Finite Group Databasebeta

← C103×#22858 #39928133

Subgroups — C103×#22858 #39928133

Order 26368.

1386 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×#447×C103C211yesmaximal, characteristic
2C2×#442×C103C211yesmaximal, characteristic, complemented
3C22×#102×C103C211yesmaximal, characteristic, complemented
4C103×#2361C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C103C211yesmaximal, characteristic, complemented
6C103×#1972C211yesmaximal, characteristic, complemented
7C103×#1936C211yesmaximal, characteristic, complemented
8C103×#1926C211yesmaximal, characteristic, complemented
9C103×#1893C211yesmaximal, characteristic, complemented
10C103×#1879C211yesmaximal, characteristic, complemented
11C103×#1879C211yesmaximal, characteristic, complemented
12C103×#1864C211yesmaximal, characteristic, complemented
13C103×#1853C211yesmaximal, characteristic, complemented
14C103×#1762C211yesmaximal, characteristic, complemented
15C103×#1752C211yesmaximal, characteristic, complemented
16C23×D4×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C22×D8×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20C2×#121×C103C2211yescharacteristic
21C2×C4×D4×C103—21no—
22C2×C4×D4×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24C2×C4×D4×C103C2211yescharacteristic, complemented
25C22×C4⋊C4×C103C2211yescharacteristic
26C22×C22⋊C4×C103—21no—
27#447×C103C418yescomplemented
28#442×C103—24no—
29C2×#106×C103C2211yescharacteristic, complemented
30C2×#106×C103C2211yescharacteristic, complemented
31C2×#102×C103—24no—
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×#102×C103C2211yescharacteristic
35C2×#102×C103C2211yescharacteristic
36C2×#102×C103C2211yescharacteristic
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic, complemented
39C2×#102×C103C2211yescharacteristic, complemented
40C2×C22⋊C8×C103C2211yescharacteristic
41C2×#97×C103C2211yescharacteristic, complemented
42C2×#97×C103C2211yescharacteristic, complemented
43#390×C103C2211yescharacteristic
44#390×C103C2211yescharacteristic
45#390×C103C2211yescharacteristic, complemented
46#389×C103C2211yescharacteristic, complemented
47#388×C103—21no—
48#386×C103—21no—
49#386×C103—21no—
50#386×C103—21no—
51#385×C103—21no—
52#380×C103C2211yescharacteristic
53#379×C103—21no—
54C4×C4⋊C4×C103C2211yescharacteristic, complemented
55C4×C22⋊C4×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic, complemented
57#340×C103C2211yescharacteristic, complemented
58#340×C103C2211yescharacteristic, complemented
59#340×C103C2211yescharacteristic, complemented
60#336×C103C2211yescharacteristic, complemented
61#336×C103C2211yescharacteristic, complemented
62C25×C103—21no—
63C22×D4×C103—22no—
64C22×D4×C103—22no—
65C22×D4×C103—21no—
66C22×D4×C103—21no—
67C22×D4×C103—22no—
68C22×D4×C103—41no—
69C22×D4×C103—41no—
70C22×D4×C103C2×C414yescomplemented
71C22×D4×C103C2311yescharacteristic
72C22×D4×C103C2311yescharacteristic
73C22×D4×C103C2311yescharacteristic
74C23×C4×C103—21no—
75C23×C4×C103—21no—
76C23×C4×C103—21no—
77C23×C4×C103—21no—
78C23×C4×C103C2311yescharacteristic
79C2×D8×C103—22no—
80C2×D8×C103—22no—
81C2×D8×C103—41no—
82C2×D8×C103—41no—
83C2×D8×C103C2×C414yescomplemented
84C2×D8×C103C2×C414yescomplemented
85C22×C8×C103—22no—
86C22×C8×C103—22no—
87C22×C8×C103—41no—
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90C22×C8×C103C2311yescharacteristic
91C22×C8×C103C2311yescharacteristic
92#121×C103—22no—
93#121×C103C2×C414yescomplemented
94C4×D4×C103—22no—
95C4×D4×C103—22no—
96C4×D4×C103—22no—
97C4×D4×C103—41no—
98C4×D4×C103—41no—
99C4×D4×C103—41no—
100C4×D4×C103—44no—
101C2×C4⋊C4×C103—22no—
102C2×C4⋊C4×C103—21no—
103C2×C4⋊C4×C103—21no—
104C2×C4⋊C4×C103—41no—
105C2×C4⋊C4×C103C2311yescharacteristic
106C2×C4⋊C4×C103C2311yescharacteristic
107C2×C4⋊C4×C103C2311yescharacteristic
108C2×C4⋊C4×C103C2311yescharacteristic
109C2×C4⋊C4×C103C2311yescharacteristic
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103—21no—
112C2×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—21no—
116C2×C22⋊C4×C103—21no—
117C2×C22⋊C4×C103—21no—
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
121C2×C22⋊C4×C103—44no—
122C2×C22⋊C4×C103D411yescharacteristic
123C2×C22⋊C4×C103D411yescharacteristic
124C2×C42×C103—21no—
125C2×C42×C103C2311yescharacteristic
126C2×C42×C103C2311yescharacteristic
127#106×C103—22no—
128#106×C103—41no—
129#102×C103—22no—
130#102×C103—22no—
131#102×C103—22no—
132#102×C103—22no—
133#102×C103—41no—
134#102×C103C2×C414yescomplemented
135#102×C103C2×C414yescomplemented
136#102×C103D414yescomplemented
137C22⋊C8×C103C2×C414yescomplemented
138#97×C103—22no—
139#97×C103—41no—
140#95×C103—21no—
141#95×C103—21no—
142#95×C103—21no—
143#95×C103D411yescharacteristic
144#95×C103D411yescharacteristic
145C24×C103—21no—
146C24×C103—21no—
147C24×C103—21no—
148C24×C103—24no—
149C24×C103—42no—
150C24×C103—42no—
151C24×C103—42no—
152C24×C103—42no—
153C24×C103—81no—
154C24×C103—81no—
155C24×C103C2×D411yescharacteristic
156C2×D4×C103—28no—
157C2×D4×C103—24no—
158C2×D4×C103—24no—
159C2×D4×C103—21no—
160C2×D4×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—44no—
173C2×D4×C103—44no—
174C2×D4×C103—44no—
175C2×D4×C103—42no—
176C2×D4×C103—42no—
177C2×D4×C103—42no—
178C2×D4×C103—42no—
179C2×D4×C103C22×C412yes—
180C2×D4×C103C22×C412yes—
181C2×D4×C103C22×C412yes—
182C2×D4×C103C2×D412yes—
183C2×D4×C103#4112yes—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—21no—
191C22×C4×C103—21no—
192C22×C4×C103—21no—
193C22×C4×C103—42no—
194C22×C4×C103—42no—
195C22×C4×C103—42no—
196C22×C4×C103—42no—
197C22×C4×C103—42no—
198C22×C4×C103—42no—
199C22×C4×C103—42no—
200C22×C4×C103—42no—
201C22×C4×C103—81no—
202C22×C4×C103—81no—
203C22×C4×C103—81no—
204C22×C4×C103—81no—
205C22×C4×C103C22×C412yes—
206C22×C4×C103C2×D411yescharacteristic
207C22×C4×C103C2×D411yescharacteristic
208C22×C4×C103C2×D411yescharacteristic
209C22×C4×C103C2×D411yescharacteristic
210C22×C4×C103C2×D411yescharacteristic
211C22×C4×C103#4112yes—
212C22×C4×C103C2411yescharacteristic
213D8×C103—28no—
214D8×C103—44no—
215C2×C8×C103—21no—
216C2×C8×C103—21no—
217C2×C8×C103—21no—
218C2×C8×C103—21no—
219C2×C8×C103—21no—
220C2×C8×C103—21no—
221C2×C8×C103—21no—
222C2×C8×C103—21no—
223C2×C8×C103—21no—
224C2×C8×C103—44no—
225C2×C8×C103C22×C412yes—
226C2×C8×C103C22×C412yes—
227C2×C8×C103C2×D412yes—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—21no—
233C4⋊C4×C103—21no—
234C4⋊C4×C103—21no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—42no—
237C4⋊C4×C103—42no—
238C4⋊C4×C103C22×C412yes—
239C4⋊C4×C103C2×D412yes—
240C22⋊C4×C103—22no—
241C22⋊C4×C103—22no—
242C22⋊C4×C103—24no—
243C22⋊C4×C103—42no—
244C22⋊C4×C103—42no—
245C22⋊C4×C103—42no—
246C22⋊C4×C103—42no—
247C22⋊C4×C103—42no—
248C22⋊C4×C103—42no—
249C22⋊C4×C103—42no—
250C22⋊C4×C103—81no—
251C22⋊C4×C103—81no—
252C22⋊C4×C103—81no—
253C42×C103—21no—
254C42×C103—21no—
255C42×C103—21no—
256C42×C103—21no—
257C42×C103—42no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—21no—
262C23×C103—22no—
263C23×C103—22no—
264C23×C103—22no—
265C23×C103—22no—
266C23×C103—22no—
267C23×C103—48no—
268C23×C103—41no—
269C23×C103—41no—
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—48no—
285C23×C103—84no—
286C23×C103—84no—
287C23×C103—84no—
288C23×C103—84no—
289C23×C103—84no—
290C23×C103C4×D412yes—
291C23×C103AGL(1,ℤ/8)12yes—
292C23×C103AGL(1,ℤ/8)12yes—
293C23×C103C22×D411yescharacteristic
294D4×C103—22no—
295D4×C103—22no—
296D4×C103—22no—
297D4×C103—22no—
298D4×C103—22no—
299D4×C103—22no—
300D4×C103—22no—
301D4×C103—48no—
302D4×C103—48no—
303D4×C103—41no—
304D4×C103—41no—
305D4×C103—41no—
306D4×C103—41no—
307D4×C103C4×D414yescomplemented
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—22no—
311C2×C4×C103—22no—
312C2×C4×C103—22no—
313C2×C4×C103—22no—
314C2×C4×C103—22no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—22no—
318C2×C4×C103—21no—
319C2×C4×C103—21no—
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—21no—
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—84no—
342C2×C4×C103—84no—
343C2×C4×C103—84no—
344C2×C4×C103—84no—
345C2×C4×C103C4×D412yes—
346C2×C4×C103C23×C411yescharacteristic
347C2×C4×C103C22×D411yescharacteristic
348C2×C4×C103C2×#4111yescharacteristic
349C2×C4×C103C2×#4111yescharacteristic
350C2×C4×C103H(5,𝔽2)11yescharacteristic
351C2×C4×C103H(5,𝔽2)11yescharacteristic
352C8×C103—22no—
353C8×C103—22no—
354C8×C103—22no—
355C8×C103—41no—
356C22×C103—22no—
357C22×C103—22no—
358C22×C103—22no—
359C22×C103—22no—
360C22×C103—22no—
361C22×C103—22no—
362C22×C103—24no—
363C22×C103—42no—
364C22×C103—42no—
365C22×C103—42no—
366C22×C103—42no—
367C22×C103—42no—
368C22×C103—42no—
369C22×C103—42no—
370C22×C103—42no—
371C22×C103—42no—
372C22×C103—42no—
373C22×C103—42no—
374C22×C103—42no—
375C22×C103—816no—
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#44214yescomplemented
385C22×C103C2×C4×D411yescharacteristic
386C22×C103D4211yescharacteristic
387C22×C103#54611yescharacteristic
388C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
390C22×C103#57611yescharacteristic
391C22×C103#57711yescharacteristic
392C4×C103—22no—
393C4×C103—42no—
394C4×C103—41no—
395C4×C103—42no—
396C4×C103—41no—
397C4×C103—41no—
398C4×C103—41no—
399C4×C103—81no—
400C4×C103—81no—
401C4×C103—81no—
402C4×C103C2×C4×D411yescharacteristic
403C4×C103#51811yescharacteristic
404C4×C103#54611yescharacteristic
405C4×C103#55111yescharacteristic
406#22858C10311yesmaximal, characteristic, direct product factor, Sylow
407C2×C103—24no—
408C2×C103—44no—
409C2×C103—82no—
410C2×C103—82no—
411C2×C103#235811yescharacteristic
412C2×C103C2×#44211yescharacteristic
413C2×C103#294611yescharacteristic
414C2×C103#326411yescharacteristic
415C2×C103#326511yescharacteristic
416C2×C103#330611yescharacteristic
417C2×C103#331811yescharacteristic
418C2×#447C2×C10311yescharacteristic
419C2×#442C2×C10311yescharacteristic, complemented
420C22×#102C2×C10311yescharacteristic, complemented
421#2361C2×C10311yescharacteristic, complemented
422D4×C22⋊C4C2×C10311yescharacteristic, complemented
423#1972C2×C10311yescharacteristic, complemented
424#1936C2×C10311yescharacteristic, complemented
425#1926C2×C10311yescharacteristic, complemented
426#1893C2×C10311yescharacteristic, complemented
427#1879C2×C10311yescharacteristic, complemented
428#1879C2×C10311yescharacteristic, complemented
429#1864C2×C10311yescharacteristic, complemented
430#1853C2×C10311yescharacteristic, complemented
431#1762C2×C10311yescharacteristic, complemented
432#1752C2×C10311yescharacteristic, complemented
433C103#2285811yescharacteristic, direct product factor, Sylow
434C23×D4C22×C10311yescharacteristic
435C22×D8C22×C10311yescharacteristic
436C22×D8C22×C10311yescharacteristic
437C23×C8C22×C10311yescharacteristic
438C2×#121C22×C10311yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C10311yescharacteristic
441C2×C4×D4C22×C10311yescharacteristic
442C2×C4×D4C22×C10311yescharacteristic, complemented
443C22×C4⋊C4C22×C10311yescharacteristic
444C22×C22⋊C4—21no—
445#447C4×C10318yescomplemented
446#442—24no—
447C2×#106C22×C10311yescharacteristic, complemented
448C2×#106C22×C10311yescharacteristic, complemented
449C2×#102—24no—
450C2×#102C22×C10311yescharacteristic
451C2×#102C22×C10311yescharacteristic
452C2×#102C22×C10311yescharacteristic
453C2×#102C22×C10311yescharacteristic
454C2×#102C22×C10311yescharacteristic
455C2×#102C22×C10311yescharacteristic
456C2×#102C22×C10311yescharacteristic, complemented
457C2×#102C22×C10311yescharacteristic, complemented
458C2×C22⋊C8C22×C10311yescharacteristic
459C2×#97C22×C10311yescharacteristic, complemented
460C2×#97C22×C10311yescharacteristic, complemented
461#390C22×C10311yescharacteristic
462#390C22×C10311yescharacteristic
463#390C22×C10311yescharacteristic, complemented
464#389C22×C10311yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#386—21no—
469#385—21no—
470#380C22×C10311yescharacteristic
471#379—21no—
472C4×C4⋊C4C22×C10311yescharacteristic, complemented
473C4×C22⋊C4C22×C10311yescharacteristic
474#340C22×C10311yescharacteristic, complemented
475#340C22×C10311yescharacteristic, complemented
476#340C22×C10311yescharacteristic, complemented
477#340C22×C10311yescharacteristic, complemented
478#336C22×C10311yescharacteristic, complemented
479#336C22×C10311yescharacteristic, complemented
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—22no—
486C22×D4—41no—
487C22×D4—41no—
488C22×D4C2×C4×C10314yescomplemented
489C22×D4C23×C10311yescharacteristic
490C22×D4C23×C10311yescharacteristic
491C22×D4C23×C10311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C10311yescharacteristic
497C2×D8—22no—
498C2×D8—22no—
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×C4×C10314yescomplemented
502C2×D8C2×C4×C10314yescomplemented
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8C23×C10311yescharacteristic
507C22×C8C23×C10311yescharacteristic
508C22×C8C23×C10311yescharacteristic
509C22×C8C23×C10311yescharacteristic
510#121—22no—
511#121C2×C4×C10314yescomplemented
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—41no—
516C4×D4—41no—
517C4×D4—41no—
518C4×D4—44no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4C23×C10311yescharacteristic
524C2×C4⋊C4C23×C10311yescharacteristic
525C2×C4⋊C4C23×C10311yescharacteristic
526C2×C4⋊C4C23×C10311yescharacteristic
527C2×C4⋊C4C23×C10311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4D4×C10311yescharacteristic
541C2×C22⋊C4D4×C10311yescharacteristic
542C2×C42—21no—
543C2×C42C23×C10311yescharacteristic
544C2×C42C23×C10311yescharacteristic
545#106—22no—
546#106—41no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—41no—
552#102C2×C4×C10314yescomplemented
553#102C2×C4×C10314yescomplemented
554#102D4×C10314yescomplemented
555C22⋊C8C2×C4×C10314yescomplemented
556#97—22no—
557#97—41no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C10311yescharacteristic
562#95D4×C10311yescharacteristic
563C24—21no—
564C24—21no—
565C24—21no—
566C24—24no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—42no—
571C24—81no—
572C24—81no—
573C24C2×D4×C10311yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—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—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4C22×C4×C10312yes—
598C2×D4C22×C4×C10312yes—
599C2×D4C22×C4×C10312yes—
600C2×D4C2×D4×C10312yes—
601C2×D4#41×C10312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4—81no—
623C22×C4C22×C4×C10312yes—
624C22×C4C2×D4×C10311yescharacteristic
625C22×C4C2×D4×C10311yescharacteristic
626C22×C4C2×D4×C10311yescharacteristic
627C22×C4C2×D4×C10311yescharacteristic
628C22×C4C2×D4×C10311yescharacteristic
629C22×C4#41×C10312yes—
630C22×C4C24×C10311yescharacteristic
631D8—28no—
632D8—44no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—44no—
643C2×C8C22×C4×C10312yes—
644C2×C8C22×C4×C10312yes—
645C2×C8C2×D4×C10312yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4C22×C4×C10312yes—
657C4⋊C4C2×D4×C10312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4—81no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—48no—
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—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23C4×D4×C10312yes—
709C23AGL(1,ℤ/8)×C10312yes—
710C23AGL(1,ℤ/8)×C10312yes—
711C23C22×D4×C10311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4C4×D4×C10314yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
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—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4C4×D4×C10312yes—
764C2×C4C23×C4×C10311yescharacteristic
765C2×C4C22×D4×C10311yescharacteristic
766C2×C4C2×#41×C10311yescharacteristic
767C2×C4C2×#41×C10311yescharacteristic
768C2×C4H(5,𝔽2)×C10311yescharacteristic
769C2×C4H(5,𝔽2)×C10311yescharacteristic
770C8—22no—
771C8—22no—
772C8—22no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—816no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22#442×C10314yescomplemented
803C22C2×C4×D4×C10311yescharacteristic
804C22D42×C10311yescharacteristic
805C22#546×C10311yescharacteristic
806C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
807C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
808C22#576×C10311yescharacteristic
809C22#577×C10311yescharacteristic
810C4—22no—
811C4—41no—
812C4—42no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C2×C4×D4×C10311yescharacteristic
821C4#518×C10311yescharacteristic
822C4#546×C10311yescharacteristic
823C4#551×C10311yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—82no—
828C2C103×#235811yescharacteristic
829C2C2×#442×C10311yescharacteristic
830C2C103×#294611yescharacteristic
831C2C103×#326411yescharacteristic
832C2C103×#326511yescharacteristic
833C2C103×#330611yescharacteristic
834C2C103×#331811yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC2×#447×C103C2
LCSG ▷ C2×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
2. C2×#442×C103C2semidirect
3. C22×#102×C103C2semidirect
4. C103×#2361C2semidirect
5. D4×C22⋊C4×C103C2semidirect
6. C103×#1972C2semidirect
7. C103×#1936C2semidirect
8. C103×#1926C2semidirect
9. C103×#1893C2semidirect
10. C103×#1879C2semidirect
11. C103×#1879C2semidirect
12. C103×#1864C2semidirect
13. C103×#1853C2semidirect
14. C103×#1762C2semidirect
15. C103×#1752C2semidirect
24. C2×C4×D4×C103C22semidirect
27. #447×C103C4semidirect
29. C2×#106×C103C22semidirect
30. C2×#106×C103C22semidirect
38. C2×#102×C103C22semidirect
39. C2×#102×C103C22semidirect
41. C2×#97×C103C22semidirect
42. C2×#97×C103C22semidirect
45. #390×C103C22semidirect
46. #389×C103C22semidirect
54. C4×C4⋊C4×C103C22semidirect
56. #340×C103C22semidirect
57. #340×C103C22semidirect
58. #340×C103C22semidirect
59. #340×C103C22semidirect
60. #336×C103C22semidirect
61. #336×C103C22semidirect
70. C22×D4×C103C2×C4semidirect
83. C2×D8×C103C2×C4semidirect
84. C2×D8×C103C2×C4semidirect
93. #121×C103C2×C4semidirect
134. #102×C103C2×C4semidirect
135. #102×C103C2×C4semidirect
136. #102×C103D4semidirect
137. C22⋊C8×C103C2×C4semidirect
307. D4×C103C4×D4semidirect
384. C22×C103#442semidirect
406. #22858C103direct (N × H)
419. C2×#442C2×C103semidirect
420. C22×#102C2×C103semidirect
421. #2361C2×C103semidirect
422. D4×C22⋊C4C2×C103semidirect
423. #1972C2×C103semidirect
424. #1936C2×C103semidirect
425. #1926C2×C103semidirect
426. #1893C2×C103semidirect
427. #1879C2×C103semidirect
428. #1879C2×C103semidirect
429. #1864C2×C103semidirect
430. #1853C2×C103semidirect
431. #1762C2×C103semidirect
432. #1752C2×C103semidirect
433. C103#22858direct (N × H)
442. C2×C4×D4C22×C103semidirect
445. #447C4×C103semidirect
447. C2×#106C22×C103semidirect
448. C2×#106C22×C103semidirect
456. C2×#102C22×C103semidirect
457. C2×#102C22×C103semidirect
459. C2×#97C22×C103semidirect
460. C2×#97C22×C103semidirect
463. #390C22×C103semidirect
464. #389C22×C103semidirect
472. C4×C4⋊C4C22×C103semidirect
474. #340C22×C103semidirect
475. #340C22×C103semidirect
476. #340C22×C103semidirect
477. #340C22×C103semidirect
478. #336C22×C103semidirect
479. #336C22×C103semidirect
488. C22×D4C2×C4×C103semidirect
501. C2×D8C2×C4×C103semidirect
502. C2×D8C2×C4×C103semidirect
511. #121C2×C4×C103semidirect
552. #102C2×C4×C103semidirect
553. #102C2×C4×C103semidirect
554. #102D4×C103semidirect
555. C22⋊C8C2×C4×C103semidirect
725. D4C4×D4×C103semidirect
802. C22#442×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1032
C2×#442×C1032
C22×#102×C1032
C103×#23612
D4×C22⋊C4×C1032
C103×#19722
C103×#19362
C103×#19262
C103×#18932
C103×#18792
C103×#18642
C103×#18532
C103×#17622
C103×#17522
#22858103