Finite Group Databasebeta

← C103×#22559 #39927834

Subgroups — C103×#22559 #39927834

Order 26368.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C103C211yesmaximal, characteristic, complemented
2C2×#407×C103C211yesmaximal, characteristic
3C103×#2280C211yesmaximal, characteristic
4C103×#1924C211yesmaximal, characteristic, complemented
5C103×#1924C211yesmaximal, characteristic, complemented
6C103×#1923C211yesmaximal, characteristic, complemented
7C103×#1923C211yesmaximal, characteristic, complemented
8C103×#1851C211yesmaximal, characteristic, complemented
9C103×#1851C211yesmaximal, characteristic, complemented
10C103×#1818C211yesmaximal, characteristic, complemented
11C103×#1798C211yesmaximal, characteristic, complemented
12C103×#1779C211yesmaximal, characteristic
13C103×#1753C211yesmaximal, characteristic, complemented
14C103×#1753C211yesmaximal, characteristic, complemented
15C103×#1750C211yesmaximal, characteristic, complemented
16C24×C4×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C2×#117×C103C2211yescharacteristic
20C2×#117×C103C2211yescharacteristic
21#433×C103—24no—
22C2×C4⋊C8×C103C2211yescharacteristic, complemented
23C2×C4⋊C8×C103C2211yescharacteristic, complemented
24C2×C4⋊C8×C103C2211yescharacteristic, complemented
25C2×C4⋊C8×C103C2211yescharacteristic, complemented
26#407×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, complemented
38C2×#97×C103C2211yescharacteristic, complemented
39C2×C4×C8×C103C2211yescharacteristic, complemented
40C2×C4×C8×C103C2211yescharacteristic, complemented
41#381×C103C411yescharacteristic
42#381×C103C411yescharacteristic
43#380×C103C411yescharacteristic
44#380×C103C411yescharacteristic
45#380×C103C411yescharacteristic
46#380×C103C411yescharacteristic
47#379×C103C411yescharacteristic
48#379×C103C411yescharacteristic
49C4×C22⋊C4×C103C2211yescharacteristic
50C4×C22⋊C4×C103C2211yescharacteristic
51C4×C22⋊C4×C103C2211yescharacteristic
52C4×C22⋊C4×C103C2211yescharacteristic
53#336×C103C2211yescharacteristic, complemented
54#336×C103C2211yescharacteristic, complemented
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
62C23×C4×C103—22no—
63C23×C4×C103—22no—
64C23×C4×C103—22no—
65C23×C4×C103—22no—
66C23×C4×C103—41no—
67C23×C4×C103—41no—
68C23×C4×C103C2×C411yescharacteristic
69C23×C4×C103C2×C411yescharacteristic
70C23×C4×C103C2×C411yescharacteristic
71C23×C4×C103C2311yescharacteristic
72C23×C4×C103C2311yescharacteristic
73C23×C4×C103C2311yescharacteristic
74C2×M16×C103—22no—
75C2×M16×C103—22no—
76C2×M16×C103—22no—
77C2×M16×C103—22no—
78C2×M16×C103—41no—
79C2×M16×C103—41no—
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88#117×C103—22no—
89#117×C103—22no—
90#117×C103—41no—
91#117×C103—41no—
92C2×C4⋊C4×C103C2×C411yescharacteristic
93C2×C4⋊C4×C103C2×C411yescharacteristic
94C2×C4⋊C4×C103C2×C411yescharacteristic
95C2×C4⋊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×C22⋊C4×C103C2×C411yescharacteristic
105C2×C22⋊C4×C103C2×C411yescharacteristic
106C2×C22⋊C4×C103C2×C411yescharacteristic
107C2×C22⋊C4×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—
127#97×C103—41no—
128C4×C8×C103—22no—
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×C103—22no—
139C24×C103—22no—
140C24×C103—22no—
141C24×C103—41no—
142C24×C103—41no—
143C24×C103—41no—
144C24×C103—41no—
145C24×C103C22×C411yescharacteristic
146C24×C103C22×C411yescharacteristic
147C24×C103C22×C411yescharacteristic
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—22no—
157C22×C4×C103—22no—
158C22×C4×C103—22no—
159C22×C4×C103—22no—
160C22×C4×C103—22no—
161C22×C4×C103—22no—
162C22×C4×C103—21no—
163C22×C4×C103—21no—
164C22×C4×C103—21no—
165C22×C4×C103—21no—
166C22×C4×C103—21no—
167C22×C4×C103—21no—
168C22×C4×C103—41no—
169C22×C4×C103—41no—
170C22×C4×C103—41no—
171C22×C4×C103—44no—
172C22×C4×C103—44no—
173C22×C4×C103—44no—
174C22×C4×C103—44no—
175C22×C4×C103C22×C411yescharacteristic
176C22×C4×C103C22×C411yescharacteristic
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×C103C2×D412yes—
187C22×C4×C103#4112yes—
188C22×C4×C103#4112yes—
189C22×C4×C103#4112yes—
190C22×C4×C103C2411yescharacteristic
191M16×C103—44no—
192M16×C103—44no—
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—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×C103C2×D412yes—
216C2×C8×C103C2×D412yes—
217C4⋊C4×C103—22no—
218C4⋊C4×C103—22no—
219C4⋊C4×C103—41no—
220C4⋊C4×C103—41no—
221C22⋊C4×C103—22no—
222C22⋊C4×C103—22no—
223C22⋊C4×C103—22no—
224C22⋊C4×C103—22no—
225C22⋊C4×C103—41no—
226C22⋊C4×C103—41no—
227C22⋊C4×C103—41no—
228C22⋊C4×C103—41no—
229C22⋊C4×C103—41no—
230C22⋊C4×C103—41no—
231C22⋊C4×C103—41no—
232C22⋊C4×C103—41no—
233C42×C103—21no—
234C42×C103—21no—
235C42×C103—21no—
236C42×C103—21no—
237C42×C103—21no—
238C42×C103—21no—
239C42×C103—21no—
240C42×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×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—44no—
260C23×C103—44no—
261C23×C103—44no—
262C23×C103—44no—
263C23×C103—44no—
264C23×C103—44no—
265C23×C103—44no—
266C23×C103#11712yes—
267C23×C103C4×D412yes—
268C23×C103#13112yes—
269C23×C103C23×C411yescharacteristic
270C2×C4×C103—21no—
271C2×C4×C103—21no—
272C2×C4×C103—21no—
273C2×C4×C103—21no—
274C2×C4×C103—22no—
275C2×C4×C103—22no—
276C2×C4×C103—22no—
277C2×C4×C103—22no—
278C2×C4×C103—22no—
279C2×C4×C103—22no—
280C2×C4×C103—22no—
281C2×C4×C103—22no—
282C2×C4×C103—21no—
283C2×C4×C103—21no—
284C2×C4×C103—21no—
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—21no—
304C2×C4×C103—21no—
305C2×C4×C103—21no—
306C2×C4×C103—21no—
307C2×C4×C103—21no—
308C2×C4×C103—21no—
309C2×C4×C103—44no—
310C2×C4×C103—44no—
311C2×C4×C103—44no—
312C2×C4×C103—41no—
313C2×C4×C103—41no—
314C2×C4×C103—41no—
315C2×C4×C103—41no—
316C2×C4×C103#11712yes—
317C2×C4×C103C4×D412yes—
318C2×C4×C103C22×D411yescharacteristic
319C2×C4×C103C2×#4111yescharacteristic
320C2×C4×C103C2×#4111yescharacteristic
321C2×C4×C103C2×#4111yescharacteristic
322C2×C4×C103H(5,𝔽2)11yescharacteristic
323C2×C4×C103H(5,𝔽2)11yescharacteristic
324C8×C103—22no—
325C8×C103—22no—
326C8×C103—41no—
327C8×C103—41no—
328C8×C103—41no—
329C8×C103—41no—
330C8×C103—41no—
331C8×C103—41no—
332C22×C103—22no—
333C22×C103—22no—
334C22×C103—22no—
335C22×C103—22no—
336C22×C103—22no—
337C22×C103—22no—
338C22×C103—22no—
339C22×C103—22no—
340C22×C103—22no—
341C22×C103—416no—
342C22×C103—41no—
343C22×C103—41no—
344C22×C103—41no—
345C22×C103—41no—
346C22×C103—41no—
347C22×C103—41no—
348C22×C103—41no—
349C22×C103—41no—
350C22×C103—41no—
351C22×C103—41no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103C2×#11711yescharacteristic
355C22×C103C2×C4×D411yescharacteristic
356C22×C103#51811yescharacteristic
357C22×C103C2×#13111yescharacteristic
358C22×C103#56811yescharacteristic
359C22×C103#56811yescharacteristic
360C22×C103#56811yescharacteristic
361C4×C103—22no—
362C4×C103—22no—
363C4×C103—41no—
364C4×C103—41no—
365C4×C103—41no—
366C4×C103—41no—
367C4×C103—41no—
368C4×C103—41no—
369C4×C103—41no—
370C4×C103—41no—
371C4×C103—41no—
372C4×C103#54611yescharacteristic
373C4×C103#54611yescharacteristic
374C4×C103#55111yescharacteristic
375C4×C103#55111yescharacteristic
376#22559C10311yesmaximal, characteristic, direct product factor, Sylow
377C2×C103—42no—
378C2×C103—42no—
379C2×C103—42no—
380C2×C103#234211yescharacteristic
381C2×C103#292111yescharacteristic
382C2×C103#292411yescharacteristic
383C2×C103#293011yescharacteristic
384C2×C103#293311yescharacteristic
385C2×C103#297611yescharacteristic
386C2×C103#297811yescharacteristic
387C2×#433C2×C10311yescharacteristic, complemented
388C2×#407C2×C10311yescharacteristic
389#2280C2×C10311yescharacteristic
390#1924C2×C10311yescharacteristic, complemented
391#1924C2×C10311yescharacteristic, complemented
392#1923C2×C10311yescharacteristic, complemented
393#1923C2×C10311yescharacteristic, complemented
394#1851C2×C10311yescharacteristic, complemented
395#1851C2×C10311yescharacteristic, complemented
396#1818C2×C10311yescharacteristic, complemented
397#1798C2×C10311yescharacteristic, complemented
398#1779C2×C10311yescharacteristic
399#1753C2×C10311yescharacteristic, complemented
400#1753C2×C10311yescharacteristic, complemented
401#1750C2×C10311yescharacteristic, complemented
402C103#2255911yescharacteristic, direct product factor, Sylow
403C24×C4C22×C10311yescharacteristic
404C22×M16C22×C10311yescharacteristic
405C22×M16C22×C10311yescharacteristic
406C2×#117C22×C10311yescharacteristic
407C2×#117C22×C10311yescharacteristic
408#433—24no—
409C2×C4⋊C8C22×C10311yescharacteristic, complemented
410C2×C4⋊C8C22×C10311yescharacteristic, complemented
411C2×C4⋊C8C22×C10311yescharacteristic, complemented
412C2×C4⋊C8C22×C10311yescharacteristic, complemented
413#407—24no—
414C2×C22⋊C8C22×C10311yescharacteristic
415C2×C22⋊C8C22×C10311yescharacteristic
416C2×C22⋊C8C22×C10311yescharacteristic
417C2×C22⋊C8C22×C10311yescharacteristic
418C2×C22⋊C8C22×C10311yescharacteristic
419C2×C22⋊C8C22×C10311yescharacteristic
420C2×C22⋊C8C22×C10311yescharacteristic
421C2×C22⋊C8C22×C10311yescharacteristic
422C2×C22⋊C8C22×C10311yescharacteristic
423C2×C22⋊C8C22×C10311yescharacteristic
424C2×#97C22×C10311yescharacteristic, complemented
425C2×#97C22×C10311yescharacteristic, complemented
426C2×C4×C8C22×C10311yescharacteristic, complemented
427C2×C4×C8C22×C10311yescharacteristic, complemented
428#381C4×C10311yescharacteristic
429#381C4×C10311yescharacteristic
430#380C4×C10311yescharacteristic
431#380C4×C10311yescharacteristic
432#380C4×C10311yescharacteristic
433#380C4×C10311yescharacteristic
434#379C4×C10311yescharacteristic
435#379C4×C10311yescharacteristic
436C4×C22⋊C4C22×C10311yescharacteristic
437C4×C22⋊C4C22×C10311yescharacteristic
438C4×C22⋊C4C22×C10311yescharacteristic
439C4×C22⋊C4C22×C10311yescharacteristic
440#336C22×C10311yescharacteristic, complemented
441#336C22×C10311yescharacteristic, complemented
442#336C22×C10311yescharacteristic, complemented
443#336C22×C10311yescharacteristic, complemented
444#336C22×C10311yescharacteristic, complemented
445#336C22×C10311yescharacteristic, complemented
446#336C22×C10311yescharacteristic, complemented
447#336C22×C10311yescharacteristic, complemented
448C25C2×C4×C10311yescharacteristic
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—22no—
453C23×C4—41no—
454C23×C4—41no—
455C23×C4C2×C4×C10311yescharacteristic
456C23×C4C2×C4×C10311yescharacteristic
457C23×C4C2×C4×C10311yescharacteristic
458C23×C4C23×C10311yescharacteristic
459C23×C4C23×C10311yescharacteristic
460C23×C4C23×C10311yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—41no—
467C22×C8C23×C10311yescharacteristic
468C22×C8C23×C10311yescharacteristic
469C22×C8C23×C10311yescharacteristic
470C22×C8C23×C10311yescharacteristic
471C22×C8C23×C10311yescharacteristic
472C22×C8C23×C10311yescharacteristic
473C22×C8C23×C10311yescharacteristic
474C22×C8C23×C10311yescharacteristic
475#117—22no—
476#117—22no—
477#117—41no—
478#117—41no—
479C2×C4⋊C4C2×C4×C10311yescharacteristic
480C2×C4⋊C4C2×C4×C10311yescharacteristic
481C2×C4⋊C4C2×C4×C10311yescharacteristic
482C2×C4⋊C4C2×C4×C10311yescharacteristic
483C2×C22⋊C4C2×C4×C10311yescharacteristic
484C2×C22⋊C4C2×C4×C10311yescharacteristic
485C2×C22⋊C4C2×C4×C10311yescharacteristic
486C2×C22⋊C4C2×C4×C10311yescharacteristic
487C2×C22⋊C4C2×C4×C10311yescharacteristic
488C2×C22⋊C4C2×C4×C10311yescharacteristic
489C2×C22⋊C4C2×C4×C10311yescharacteristic
490C2×C22⋊C4C2×C4×C10311yescharacteristic
491C2×C22⋊C4C2×C4×C10311yescharacteristic
492C2×C22⋊C4C2×C4×C10311yescharacteristic
493C2×C22⋊C4C2×C4×C10311yescharacteristic
494C2×C22⋊C4C2×C4×C10311yescharacteristic
495C2×C42C23×C10311yescharacteristic
496C2×C42C23×C10311yescharacteristic
497C2×C42C23×C10311yescharacteristic
498C2×C42C23×C10311yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—41no—
502C4⋊C8—41no—
503C22⋊C8—22no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—41no—
511C22⋊C8—41no—
512C22⋊C8D4×C10314yes—
513#97—22no—
514#97—41no—
515C4×C8—22no—
516C4×C8—41no—
517#95C2×C4×C10311yescharacteristic
518#95C2×C4×C10311yescharacteristic
519#95C2×C4×C10311yescharacteristic
520#95C2×C4×C10311yescharacteristic
521#95C2×C4×C10311yescharacteristic
522#95C2×C4×C10311yescharacteristic
523#95C2×C4×C10311yescharacteristic
524#95C2×C4×C10311yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24C22×C4×C10311yescharacteristic
533C24C22×C4×C10311yescharacteristic
534C24C22×C4×C10311yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
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×C4C22×C4×C10311yescharacteristic
571C22×C4C22×C4×C10311yescharacteristic
572C22×C4C22×C4×C10311yescharacteristic
573C22×C4C2×D4×C10312yes—
574C22×C4#41×C10312yes—
575C22×C4#41×C10312yes—
576C22×C4#41×C10312yes—
577C22×C4C24×C10311yescharacteristic
578M16—44no—
579M16—44no—
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—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8C2×D4×C10312yes—
603C2×C8C2×D4×C10312yes—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—41no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—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—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#117×C10312yes—
654C23C4×D4×C10312yes—
655C23#131×C10312yes—
656C23C23×C4×C10311yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4#117×C10312yes—
704C2×C4C4×D4×C10312yes—
705C2×C4C22×D4×C10311yescharacteristic
706C2×C4C2×#41×C10311yescharacteristic
707C2×C4C2×#41×C10311yescharacteristic
708C2×C4C2×#41×C10311yescharacteristic
709C2×C4H(5,𝔽2)×C10311yescharacteristic
710C2×C4H(5,𝔽2)×C10311yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C8—41no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—416no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×#117×C10311yescharacteristic
742C22C2×C4×D4×C10311yescharacteristic
743C22#518×C10311yescharacteristic
744C22C2×#131×C10311yescharacteristic
745C22#568×C10311yescharacteristic
746C22#568×C10311yescharacteristic
747C22#568×C10311yescharacteristic
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4#546×C10311yescharacteristic
760C4#546×C10311yescharacteristic
761C4#551×C10311yescharacteristic
762C4#551×C10311yescharacteristic
763C2—42no—
764C2—42no—
765C2—42no—
766C2C103×#234211yescharacteristic
767C2C103×#292111yescharacteristic
768C2C103×#292411yescharacteristic
769C2C103×#293011yescharacteristic
770C2C103×#293311yescharacteristic
771C2C103×#297611yescharacteristic
772C2C103×#297811yescharacteristic
subgroupG/H
centerC22×C4×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C23×C4
prime radicalC25×C103C2×C4
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×#1924C2semidirect
6. C103×#1923C2semidirect
7. C103×#1923C2semidirect
8. C103×#1851C2semidirect
9. C103×#1851C2semidirect
10. C103×#1818C2semidirect
11. C103×#1798C2semidirect
13. C103×#1753C2semidirect
14. C103×#1753C2semidirect
15. C103×#1750C2semidirect
22. C2×C4⋊C8×C103C22semidirect
23. C2×C4⋊C8×C103C22semidirect
24. C2×C4⋊C8×C103C22semidirect
25. C2×C4⋊C8×C103C22semidirect
37. C2×#97×C103C22semidirect
38. C2×#97×C103C22semidirect
39. C2×C4×C8×C103C22semidirect
40. C2×C4×C8×C103C22semidirect
53. #336×C103C22semidirect
54. #336×C103C22semidirect
55. #336×C103C22semidirect
56. #336×C103C22semidirect
57. #336×C103C22semidirect
58. #336×C103C22semidirect
59. #336×C103C22semidirect
60. #336×C103C22semidirect
376. #22559C103direct (N × H)
387. C2×#433C2×C103semidirect
390. #1924C2×C103semidirect
391. #1924C2×C103semidirect
392. #1923C2×C103semidirect
393. #1923C2×C103semidirect
394. #1851C2×C103semidirect
395. #1851C2×C103semidirect
396. #1818C2×C103semidirect
397. #1798C2×C103semidirect
399. #1753C2×C103semidirect
400. #1753C2×C103semidirect
401. #1750C2×C103semidirect
402. C103#22559direct (N × H)
409. C2×C4⋊C8C22×C103semidirect
410. C2×C4⋊C8C22×C103semidirect
411. C2×C4⋊C8C22×C103semidirect
412. C2×C4⋊C8C22×C103semidirect
424. C2×#97C22×C103semidirect
425. C2×#97C22×C103semidirect
426. C2×C4×C8C22×C103semidirect
427. C2×C4×C8C22×C103semidirect
440. #336C22×C103semidirect
441. #336C22×C103semidirect
442. #336C22×C103semidirect
443. #336C22×C103semidirect
444. #336C22×C103semidirect
445. #336C22×C103semidirect
446. #336C22×C103semidirect
447. #336C22×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#433×C1032
C2×#407×C1032
C103×#22802
C103×#19242
C103×#19232
C103×#18512
C103×#18182
C103×#17982
C103×#17792
C103×#17532
C103×#17502
#22559103