Finite Group Databasebeta

← C103×#22560 #39927835

Subgroups — C103×#22560 #39927835

Order 26368.

1010 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C103C211yesmaximal, characteristic, complemented
2C2×#408×C103C211yesmaximal, characteristic
3C103×#2297C211yesmaximal, characteristic
4C103×#1924C211yesmaximal, characteristic, complemented
5C103×#1923C211yesmaximal, characteristic, complemented
6C103×#1923C211yesmaximal, characteristic, complemented
7C103×#1923C211yesmaximal, characteristic, complemented
8C103×#1851C211yesmaximal, characteristic, complemented
9C103×#1850C211yesmaximal, characteristic, complemented
10C103×#1818C211yesmaximal, characteristic, complemented
11C103×#1797C211yesmaximal, characteristic, complemented
12C103×#1780C211yesmaximal, characteristic
13C103×#1753C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C103C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C103C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18C23×C8×C103C2211yescharacteristic
19C2×#117×C103C2211yescharacteristic
20C22×C42×C103C2211yescharacteristic
21#433×C103—24no—
22C2×C4⋊C8×C103C2211yescharacteristic
23C2×C4⋊C8×C103C2211yescharacteristic
24C2×C4⋊C8×C103C2211yescharacteristic
25C2×C4⋊C8×C103C2211yescharacteristic
26#408×C103—24no—
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
39C2×C4×C8×C103C2211yescharacteristic
40C2×C4×C8×C103C2211yescharacteristic
41#391×C103C411yescharacteristic
42#391×C103C411yescharacteristic
43#390×C103C411yescharacteristic
44#390×C103C411yescharacteristic
45#386×C103C411yescharacteristic
46#386×C103C411yescharacteristic
47#386×C103C411yescharacteristic
48#386×C103C411yescharacteristic
49C4×C22⋊C4×C103C2211yescharacteristic
50C4×C22⋊C4×C103C2211yescharacteristic
51C4×C22⋊C4×C103C2211yescharacteristic
52C4×C22⋊C4×C103C2211yescharacteristic
53#336×C103C2211yescharacteristic
54#336×C103C2211yescharacteristic
55#336×C103C2211yescharacteristic
56#336×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60#336×C103C2211yescharacteristic
61C2×#41×C103—22no—
62C2×#41×C103—22no—
63C2×#41×C103—22no—
64C2×#41×C103—22no—
65C2×#41×C103—41no—
66C2×#41×C103—41no—
67C22×Q8×C103C2×C411yescharacteristic
68C22×D4×C103C2×C411yescharacteristic
69C22×D4×C103C2×C411yescharacteristic
70C22×D4×C103C2×C411yescharacteristic
71C23×C4×C103C2×C411yescharacteristic
72C23×C4×C103C2×C411yescharacteristic
73C23×C4×C103C2311yescharacteristic
74C23×C4×C103C2311yescharacteristic
75C23×C4×C103C2311yescharacteristic
76C2×M16×C103—22no—
77C2×M16×C103—22no—
78C2×M16×C103—41no—
79C22×C8×C103—22no—
80C22×C8×C103—22no—
81C22×C8×C103—41no—
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90#117×C103—22no—
91#117×C103—22no—
92C2×C4⋊C4×C103C2×C411yescharacteristic
93C2×C4⋊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×C22⋊C4×C103C2×C411yescharacteristic
104C2×C42×C103—41no—
105C2×C42×C103—41no—
106C2×C42×C103C2×C411yescharacteristic
107C2×C42×C103C2×C411yescharacteristic
108C2×C42×C103C2311yescharacteristic
109C2×C42×C103C2311yescharacteristic
110C2×C42×C103C2311yescharacteristic
111C2×C42×C103C2311yescharacteristic
112C4⋊C8×C103—22no—
113C4⋊C8×C103—22no—
114C4⋊C8×C103—41no—
115C4⋊C8×C103—41no—
116C22⋊C8×C103—22no—
117C22⋊C8×C103—22no—
118C22⋊C8×C103—22no—
119C22⋊C8×C103—22no—
120C22⋊C8×C103—22no—
121C22⋊C8×C103—22no—
122C22⋊C8×C103—22no—
123C22⋊C8×C103—41no—
124C22⋊C8×C103—41no—
125C22⋊C8×C103D414yes—
126#97×C103—22no—
127C4×C8×C103—22no—
128C4×C8×C103—41no—
129C4×C8×C103—41no—
130#95×C103C2×C411yescharacteristic
131#95×C103C2×C411yescharacteristic
132#95×C103C2×C411yescharacteristic
133#95×C103C2×C411yescharacteristic
134#95×C103C2×C411yescharacteristic
135#95×C103C2×C411yescharacteristic
136#95×C103C2×C411yescharacteristic
137#95×C103C2×C411yescharacteristic
138C24×C103C22×C411yescharacteristic
139C24×C103C22×C411yescharacteristic
140C24×C103C22×C411yescharacteristic
141#41×C103—44no—
142#41×C103—44no—
143#41×C103—44no—
144#41×C103—44no—
145C2×Q8×C103—22no—
146C2×Q8×C103—22no—
147C2×Q8×C103—41no—
148C2×D4×C103—22no—
149C2×D4×C103—22no—
150C2×D4×C103—22no—
151C2×D4×C103—22no—
152C2×D4×C103—22no—
153C2×D4×C103—22no—
154C2×D4×C103—41no—
155C2×D4×C103—41no—
156C2×D4×C103—41no—
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—22no—
166C22×C4×C103—22no—
167C22×C4×C103—22no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—21no—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—41no—
175C22×C4×C103—41no—
176C22×C4×C103—41no—
177C22×C4×C103C22×C411yescharacteristic
178C22×C4×C103C22×C411yescharacteristic
179C22×C4×C103C22×C411yescharacteristic
180C22×C4×C103C22×C411yescharacteristic
181C22×C4×C103C22×C411yescharacteristic
182C22×C4×C103C22×C411yescharacteristic
183C22×C4×C103C22×C411yescharacteristic
184C22×C4×C103C22×C411yescharacteristic
185C22×C4×C103C22×C411yescharacteristic
186C22×C4×C103C22×C411yescharacteristic
187C22×C4×C103C22×C411yescharacteristic
188C22×C4×C103C2×D412yes—
189C22×C4×C103#4112yes—
190C22×C4×C103#4112yes—
191C22×C4×C103#4112yes—
192C22×C4×C103C2411yescharacteristic
193M16×C103—44no—
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—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103—21no—
213C2×C8×C103—21no—
214C2×C8×C103—21no—
215C2×C8×C103—21no—
216C2×C8×C103—44no—
217C2×C8×C103C2×D412yes—
218C2×C8×C103C2×D412yes—
219C4⋊C4×C103—22no—
220C4⋊C4×C103—22no—
221C22⋊C4×C103—22no—
222C22⋊C4×C103—22no—
223C22⋊C4×C103—22no—
224C22⋊C4×C103—22no—
225C22⋊C4×C103—22no—
226C22⋊C4×C103—22no—
227C22⋊C4×C103—22no—
228C22⋊C4×C103—22no—
229C22⋊C4×C103—41no—
230C22⋊C4×C103—41no—
231C42×C103—21no—
232C42×C103—21no—
233C42×C103—21no—
234C42×C103—21no—
235C42×C103—21no—
236C42×C103—21no—
237C42×C103—21no—
238C42×C103—21no—
239C42×C103—41no—
240C42×C103—41no—
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×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103—21no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103#11712yes—
261C23×C103C4×D412yes—
262C23×C103C23×C411yescharacteristic
263Q8×C103—44no—
264D4×C103—44no—
265D4×C103—44no—
266D4×C103—44no—
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—22no—
278C2×C4×C103—22no—
279C2×C4×C103—22no—
280C2×C4×C103—22no—
281C2×C4×C103—22no—
282C2×C4×C103—22no—
283C2×C4×C103—22no—
284C2×C4×C103—22no—
285C2×C4×C103—21no—
286C2×C4×C103—21no—
287C2×C4×C103—21no—
288C2×C4×C103—21no—
289C2×C4×C103—21no—
290C2×C4×C103—21no—
291C2×C4×C103—21no—
292C2×C4×C103—21no—
293C2×C4×C103—21no—
294C2×C4×C103—21no—
295C2×C4×C103—21no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—21no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—44no—
304C2×C4×C103—44no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103—41no—
309C2×C4×C103#11712yes—
310C2×C4×C103C4×D412yes—
311C2×C4×C103#13112yes—
312C2×C4×C103#13112yes—
313C2×C4×C103#13112yes—
314C2×C4×C103C22×D411yescharacteristic
315C2×C4×C103C2×#4111yescharacteristic
316C2×C4×C103C2×#4111yescharacteristic
317C2×C4×C103C2×#4111yescharacteristic
318C2×C4×C103H(5,𝔽2)11yescharacteristic
319C2×C4×C103H(5,𝔽2)11yescharacteristic
320C8×C103—22no—
321C8×C103—22no—
322C8×C103—41no—
323C8×C103—41no—
324C8×C103—41no—
325C8×C103—41no—
326C8×C103—41no—
327C8×C103—41no—
328C22×C103—22no—
329C22×C103—22no—
330C22×C103—22no—
331C22×C103—22no—
332C22×C103—22no—
333C22×C103—22no—
334C22×C103—41no—
335C22×C103—41no—
336C22×C103—41no—
337C22×C103—41no—
338C22×C103—41no—
339C22×C103—41no—
340C22×C103—41no—
341C22×C103—41no—
342C22×C103—41no—
343C22×C103—41no—
344C22×C103—41no—
345C22×C103—41no—
346C22×C103—41no—
347C22×C103—41no—
348C22×C103—41no—
349C22×C103C2×#11711yescharacteristic
350C22×C103C2×C4×D411yescharacteristic
351C22×C103#51811yescharacteristic
352C22×C103C2×#13111yescharacteristic
353C22×C103C2×#13111yescharacteristic
354C22×C103C2×#13111yescharacteristic
355C22×C103#56811yescharacteristic
356C4×C103—22no—
357C4×C103—22no—
358C4×C103—22no—
359C4×C103—22no—
360C4×C103—22no—
361C4×C103—41no—
362C4×C103—41no—
363C4×C103—41no—
364C4×C103—41no—
365C4×C103—41no—
366C4×C103—41no—
367C4×C103#54611yescharacteristic
368C4×C103#54611yescharacteristic
369C4×C103#55111yescharacteristic
370C4×C103#55111yescharacteristic
371#22560C10311yesmaximal, characteristic, direct product factor, Sylow
372C2×C103—42no—
373C2×C103—42no—
374C2×C103—81no—
375C2×C103#234211yescharacteristic
376C2×C103#292211yescharacteristic
377C2×C103#292511yescharacteristic
378C2×C103#293111yescharacteristic
379C2×C103#293511yescharacteristic
380C2×C103#297611yescharacteristic
381C2×C103#297711yescharacteristic
382C2×#433C2×C10311yescharacteristic, complemented
383C2×#408C2×C10311yescharacteristic
384#2297C2×C10311yescharacteristic
385#1924C2×C10311yescharacteristic, complemented
386#1923C2×C10311yescharacteristic, complemented
387#1923C2×C10311yescharacteristic, complemented
388#1923C2×C10311yescharacteristic, complemented
389#1851C2×C10311yescharacteristic, complemented
390#1850C2×C10311yescharacteristic, complemented
391#1818C2×C10311yescharacteristic, complemented
392#1797C2×C10311yescharacteristic, complemented
393#1780C2×C10311yescharacteristic
394#1753C2×C10311yescharacteristic, complemented
395C8×C22⋊C4C2×C10311yescharacteristic, complemented
396C4×C22⋊C8C2×C10311yescharacteristic, complemented
397C103#2256011yescharacteristic, direct product factor, Sylow
398C22×#41C22×C10311yescharacteristic
399C22×M16C22×C10311yescharacteristic
400C23×C8C22×C10311yescharacteristic
401C2×#117C22×C10311yescharacteristic
402C22×C42C22×C10311yescharacteristic
403#433—24no—
404C2×C4⋊C8C22×C10311yescharacteristic
405C2×C4⋊C8C22×C10311yescharacteristic
406C2×C4⋊C8C22×C10311yescharacteristic
407C2×C4⋊C8C22×C10311yescharacteristic
408#408—24no—
409C2×C22⋊C8C22×C10311yescharacteristic
410C2×C22⋊C8C22×C10311yescharacteristic
411C2×C22⋊C8C22×C10311yescharacteristic
412C2×C22⋊C8C22×C10311yescharacteristic
413C2×C22⋊C8C22×C10311yescharacteristic
414C2×C22⋊C8C22×C10311yescharacteristic
415C2×C22⋊C8C22×C10311yescharacteristic
416C2×C22⋊C8C22×C10311yescharacteristic
417C2×C22⋊C8C22×C10311yescharacteristic
418C2×C22⋊C8C22×C10311yescharacteristic
419C2×#97C22×C10311yescharacteristic
420C2×C4×C8C22×C10311yescharacteristic
421C2×C4×C8C22×C10311yescharacteristic
422C2×C4×C8C22×C10311yescharacteristic
423#391C4×C10311yescharacteristic
424#391C4×C10311yescharacteristic
425#390C4×C10311yescharacteristic
426#390C4×C10311yescharacteristic
427#386C4×C10311yescharacteristic
428#386C4×C10311yescharacteristic
429#386C4×C10311yescharacteristic
430#386C4×C10311yescharacteristic
431C4×C22⋊C4C22×C10311yescharacteristic
432C4×C22⋊C4C22×C10311yescharacteristic
433C4×C22⋊C4C22×C10311yescharacteristic
434C4×C22⋊C4C22×C10311yescharacteristic
435#336C22×C10311yescharacteristic
436#336C22×C10311yescharacteristic
437#336C22×C10311yescharacteristic
438#336C22×C10311yescharacteristic
439#336C22×C10311yescharacteristic
440#336C22×C10311yescharacteristic
441#336C22×C10311yescharacteristic
442#336C22×C10311yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C22×Q8C2×C4×C10311yescharacteristic
450C22×D4C2×C4×C10311yescharacteristic
451C22×D4C2×C4×C10311yescharacteristic
452C22×D4C2×C4×C10311yescharacteristic
453C23×C4C2×C4×C10311yescharacteristic
454C23×C4C2×C4×C10311yescharacteristic
455C23×C4C23×C10311yescharacteristic
456C23×C4C23×C10311yescharacteristic
457C23×C4C23×C10311yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—41no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8C23×C10311yescharacteristic
465C22×C8C23×C10311yescharacteristic
466C22×C8C23×C10311yescharacteristic
467C22×C8C23×C10311yescharacteristic
468C22×C8C23×C10311yescharacteristic
469C22×C8C23×C10311yescharacteristic
470C22×C8C23×C10311yescharacteristic
471C22×C8C23×C10311yescharacteristic
472#117—22no—
473#117—22no—
474C2×C4⋊C4C2×C4×C10311yescharacteristic
475C2×C4⋊C4C2×C4×C10311yescharacteristic
476C2×C22⋊C4C2×C4×C10311yescharacteristic
477C2×C22⋊C4C2×C4×C10311yescharacteristic
478C2×C22⋊C4C2×C4×C10311yescharacteristic
479C2×C22⋊C4C2×C4×C10311yescharacteristic
480C2×C22⋊C4C2×C4×C10311yescharacteristic
481C2×C22⋊C4C2×C4×C10311yescharacteristic
482C2×C22⋊C4C2×C4×C10311yescharacteristic
483C2×C22⋊C4C2×C4×C10311yescharacteristic
484C2×C22⋊C4C2×C4×C10311yescharacteristic
485C2×C22⋊C4C2×C4×C10311yescharacteristic
486C2×C42—41no—
487C2×C42—41no—
488C2×C42C2×C4×C10311yescharacteristic
489C2×C42C2×C4×C10311yescharacteristic
490C2×C42C23×C10311yescharacteristic
491C2×C42C23×C10311yescharacteristic
492C2×C42C23×C10311yescharacteristic
493C2×C42C23×C10311yescharacteristic
494C4⋊C8—22no—
495C4⋊C8—22no—
496C4⋊C8—41no—
497C4⋊C8—41no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—41no—
506C22⋊C8—41no—
507C22⋊C8D4×C10314yes—
508#97—22no—
509C4×C8—22no—
510C4×C8—41no—
511C4×C8—41no—
512#95C2×C4×C10311yescharacteristic
513#95C2×C4×C10311yescharacteristic
514#95C2×C4×C10311yescharacteristic
515#95C2×C4×C10311yescharacteristic
516#95C2×C4×C10311yescharacteristic
517#95C2×C4×C10311yescharacteristic
518#95C2×C4×C10311yescharacteristic
519#95C2×C4×C10311yescharacteristic
520C24C22×C4×C10311yescharacteristic
521C24C22×C4×C10311yescharacteristic
522C24C22×C4×C10311yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C22×C4×C10311yescharacteristic
560C22×C4C22×C4×C10311yescharacteristic
561C22×C4C22×C4×C10311yescharacteristic
562C22×C4C22×C4×C10311yescharacteristic
563C22×C4C22×C4×C10311yescharacteristic
564C22×C4C22×C4×C10311yescharacteristic
565C22×C4C22×C4×C10311yescharacteristic
566C22×C4C22×C4×C10311yescharacteristic
567C22×C4C22×C4×C10311yescharacteristic
568C22×C4C22×C4×C10311yescharacteristic
569C22×C4C22×C4×C10311yescharacteristic
570C22×C4C2×D4×C10312yes—
571C22×C4#41×C10312yes—
572C22×C4#41×C10312yes—
573C22×C4#41×C10312yes—
574C22×C4C24×C10311yescharacteristic
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—44no—
599C2×C8C2×D4×C10312yes—
600C2×C8C2×D4×C10312yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23#117×C10312yes—
643C23C4×D4×C10312yes—
644C23C23×C4×C10311yescharacteristic
645Q8—44no—
646D4—44no—
647D4—44no—
648D4—44no—
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—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4#117×C10312yes—
692C2×C4C4×D4×C10312yes—
693C2×C4#131×C10312yes—
694C2×C4#131×C10312yes—
695C2×C4#131×C10312yes—
696C2×C4C22×D4×C10311yescharacteristic
697C2×C4C2×#41×C10311yescharacteristic
698C2×C4C2×#41×C10311yescharacteristic
699C2×C4C2×#41×C10311yescharacteristic
700C2×C4H(5,𝔽2)×C10311yescharacteristic
701C2×C4H(5,𝔽2)×C10311yescharacteristic
702C8—22no—
703C8—22no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22C2×#117×C10311yescharacteristic
732C22C2×C4×D4×C10311yescharacteristic
733C22#518×C10311yescharacteristic
734C22C2×#131×C10311yescharacteristic
735C22C2×#131×C10311yescharacteristic
736C22C2×#131×C10311yescharacteristic
737C22#568×C10311yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—22no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4#546×C10311yescharacteristic
750C4#546×C10311yescharacteristic
751C4#551×C10311yescharacteristic
752C4#551×C10311yescharacteristic
753C2—42no—
754C2—42no—
755C2—81no—
756C2C103×#234211yescharacteristic
757C2C103×#292211yescharacteristic
758C2C103×#292511yescharacteristic
759C2C103×#293111yescharacteristic
760C2C103×#293511yescharacteristic
761C2C103×#297611yescharacteristic
762C2C103×#297711yescharacteristic
subgroupG/H
centerC22×C4×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C23×C4
prime radicalC22×#41×C103C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#433×C103C2semidirect
4. C103×#1924C2semidirect
5. C103×#1923C2semidirect
6. C103×#1923C2semidirect
7. C103×#1923C2semidirect
8. C103×#1851C2semidirect
9. C103×#1850C2semidirect
10. C103×#1818C2semidirect
11. C103×#1797C2semidirect
13. C103×#1753C2semidirect
14. C8×C22⋊C4×C103C2semidirect
15. C4×C22⋊C8×C103C2semidirect
371. #22560C103direct (N × H)
382. C2×#433C2×C103semidirect
385. #1924C2×C103semidirect
386. #1923C2×C103semidirect
387. #1923C2×C103semidirect
388. #1923C2×C103semidirect
389. #1851C2×C103semidirect
390. #1850C2×C103semidirect
391. #1818C2×C103semidirect
392. #1797C2×C103semidirect
394. #1753C2×C103semidirect
395. C8×C22⋊C4C2×C103semidirect
396. C4×C22⋊C8C2×C103semidirect
397. C103#22560direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#433×C1032
C2×#408×C1032
C103×#22972
C103×#19242
C103×#19232
C103×#18512
C103×#18502
C103×#18182
C103×#17972
C103×#17802
C103×#17532
C8×C22⋊C4×C1032
C4×C22⋊C8×C1032
#22560103