Finite Group Databasebeta

← C103×#24427 #39929702

Subgroups — C103×#24427 #39929702

Order 26368.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C103C211yesmaximal, characteristic
2C2×#465×C103C211yesmaximal, characteristic, complemented
3C2×#452×C103C211yesmaximal, characteristic, complemented
4C2×#452×C103C211yesmaximal, characteristic, complemented
5C2×#416×C103C211yesmaximal, characteristic, complemented
6C103×#2415C211yesmaximal, characteristic, complemented
7C103×#2041C211yesmaximal, characteristic, complemented
8C103×#2034C211yesmaximal, characteristic, complemented
9C103×#2014C211yesmaximal, characteristic, complemented
10C103×#2000C211yesmaximal, characteristic, complemented
11C103×#1878C211yesmaximal, characteristic, complemented
12C103×#1875C211yesmaximal, characteristic, complemented
13C103×#1869C211yesmaximal, characteristic, complemented
14C103×#1865C211yesmaximal, characteristic, complemented
15C103×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C22×Q16×C103C2211yescharacteristic
19C22×SD16×C103C2211yescharacteristic
20C22×SD16×C103C2211yescharacteristic
21C23×C8×C103C2211yescharacteristic
22#550×C103—24no—
23#550×C103—24no—
24C2×#127×C103—21no—
25C2×#127×C103C2211yescharacteristic
26C2×C22⋊Q8×C103C2211yescharacteristic
27C2×C22⋊Q8×C103C2211yescharacteristic
28C2×#121×C103—21no—
29C2×#121×C103—21no—
30C2×#121×C103C2211yescharacteristic
31C2×#121×C103C2211yescharacteristic
32C2×C4×Q8×C103C2211yescharacteristic
33C2×C4×D4×C103—21no—
34C2×C4×D4×C103C2211yescharacteristic
35C2×#117×C103C2211yescharacteristic
36#465×C103—24no—
37#452×C103—24no—
38#452×C103—24no—
39C2×#106×C103C2211yescharacteristic
40#416×C103—24no—
41C2×#103×C103C2211yescharacteristic
42C2×#103×C103C2211yescharacteristic
43C2×#103×C103C2211yescharacteristic
44C2×#103×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×#102×C103C2211yescharacteristic
47C2×#102×C103C2211yescharacteristic
48C2×#102×C103C2211yescharacteristic
49C2×#102×C103C2211yescharacteristic
50C2×#102×C103C2211yescharacteristic
51C2×C22⋊C8×C103C2211yescharacteristic
52C2×C22⋊C8×C103C2211yescharacteristic
53C2×C22⋊C8×C103C2211yescharacteristic
54#397×C103—21no—
55#394×C103—21no—
56#391×C103C2211yescharacteristic
57#389×C103—21no—
58#389×C103C2211yescharacteristic
59#388×C103—21no—
60#380×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic
62#340×C103C2211yescharacteristic
63#336×C103C2211yescharacteristic
64#336×C103C2211yescharacteristic
65C2×#41×C103—22no—
66C2×#41×C103—22no—
67C2×#41×C103—22no—
68C2×#41×C103—22no—
69C2×#41×C103—22no—
70C2×#41×C103—22no—
71C2×#41×C103—22no—
72C2×#41×C103—41no—
73C2×#41×C103—41no—
74C2×#41×C103—41no—
75C2×#41×C103—41no—
76C2×#41×C103D414yes—
77C22×Q8×C103C2311yescharacteristic
78C22×Q8×C103C2311yescharacteristic
79C22×D4×C103—21no—
80C22×D4×C103—21no—
81C22×D4×C103—21no—
82C22×D4×C103—21no—
83C22×D4×C103—21no—
84C22×D4×C103—21no—
85C22×D4×C103D411yescharacteristic
86C22×D4×C103C2311yescharacteristic
87C22×D4×C103C2311yescharacteristic
88C23×C4×C103—21no—
89C23×C4×C103—21no—
90C23×C4×C103C2311yescharacteristic
91C23×C4×C103C2311yescharacteristic
92C2×Q16×C103—22no—
93C2×Q16×C103—22no—
94C2×Q16×C103—22no—
95C2×SD16×C103—22no—
96C2×SD16×C103—22no—
97C2×SD16×C103—22no—
98C2×SD16×C103—41no—
99C2×SD16×C103—41no—
100C2×SD16×C103—41no—
101C22×C8×C103—22no—
102C22×C8×C103—22no—
103C22×C8×C103—41no—
104C22×C8×C103C2311yescharacteristic
105C22×C8×C103C2311yescharacteristic
106C22×C8×C103C2311yescharacteristic
107C22×C8×C103C2311yescharacteristic
108#127×C103—28no—
109#127×C103—22no—
110#127×C103—22no—
111C22⋊Q8×C103—22no—
112C22⋊Q8×C103—22no—
113C22⋊Q8×C103—22no—
114C22⋊Q8×C103—41no—
115#121×C103—28no—
116#121×C103—28no—
117#121×C103—22no—
118#121×C103—22no—
119#121×C103—22no—
120#121×C103D414yes—
121C4×Q8×C103—22no—
122C4×Q8×C103—22no—
123C4×D4×C103—28no—
124C4×D4×C103—22no—
125C4×D4×C103—22no—
126#117×C103—22no—
127#117×C103—41no—
128C2×C4⋊C4×C103—21no—
129C2×C4⋊C4×C103—21no—
130C2×C4⋊C4×C103—21no—
131C2×C4⋊C4×C103—21no—
132C2×C4⋊C4×C103D411yescharacteristic
133C2×C4⋊C4×C103C2311yescharacteristic
134C2×C4⋊C4×C103C2311yescharacteristic
135C2×C4⋊C4×C103C2311yescharacteristic
136C2×C4⋊C4×C103C2311yescharacteristic
137C2×C22⋊C4×C103—21no—
138C2×C22⋊C4×C103—21no—
139C2×C22⋊C4×C103—21no—
140C2×C22⋊C4×C103—21no—
141C2×C22⋊C4×C103—21no—
142C2×C22⋊C4×C103—21no—
143C2×C22⋊C4×C103D411yescharacteristic
144C2×C22⋊C4×C103D411yescharacteristic
145C2×C42×C103—21no—
146C2×C42×C103—21no—
147C2×C42×C103C2311yescharacteristic
148#106×C103—22no—
149#103×C103—22no—
150#103×C103—22no—
151#103×C103—22no—
152#103×C103D414yescomplemented
153#102×C103—22no—
154#102×C103—22no—
155#102×C103—22no—
156#102×C103—22no—
157#102×C103—22no—
158#102×C103—41no—
159C22⋊C8×C103—22no—
160C22⋊C8×C103—22no—
161C22⋊C8×C103—41no—
162#95×C103—21no—
163#95×C103—21no—
164#95×C103—21no—
165#95×C103—21no—
166C24×C103—21no—
167C24×C103—21no—
168C24×C103C2×D411yescharacteristic
169C24×C103C2×D411yescharacteristic
170#41×C103—28no—
171#41×C103—44no—
172#41×C103—44no—
173#41×C103—44no—
174#41×C103—44no—
175#41×C103—44no—
176#41×C103—44no—
177#41×C103—44no—
178C2×Q8×C103—21no—
179C2×Q8×C103—21no—
180C2×Q8×C103—21no—
181C2×Q8×C103—21no—
182C2×Q8×C103—21no—
183C2×Q8×C103—21no—
184C2×Q8×C103—21no—
185C2×Q8×C103—21no—
186C2×Q8×C103—21no—
187C2×Q8×C103C2×D412yes—
188C2×Q8×C103C2×D412yes—
189C2×Q8×C103#4112yes—
190C2×D4×C103—24no—
191C2×D4×C103—24no—
192C2×D4×C103—22no—
193C2×D4×C103—24no—
194C2×D4×C103—24no—
195C2×D4×C103—24no—
196C2×D4×C103—24no—
197C2×D4×C103—22no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—21no—
203C2×D4×C103—21no—
204C2×D4×C103—21no—
205C2×D4×C103—21no—
206C2×D4×C103—21no—
207C2×D4×C103—21no—
208C2×D4×C103—41no—
209C2×D4×C103—42no—
210C2×D4×C103—42no—
211C2×D4×C103—42no—
212C2×D4×C103—42no—
213C2×D4×C103—42no—
214C2×D4×C103—42no—
215C2×D4×C103—81no—
216C2×D4×C103—81no—
217C2×D4×C103—81no—
218C2×D4×C103—81no—
219C2×D4×C103—81no—
220C2×D4×C103—81no—
221C2×D4×C103C2×D412yes—
222C2×D4×C103C2×D412yes—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—21no—
227C22×C4×C103—21no—
228C22×C4×C103—24no—
229C22×C4×C103—21no—
230C22×C4×C103—21no—
231C22×C4×C103—24no—
232C22×C4×C103—21no—
233C22×C4×C103—21no—
234C22×C4×C103—21no—
235C22×C4×C103—21no—
236C22×C4×C103—21no—
237C22×C4×C103—21no—
238C22×C4×C103—21no—
239C22×C4×C103—21no—
240C22×C4×C103—21no—
241C22×C4×C103—42no—
242C22×C4×C103—42no—
243C22×C4×C103—42no—
244C22×C4×C103—42no—
245C22×C4×C103C2×D411yescharacteristic
246C22×C4×C103C2×D411yescharacteristic
247C22×C4×C103C2×D411yescharacteristic
248C22×C4×C103C2×D412yes—
249C22×C4×C103C2×D412yes—
250C22×C4×C103C2×D411yescharacteristic
251C22×C4×C103C2411yescharacteristic
252Q16×C103—44no—
253SD16×C103—44no—
254SD16×C103—44no—
255C2×C8×C103—21no—
256C2×C8×C103—21no—
257C2×C8×C103—21no—
258C2×C8×C103—21no—
259C2×C8×C103—21no—
260C2×C8×C103—21no—
261C2×C8×C103—21no—
262C2×C8×C103—21no—
263C2×C8×C103—21no—
264C2×C8×C103—21no—
265C2×C8×C103—21no—
266C2×C8×C103—44no—
267C2×C8×C103C2×D412yes—
268C4⋊C4×C103—24no—
269C4⋊C4×C103—22no—
270C4⋊C4×C103—21no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103—21no—
273C4⋊C4×C103—21no—
274C4⋊C4×C103—21no—
275C4⋊C4×C103—21no—
276C4⋊C4×C103—42no—
277C4⋊C4×C103—42no—
278C4⋊C4×C103—42no—
279C4⋊C4×C103C2×D412yes—
280C4⋊C4×C103C2×D412yes—
281C22⋊C4×C103—24no—
282C22⋊C4×C103—22no—
283C22⋊C4×C103—24no—
284C22⋊C4×C103—22no—
285C22⋊C4×C103—42no—
286C22⋊C4×C103—42no—
287C22⋊C4×C103—42no—
288C22⋊C4×C103—42no—
289C42×C103—24no—
290C42×C103—21no—
291C42×C103—21no—
292C42×C103—42no—
293C23×C103—21no—
294C23×C103—21no—
295C23×C103—21no—
296C23×C103—21no—
297C23×C103—21no—
298C23×C103—21no—
299C23×C103—21no—
300C23×C103—22no—
301C23×C103—22no—
302C23×C103—21no—
303C23×C103—21no—
304C23×C103—21no—
305C23×C103—21no—
306C23×C103—21no—
307C23×C103—21no—
308C23×C103—41no—
309C23×C103—41no—
310C23×C103—41no—
311C23×C103—41no—
312C23×C103—41no—
313C23×C103—41no—
314C23×C103—41no—
315C23×C103—41no—
316C23×C103—41no—
317C23×C103—41no—
318C23×C103—41no—
319C23×C103—41no—
320C23×C103#12012yes—
321C23×C103C22×D411yescharacteristic
322Q8×C103—22no—
323Q8×C103—22no—
324Q8×C103—22no—
325Q8×C103—41no—
326Q8×C103—41no—
327Q8×C103—41no—
328Q8×C103—41no—
329Q8×C103#12114yes—
330D4×C103—22no—
331D4×C103—22no—
332D4×C103—22no—
333D4×C103—22no—
334D4×C103—44no—
335D4×C103—48no—
336D4×C103—48no—
337D4×C103—48no—
338D4×C103—41no—
339D4×C103—41no—
340D4×C103—41no—
341D4×C103—41no—
342D4×C103—84no—
343D4×C103—84no—
344D4×C103—84no—
345C2×C4×C103—21no—
346C2×C4×C103—22no—
347C2×C4×C103—21no—
348C2×C4×C103—22no—
349C2×C4×C103—21no—
350C2×C4×C103—22no—
351C2×C4×C103—21no—
352C2×C4×C103—22no—
353C2×C4×C103—22no—
354C2×C4×C103—22no—
355C2×C4×C103—22no—
356C2×C4×C103—21no—
357C2×C4×C103—22no—
358C2×C4×C103—21no—
359C2×C4×C103—22no—
360C2×C4×C103—21no—
361C2×C4×C103—21no—
362C2×C4×C103—21no—
363C2×C4×C103—21no—
364C2×C4×C103—48no—
365C2×C4×C103—48no—
366C2×C4×C103—41no—
367C2×C4×C103—41no—
368C2×C4×C103—41no—
369C2×C4×C103—41no—
370C2×C4×C103—41no—
371C2×C4×C103—41no—
372C2×C4×C103—41no—
373C2×C4×C103—41no—
374C2×C4×C103—41no—
375C2×C4×C103—41no—
376C2×C4×C103—41no—
377C2×C4×C103—41no—
378C2×C4×C103—41no—
379C2×C4×C103—41no—
380C2×C4×C103—41no—
381C2×C4×C103—41no—
382C2×C4×C103—41no—
383C2×C4×C103#12012yes—
384C2×C4×C103#13512yes—
385C2×C4×C103C22×D411yescharacteristic
386C2×C4×C103C22×D411yescharacteristic
387C2×C4×C103C22×D411yescharacteristic
388C2×C4×C103C2×#4111yescharacteristic
389C2×C4×C103H(5,𝔽2)11yescharacteristic
390C2×C4×C103H(5,𝔽2)11yescharacteristic
391C8×C103—22no—
392C8×C103—41no—
393C8×C103—41no—
394C8×C103—41no—
395C22×C103—22no—
396C22×C103—22no—
397C22×C103—22no—
398C22×C103—41no—
399C22×C103—41no—
400C22×C103—41no—
401C22×C103—41no—
402C22×C103—42no—
403C22×C103—42no—
404C22×C103—41no—
405C22×C103—41no—
406C22×C103—42no—
407C22×C103—42no—
408C22×C103—41no—
409C22×C103—42no—
410C22×C103—42no—
411C22×C103—41no—
412C22×C103—41no—
413C22×C103—41no—
414C22×C103—41no—
415C22×C103—81no—
416C22×C103—81no—
417C22×C103—81no—
418C22×C103—81no—
419C22×C103—81no—
420C22×C103—81no—
421C22×C103—81no—
422C22×C103—81no—
423C22×C103C2×#12011yescharacteristic
424C22×C103D4211yescharacteristic
425C22×C103#54611yescharacteristic
426C22×C103C2×#13511yescharacteristic
427C22×C103#57511yescharacteristic
428C22×C103#57711yescharacteristic
429C22×C103#57711yescharacteristic
430C4×C103—22no—
431C4×C103—24no—
432C4×C103—22no—
433C4×C103—41no—
434C4×C103—41no—
435C4×C103—42no—
436C4×C103—42no—
437C4×C103—81no—
438C4×C103—81no—
439C4×C103—81no—
440C4×C103C2×#12111yescharacteristic
441C4×C103#53411yescharacteristic
442C4×C103D4211yescharacteristic
443C4×C103#54611yescharacteristic
444#24427C10311yesmaximal, characteristic, direct product factor, Sylow
445C2×C103—42no—
446C2×C103—81no—
447C2×C103—82no—
448C2×C103—82no—
449C2×C103#241011yescharacteristic
450C2×C103#300211yescharacteristic
451C2×C103#300911yescharacteristic
452C2×C103#327111yescharacteristic
453C2×C103#328411yescharacteristic
454C2×C103#330411yescharacteristic
455C2×C103#331711yescharacteristic
456C2×#550C2×C10311yescharacteristic
457C2×#465C2×C10311yescharacteristic, complemented
458C2×#452C2×C10311yescharacteristic, complemented
459C2×#452C2×C10311yescharacteristic, complemented
460C2×#416C2×C10311yescharacteristic, complemented
461#2415C2×C10311yescharacteristic, complemented
462#2041C2×C10311yescharacteristic, complemented
463#2034C2×C10311yescharacteristic, complemented
464#2014C2×C10311yescharacteristic, complemented
465#2000C2×C10311yescharacteristic, complemented
466#1878C2×C10311yescharacteristic, complemented
467#1875C2×C10311yescharacteristic, complemented
468#1869C2×C10311yescharacteristic, complemented
469#1865C2×C10311yescharacteristic, complemented
470#1788C2×C10311yescharacteristic, complemented
471C103#2442711yescharacteristic, direct product factor, Sylow
472C22×#41C22×C10311yescharacteristic
473C22×#41C22×C10311yescharacteristic
474C22×Q16C22×C10311yescharacteristic
475C22×SD16C22×C10311yescharacteristic
476C22×SD16C22×C10311yescharacteristic
477C23×C8C22×C10311yescharacteristic
478#550—24no—
479#550—24no—
480C2×#127—21no—
481C2×#127C22×C10311yescharacteristic
482C2×C22⋊Q8C22×C10311yescharacteristic
483C2×C22⋊Q8C22×C10311yescharacteristic
484C2×#121—21no—
485C2×#121—21no—
486C2×#121C22×C10311yescharacteristic
487C2×#121C22×C10311yescharacteristic
488C2×C4×Q8C22×C10311yescharacteristic
489C2×C4×D4—21no—
490C2×C4×D4C22×C10311yescharacteristic
491C2×#117C22×C10311yescharacteristic
492#465—24no—
493#452—24no—
494#452—24no—
495C2×#106C22×C10311yescharacteristic
496#416—24no—
497C2×#103C22×C10311yescharacteristic
498C2×#103C22×C10311yescharacteristic
499C2×#103C22×C10311yescharacteristic
500C2×#103C22×C10311yescharacteristic
501C2×#102C22×C10311yescharacteristic
502C2×#102C22×C10311yescharacteristic
503C2×#102C22×C10311yescharacteristic
504C2×#102C22×C10311yescharacteristic
505C2×#102C22×C10311yescharacteristic
506C2×#102C22×C10311yescharacteristic
507C2×C22⋊C8C22×C10311yescharacteristic
508C2×C22⋊C8C22×C10311yescharacteristic
509C2×C22⋊C8C22×C10311yescharacteristic
510#397—21no—
511#394—21no—
512#391C22×C10311yescharacteristic
513#389—21no—
514#389C22×C10311yescharacteristic
515#388—21no—
516#380C22×C10311yescharacteristic
517#340C22×C10311yescharacteristic
518#340C22×C10311yescharacteristic
519#336C22×C10311yescharacteristic
520#336C22×C10311yescharacteristic
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41D4×C10314yes—
533C22×Q8C23×C10311yescharacteristic
534C22×Q8C23×C10311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C10311yescharacteristic
542C22×D4C23×C10311yescharacteristic
543C22×D4C23×C10311yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C10311yescharacteristic
547C23×C4C23×C10311yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—41no—
560C22×C8C23×C10311yescharacteristic
561C22×C8C23×C10311yescharacteristic
562C22×C8C23×C10311yescharacteristic
563C22×C8C23×C10311yescharacteristic
564#127—28no—
565#127—22no—
566#127—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—41no—
571#121—28no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121D4×C10314yes—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582#117—22no—
583#117—41no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10311yescharacteristic
589C2×C4⋊C4C23×C10311yescharacteristic
590C2×C4⋊C4C23×C10311yescharacteristic
591C2×C4⋊C4C23×C10311yescharacteristic
592C2×C4⋊C4C23×C10311yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4D4×C10311yescharacteristic
600C2×C22⋊C4D4×C10311yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C23×C10311yescharacteristic
604#106—22no—
605#103—22no—
606#103—22no—
607#103—22no—
608#103D4×C10314yescomplemented
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—41no—
615C22⋊C8—22no—
616C22⋊C8—22no—
617C22⋊C8—41no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622C24—21no—
623C24—21no—
624C24C2×D4×C10311yescharacteristic
625C24C2×D4×C10311yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C10312yes—
644C2×Q8C2×D4×C10312yes—
645C2×Q8#41×C10312yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C10312yes—
678C2×D4C2×D4×C10312yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×D4×C10311yescharacteristic
702C22×C4C2×D4×C10311yescharacteristic
703C22×C4C2×D4×C10311yescharacteristic
704C22×C4C2×D4×C10312yes—
705C22×C4C2×D4×C10312yes—
706C22×C4C2×D4×C10311yescharacteristic
707C22×C4C24×C10311yescharacteristic
708Q16—44no—
709SD16—44no—
710SD16—44no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C10312yes—
724C4⋊C4—24no—
725C4⋊C4—22no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4C2×D4×C10312yes—
736C4⋊C4C2×D4×C10312yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—42no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#120×C10312yes—
777C23C22×D4×C10311yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8#121×C10314yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4#120×C10312yes—
840C2×C4#135×C10312yes—
841C2×C4C22×D4×C10311yescharacteristic
842C2×C4C22×D4×C10311yescharacteristic
843C2×C4C22×D4×C10311yescharacteristic
844C2×C4C2×#41×C10311yescharacteristic
845C2×C4H(5,𝔽2)×C10311yescharacteristic
846C2×C4H(5,𝔽2)×C10311yescharacteristic
847C8—22no—
848C8—41no—
849C8—41no—
850C8—41no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#120×C10311yescharacteristic
880C22D42×C10311yescharacteristic
881C22#546×C10311yescharacteristic
882C22C2×#135×C10311yescharacteristic
883C22#575×C10311yescharacteristic
884C22#577×C10311yescharacteristic
885C22#577×C10311yescharacteristic
886C4—22no—
887C4—22no—
888C4—24no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4C2×#121×C10311yescharacteristic
897C4#534×C10311yescharacteristic
898C4D42×C10311yescharacteristic
899C4#546×C10311yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2C103×#241011yescharacteristic
905C2C103×#300211yescharacteristic
906C2C103×#300911yescharacteristic
907C2C103×#327111yescharacteristic
908C2C103×#328411yescharacteristic
909C2C103×#330411yescharacteristic
910C2C103×#331711yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#550×C103C2
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
2. C2×#465×C103C2semidirect
3. C2×#452×C103C2semidirect
4. C2×#452×C103C2semidirect
5. C2×#416×C103C2semidirect
6. C103×#2415C2semidirect
7. C103×#2041C2semidirect
8. C103×#2034C2semidirect
9. C103×#2014C2semidirect
10. C103×#2000C2semidirect
11. C103×#1878C2semidirect
12. C103×#1875C2semidirect
13. C103×#1869C2semidirect
14. C103×#1865C2semidirect
15. C103×#1788C2semidirect
152. #103×C103D4semidirect
444. #24427C103direct (N × H)
457. C2×#465C2×C103semidirect
458. C2×#452C2×C103semidirect
459. C2×#452C2×C103semidirect
460. C2×#416C2×C103semidirect
461. #2415C2×C103semidirect
462. #2041C2×C103semidirect
463. #2034C2×C103semidirect
464. #2014C2×C103semidirect
465. #2000C2×C103semidirect
466. #1878C2×C103semidirect
467. #1875C2×C103semidirect
468. #1869C2×C103semidirect
469. #1865C2×C103semidirect
470. #1788C2×C103semidirect
471. C103#24427direct (N × H)
608. #103D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1032
C2×#465×C1032
C2×#452×C1032
C2×#416×C1032
C103×#24152
C103×#20412
C103×#20342
C103×#20142
C103×#20002
C103×#18782
C103×#18752
C103×#18692
C103×#18652
C103×#17882
#24427103