Finite Group Databasebeta

← C103×#25419 #39930694

Subgroups — C103×#25419 #39930694

Order 26368.

1134 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C103C211yesmaximal, characteristic, complemented
2C2×#469×C103C211yesmaximal, characteristic, complemented
3C2×#468×C103C211yesmaximal, characteristic, complemented
4C2×C4×D8×C103C211yesmaximal, characteristic, complemented
5C103×#2428C211yesmaximal, characteristic, complemented
6C103×#2427C211yesmaximal, characteristic, complemented
7C103×#2042C211yesmaximal, characteristic, complemented
8C103×#2041C211yesmaximal, characteristic, complemented
9C103×#2000C211yesmaximal, characteristic, complemented
10C103×#1999C211yesmaximal, characteristic, complemented
11C103×#1968C211yesmaximal, characteristic, complemented
12C103×#1943C211yesmaximal, characteristic, complemented
13C103×#1879C211yesmaximal, characteristic, complemented
14C103×#1877C211yesmaximal, characteristic, complemented
15C103×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18C22×D8×C103C2211yescharacteristic
19C22×D8×C103C2211yescharacteristic
20C22×M16×C103C2211yescharacteristic
21C2×#127×C103C2211yescharacteristic
22C2×#124×C103C2211yescharacteristic
23C2×C22⋊Q8×C103C2211yescharacteristic
24C2×#121×C103—21no—
25C2×#121×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×#121×C103C2211yescharacteristic
28C2×C4×D4×C103C2211yescharacteristic
29C2×C4×D4×C103C2211yescharacteristic
30#496×C103—24no—
31#469×C103—24no—
32#468×C103—24no—
33C4×D8×C103—24no—
34C2×#107×C103C2211yescharacteristic
35C2×#106×C103C2211yescharacteristic
36C2×#103×C103C2211yescharacteristic
37C2×#103×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×C22⋊C8×C103C2211yescharacteristic
45C2×#97×C103C2211yescharacteristic
46C2×C4×C8×C103C2211yescharacteristic
47#397×C103—21no—
48#394×C103—21no—
49#394×C103—21no—
50#392×C103—21no—
51#391×C103C2211yescharacteristic
52#390×C103C2211yescharacteristic
53#389×C103C2211yescharacteristic
54#389×C103C2211yescharacteristic
55#386×C103—21no—
56#386×C103—21no—
57#380×C103—21no—
58C4×C22⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103—21no—
67C22×D4×C103—21no—
68C22×D4×C103—21no—
69C22×D4×C103C2311yescharacteristic
70C22×D4×C103C2311yescharacteristic
71C22×D4×C103C2311yescharacteristic
72C23×C4×C103—21no—
73C23×C4×C103—21no—
74C23×C4×C103C2311yescharacteristic
75C2×SD16×C103—22no—
76C2×SD16×C103—22no—
77C2×SD16×C103—22no—
78C2×SD16×C103—22no—
79C2×SD16×C103—22no—
80C2×SD16×C103—41no—
81C2×D8×C103—22no—
82C2×D8×C103—22no—
83C2×D8×C103—22no—
84C2×D8×C103—22no—
85C2×D8×C103—41no—
86C2×D8×C103D414yescomplemented
87C2×M16×C103—22no—
88C2×M16×C103—22no—
89C2×M16×C103—22no—
90C22×C8×C103C2311yescharacteristic
91C22×C8×C103C2311yescharacteristic
92C22×C8×C103C2311yescharacteristic
93C22×C8×C103C2311yescharacteristic
94#127×C103—22no—
95#127×C103—41no—
96#124×C103—22no—
97#124×C103—41no—
98C22⋊Q8×C103—22no—
99C22⋊Q8×C103—41no—
100#121×C103—22no—
101#121×C103—22no—
102#121×C103—22no—
103#121×C103—44no—
104#121×C103—41no—
105#121×C103—41no—
106#121×C103—41no—
107C4×D4×C103—22no—
108C4×D4×C103—22no—
109C4×D4×C103—41no—
110C4×D4×C103—41no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—21no—
113C2×C4⋊C4×C103—21no—
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
117C2×C4⋊C4×C103C2311yescharacteristic
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
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—21no—
128C2×C22⋊C4×C103D411yescharacteristic
129C2×C22⋊C4×C103D411yescharacteristic
130C2×C42×C103C2311yescharacteristic
131C2×C42×C103C2311yescharacteristic
132#107×C103D414yescomplemented
133#106×C103—22no—
134#103×C103—22no—
135#103×C103—41no—
136#102×C103—22no—
137#102×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—41no—
142C22⋊C8×C103—22no—
143#97×C103—22no—
144C4×C8×C103—22no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148#95×C103—21no—
149#95×C103D411yescharacteristic
150#95×C103D411yescharacteristic
151C24×C103—21no—
152C24×C103—21no—
153C24×C103—21no—
154C24×C103C2×D411yescharacteristic
155C2×Q8×C103—21no—
156C2×Q8×C103—21no—
157C2×Q8×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×D4×C103—21no—
162C2×D4×C103—21no—
163C2×D4×C103—21no—
164C2×D4×C103—21no—
165C2×D4×C103—21no—
166C2×D4×C103—21no—
167C2×D4×C103—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103—42no—
178C2×D4×C103—42no—
179C2×D4×C103—42no—
180C2×D4×C103—42no—
181C2×D4×C103—42no—
182C2×D4×C103—42no—
183C2×D4×C103—42no—
184C2×D4×C103—42no—
185C2×D4×C103—42no—
186C2×D4×C103—42no—
187C2×D4×C103—81no—
188C2×D4×C103—81no—
189C2×D4×C103—81no—
190C2×D4×C103—81no—
191C2×D4×C103—81no—
192C2×D4×C103C2×D412yes—
193C2×D4×C103C2×D412yes—
194C22×C4×C103—21no—
195C22×C4×C103—21no—
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—21no—
205C22×C4×C103—42no—
206C22×C4×C103—42no—
207C22×C4×C103—42no—
208C22×C4×C103—42no—
209C22×C4×C103—81no—
210C22×C4×C103—81no—
211C22×C4×C103C2×D411yescharacteristic
212C22×C4×C103C2×D411yescharacteristic
213C22×C4×C103C2×D411yescharacteristic
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103C2×D411yescharacteristic
216C22×C4×C103C2411yescharacteristic
217SD16×C103—44no—
218SD16×C103—44no—
219D8×C103—28no—
220D8×C103—44no—
221M16×C103—44no—
222C2×C8×C103—21no—
223C2×C8×C103—21no—
224C2×C8×C103—21no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103C2×D412yes—
231C2×C8×C103C2×D412yes—
232C2×C8×C103#4112yes—
233C2×C8×C103#4112yes—
234C4⋊C4×C103—21no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—21no—
237C4⋊C4×C103—21no—
238C4⋊C4×C103—21no—
239C4⋊C4×C103—21no—
240C4⋊C4×C103—42no—
241C4⋊C4×C103—42no—
242C4⋊C4×C103—81no—
243C4⋊C4×C103C2×D412yes—
244C4⋊C4×C103C2×D412yes—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—41no—
247C22⋊C4×C103—42no—
248C22⋊C4×C103—42no—
249C22⋊C4×C103—42no—
250C22⋊C4×C103—42no—
251C22⋊C4×C103—42no—
252C22⋊C4×C103—42no—
253C22⋊C4×C103—42no—
254C22⋊C4×C103—42no—
255C22⋊C4×C103—42no—
256C22⋊C4×C103—81no—
257C42×C103—21no—
258C42×C103—21no—
259C42×C103—21no—
260C42×C103—21no—
261C23×C103—21no—
262C23×C103—22no—
263C23×C103—21no—
264C23×C103—22no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—21no—
269C23×C103—21no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103—41no—
273C23×C103—41no—
274C23×C103—41no—
275C23×C103—41no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103—41no—
279C23×C103—41no—
280C23×C103—41no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103—41no—
284C23×C103—41no—
285C23×C103—41no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—41no—
289C23×C103C22×D411yescharacteristic
290Q8×C103—41no—
291Q8×C103—41no—
292Q8×C103—41no—
293Q8×C103—41no—
294D4×C103—22no—
295D4×C103—22no—
296D4×C103—22no—
297D4×C103—22no—
298D4×C103—41no—
299D4×C103—41no—
300D4×C103—41no—
301D4×C103—41no—
302D4×C103—41no—
303D4×C103—41no—
304D4×C103—41no—
305D4×C103—41no—
306D4×C103—84no—
307D4×C103—84no—
308D4×C103—84no—
309D4×C103—84no—
310D4×C103—84no—
311C2×C4×C103—21no—
312C2×C4×C103—21no—
313C2×C4×C103—21no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—22no—
319C2×C4×C103—22no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—21no—
326C2×C4×C103—21no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—41no—
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—41no—
338C2×C4×C103—41no—
339C2×C4×C103—41no—
340C2×C4×C103—41no—
341C2×C4×C103—41no—
342C2×C4×C103—41no—
343C2×C4×C103—41no—
344C2×C4×C103—84no—
345C2×C4×C103—84no—
346C2×C4×C103AGL(1,ℤ/8)12yes—
347C2×C4×C103C22×D411yescharacteristic
348C2×C4×C103C22×D411yescharacteristic
349C2×C4×C103C2×#4111yescharacteristic
350C2×C4×C103C2×#4111yescharacteristic
351C2×C4×C103H(5,𝔽2)11yescharacteristic
352C2×C4×C103H(5,𝔽2)11yescharacteristic
353C8×C103—22no—
354C8×C103—41no—
355C8×C103—41no—
356C8×C103#12114yescomplemented
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—42no—
361C22×C103—42no—
362C22×C103—41no—
363C22×C103—41no—
364C22×C103—41no—
365C22×C103—42no—
366C22×C103—42no—
367C22×C103—41no—
368C22×C103—42no—
369C22×C103—42no—
370C22×C103—81no—
371C22×C103—81no—
372C22×C103—81no—
373C22×C103—81no—
374C22×C103—81no—
375C22×C103—81no—
376C22×C103—81no—
377C22×C103—81no—
378C22×C103—81no—
379C22×C103—81no—
380C22×C103—81no—
381C22×C103—81no—
382C22×C103—81no—
383C22×C103—81no—
384C22×C103—81no—
385C22×C103#53211yescharacteristic
386C22×C103D4211yescharacteristic
387C22×C103D4211yescharacteristic
388C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C103#57511yescharacteristic
390C22×C103#57611yescharacteristic
391C22×C103#57711yescharacteristic
392C4×C103—22no—
393C4×C103—41no—
394C4×C103—42no—
395C4×C103—42no—
396C4×C103—41no—
397C4×C103—41no—
398C4×C103—41no—
399C4×C103—81no—
400C4×C103—81no—
401C4×C103—81no—
402C4×C103C2×#12111yescharacteristic
403C4×C103#54011yescharacteristic
404C4×C103#54611yescharacteristic
405C4×C103#55011yescharacteristic
406#25419C10311yesmaximal, characteristic, direct product factor, Sylow
407C2×C103—81no—
408C2×C103—82no—
409C2×C103—82no—
410C2×C103—161no—
411C2×C103#242811yescharacteristic
412C2×C103#317111yescharacteristic
413C2×C103#317911yescharacteristic
414C2×C103#326411yescharacteristic
415C2×C103#327111yescharacteristic
416C2×C103#327211yescharacteristic
417C2×C103#327311yescharacteristic
418C2×#496C2×C10311yescharacteristic, complemented
419C2×#469C2×C10311yescharacteristic, complemented
420C2×#468C2×C10311yescharacteristic, complemented
421C2×C4×D8C2×C10311yescharacteristic, complemented
422#2428C2×C10311yescharacteristic, complemented
423#2427C2×C10311yescharacteristic, complemented
424#2042C2×C10311yescharacteristic, complemented
425#2041C2×C10311yescharacteristic, complemented
426#2000C2×C10311yescharacteristic, complemented
427#1999C2×C10311yescharacteristic, complemented
428#1968C2×C10311yescharacteristic, complemented
429#1943C2×C10311yescharacteristic, complemented
430#1879C2×C10311yescharacteristic, complemented
431#1877C2×C10311yescharacteristic, complemented
432#1753C2×C10311yescharacteristic, complemented
433C103#2541911yescharacteristic, direct product factor, Sylow
434C22×SD16C22×C10311yescharacteristic
435C22×SD16C22×C10311yescharacteristic
436C22×D8C22×C10311yescharacteristic
437C22×D8C22×C10311yescharacteristic
438C22×M16C22×C10311yescharacteristic
439C2×#127C22×C10311yescharacteristic
440C2×#124C22×C10311yescharacteristic
441C2×C22⋊Q8C22×C10311yescharacteristic
442C2×#121—21no—
443C2×#121C22×C10311yescharacteristic
444C2×#121C22×C10311yescharacteristic
445C2×#121C22×C10311yescharacteristic
446C2×C4×D4C22×C10311yescharacteristic
447C2×C4×D4C22×C10311yescharacteristic
448#496—24no—
449#469—24no—
450#468—24no—
451C4×D8—24no—
452C2×#107C22×C10311yescharacteristic
453C2×#106C22×C10311yescharacteristic
454C2×#103C22×C10311yescharacteristic
455C2×#103C22×C10311yescharacteristic
456C2×#102C22×C10311yescharacteristic
457C2×#102C22×C10311yescharacteristic
458C2×#102C22×C10311yescharacteristic
459C2×#102C22×C10311yescharacteristic
460C2×#102C22×C10311yescharacteristic
461C2×#102C22×C10311yescharacteristic
462C2×C22⋊C8C22×C10311yescharacteristic
463C2×#97C22×C10311yescharacteristic
464C2×C4×C8C22×C10311yescharacteristic
465#397—21no—
466#394—21no—
467#394—21no—
468#392—21no—
469#391C22×C10311yescharacteristic
470#390C22×C10311yescharacteristic
471#389C22×C10311yescharacteristic
472#389C22×C10311yescharacteristic
473#386—21no—
474#386—21no—
475#380—21no—
476C4×C22⋊C4C22×C10311yescharacteristic
477#340C22×C10311yescharacteristic
478#340C22×C10311yescharacteristic
479#336C22×C10311yescharacteristic
480#336C22×C10311yescharacteristic
481C22×Q8C23×C10311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4C23×C10311yescharacteristic
488C22×D4C23×C10311yescharacteristic
489C22×D4C23×C10311yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C23×C10311yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×D8—22no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×D8D4×C10314yescomplemented
505C2×M16—22no—
506C2×M16—22no—
507C2×M16—22no—
508C22×C8C23×C10311yescharacteristic
509C22×C8C23×C10311yescharacteristic
510C22×C8C23×C10311yescharacteristic
511C22×C8C23×C10311yescharacteristic
512#127—22no—
513#127—41no—
514#124—22no—
515#124—41no—
516C22⋊Q8—22no—
517C22⋊Q8—41no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—44no—
522#121—41no—
523#121—41no—
524#121—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C10311yescharacteristic
533C2×C4⋊C4C23×C10311yescharacteristic
534C2×C4⋊C4C23×C10311yescharacteristic
535C2×C4⋊C4C23×C10311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4D4×C10311yescharacteristic
547C2×C22⋊C4D4×C10311yescharacteristic
548C2×C42C23×C10311yescharacteristic
549C2×C42C23×C10311yescharacteristic
550#107D4×C10314yescomplemented
551#106—22no—
552#103—22no—
553#103—41no—
554#102—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561#97—22no—
562C4×C8—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95D4×C10311yescharacteristic
568#95D4×C10311yescharacteristic
569C24—21no—
570C24—21no—
571C24—21no—
572C24C2×D4×C10311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4C2×D4×C10312yes—
611C2×D4C2×D4×C10312yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4C2×D4×C10311yescharacteristic
630C22×C4C2×D4×C10311yescharacteristic
631C22×C4C2×D4×C10311yescharacteristic
632C22×C4C2×D4×C10311yescharacteristic
633C22×C4C2×D4×C10311yescharacteristic
634C22×C4C24×C10311yescharacteristic
635SD16—44no—
636SD16—44no—
637D8—28no—
638D8—44no—
639M16—44no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8C2×D4×C10312yes—
649C2×C8C2×D4×C10312yes—
650C2×C8#41×C10312yes—
651C2×C8#41×C10312yes—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C10312yes—
662C4⋊C4C2×D4×C10312yes—
663C22⋊C4—22no—
664C22⋊C4—41no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23C22×D4×C10311yescharacteristic
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—84no—
725D4—84no—
726D4—84no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4AGL(1,ℤ/8)×C10312yes—
765C2×C4C22×D4×C10311yescharacteristic
766C2×C4C22×D4×C10311yescharacteristic
767C2×C4C2×#41×C10311yescharacteristic
768C2×C4C2×#41×C10311yescharacteristic
769C2×C4H(5,𝔽2)×C10311yescharacteristic
770C2×C4H(5,𝔽2)×C10311yescharacteristic
771C8—22no—
772C8—41no—
773C8—41no—
774C8#121×C10314yescomplemented
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22#532×C10311yescharacteristic
804C22D42×C10311yescharacteristic
805C22D42×C10311yescharacteristic
806C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
807C22#575×C10311yescharacteristic
808C22#576×C10311yescharacteristic
809C22#577×C10311yescharacteristic
810C4—22no—
811C4—42no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C2×#121×C10311yescharacteristic
821C4#540×C10311yescharacteristic
822C4#546×C10311yescharacteristic
823C4#550×C10311yescharacteristic
824C2—81no—
825C2—82no—
826C2—82no—
827C2—161no—
828C2C103×#242811yescharacteristic
829C2C103×#317111yescharacteristic
830C2C103×#317911yescharacteristic
831C2C103×#326411yescharacteristic
832C2C103×#327111yescharacteristic
833C2C103×#327211yescharacteristic
834C2C103×#327311yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#496×C103C2semidirect
2. C2×#469×C103C2semidirect
3. C2×#468×C103C2semidirect
4. C2×C4×D8×C103C2semidirect
5. C103×#2428C2semidirect
6. C103×#2427C2semidirect
7. C103×#2042C2semidirect
8. C103×#2041C2semidirect
9. C103×#2000C2semidirect
10. C103×#1999C2semidirect
11. C103×#1968C2semidirect
12. C103×#1943C2semidirect
13. C103×#1879C2semidirect
14. C103×#1877C2semidirect
15. C103×#1753C2semidirect
86. C2×D8×C103D4semidirect
132. #107×C103D4semidirect
356. C8×C103#121semidirect
406. #25419C103direct (N × H)
418. C2×#496C2×C103semidirect
419. C2×#469C2×C103semidirect
420. C2×#468C2×C103semidirect
421. C2×C4×D8C2×C103semidirect
422. #2428C2×C103semidirect
423. #2427C2×C103semidirect
424. #2042C2×C103semidirect
425. #2041C2×C103semidirect
426. #2000C2×C103semidirect
427. #1999C2×C103semidirect
428. #1968C2×C103semidirect
429. #1943C2×C103semidirect
430. #1879C2×C103semidirect
431. #1877C2×C103semidirect
432. #1753C2×C103semidirect
433. C103#25419direct (N × H)
504. C2×D8D4×C103semidirect
550. #107D4×C103semidirect
774. C8#121×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C1032
C2×#469×C1032
C2×#468×C1032
C2×C4×D8×C1032
C103×#24282
C103×#24272
C103×#20422
C103×#20412
C103×#20002
C103×#19992
C103×#19682
C103×#19432
C103×#18792
C103×#18772
C103×#17532
#25419103