Finite Group Databasebeta

← C103×#22036 #39927311

Subgroups — C103×#22036 #39927311

Order 26368.

1162 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C103C211yesmaximal, characteristic, complemented
2C2×#407×C103C211yesmaximal, characteristic, complemented
3C4×#120×C103C211yesmaximal, characteristic
4C103×#1955C211yesmaximal, characteristic, complemented
5C103×#1954C211yesmaximal, characteristic, complemented
6C103×#1924C211yesmaximal, characteristic, complemented
7C103×#1924C211yesmaximal, characteristic, complemented
8C103×#1924C211yesmaximal, characteristic, complemented
9C103×#1923C211yesmaximal, characteristic, complemented
10C103×#1870C211yesmaximal, characteristic, complemented
11C103×#1869C211yesmaximal, characteristic, complemented
12C103×#1869C211yesmaximal, characteristic, complemented
13C103×#1851C211yesmaximal, characteristic, complemented
14C103×#1779C211yesmaximal, characteristic, complemented
15C103×#1753C211yesmaximal, characteristic, complemented
16C24×C4×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic, complemented
20C2×#120×C103C411yescharacteristic
21C2×C4×D4×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24#435×C103—24no—
25C2×C4⋊C8×C103C2211yescharacteristic, complemented
26C2×C4⋊C8×C103C2211yescharacteristic, complemented
27C2×C4⋊C8×C103C2211yescharacteristic, complemented
28#407×C103—24no—
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×C22⋊C8×C103C2211yescharacteristic
38C2×C22⋊C8×C103C2211yescharacteristic
39C2×C22⋊C8×C103C2211yescharacteristic, complemented
40C2×C22⋊C8×C103C2211yescharacteristic, complemented
41C2×C22⋊C8×C103C2211yescharacteristic, complemented
42C2×#97×C103C2211yescharacteristic, complemented
43C2×#97×C103C2211yescharacteristic, complemented
44C2×C4×C8×C103C2211yescharacteristic, complemented
45#386×C103C411yescharacteristic
46#386×C103C411yescharacteristic
47#386×C103C411yescharacteristic
48#385×C103C411yescharacteristic
49#385×C103C411yescharacteristic
50#385×C103C411yescharacteristic
51#379×C103C411yescharacteristic
52C4×C22⋊C4×C103C2211yescharacteristic
53C4×C22⋊C4×C103C2211yescharacteristic
54C4×C22⋊C4×C103C2211yescharacteristic
55#336×C103C2211yescharacteristic, complemented
56#336×C103C2211yescharacteristic, complemented
57#336×C103C2211yescharacteristic, complemented
58#336×C103C2211yescharacteristic, complemented
59#336×C103C2211yescharacteristic, complemented
60#336×C103C2211yescharacteristic, complemented
61C25×C103C2×C411yescharacteristic
62C22×D4×C103C2×C411yescharacteristic
63C22×D4×C103C2×C411yescharacteristic
64C22×D4×C103C2×C411yescharacteristic
65C23×C4×C103—22no—
66C23×C4×C103—22no—
67C23×C4×C103—41no—
68C23×C4×C103—41no—
69C23×C4×C103—41no—
70C23×C4×C103—41no—
71C23×C4×C103C2×C411yescharacteristic
72C23×C4×C103C2×C411yescharacteristic
73C23×C4×C103C2×C411yescharacteristic
74C23×C4×C103C2311yescharacteristic
75C23×C4×C103C2311yescharacteristic
76C23×C4×C103C2311yescharacteristic
77C23×C4×C103C2311yescharacteristic
78C2×M16×C103—22no—
79C2×M16×C103—41no—
80C2×M16×C103—41no—
81C2×M16×C103—41no—
82C2×M16×C103—41no—
83C2×M16×C103D414yescomplemented
84C22×C8×C103—22no—
85C22×C8×C103—41no—
86C22×C8×C103—41no—
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90C22×C8×C103C2311yescharacteristic
91C22×C8×C103C2311yescharacteristic
92C22×C8×C103C2311yescharacteristic
93C22×C8×C103C2311yescharacteristic
94C22×C8×C103C2311yescharacteristic
95#120×C103—24no—
96C4×D4×C103—22no—
97C4×D4×C103—22no—
98C4×D4×C103—41no—
99C4×D4×C103—41no—
100C4×D4×C103—41no—
101C4×D4×C103—41no—
102C2×C4⋊C4×C103C2×C411yescharacteristic
103C2×C4⋊C4×C103C2×C411yescharacteristic
104C2×C4⋊C4×C103C2×C411yescharacteristic
105C2×C22⋊C4×C103C2×C411yescharacteristic
106C2×C22⋊C4×C103C2×C411yescharacteristic
107C2×C22⋊C4×C103C2×C411yescharacteristic
108C2×C22⋊C4×C103C2×C411yescharacteristic
109C2×C22⋊C4×C103C2×C411yescharacteristic
110C2×C22⋊C4×C103C2×C411yescharacteristic
111C2×C22⋊C4×C103C2×C411yescharacteristic
112C2×C22⋊C4×C103C2×C411yescharacteristic
113C2×C22⋊C4×C103C2×C411yescharacteristic
114C2×C22⋊C4×C103C2×C411yescharacteristic
115C2×C22⋊C4×C103C2×C411yescharacteristic
116C2×C22⋊C4×C103C2×C411yescharacteristic
117C2×C42×C103C2311yescharacteristic
118C2×C42×C103C2311yescharacteristic
119C2×C42×C103C2311yescharacteristic
120C4⋊C8×C103—22no—
121C4⋊C8×C103—41no—
122C4⋊C8×C103—41no—
123C22⋊C8×C103—22no—
124C22⋊C8×C103—22no—
125C22⋊C8×C103—22no—
126C22⋊C8×C103—22no—
127C22⋊C8×C103—22no—
128C22⋊C8×C103—22no—
129C22⋊C8×C103—22no—
130C22⋊C8×C103—41no—
131C22⋊C8×C103—41no—
132C22⋊C8×C103—41no—
133C22⋊C8×C103—41no—
134C22⋊C8×C103—41no—
135C22⋊C8×C103—41no—
136#97×C103—22no—
137#97×C103—41no—
138C4×C8×C103—41no—
139#95×C103C2×C411yescharacteristic
140#95×C103C2×C411yescharacteristic
141#95×C103C2×C411yescharacteristic
142#95×C103C2×C411yescharacteristic
143#95×C103C2×C411yescharacteristic
144#95×C103C2×C411yescharacteristic
145C24×C103—22no—
146C24×C103—22no—
147C24×C103—22no—
148C24×C103—41no—
149C24×C103—41no—
150C24×C103—41no—
151C24×C103—41no—
152C24×C103C22×C411yescharacteristic
153C24×C103C22×C411yescharacteristic
154C24×C103C22×C411yescharacteristic
155C24×C103C22×C411yescharacteristic
156C2×D4×C103—22no—
157C2×D4×C103—22no—
158C2×D4×C103—22no—
159C2×D4×C103—22no—
160C2×D4×C103—41no—
161C2×D4×C103—41no—
162C2×D4×C103—41no—
163C2×D4×C103—41no—
164C2×D4×C103M1614yescomplemented
165C22×C4×C103—21no—
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—22no—
170C22×C4×C103—22no—
171C22×C4×C103—22no—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
183C22×C4×C103—21no—
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—41no—
191C22×C4×C103—41no—
192C22×C4×C103—41no—
193C22×C4×C103—41no—
194C22×C4×C103—41no—
195C22×C4×C103—41no—
196C22×C4×C103—44no—
197C22×C4×C103—44no—
198C22×C4×C103—44no—
199C22×C4×C103—44no—
200C22×C4×C103C22×C411yescharacteristic
201C22×C4×C103C22×C411yescharacteristic
202C22×C4×C103C22×C411yescharacteristic
203C22×C4×C103C22×C411yescharacteristic
204C22×C4×C103C22×C411yescharacteristic
205C22×C4×C103C22×C411yescharacteristic
206C22×C4×C103C22×C411yescharacteristic
207C22×C4×C103C22×C411yescharacteristic
208C22×C4×C103C22×C411yescharacteristic
209C22×C4×C103C22×C411yescharacteristic
210C22×C4×C103C2×D412yes—
211C22×C4×C103#4112yes—
212C22×C4×C103C2411yescharacteristic
213M16×C103—44no—
214M16×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—21no—
225C2×C8×C103—21no—
226C2×C8×C103—21no—
227C2×C8×C103—21no—
228C2×C8×C103—21no—
229C2×C8×C103—21no—
230C2×C8×C103—21no—
231C2×C8×C103—21no—
232C2×C8×C103—21no—
233C2×C8×C103—21no—
234C2×C8×C103—21no—
235C2×C8×C103—21no—
236C2×C8×C103—21no—
237C2×C8×C103—44no—
238C2×C8×C103C2×D412yes—
239C2×C8×C103C2×D412yes—
240C4⋊C4×C103—22no—
241C4⋊C4×C103—41no—
242C4⋊C4×C103—41no—
243C22⋊C4×C103—22no—
244C22⋊C4×C103—22no—
245C22⋊C4×C103—22no—
246C22⋊C4×C103—22no—
247C22⋊C4×C103—22no—
248C22⋊C4×C103—22no—
249C22⋊C4×C103—41no—
250C22⋊C4×C103—41no—
251C22⋊C4×C103—41no—
252C22⋊C4×C103—41no—
253C22⋊C4×C103—41no—
254C22⋊C4×C103—41no—
255C42×C103—21no—
256C42×C103—21no—
257C42×C103—21no—
258C42×C103—21no—
259C42×C103—21no—
260C42×C103—21no—
261C23×C103—21no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—21no—
266C23×C103—21no—
267C23×C103—21no—
268C23×C103—21no—
269C23×C103—21no—
270C23×C103—21no—
271C23×C103—21no—
272C23×C103—21no—
273C23×C103—21no—
274C23×C103—21no—
275C23×C103—21no—
276C23×C103—21no—
277C23×C103—21no—
278C23×C103—21no—
279C23×C103—21no—
280C23×C103—21no—
281C23×C103—21no—
282C23×C103—21no—
283C23×C103—21no—
284C23×C103—21no—
285C23×C103—44no—
286C23×C103—44no—
287C23×C103—44no—
288C23×C103—44no—
289C23×C103—44no—
290C23×C103—44no—
291C23×C103—44no—
292C23×C103C4×D412yes—
293C23×C103C2×M1612yes—
294C23×C103C2×M1612yes—
295C23×C103#13112yes—
296C23×C103C23×C411yescharacteristic
297D4×C103—44no—
298D4×C103—44no—
299D4×C103—44no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—22no—
305C2×C4×C103—22no—
306C2×C4×C103—22no—
307C2×C4×C103—22no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
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—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—21no—
329C2×C4×C103—21no—
330C2×C4×C103—21no—
331C2×C4×C103—21no—
332C2×C4×C103—44no—
333C2×C4×C103—44no—
334C2×C4×C103—44no—
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—41no—
345C2×C4×C103—41no—
346C2×C4×C103—41no—
347C2×C4×C103C4×D412yes—
348C2×C4×C103C2×M1612yes—
349C2×C4×C103C22×D411yescharacteristic
350C2×C4×C103C2×#4111yescharacteristic
351C2×C4×C103H(5,𝔽2)11yescharacteristic
352C2×C4×C103H(5,𝔽2)11yescharacteristic
353C2×C4×C103H(5,𝔽2)11yescharacteristic
354C2×C4×C103H(5,𝔽2)11yescharacteristic
355C8×C103—22no—
356C8×C103—22no—
357C8×C103—41no—
358C8×C103—41no—
359C8×C103—41no—
360C8×C103—41no—
361C8×C103—41no—
362C8×C103—41no—
363C22×C103—22no—
364C22×C103—22no—
365C22×C103—22no—
366C22×C103—22no—
367C22×C103—22no—
368C22×C103—22no—
369C22×C103—22no—
370C22×C103—22no—
371C22×C103—22no—
372C22×C103—22no—
373C22×C103—22no—
374C22×C103—22no—
375C22×C103—416no—
376C22×C103—41no—
377C22×C103—41no—
378C22×C103—41no—
379C22×C103—41no—
380C22×C103—41no—
381C22×C103—41no—
382C22×C103—41no—
383C22×C103—41no—
384C22×C103—41no—
385C22×C103—41no—
386C22×C103—41no—
387C22×C103—41no—
388C22×C103—41no—
389C22×C103—41no—
390C22×C103—41no—
391C22×C103—41no—
392C22×C103C2×C4×D411yescharacteristic
393C22×C103#51811yescharacteristic
394C22×C103#51811yescharacteristic
395C22×C103C22×M1611yescharacteristic
396C22×C103C2×#13111yescharacteristic
397C22×C103#56811yescharacteristic
398C22×C103#56811yescharacteristic
399C4×C103—22no—
400C4×C103—22no—
401C4×C103—41no—
402C4×C103—41no—
403C4×C103—41no—
404C4×C103—41no—
405C4×C103—41no—
406C4×C103—41no—
407C4×C103—41no—
408C4×C103—41no—
409C4×C103#53411yescharacteristic
410C4×C103#53511yescharacteristic
411C4×C103#53811yescharacteristic
412C4×C103#53811yescharacteristic
413#22036C10311yesmaximal, characteristic, direct product factor, Sylow
414C2×C103—42no—
415C2×C103—42no—
416C2×C103—42no—
417C2×C103—42no—
418C2×C103#232111yescharacteristic
419C2×C103#293311yescharacteristic
420C2×C103D4×M1611yescharacteristic
421C2×C103#297311yescharacteristic
422C2×C103#297411yescharacteristic
423C2×C103#297611yescharacteristic
424C2×C103#297811yescharacteristic
425C2×#435C2×C10311yescharacteristic, complemented
426C2×#407C2×C10311yescharacteristic, complemented
427C4×#120C2×C10311yescharacteristic
428#1955C2×C10311yescharacteristic, complemented
429#1954C2×C10311yescharacteristic, complemented
430#1924C2×C10311yescharacteristic, complemented
431#1924C2×C10311yescharacteristic, complemented
432#1924C2×C10311yescharacteristic, complemented
433#1923C2×C10311yescharacteristic, complemented
434#1870C2×C10311yescharacteristic, complemented
435#1869C2×C10311yescharacteristic, complemented
436#1869C2×C10311yescharacteristic, complemented
437#1851C2×C10311yescharacteristic, complemented
438#1779C2×C10311yescharacteristic, complemented
439#1753C2×C10311yescharacteristic, complemented
440C103#2203611yescharacteristic, direct product factor, Sylow
441C24×C4C22×C10311yescharacteristic
442C22×M16C22×C10311yescharacteristic
443C22×M16C22×C10311yescharacteristic
444C23×C8C22×C10311yescharacteristic, complemented
445C2×#120C4×C10311yescharacteristic
446C2×C4×D4C22×C10311yescharacteristic
447C2×C4×D4C22×C10311yescharacteristic
448C2×C4×D4C22×C10311yescharacteristic
449#435—24no—
450C2×C4⋊C8C22×C10311yescharacteristic, complemented
451C2×C4⋊C8C22×C10311yescharacteristic, complemented
452C2×C4⋊C8C22×C10311yescharacteristic, complemented
453#407—24no—
454C2×C22⋊C8C22×C10311yescharacteristic
455C2×C22⋊C8C22×C10311yescharacteristic
456C2×C22⋊C8C22×C10311yescharacteristic
457C2×C22⋊C8C22×C10311yescharacteristic
458C2×C22⋊C8C22×C10311yescharacteristic
459C2×C22⋊C8C22×C10311yescharacteristic
460C2×C22⋊C8C22×C10311yescharacteristic
461C2×C22⋊C8C22×C10311yescharacteristic
462C2×C22⋊C8C22×C10311yescharacteristic
463C2×C22⋊C8C22×C10311yescharacteristic
464C2×C22⋊C8C22×C10311yescharacteristic, complemented
465C2×C22⋊C8C22×C10311yescharacteristic, complemented
466C2×C22⋊C8C22×C10311yescharacteristic, complemented
467C2×#97C22×C10311yescharacteristic, complemented
468C2×#97C22×C10311yescharacteristic, complemented
469C2×C4×C8C22×C10311yescharacteristic, complemented
470#386C4×C10311yescharacteristic
471#386C4×C10311yescharacteristic
472#386C4×C10311yescharacteristic
473#385C4×C10311yescharacteristic
474#385C4×C10311yescharacteristic
475#385C4×C10311yescharacteristic
476#379C4×C10311yescharacteristic
477C4×C22⋊C4C22×C10311yescharacteristic
478C4×C22⋊C4C22×C10311yescharacteristic
479C4×C22⋊C4C22×C10311yescharacteristic
480#336C22×C10311yescharacteristic, complemented
481#336C22×C10311yescharacteristic, complemented
482#336C22×C10311yescharacteristic, complemented
483#336C22×C10311yescharacteristic, complemented
484#336C22×C10311yescharacteristic, complemented
485#336C22×C10311yescharacteristic, complemented
486C25C2×C4×C10311yescharacteristic
487C22×D4C2×C4×C10311yescharacteristic
488C22×D4C2×C4×C10311yescharacteristic
489C22×D4C2×C4×C10311yescharacteristic
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—41no—
495C23×C4—41no—
496C23×C4C2×C4×C10311yescharacteristic
497C23×C4C2×C4×C10311yescharacteristic
498C23×C4C2×C4×C10311yescharacteristic
499C23×C4C23×C10311yescharacteristic
500C23×C4C23×C10311yescharacteristic
501C23×C4C23×C10311yescharacteristic
502C23×C4C23×C10311yescharacteristic
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16D4×C10314yescomplemented
509C22×C8—22no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8C23×C10311yescharacteristic
513C22×C8C23×C10311yescharacteristic
514C22×C8C23×C10311yescharacteristic
515C22×C8C23×C10311yescharacteristic
516C22×C8C23×C10311yescharacteristic
517C22×C8C23×C10311yescharacteristic
518C22×C8C23×C10311yescharacteristic
519C22×C8C23×C10311yescharacteristic
520#120—24no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—41no—
524C4×D4—41no—
525C4×D4—41no—
526C4×D4—41no—
527C2×C4⋊C4C2×C4×C10311yescharacteristic
528C2×C4⋊C4C2×C4×C10311yescharacteristic
529C2×C4⋊C4C2×C4×C10311yescharacteristic
530C2×C22⋊C4C2×C4×C10311yescharacteristic
531C2×C22⋊C4C2×C4×C10311yescharacteristic
532C2×C22⋊C4C2×C4×C10311yescharacteristic
533C2×C22⋊C4C2×C4×C10311yescharacteristic
534C2×C22⋊C4C2×C4×C10311yescharacteristic
535C2×C22⋊C4C2×C4×C10311yescharacteristic
536C2×C22⋊C4C2×C4×C10311yescharacteristic
537C2×C22⋊C4C2×C4×C10311yescharacteristic
538C2×C22⋊C4C2×C4×C10311yescharacteristic
539C2×C22⋊C4C2×C4×C10311yescharacteristic
540C2×C22⋊C4C2×C4×C10311yescharacteristic
541C2×C22⋊C4C2×C4×C10311yescharacteristic
542C2×C42C23×C10311yescharacteristic
543C2×C42C23×C10311yescharacteristic
544C2×C42C23×C10311yescharacteristic
545C4⋊C8—22no—
546C4⋊C8—41no—
547C4⋊C8—41no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—41no—
556C22⋊C8—41no—
557C22⋊C8—41no—
558C22⋊C8—41no—
559C22⋊C8—41no—
560C22⋊C8—41no—
561#97—22no—
562#97—41no—
563C4×C8—41no—
564#95C2×C4×C10311yescharacteristic
565#95C2×C4×C10311yescharacteristic
566#95C2×C4×C10311yescharacteristic
567#95C2×C4×C10311yescharacteristic
568#95C2×C4×C10311yescharacteristic
569#95C2×C4×C10311yescharacteristic
570C24—22no—
571C24—22no—
572C24—22no—
573C24—41no—
574C24—41no—
575C24—41no—
576C24—41no—
577C24C22×C4×C10311yescharacteristic
578C24C22×C4×C10311yescharacteristic
579C24C22×C4×C10311yescharacteristic
580C24C22×C4×C10311yescharacteristic
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4M16×C10314yescomplemented
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
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—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4C22×C4×C10311yescharacteristic
626C22×C4C22×C4×C10311yescharacteristic
627C22×C4C22×C4×C10311yescharacteristic
628C22×C4C22×C4×C10311yescharacteristic
629C22×C4C22×C4×C10311yescharacteristic
630C22×C4C22×C4×C10311yescharacteristic
631C22×C4C22×C4×C10311yescharacteristic
632C22×C4C22×C4×C10311yescharacteristic
633C22×C4C22×C4×C10311yescharacteristic
634C22×C4C22×C4×C10311yescharacteristic
635C22×C4C2×D4×C10312yes—
636C22×C4#41×C10312yes—
637C22×C4C24×C10311yescharacteristic
638M16—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×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—44no—
663C2×C8C2×D4×C10312yes—
664C2×C8C2×D4×C10312yes—
665C4⋊C4—22no—
666C4⋊C4—41no—
667C4⋊C4—41no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C4×D4×C10312yes—
718C23C2×M16×C10312yes—
719C23C2×M16×C10312yes—
720C23#131×C10312yes—
721C23C23×C4×C10311yescharacteristic
722D4—44no—
723D4—44no—
724D4—44no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
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—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4C4×D4×C10312yes—
773C2×C4C2×M16×C10312yes—
774C2×C4C22×D4×C10311yescharacteristic
775C2×C4C2×#41×C10311yescharacteristic
776C2×C4H(5,𝔽2)×C10311yescharacteristic
777C2×C4H(5,𝔽2)×C10311yescharacteristic
778C2×C4H(5,𝔽2)×C10311yescharacteristic
779C2×C4H(5,𝔽2)×C10311yescharacteristic
780C8—22no—
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—416no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22C2×C4×D4×C10311yescharacteristic
818C22#518×C10311yescharacteristic
819C22#518×C10311yescharacteristic
820C22C22×M16×C10311yescharacteristic
821C22C2×#131×C10311yescharacteristic
822C22#568×C10311yescharacteristic
823C22#568×C10311yescharacteristic
824C4—22no—
825C4—22no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—41no—
834C4#534×C10311yescharacteristic
835C4#535×C10311yescharacteristic
836C4#538×C10311yescharacteristic
837C4#538×C10311yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—42no—
842C2C103×#232111yescharacteristic
843C2C103×#293311yescharacteristic
844C2D4×M16×C10311yescharacteristic
845C2C103×#297311yescharacteristic
846C2C103×#297411yescharacteristic
847C2C103×#297611yescharacteristic
848C2C103×#297811yescharacteristic
subgroupG/H
centerC22×C4×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C23×C4
prime radicalC2×#120×C103C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C103C2semidirect
2. C2×#407×C103C2semidirect
4. C103×#1955C2semidirect
5. C103×#1954C2semidirect
6. C103×#1924C2semidirect
7. C103×#1924C2semidirect
8. C103×#1924C2semidirect
9. C103×#1923C2semidirect
10. C103×#1870C2semidirect
11. C103×#1869C2semidirect
12. C103×#1869C2semidirect
13. C103×#1851C2semidirect
14. C103×#1779C2semidirect
15. C103×#1753C2semidirect
19. C23×C8×C103C22semidirect
25. C2×C4⋊C8×C103C22semidirect
26. C2×C4⋊C8×C103C22semidirect
27. C2×C4⋊C8×C103C22semidirect
39. C2×C22⋊C8×C103C22semidirect
40. C2×C22⋊C8×C103C22semidirect
41. C2×C22⋊C8×C103C22semidirect
42. C2×#97×C103C22semidirect
43. C2×#97×C103C22semidirect
44. C2×C4×C8×C103C22semidirect
55. #336×C103C22semidirect
56. #336×C103C22semidirect
57. #336×C103C22semidirect
58. #336×C103C22semidirect
59. #336×C103C22semidirect
60. #336×C103C22semidirect
83. C2×M16×C103D4semidirect
164. C2×D4×C103M16semidirect
413. #22036C103direct (N × H)
425. C2×#435C2×C103semidirect
426. C2×#407C2×C103semidirect
428. #1955C2×C103semidirect
429. #1954C2×C103semidirect
430. #1924C2×C103semidirect
431. #1924C2×C103semidirect
432. #1924C2×C103semidirect
433. #1923C2×C103semidirect
434. #1870C2×C103semidirect
435. #1869C2×C103semidirect
436. #1869C2×C103semidirect
437. #1851C2×C103semidirect
438. #1779C2×C103semidirect
439. #1753C2×C103semidirect
440. C103#22036direct (N × H)
444. C23×C8C22×C103semidirect
450. C2×C4⋊C8C22×C103semidirect
451. C2×C4⋊C8C22×C103semidirect
452. C2×C4⋊C8C22×C103semidirect
464. C2×C22⋊C8C22×C103semidirect
465. C2×C22⋊C8C22×C103semidirect
466. C2×C22⋊C8C22×C103semidirect
467. C2×#97C22×C103semidirect
468. C2×#97C22×C103semidirect
469. C2×C4×C8C22×C103semidirect
480. #336C22×C103semidirect
481. #336C22×C103semidirect
482. #336C22×C103semidirect
483. #336C22×C103semidirect
484. #336C22×C103semidirect
485. #336C22×C103semidirect
508. C2×M16D4×C103semidirect
589. C2×D4M16×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1032
C2×#407×C1032
C4×#120×C1032
C103×#19552
C103×#19542
C103×#19242
C103×#19232
C103×#18702
C103×#18692
C103×#18512
C103×#17792
C103×#17532
#22036103