Finite Group Databasebeta

← C103×#23331 #39928606

Subgroups — C103×#23331 #39928606

Order 26368.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C103C211yesmaximal, characteristic
2C103×#1955C211yesmaximal, characteristic, complemented
3C103×#1954C211yesmaximal, characteristic, complemented
4C103×#1924C211yesmaximal, characteristic, complemented
5C103×#1923C211yesmaximal, characteristic, complemented
6C103×#1917C211yesmaximal, characteristic, complemented
7C103×#1916C211yesmaximal, characteristic, complemented
8C103×#1870C211yesmaximal, characteristic, complemented
9C103×#1870C211yesmaximal, characteristic, complemented
10C103×#1869C211yesmaximal, characteristic, complemented
11C103×#1869C211yesmaximal, characteristic, complemented
12C103×#1851C211yesmaximal, characteristic, complemented
13C103×#1850C211yesmaximal, characteristic, complemented
14C103×#1817C211yesmaximal, characteristic, complemented
15C103×#1797C211yesmaximal, characteristic, complemented
16C22×M16×C103C2211yescharacteristic
17C23×C8×C103C2211yescharacteristic
18C2×#121×C103C411yescharacteristic
19C2×C4×D4×C103C2211yescharacteristic
20C2×C4×D4×C103C2211yescharacteristic
21C2×C4×D4×C103C2211yescharacteristic
22C22×C42×C103C2211yescharacteristic
23C2×C4⋊C8×C103C2211yescharacteristic
24C2×C4⋊C8×C103C2211yescharacteristic
25C2×C4⋊C8×C103C2211yescharacteristic
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×C22⋊C8×C103C2211yescharacteristic
28C2×C22⋊C8×C103C2211yescharacteristic
29C2×C22⋊C8×C103C2211yescharacteristic
30C2×C22⋊C8×C103C2211yescharacteristic
31C2×C22⋊C8×C103C2211yescharacteristic
32C2×C22⋊C8×C103C2211yescharacteristic
33C2×C22⋊C8×C103C2211yescharacteristic
34C2×C22⋊C8×C103C2211yescharacteristic
35C2×C22⋊C8×C103C2211yescharacteristic
36C2×C22⋊C8×C103C2211yescharacteristic
37C2×#97×C103C2211yescharacteristic
38C2×C4×C8×C103C2211yescharacteristic
39#390×C103C411yescharacteristic
40#389×C103C411yescharacteristic
41#388×C103C411yescharacteristic
42#388×C103C411yescharacteristic
43#386×C103C411yescharacteristic
44#386×C103C411yescharacteristic
45#380×C103C411yescharacteristic
46C4×C4⋊C4×C103C2211yescharacteristic
47C4×C22⋊C4×C103C2211yescharacteristic
48C4×C22⋊C4×C103C2211yescharacteristic
49#336×C103C2211yescharacteristic
50#336×C103C2211yescharacteristic
51#336×C103C2211yescharacteristic
52#336×C103C2211yescharacteristic
53#336×C103C2211yescharacteristic
54#336×C103C2211yescharacteristic
55#336×C103C2211yescharacteristic
56#336×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×D4×C103C2×C411yescharacteristic
60C22×D4×C103C2×C411yescharacteristic
61C22×D4×C103C2×C411yescharacteristic
62C23×C4×C103C2×C411yescharacteristic
63C23×C4×C103C2×C411yescharacteristic
64C23×C4×C103C2311yescharacteristic
65C23×C4×C103C2311yescharacteristic
66C23×C4×C103C2311yescharacteristic
67C2×M16×C103—41no—
68C2×M16×C103—41no—
69C2×M16×C103—41no—
70C22×C8×C103—41no—
71C22×C8×C103—41no—
72C22×C8×C103—41no—
73C22×C8×C103C2311yescharacteristic
74C22×C8×C103C2311yescharacteristic
75C22×C8×C103C2311yescharacteristic
76C22×C8×C103C2311yescharacteristic
77C22×C8×C103C2311yescharacteristic
78C22×C8×C103C2311yescharacteristic
79C22×C8×C103C2311yescharacteristic
80C22×C8×C103C2311yescharacteristic
81#121×C103—24no—
82C4×D4×C103—41no—
83C4×D4×C103—41no—
84C4×D4×C103—41no—
85C4×D4×C103—41no—
86C4×D4×C103—41no—
87C4×D4×C103—41no—
88C2×C4⋊C4×C103C2×C411yescharacteristic
89C2×C4⋊C4×C103C2×C411yescharacteristic
90C2×C4⋊C4×C103C2×C411yescharacteristic
91C2×C4⋊C4×C103C2×C411yescharacteristic
92C2×C4⋊C4×C103C2×C411yescharacteristic
93C2×C22⋊C4×C103C2×C411yescharacteristic
94C2×C22⋊C4×C103C2×C411yescharacteristic
95C2×C22⋊C4×C103C2×C411yescharacteristic
96C2×C22⋊C4×C103C2×C411yescharacteristic
97C2×C22⋊C4×C103C2×C411yescharacteristic
98C2×C22⋊C4×C103C2×C411yescharacteristic
99C2×C22⋊C4×C103C2×C411yescharacteristic
100C2×C22⋊C4×C103C2×C411yescharacteristic
101C2×C22⋊C4×C103C2×C411yescharacteristic
102C2×C22⋊C4×C103C2×C411yescharacteristic
103C2×C42×C103—41no—
104C2×C42×C103—41no—
105C2×C42×C103C2×C411yescharacteristic
106C2×C42×C103C2×C411yescharacteristic
107C2×C42×C103C2311yescharacteristic
108C2×C42×C103C2311yescharacteristic
109C2×C42×C103C2311yescharacteristic
110C2×C42×C103C2311yescharacteristic
111C4⋊C8×C103—41no—
112C4⋊C8×C103—41no—
113C4⋊C8×C103—41no—
114C4⋊C8×C103—41no—
115C22⋊C8×C103—41no—
116C22⋊C8×C103—41no—
117C22⋊C8×C103—41no—
118C22⋊C8×C103—41no—
119C22⋊C8×C103—41no—
120C22⋊C8×C103—41no—
121C22⋊C8×C103—41no—
122C22⋊C8×C103—41no—
123C22⋊C8×C103—41no—
124C22⋊C8×C103—41no—
125#97×C103—41no—
126C4×C8×C103—41no—
127#95×C103C2×C411yescharacteristic
128#95×C103C2×C411yescharacteristic
129#95×C103C2×C411yescharacteristic
130#95×C103C2×C411yescharacteristic
131#95×C103C2×C411yescharacteristic
132#95×C103C2×C411yescharacteristic
133C24×C103C22×C411yescharacteristic
134C24×C103C22×C411yescharacteristic
135C24×C103C22×C411yescharacteristic
136C2×D4×C103—22no—
137C2×D4×C103—22no—
138C2×D4×C103—22no—
139C2×D4×C103—41no—
140C2×D4×C103—41no—
141C2×D4×C103—41no—
142C2×D4×C103—41no—
143C2×D4×C103—41no—
144C2×D4×C103M1614yescomplemented
145C22×C4×C103—22no—
146C22×C4×C103—22no—
147C22×C4×C103—22no—
148C22×C4×C103—21no—
149C22×C4×C103—21no—
150C22×C4×C103—21no—
151C22×C4×C103—21no—
152C22×C4×C103—21no—
153C22×C4×C103—21no—
154C22×C4×C103—21no—
155C22×C4×C103—21no—
156C22×C4×C103—21no—
157C22×C4×C103—21no—
158C22×C4×C103—21no—
159C22×C4×C103—21no—
160C22×C4×C103—21no—
161C22×C4×C103—21no—
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—21no—
166C22×C4×C103—41no—
167C22×C4×C103—41no—
168C22×C4×C103—41no—
169C22×C4×C103C22×C411yescharacteristic
170C22×C4×C103C22×C411yescharacteristic
171C22×C4×C103C22×C411yescharacteristic
172C22×C4×C103C22×C411yescharacteristic
173C22×C4×C103C22×C411yescharacteristic
174C22×C4×C103C22×C411yescharacteristic
175C22×C4×C103C22×C411yescharacteristic
176C22×C4×C103C22×C411yescharacteristic
177C22×C4×C103C22×C411yescharacteristic
178C22×C4×C103C22×C411yescharacteristic
179C22×C4×C103C22×C411yescharacteristic
180C22×C4×C103C2411yescharacteristic
181M16×C103—44no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103—21no—
185C2×C8×C103—21no—
186C2×C8×C103—21no—
187C2×C8×C103—21no—
188C2×C8×C103—21no—
189C2×C8×C103—21no—
190C2×C8×C103—21no—
191C2×C8×C103—21no—
192C2×C8×C103—21no—
193C2×C8×C103—21no—
194C2×C8×C103—21no—
195C2×C8×C103—21no—
196C2×C8×C103—21no—
197C2×C8×C103—21no—
198C2×C8×C103—21no—
199C2×C8×C103—21no—
200C2×C8×C103—21no—
201C2×C8×C103—21no—
202C2×C8×C103—21no—
203C2×C8×C103—21no—
204C2×C8×C103—21no—
205C2×C8×C103—21no—
206C2×C8×C103—44no—
207C4⋊C4×C103—22no—
208C4⋊C4×C103—22no—
209C4⋊C4×C103—41no—
210C4⋊C4×C103—41no—
211C4⋊C4×C103—41no—
212C22⋊C4×C103—22no—
213C22⋊C4×C103—22no—
214C22⋊C4×C103—22no—
215C22⋊C4×C103—22no—
216C22⋊C4×C103—41no—
217C22⋊C4×C103—41no—
218C22⋊C4×C103—41no—
219C22⋊C4×C103—41no—
220C22⋊C4×C103—41no—
221C22⋊C4×C103—41no—
222C42×C103—21no—
223C42×C103—21no—
224C42×C103—21no—
225C42×C103—21no—
226C42×C103—21no—
227C42×C103—21no—
228C42×C103—21no—
229C42×C103—21no—
230C42×C103—41no—
231C42×C103—41no—
232C23×C103—21no—
233C23×C103—21no—
234C23×C103—21no—
235C23×C103—21no—
236C23×C103—21no—
237C23×C103—21no—
238C23×C103—21no—
239C23×C103—21no—
240C23×C103—21no—
241C23×C103—21no—
242C23×C103—21no—
243C23×C103—21no—
244C23×C103—21no—
245C23×C103—21no—
246C23×C103—21no—
247C23×C103—21no—
248C23×C103—21no—
249C23×C103—21no—
250C23×C103—21no—
251C23×C103C2×M1612yes—
252C23×C103C2×M1612yes—
253C23×C103C23×C411yescharacteristic
254D4×C103—44no—
255D4×C103—44no—
256D4×C103—44no—
257C2×C4×C103—21no—
258C2×C4×C103—21no—
259C2×C4×C103—21no—
260C2×C4×C103—21no—
261C2×C4×C103—21no—
262C2×C4×C103—21no—
263C2×C4×C103—21no—
264C2×C4×C103—21no—
265C2×C4×C103—21no—
266C2×C4×C103—21no—
267C2×C4×C103—21no—
268C2×C4×C103—21no—
269C2×C4×C103—21no—
270C2×C4×C103—21no—
271C2×C4×C103—21no—
272C2×C4×C103—21no—
273C2×C4×C103—21no—
274C2×C4×C103—21no—
275C2×C4×C103—21no—
276C2×C4×C103—21no—
277C2×C4×C103—21no—
278C2×C4×C103—21no—
279C2×C4×C103—21no—
280C2×C4×C103—21no—
281C2×C4×C103—21no—
282C2×C4×C103—21no—
283C2×C4×C103—21no—
284C2×C4×C103—21no—
285C2×C4×C103—21no—
286C2×C4×C103—21no—
287C2×C4×C103—44no—
288C2×C4×C103—44no—
289C2×C4×C103—41no—
290C2×C4×C103—41no—
291C2×C4×C103—41no—
292C2×C4×C103—41no—
293C2×C4×C103—41no—
294C2×C4×C103—41no—
295C2×C4×C103—41no—
296C2×C4×C103—41no—
297C2×C4×C103—41no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
301C2×C4×C103C2×M1612yes—
302C2×C4×C103#13112yes—
303C2×C4×C103#13112yes—
304C2×C4×C103H(5,𝔽2)11yescharacteristic
305C2×C4×C103H(5,𝔽2)11yescharacteristic
306C2×C4×C103H(5,𝔽2)11yescharacteristic
307C2×C4×C103H(5,𝔽2)11yescharacteristic
308C2×C4×C103H(5,𝔽2)11yescharacteristic
309C2×C4×C1032−1+411yescharacteristic
310C8×C103—41no—
311C8×C103—41no—
312C8×C103—41no—
313C8×C103—41no—
314C8×C103—41no—
315C8×C103—41no—
316C8×C103—41no—
317C8×C103—41no—
318C22×C103—22no—
319C22×C103—22no—
320C22×C103—22no—
321C22×C103—22no—
322C22×C103—22no—
323C22×C103—22no—
324C22×C103—41no—
325C22×C103—41no—
326C22×C103—41no—
327C22×C103—41no—
328C22×C103—41no—
329C22×C103—41no—
330C22×C103—41no—
331C22×C103—41no—
332C22×C103—41no—
333C22×C103—41no—
334C22×C103—41no—
335C22×C103—41no—
336C22×C103—41no—
337C22×C103—41no—
338C22×C103—41no—
339C22×C103#51811yescharacteristic
340C22×C103#51811yescharacteristic
341C22×C103#52011yescharacteristic
342C22×C103C22×M1611yescharacteristic
343C22×C103C2×#13111yescharacteristic
344C22×C103C2×#13111yescharacteristic
345C22×C103#56811yescharacteristic
346C4×C103—22no—
347C4×C103—22no—
348C4×C103—22no—
349C4×C103—41no—
350C4×C103—41no—
351C4×C103—41no—
352C4×C103—41no—
353C4×C103—41no—
354C4×C103—41no—
355C4×C103—41no—
356C4×C103—41no—
357C4×C103#56011yescharacteristic
358C4×C103#56011yescharacteristic
359C4×C103#56211yescharacteristic
360C4×C103#56211yescharacteristic
361#23331C10311yesmaximal, characteristic, direct product factor, Sylow
362C2×C103—42no—
363C2×C103—42no—
364C2×C103—81no—
365C2×C103#237711yescharacteristic
366C2×C103#297311yescharacteristic
367C2×C103#297411yescharacteristic
368C2×C103#297611yescharacteristic
369C2×C103#297911yescharacteristic
370C2×C103#299011yescharacteristic
371C2×C103#299311yescharacteristic
372C4×#121C2×C10311yescharacteristic
373#1955C2×C10311yescharacteristic, complemented
374#1954C2×C10311yescharacteristic, complemented
375#1924C2×C10311yescharacteristic, complemented
376#1923C2×C10311yescharacteristic, complemented
377#1917C2×C10311yescharacteristic, complemented
378#1916C2×C10311yescharacteristic, complemented
379#1870C2×C10311yescharacteristic, complemented
380#1870C2×C10311yescharacteristic, complemented
381#1869C2×C10311yescharacteristic, complemented
382#1869C2×C10311yescharacteristic, complemented
383#1851C2×C10311yescharacteristic, complemented
384#1850C2×C10311yescharacteristic, complemented
385#1817C2×C10311yescharacteristic, complemented
386#1797C2×C10311yescharacteristic, complemented
387C103#2333111yescharacteristic, direct product factor, Sylow
388C22×M16C22×C10311yescharacteristic
389C23×C8C22×C10311yescharacteristic
390C2×#121C4×C10311yescharacteristic
391C2×C4×D4C22×C10311yescharacteristic
392C2×C4×D4C22×C10311yescharacteristic
393C2×C4×D4C22×C10311yescharacteristic
394C22×C42C22×C10311yescharacteristic
395C2×C4⋊C8C22×C10311yescharacteristic
396C2×C4⋊C8C22×C10311yescharacteristic
397C2×C4⋊C8C22×C10311yescharacteristic
398C2×C4⋊C8C22×C10311yescharacteristic
399C2×C22⋊C8C22×C10311yescharacteristic
400C2×C22⋊C8C22×C10311yescharacteristic
401C2×C22⋊C8C22×C10311yescharacteristic
402C2×C22⋊C8C22×C10311yescharacteristic
403C2×C22⋊C8C22×C10311yescharacteristic
404C2×C22⋊C8C22×C10311yescharacteristic
405C2×C22⋊C8C22×C10311yescharacteristic
406C2×C22⋊C8C22×C10311yescharacteristic
407C2×C22⋊C8C22×C10311yescharacteristic
408C2×C22⋊C8C22×C10311yescharacteristic
409C2×#97C22×C10311yescharacteristic
410C2×C4×C8C22×C10311yescharacteristic
411#390C4×C10311yescharacteristic
412#389C4×C10311yescharacteristic
413#388C4×C10311yescharacteristic
414#388C4×C10311yescharacteristic
415#386C4×C10311yescharacteristic
416#386C4×C10311yescharacteristic
417#380C4×C10311yescharacteristic
418C4×C4⋊C4C22×C10311yescharacteristic
419C4×C22⋊C4C22×C10311yescharacteristic
420C4×C22⋊C4C22×C10311yescharacteristic
421#336C22×C10311yescharacteristic
422#336C22×C10311yescharacteristic
423#336C22×C10311yescharacteristic
424#336C22×C10311yescharacteristic
425#336C22×C10311yescharacteristic
426#336C22×C10311yescharacteristic
427#336C22×C10311yescharacteristic
428#336C22×C10311yescharacteristic
429#336C22×C10311yescharacteristic
430#336C22×C10311yescharacteristic
431C22×D4C2×C4×C10311yescharacteristic
432C22×D4C2×C4×C10311yescharacteristic
433C22×D4C2×C4×C10311yescharacteristic
434C23×C4C2×C4×C10311yescharacteristic
435C23×C4C2×C4×C10311yescharacteristic
436C23×C4C23×C10311yescharacteristic
437C23×C4C23×C10311yescharacteristic
438C23×C4C23×C10311yescharacteristic
439C2×M16—41no—
440C2×M16—41no—
441C2×M16—41no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C10311yescharacteristic
446C22×C8C23×C10311yescharacteristic
447C22×C8C23×C10311yescharacteristic
448C22×C8C23×C10311yescharacteristic
449C22×C8C23×C10311yescharacteristic
450C22×C8C23×C10311yescharacteristic
451C22×C8C23×C10311yescharacteristic
452C22×C8C23×C10311yescharacteristic
453#121—24no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C4×D4—41no—
460C2×C4⋊C4C2×C4×C10311yescharacteristic
461C2×C4⋊C4C2×C4×C10311yescharacteristic
462C2×C4⋊C4C2×C4×C10311yescharacteristic
463C2×C4⋊C4C2×C4×C10311yescharacteristic
464C2×C4⋊C4C2×C4×C10311yescharacteristic
465C2×C22⋊C4C2×C4×C10311yescharacteristic
466C2×C22⋊C4C2×C4×C10311yescharacteristic
467C2×C22⋊C4C2×C4×C10311yescharacteristic
468C2×C22⋊C4C2×C4×C10311yescharacteristic
469C2×C22⋊C4C2×C4×C10311yescharacteristic
470C2×C22⋊C4C2×C4×C10311yescharacteristic
471C2×C22⋊C4C2×C4×C10311yescharacteristic
472C2×C22⋊C4C2×C4×C10311yescharacteristic
473C2×C22⋊C4C2×C4×C10311yescharacteristic
474C2×C22⋊C4C2×C4×C10311yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C10311yescharacteristic
478C2×C42C2×C4×C10311yescharacteristic
479C2×C42C23×C10311yescharacteristic
480C2×C42C23×C10311yescharacteristic
481C2×C42C23×C10311yescharacteristic
482C2×C42C23×C10311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C4⋊C8—41no—
486C4⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497#97—41no—
498C4×C8—41no—
499#95C2×C4×C10311yescharacteristic
500#95C2×C4×C10311yescharacteristic
501#95C2×C4×C10311yescharacteristic
502#95C2×C4×C10311yescharacteristic
503#95C2×C4×C10311yescharacteristic
504#95C2×C4×C10311yescharacteristic
505C24C22×C4×C10311yescharacteristic
506C24C22×C4×C10311yescharacteristic
507C24C22×C4×C10311yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4M16×C10314yescomplemented
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4C22×C4×C10311yescharacteristic
542C22×C4C22×C4×C10311yescharacteristic
543C22×C4C22×C4×C10311yescharacteristic
544C22×C4C22×C4×C10311yescharacteristic
545C22×C4C22×C4×C10311yescharacteristic
546C22×C4C22×C4×C10311yescharacteristic
547C22×C4C22×C4×C10311yescharacteristic
548C22×C4C22×C4×C10311yescharacteristic
549C22×C4C22×C4×C10311yescharacteristic
550C22×C4C22×C4×C10311yescharacteristic
551C22×C4C22×C4×C10311yescharacteristic
552C22×C4C24×C10311yescharacteristic
553M16—44no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—44no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—41no—
603C42—41no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×M16×C10312yes—
624C23C2×M16×C10312yes—
625C23C23×C4×C10311yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4C2×M16×C10312yes—
674C2×C4#131×C10312yes—
675C2×C4#131×C10312yes—
676C2×C4H(5,𝔽2)×C10311yescharacteristic
677C2×C4H(5,𝔽2)×C10311yescharacteristic
678C2×C4H(5,𝔽2)×C10311yescharacteristic
679C2×C4H(5,𝔽2)×C10311yescharacteristic
680C2×C4H(5,𝔽2)×C10311yescharacteristic
681C2×C42−1+4×C10311yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22#518×C10311yescharacteristic
712C22#518×C10311yescharacteristic
713C22#520×C10311yescharacteristic
714C22C22×M16×C10311yescharacteristic
715C22C2×#131×C10311yescharacteristic
716C22C2×#131×C10311yescharacteristic
717C22#568×C10311yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4#560×C10311yescharacteristic
730C4#560×C10311yescharacteristic
731C4#562×C10311yescharacteristic
732C4#562×C10311yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2C103×#237711yescharacteristic
737C2C103×#297311yescharacteristic
738C2C103×#297411yescharacteristic
739C2C103×#297611yescharacteristic
740C2C103×#297911yescharacteristic
741C2C103×#299011yescharacteristic
742C2C103×#299311yescharacteristic
subgroupG/H
centerC22×C4×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C23×C4
prime radicalC2×#121×C103C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1955C2semidirect
3. C103×#1954C2semidirect
4. C103×#1924C2semidirect
5. C103×#1923C2semidirect
6. C103×#1917C2semidirect
7. C103×#1916C2semidirect
8. C103×#1870C2semidirect
9. C103×#1870C2semidirect
10. C103×#1869C2semidirect
11. C103×#1869C2semidirect
12. C103×#1851C2semidirect
13. C103×#1850C2semidirect
14. C103×#1817C2semidirect
15. C103×#1797C2semidirect
144. C2×D4×C103M16semidirect
361. #23331C103direct (N × H)
373. #1955C2×C103semidirect
374. #1954C2×C103semidirect
375. #1924C2×C103semidirect
376. #1923C2×C103semidirect
377. #1917C2×C103semidirect
378. #1916C2×C103semidirect
379. #1870C2×C103semidirect
380. #1870C2×C103semidirect
381. #1869C2×C103semidirect
382. #1869C2×C103semidirect
383. #1851C2×C103semidirect
384. #1850C2×C103semidirect
385. #1817C2×C103semidirect
386. #1797C2×C103semidirect
387. C103#23331direct (N × H)
516. C2×D4M16×C103semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1032
C103×#19552
C103×#19542
C103×#19242
C103×#19232
C103×#19172
C103×#19162
C103×#18702
C103×#18692
C103×#18512
C103×#18502
C103×#18172
C103×#17972
#23331103