD16×C103D414yescomplemented
117C2×D8×C103—22no—
118C2×D8×C103—22no—
119C2×D8×C103—22no—
120C2×D8×C103—22no—
121C2×D8×C103—22no—
122C2×D8×C103—41no—
123C22×C8×C103—22no—
124C22×C8×C103—22no—
125C22×C8×C103—22no—
126C22×C8×C103C2311yescharacteristic
127C22×C8×C103C2311yescharacteristic
128C22×C8×C103C2311yescharacteristic
129C22×C8×C103C2311yescharacteristic
130#127×C103—28no—
131#127×C103—22no—
132#127×C103—22no—
133C22⋊Q8×C103—22no—
134C22⋊Q8×C103—41no—
135#121×C103—28no—
136#121×C103—28no—
137#121×C103—22no—
138#121×C103—22no—
139#121×C103—22no—
140#121×C103—22no—
141#121×C103—41no—
142#121×C103D414yescomplemented
143C4×Q8×C103—22no—
144C4×Q8×C103—22no—
145C4×D4×C103—28no—
146C4×D4×C103—22no—
147C4×D4×C103—22no—
148C2×C4⋊C4×C103—21no—
149C2×C4⋊C4×C103—21no—
150C2×C4⋊C4×C103D411yescharacteristic
151C2×C4⋊C4×C103C2311yescharacteristic
152C2×C4⋊C4×C103C2311yescharacteristic
153C2×C4⋊C4×C103C2311yescharacteristic
154C2×C22⋊C4×C103—21no—
155C2×C22⋊C4×C103—21no—
156C2×C22⋊C4×C103—21no—
157C2×C22⋊C4×C103—21no—
158C2×C22⋊C4×C103—21no—
159C2×C22⋊C4×C103—21no—
160C2×C22⋊C4×C103—21no—
161C2×C22⋊C4×C103D411yescharacteristic
162C2×C22⋊C4×C103D411yescharacteristic
163C2×C42×C103—21no—
164C2×C42×C103C2311yescharacteristic
165#103×C103—22no—
166#103×C103—22no—
167#103×C103—22no—
168#102×C103—22no—
169#102×C103—22no—
170#102×C103—22no—
171#102×C103—41no—
172#102×C103—41no—
173C22⋊C8×C103—22no—
174C22⋊C8×C103—22no—
175C22⋊C8×C103—22no—
176#95×C103—21no—
177#95×C103—21no—
178#95×C103—21no—
179C24×C103—21no—
180C24×C103—21no—
181C24×C103—21no—
182C24×C103C2×D411yescharacteristic
183C24×C103C2×D411yescharacteristic
184#41×C103—28no—
185#41×C103—28no—
186#41×C103—44no—
187#41×C103—44no—
188#41×C103—44no—
189#41×C103—44no—
190#41×C103—44no—
191#41×C103—44no—
192#41×C103—44no—
193#41×C103—44no—
194#41×C103—44no—
195#41×C103—44no—
196C2×Q8×C103—21no—
197C2×Q8×C103—21no—
198C2×Q8×C103—21no—
199C2×Q8×C103—21no—
200C2×Q8×C103—21no—
201C2×Q8×C103—21no—
202C2×Q8×C103—21no—
203C2×Q8×C103—21no—
204C2×Q8×C103C2×D412yes—
205C2×Q8×C103C2×D412yes—
206C2×Q8×C103C2×D412yes—
207C2×Q8×C103C2×D412yes—
208C2×D4×C103—24no—
209C2×D4×C103—24no—
210C2×D4×C103—22no—
211C2×D4×C103—24no—
212C2×D4×C103—24no—
213C2×D4×C103—24no—
214C2×D4×C103—24no—
215C2×D4×C103—22no—
216C2×D4×C103—21no—
217C2×D4×C103—21no—
218C2×D4×C103—21no—
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—21no—
224C2×D4×C103—21no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—21no—
230C2×D4×C103—21no—
231C2×D4×C103—41no—
232C2×D4×C103—42no—
233C2×D4×C103—42no—
234C2×D4×C103—42no—
235C2×D4×C103—42no—
236C2×D4×C103—42no—
237C2×D4×C103—42no—
238C2×D4×C103—42no—
239C2×D4×C103—42no—
240C2×D4×C103—42no—
241C2×D4×C103—42no—
242C2×D4×C103—42no—
243C2×D4×C103—81no—
244C2×D4×C103—81no—
245C2×D4×C103—81no—
246C2×D4×C103—81no—
247C2×D4×C103—81no—
248C2×D4×C103—81no—
249C2×D4×C103—81no—
250C2×D4×C103C2×D412yes—
251C2×D4×C103C2×D412yes—
252C2×D4×C103C2×D412yes—
253C22×C4×C103—21no—
254C22×C4×C103—21no—
255C22×C4×C103—21no—
256C22×C4×C103—21no—
257C22×C4×C103—21no—
258C22×C4×C103—24no—
259C22×C4×C103—21no—
260C22×C4×C103—21no—
261C22×C4×C103—24no—
262C22×C4×C103—21no—
263C22×C4×C103—21no—
264C22×C4×C103—21no—
265C22×C4×C103—21no—
266C22×C4×C103—21no—
267C22×C4×C103—21no—
268C22×C4×C103—21no—
269C22×C4×C103—21no—
270C22×C4×C103—42no—
271C22×C4×C103—42no—
272C22×C4×C103—42no—
273C22×C4×C103—42no—
274C22×C4×C103—42no—
275C22×C4×C103—42no—
276C22×C4×C103—42no—
277C22×C4×C103C2×D411yescharacteristic
278C22×C4×C103C2×D411yescharacteristic
279C22×C4×C103C2×D411yescharacteristic
280C22×C4×C103C2×D412yes—
281C22×C4×C103C2×D412yes—
282C22×C4×C103C2×D411yescharacteristic
283C22×C4×C103C2411yescharacteristic
284Q16×C103—28no—
285SD16×C103—28no—
286SD16×C103—28no—
287SD16×C103—44no—
288D8×C103—28no—
289D8×C103—44no—
290C2×C8×C103—28no—
291C2×C8×C103—21no—
292C2×C8×C103—21no—
293C2×C8×C103—21no—
294C2×C8×C103—21no—
295C2×C8×C103—21no—
296C2×C8×C103—21no—
297C2×C8×C103—21no—
298C2×C8×C103—21no—
299C2×C8×C103—21no—
300C2×C8×C103—21no—
301C2×C8×C103C2×D412yes—
302C2×C8×C103C2×D412yes—
303C4⋊C4×C103—24no—
304C4⋊C4×C103—22no—
305C4⋊C4×C103—21no—
306C4⋊C4×C103—21no—
307C4⋊C4×C103—21no—
308C4⋊C4×C103—21no—
309C4⋊C4×C103—21no—
310C4⋊C4×C103—42no—
311C4⋊C4×C103C2×D412yes—
312C22⋊C4×C103—24no—
313C22⋊C4×C103—22no—
314C22⋊C4×C103—24no—
315C22⋊C4×C103—22no—
316C22⋊C4×C103—42no—
317C22⋊C4×C103—42no—
318C22⋊C4×C103—42no—
319C22⋊C4×C103—81no—
320C22⋊C4×C103—81no—
321C42×C103—24no—
322C42×C103—21no—
323C42×C103—21no—
324C23×C103—21no—
325C23×C103—21no—
326C23×C103—21no—
327C23×C103—21no—
328C23×C103—21no—
329C23×C103—21no—
330C23×C103—21no—
331C23×C103—22no—
332C23×C103—22no—
333C23×C103—21no—
334C23×C103—22no—
335C23×C103—21no—
336C23×C103—21no—
337C23×C103—21no—
338C23×C103—21no—
339C23×C103—21no—
340C23×C103—41no—
341C23×C103—41no—
342C23×C103—41no—
343C23×C103—41no—
344C23×C103—41no—
345C23×C103—41no—
346C23×C103—41no—
347C23×C103—41no—
348C23×C103—41no—
349C23×C103—41no—
350C23×C103—41no—
351C23×C103—41no—
352C23×C103—41no—
353C23×C103—41no—
354C23×C103—41no—
355C23×C103—41no—
356C23×C103—41no—
357C23×C103—41no—
358C23×C103#12012yes—
359C23×C103C22×D411yescharacteristic
360Q8×C103—22no—
361Q8×C103—22no—
362Q8×C103—22no—
363Q8×C103—22no—
364Q8×C103—22no—
365Q8×C103—41no—
366Q8×C103—41no—
367Q8×C103#12014yes—
368D4×C103—22no—
369D4×C103—22no—
370D4×C103—22no—
371D4×C103—22no—
372D4×C103—22no—
373D4×C103—22no—
374D4×C103—44no—
375D4×C103—48no—
376D4×C103—48no—
377D4×C103—48no—
378D4×C103—48no—
379D4×C103—41no—
380D4×C103—41no—
381D4×C103—41no—
382D4×C103—41no—
383D4×C103—41no—
384D4×C103—41no—
385D4×C103—84no—
386D4×C103—84no—
387D4×C103—84no—
388D4×C103—84no—
389C2×C4×C103—21no—
390C2×C4×C103—22no—
391C2×C4×C103—21no—
392C2×C4×C103—21no—
393C2×C4×C103—22no—
394C2×C4×C103—22no—
395C2×C4×C103—21no—
396C2×C4×C103—22no—
397C2×C4×C103—22no—
398C2×C4×C103—22no—
399C2×C4×C103—22no—
400C2×C4×C103—21no—
401C2×C4×C103—22no—
402C2×C4×C103—21no—
403C2×C4×C103—21no—
404C2×C4×C103—22no—
405C2×C4×C103—21no—
406C2×C4×C103—21no—
407C2×C4×C103—21no—
408C2×C4×C103—48no—
409C2×C4×C103—48no—
410C2×C4×C103—48no—
411C2×C4×C103—41no—
412C2×C4×C103—41no—
413C2×C4×C103—41no—
414C2×C4×C103—41no—
415C2×C4×C103—41no—
416C2×C4×C103—41no—
417C2×C4×C103—41no—
418C2×C4×C103—41no—
419C2×C4×C103—41no—
420C2×C4×C103—41no—
421C2×C4×C103—41no—
422C2×C4×C103—41no—
423C2×C4×C103—41no—
424C2×C4×C103—41no—
425C2×C4×C103#12012yes—
426C2×C4×C103#13512yescomplemented
427C2×C4×C103C22×D411yescharacteristic
428C2×C4×C103C22×D411yescharacteristic
429C2×C4×C103C22×D411yescharacteristic
430C2×C4×C103C22×D411yescharacteristic
431C2×C4×C103H(5,𝔽2)11yescharacteristic
432C2×C4×C103H(5,𝔽2)11yescharacteristic
433C8×C103—22no—
434C8×C103—22no—
435C8×C103—41no—
436C8×C103—41no—
437C22×C103—22no—
438C22×C103—22no—
439C22×C103—22no—
440C22×C103—41no—
441C22×C103—41no—
442C22×C103—41no—
443C22×C103—41no—
444C22×C103—42no—
445C22×C103—42no—
446C22×C103—42no—
447C22×C103—41no—
448C22×C103—41no—
449C22×C103—42no—
450C22×C103—42no—
451C22×C103—41no—
452C22×C103—42no—
453C22×C103—42no—
454C22×C103—41no—
455C22×C103—42no—
456C22×C103—41no—
457C22×C103—41no—
458C22×C103—42no—
459C22×C103—41no—
460C22×C103—81no—
461C22×C103—81no—
462C22×C103—81no—
463C22×C103—81no—
464C22×C103—81no—
465C22×C103—81no—
466C22×C103—81no—
467C22×C103—81no—
468C22×C103—81no—
469C22×C103—81no—
470C22×C103—81no—
471C22×C103—81no—
472C22×C103C2×#12011yescharacteristic
473C22×C103D4211yescharacteristic
474C22×C103D4211yescharacteristic
475C22×C103C2×#13511yescharacteristic
476C22×C103#57511yescharacteristic
477C22×C103#57611yescharacteristic
478C22×C103#57711yescharacteristic
479C4×C103—22no—
480C4×C103—24no—
481C4×C103—22no—
482C4×C103—41no—
483C4×C103—42no—
484C4×C103—41no—
485C4×C103—42no—
486C4×C103—81no—
487C4×C103—81no—
488C4×C103C2×#12011yescharacteristic
489C4×C103#53411yescharacteristic
490C4×C103D4211yescharacteristic
491C4×C103D4211yescharacteristic
492#23857C10311yesmaximal, characteristic, direct product factor, Sylow
493C2×C103—42no—
494C2×C103—81no—
495C2×C103—82no—
496C2×C103—82no—
497C2×C103—82no—
498C2×C103#240311yescharacteristic
499C2×C103#300211yescharacteristic
500C2×C103#301211yescharacteristic
501C2×C103#326811yescharacteristic
502C2×C103#327111yescharacteristic
503C2×C103#328411yescharacteristic
504C2×C103#328711yescharacteristic
505C22×#135C2×C10311yescharacteristic, complemented
506C2×#550C2×C10311yescharacteristic, complemented
507C2×#452C2×C10311yescharacteristic, complemented
508C2×#449C2×C10311yescharacteristic, complemented
509C2×#449C2×C10311yescharacteristic, complemented
510#2407C2×C10311yescharacteristic, complemented
511#2014C2×C10311yescharacteristic, complemented
512#2011C2×C10311yescharacteristic, complemented
513#2000C2×C10311yescharacteristic, complemented
514#1999C2×C10311yescharacteristic, complemented
515#1893C2×C10311yescharacteristic, complemented
516#1880C2×C10311yescharacteristic, complemented
517#1878C2×C10311yescharacteristic, complemented
518#1869C2×C10311yescharacteristic, complemented
519#1788C2×C10311yescharacteristic, complemented
520C103#2385711yescharacteristic, direct product factor, Sylow
521C22×#41C22×C10311yescharacteristic
522C22×#41C22×C10311yescharacteristic
523C22×#41C22×C10311yescharacteristic
524C2×#135—24no—
525C2×#135—24no—
526C2×#135—24no—
527C22×Q16C22×C10311yescharacteristic
528C22×SD16C22×C10311yescharacteristic
529C22×SD16C22×C10311yescharacteristic
530C22×SD16C22×C10311yescharacteristic
531C22×D8C22×C10311yescharacteristic
532C22×D8C22×C10311yescharacteristic
533C23×C8C22×C10311yescharacteristic
534#550—24no—
535#550—24no—
536C2×#127—21no—
537C2×#127C22×C10311yescharacteristic
538C2×C22⋊Q8C22×C10311yescharacteristic
539C2×#121—21no—
540C2×#121—21no—
541C2×#121C22×C10311yescharacteristic
542C2×#121C22×C10311yescharacteristic
543C2×#121C22×C10311yescharacteristic
544C2×C4×Q8C22×C10311yescharacteristic
545C2×C4×D4—21no—
546C2×C4×D4C22×C10311yescharacteristic
547#452—24no—
548#449—24no—
549#449—24no—
550C2×#103C22×C10311yescharacteristic
551C2×#103C22×C10311yescharacteristic
552C2×#103C22×C10311yescharacteristic
553C2×#102C22×C10311yescharacteristic
554C2×#102C22×C10311yescharacteristic
555C2×#102C22×C10311yescharacteristic
556C2×#102C22×C10311yescharacteristic
557C2×#102C22×C10311yescharacteristic
558C2×C22⋊C8C22×C10311yescharacteristic
559C2×C22⋊C8C22×C10311yescharacteristic
560C2×C22⋊C8C22×C10311yescharacteristic
561#394—21no—
562#392—21no—
563#391C22×C10311yescharacteristic
564#390C22×C10311yescharacteristic
565#386—21no—
566#385—21no—
567#380C22×C10311yescharacteristic
568#340C22×C10311yescharacteristic
569#340C22×C10311yescharacteristic
570#336C22×C10311yescharacteristic
571#336C22×C10311yescharacteristic
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C10314yescomplemented
590C22×Q8C23×C10311yescharacteristic
591C22×Q8C23×C10311yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C10311yescharacteristic
601C22×D4C23×C10311yescharacteristic
602C22×D4C23×C10311yescharacteristic
603C22×D4C23×C10311yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C10311yescharacteristic
608C23×C4C23×C10311yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C10314yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C10314yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C10311yescharacteristic
632C22×C8C23×C10311yescharacteristic
633C22×C8C23×C10311yescharacteristic
634C22×C8C23×C10311yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C10314yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C10311yescharacteristic
656C2×C4⋊C4C23×C10311yescharacteristic
657C2×C4⋊C4C23×C10311yescharacteristic
658C2×C4⋊C4C23×C10311yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C10311yescharacteristic
667C2×C22⋊C4D4×C10311yescharacteristic
668C2×C42—21no—
669C2×C42C23×C10311yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C10311yescharacteristic
688C24C2×D4×C10311yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C10312yes—
710C2×Q8C2×D4×C10312yes—
711C2×Q8C2×D4×C10312yes—
712C2×Q8C2×D4×C10312yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C10312yes—
756C2×D4C2×D4×C10312yes—
757C2×D4C2×D4×C10312yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C10311yescharacteristic
783C22×C4C2×D4×C10311yescharacteristic
784C22×C4C2×D4×C10311yescharacteristic
785C22×C4C2×D4×C10312yes—
786C22×C4C2×D4×C10312yes—
787C22×C4C2×D4×C10311yescharacteristic
788C22×C4C24×C10311yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C10312yes—
807C2×C8C2×D4×C10312yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C10312yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C10312yes—
864C23C22×D4×C10311yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C10314yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C10312yes—
931C2×C4#135×C10312yescomplemented
932C2×C4C22×D4×C10311yescharacteristic
933C2×C4C22×D4×C10311yescharacteristic
934C2×C4C22×D4×C10311yescharacteristic
935C2×C4C22×D4×C10311yescharacteristic
936C2×C4H(5,𝔽2)×C10311yescharacteristic
937C2×C4H(5,𝔽2)×C10311yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—41no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C10311yescharacteristic
978C22D42×C10311yescharacteristic
979C22D42×C10311yescharacteristic
980C22C2×#135×C10311yescharacteristic
981C22#575×C10311yescharacteristic
982C22#576×C10311yescharacteristic
983C22#577×C10311yescharacteristic
984C4—22no—
985C4—22no—
986C4—24no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C10311yescharacteristic
994C4#534×C10311yescharacteristic
995C4D42×C10311yescharacteristic
996C4D42×C10311yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C103×#240311yescharacteristic
1003C2C103×#300211yescharacteristic
1004C2C103×#301211yescharacteristic
1005C2C103×#326811yescharacteristic
1006C2C103×#327111yescharacteristic
1007C2C103×#328411yescharacteristic
1008C2C103×#328711yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C103C2semidirect
2. C2×#550×C103C2semidirect
3. C2×#452×C103C2semidirect
4. C2×#449×C103C2semidirect
5. C2×#449×C103C2semidirect
6. C103×#2407C2semidirect
7. C103×#2014C2semidirect
8. C103×#2011C2semidirect
9. C103×#2000C2semidirect
10. C103×#1999C2semidirect
11. C103×#1893C2semidirect
12. C103×#1880C2semidirect
13. C103×#1878C2semidirect
14. C103×#1869C2semidirect
15. C103×#1788C2semidirect
84. C2×#41×C103D4semidirect
107. C2×Q16×C103D4semidirect
116. C2×SD16×C103D4semidirect
142. #121×C103D4semidirect
426. C2×C4×C103#135semidirect
492. #23857C103direct (N × H)
505. C22×#135C2×C103semidirect
506. C2×#550C2×C103semidirect
507. C2×#452C2×C103semidirect
508. C2×#449C2×C103semidirect
509. C2×#449C2×C103semidirect
510. #2407C2×C103semidirect
511. #2014C2×C103semidirect
512. #2011C2×C103semidirect
513. #2000C2×C103semidirect
514. #1999C2×C103semidirect
515. #1893C2×C103semidirect
516. #1880C2×C103semidirect
517. #1878C2×C103semidirect
518. #1869C2×C103semidirect
519. #1788C2×C103semidirect
520. C103#23857direct (N × H)
589. C2×#41D4×C103semidirect
612. C2×Q16D4×C103semidirect
621. C2×SD16D4×C103semidirect
647. #121D4×C103semidirect
931. C2×C4#135×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1032
C2×#550×C1032
C2×#452×C1032
C2×#449×C1032
C103×#24072
C103×#20142
C103×#20112
C103×#20002
C103×#19992
C103×#18932
C103×#18802
C103×#18782
C103×#18692
C103×#17882
#23857103