Finite Group Databasebeta

← C103×#22173 #39927448

Subgroups — C103×#22173 #39927448

Order 26368.

920 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C103C211yesmaximal, characteristic, complemented
2C2×C8×D4×C103C211yesmaximal, characteristic, complemented
3C103×#2392C211yesmaximal, characteristic
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×#1870C211yesmaximal, characteristic, complemented
11C103×#1869C211yesmaximal, characteristic, complemented
12C103×#1851C211yesmaximal, characteristic, complemented
13C103×#1850C211yesmaximal, characteristic, complemented
14C103×#1798C211yesmaximal, characteristic, complemented
15C103×#1729C211yesmaximal, characteristic, complemented
16C22×M16×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18C23×C8×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20C2×C4×D4×C103C2211yescharacteristic
21C2×C4×D4×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×#117×C103C2211yescharacteristic
24#435×C103—24no—
25C8×D4×C103—24no—
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×C4⋊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×#97×C103C2211yescharacteristic
39C2×C4×C8×C103C2211yescharacteristic
40#398×C103C411yescharacteristic
41#397×C103C411yescharacteristic
42#396×C103C411yescharacteristic
43#396×C103C411yescharacteristic
44#394×C103C411yescharacteristic
45#394×C103C411yescharacteristic
46#394×C103C411yescharacteristic
47#392×C103C411yescharacteristic
48C4×C4⋊C4×C103C2211yescharacteristic
49C4×C22⋊C4×C103C2211yescharacteristic
50C4×C22⋊C4×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
59#336×C103C2211yescharacteristic
60#336×C103C2211yescharacteristic
61C22×D4×C103C2×C411yescharacteristic
62C22×D4×C103C2×C411yescharacteristic
63C22×D4×C103C2×C411yescharacteristic
64C23×C4×C103C2311yescharacteristic
65C23×C4×C103C2311yescharacteristic
66C23×C4×C103C2311yescharacteristic
67C2×M16×C103—22no—
68C2×M16×C103—22no—
69C2×M16×C103—41no—
70C2×M16×C103—41no—
71C2×M16×C103—41no—
72C2×M16×C103—41no—
73C22×C8×C103—22no—
74C22×C8×C103—41no—
75C22×C8×C103—41no—
76C22×C8×C103—41no—
77C22×C8×C103—41no—
78C22×C8×C103D414yescomplemented
79C22×C8×C103C2311yescharacteristic
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C4×D4×C103—22no—
88C4×D4×C103—22no—
89C4×D4×C103—22no—
90C4×D4×C103—22no—
91C4×D4×C103—41no—
92C4×D4×C103—41no—
93#117×C103—41no—
94#117×C103—41no—
95C2×C4⋊C4×C103C2×C411yescharacteristic
96C2×C4⋊C4×C103C2×C411yescharacteristic
97C2×C4⋊C4×C103C2×C411yescharacteristic
98C2×C4⋊C4×C103C2×C411yescharacteristic
99C2×C4⋊C4×C103C2×C411yescharacteristic
100C2×C4⋊C4×C103C2×C411yescharacteristic
101C2×C4⋊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×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×C42×C103C2311yescharacteristic
115C2×C42×C103C2311yescharacteristic
116C2×C42×C103C2311yescharacteristic
117C2×C42×C103C2311yescharacteristic
118C4⋊C8×C103—22no—
119C4⋊C8×C103—22no—
120C4⋊C8×C103—41no—
121C4⋊C8×C103—41no—
122C22⋊C8×C103—22no—
123C22⋊C8×C103—22no—
124C22⋊C8×C103—22no—
125C22⋊C8×C103—22no—
126C22⋊C8×C103—41no—
127C22⋊C8×C103—41no—
128C22⋊C8×C103—41no—
129C22⋊C8×C103—41no—
130#97×C103—22no—
131C4×C8×C103—22no—
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
141C2×D4×C103—22no—
142C2×D4×C103—22no—
143C2×D4×C103—22no—
144C2×D4×C103—22no—
145C2×D4×C103—22no—
146C2×D4×C103—41no—
147C2×D4×C103—41no—
148C2×D4×C103—41no—
149C2×D4×C103—41no—
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×C103C22×C411yescharacteristic
167C22×C4×C103C22×C411yescharacteristic
168C22×C4×C103C22×C411yescharacteristic
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×C103C2×D412yes—
178C22×C4×C103#4112yes—
179C22×C4×C103C2411yescharacteristic
180M16×C103—44no—
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—44no—
205C2×C8×C103—44no—
206C2×C8×C103C2×D412yes—
207C2×C8×C103C2×D412yes—
208C4⋊C4×C103—22no—
209C4⋊C4×C103—22no—
210C4⋊C4×C103—22no—
211C4⋊C4×C103—41no—
212C4⋊C4×C103—41no—
213C4⋊C4×C103—41no—
214C4⋊C4×C103—41no—
215C22⋊C4×C103—22no—
216C22⋊C4×C103—22no—
217C22⋊C4×C103—22no—
218C22⋊C4×C103—22no—
219C22⋊C4×C103—22no—
220C22⋊C4×C103—22no—
221C22⋊C4×C103—41no—
222C22⋊C4×C103—41no—
223C22⋊C4×C103—41no—
224C22⋊C4×C103—41no—
225C22⋊C4×C103—41no—
226C22⋊C4×C103—41no—
227C42×C103—21no—
228C42×C103—21no—
229C42×C103—21no—
230C42×C103—21no—
231C42×C103—21no—
232C42×C103—21no—
233C42×C103—21no—
234C42×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×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103C4×D412yes—
255C23×C103#13112yes—
256C23×C103C23×C411yescharacteristic
257D4×C103—28no—
258D4×C103—44no—
259D4×C103—44no—
260C2×C4×C103—21no—
261C2×C4×C103—21no—
262C2×C4×C103—21no—
263C2×C4×C103—21no—
264C2×C4×C103—22no—
265C2×C4×C103—22no—
266C2×C4×C103—22no—
267C2×C4×C103—22no—
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—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—41no—
296C2×C4×C103—41no—
297C2×C4×C103—41no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
301C2×C4×C103—41no—
302C2×C4×C103—41no—
303C2×C4×C103C4×D412yes—
304C2×C4×C103#13112yes—
305C2×C4×C103C22×D411yescharacteristic
306C2×C4×C103C2×#4111yescharacteristic
307C2×C4×C103H(5,𝔽2)11yescharacteristic
308C2×C4×C103H(5,𝔽2)11yescharacteristic
309C2×C4×C103H(5,𝔽2)11yescharacteristic
310C2×C4×C1032−1+411yescharacteristic
311C8×C103—22no—
312C8×C103—22no—
313C8×C103—41no—
314C8×C103—41no—
315C8×C103—41no—
316C8×C103—41no—
317C8×C103—41no—
318C8×C103—41no—
319C22×C103—22no—
320C22×C103—22no—
321C22×C103—22no—
322C22×C103—22no—
323C22×C103—22no—
324C22×C103—22no—
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—41no—
340C22×C103C2×C4×D411yescharacteristic
341C22×C103#51811yescharacteristic
342C22×C103#52011yescharacteristic
343C22×C103C2×#13111yescharacteristic
344C22×C103C2×#13111yescharacteristic
345C22×C103#56811yescharacteristic
346C22×C103#56811yescharacteristic
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—41no—
358C4×C103#53411yescharacteristic
359C4×C103#53711yescharacteristic
360C4×C103#53811yescharacteristic
361C4×C103#53911yescharacteristic
362#22173C10311yesmaximal, characteristic, direct product factor, Sylow
363C2×C103—42no—
364C2×C103—42no—
365C2×C103—81no—
366C2×C103#232511yescharacteristic
367C2×C103#292911yescharacteristic
368C2×C103#293011yescharacteristic
369C2×C103#297611yescharacteristic
370C2×C103#298111yescharacteristic
371C2×C103#299211yescharacteristic
372C2×C103#299311yescharacteristic
373C2×#435C2×C10311yescharacteristic, complemented
374C2×C8×D4C2×C10311yescharacteristic, complemented
375#2392C2×C10311yescharacteristic
376#1924C2×C10311yescharacteristic, complemented
377#1923C2×C10311yescharacteristic, complemented
378#1917C2×C10311yescharacteristic, complemented
379#1916C2×C10311yescharacteristic, complemented
380#1870C2×C10311yescharacteristic, complemented
381#1870C2×C10311yescharacteristic, complemented
382#1870C2×C10311yescharacteristic, complemented
383#1869C2×C10311yescharacteristic, complemented
384#1851C2×C10311yescharacteristic, complemented
385#1850C2×C10311yescharacteristic, complemented
386#1798C2×C10311yescharacteristic, complemented
387#1729C2×C10311yescharacteristic, complemented
388C103#2217311yescharacteristic, direct product factor, Sylow
389C22×M16C22×C10311yescharacteristic
390C22×M16C22×C10311yescharacteristic
391C23×C8C22×C10311yescharacteristic
392C23×C8C22×C10311yescharacteristic
393C2×C4×D4C22×C10311yescharacteristic
394C2×C4×D4C22×C10311yescharacteristic
395C2×C4×D4C22×C10311yescharacteristic
396C2×#117C22×C10311yescharacteristic
397#435—24no—
398C8×D4—24no—
399C2×C4⋊C8C22×C10311yescharacteristic
400C2×C4⋊C8C22×C10311yescharacteristic
401C2×C4⋊C8C22×C10311yescharacteristic
402C2×C4⋊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×C22⋊C8C22×C10311yescharacteristic
410C2×C22⋊C8C22×C10311yescharacteristic
411C2×#97C22×C10311yescharacteristic
412C2×C4×C8C22×C10311yescharacteristic
413#398C4×C10311yescharacteristic
414#397C4×C10311yescharacteristic
415#396C4×C10311yescharacteristic
416#396C4×C10311yescharacteristic
417#394C4×C10311yescharacteristic
418#394C4×C10311yescharacteristic
419#394C4×C10311yescharacteristic
420#392C4×C10311yescharacteristic
421C4×C4⋊C4C22×C10311yescharacteristic
422C4×C22⋊C4C22×C10311yescharacteristic
423C4×C22⋊C4C22×C10311yescharacteristic
424#336C22×C10311yescharacteristic
425#336C22×C10311yescharacteristic
426#336C22×C10311yescharacteristic
427#336C22×C10311yescharacteristic
428#336C22×C10311yescharacteristic
429#336C22×C10311yescharacteristic
430#336C22×C10311yescharacteristic
431#336C22×C10311yescharacteristic
432#336C22×C10311yescharacteristic
433#336C22×C10311yescharacteristic
434C22×D4C2×C4×C10311yescharacteristic
435C22×D4C2×C4×C10311yescharacteristic
436C22×D4C2×C4×C10311yescharacteristic
437C23×C4C23×C10311yescharacteristic
438C23×C4C23×C10311yescharacteristic
439C23×C4C23×C10311yescharacteristic
440C2×M16—22no—
441C2×M16—22no—
442C2×M16—41no—
443C2×M16—41no—
444C2×M16—41no—
445C2×M16—41no—
446C22×C8—22no—
447C22×C8—41no—
448C22×C8—41no—
449C22×C8—41no—
450C22×C8—41no—
451C22×C8D4×C10314yescomplemented
452C22×C8C23×C10311yescharacteristic
453C22×C8C23×C10311yescharacteristic
454C22×C8C23×C10311yescharacteristic
455C22×C8C23×C10311yescharacteristic
456C22×C8C23×C10311yescharacteristic
457C22×C8C23×C10311yescharacteristic
458C22×C8C23×C10311yescharacteristic
459C22×C8C23×C10311yescharacteristic
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466#117—41no—
467#117—41no—
468C2×C4⋊C4C2×C4×C10311yescharacteristic
469C2×C4⋊C4C2×C4×C10311yescharacteristic
470C2×C4⋊C4C2×C4×C10311yescharacteristic
471C2×C4⋊C4C2×C4×C10311yescharacteristic
472C2×C4⋊C4C2×C4×C10311yescharacteristic
473C2×C4⋊C4C2×C4×C10311yescharacteristic
474C2×C4⋊C4C2×C4×C10311yescharacteristic
475C2×C22⋊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×C22⋊C4C2×C4×C10311yescharacteristic
487C2×C42C23×C10311yescharacteristic
488C2×C42C23×C10311yescharacteristic
489C2×C42C23×C10311yescharacteristic
490C2×C42C23×C10311yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—22no—
493C4⋊C8—41no—
494C4⋊C8—41no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—41no—
501C22⋊C8—41no—
502C22⋊C8—41no—
503#97—22no—
504C4×C8—22no—
505#95C2×C4×C10311yescharacteristic
506#95C2×C4×C10311yescharacteristic
507#95C2×C4×C10311yescharacteristic
508#95C2×C4×C10311yescharacteristic
509#95C2×C4×C10311yescharacteristic
510#95C2×C4×C10311yescharacteristic
511C24C22×C4×C10311yescharacteristic
512C24C22×C4×C10311yescharacteristic
513C24C22×C4×C10311yescharacteristic
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
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—21no—
539C22×C4C22×C4×C10311yescharacteristic
540C22×C4C22×C4×C10311yescharacteristic
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×C4C2×D4×C10312yes—
551C22×C4#41×C10312yes—
552C22×C4C24×C10311yescharacteristic
553M16—44no—
554M16—44no—
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—44no—
578C2×C8—44no—
579C2×C8C2×D4×C10312yes—
580C2×C8C2×D4×C10312yes—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—22no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—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—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23C4×D4×C10312yes—
628C23#131×C10312yes—
629C23C23×C4×C10311yescharacteristic
630D4—28no—
631D4—44no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
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—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4C4×D4×C10312yes—
677C2×C4#131×C10312yes—
678C2×C4C22×D4×C10311yescharacteristic
679C2×C4C2×#41×C10311yescharacteristic
680C2×C4H(5,𝔽2)×C10311yescharacteristic
681C2×C4H(5,𝔽2)×C10311yescharacteristic
682C2×C4H(5,𝔽2)×C10311yescharacteristic
683C2×C42−1+4×C10311yescharacteristic
684C8—22no—
685C8—22no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
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—41no—
712C22—41no—
713C22C2×C4×D4×C10311yescharacteristic
714C22#518×C10311yescharacteristic
715C22#520×C10311yescharacteristic
716C22C2×#131×C10311yescharacteristic
717C22C2×#131×C10311yescharacteristic
718C22#568×C10311yescharacteristic
719C22#568×C10311yescharacteristic
720C4—22no—
721C4—22no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4#534×C10311yescharacteristic
732C4#537×C10311yescharacteristic
733C4#538×C10311yescharacteristic
734C4#539×C10311yescharacteristic
735C2—42no—
736C2—42no—
737C2—81no—
738C2C103×#232511yescharacteristic
739C2C103×#292911yescharacteristic
740C2C103×#293011yescharacteristic
741C2C103×#297611yescharacteristic
742C2C103×#298111yescharacteristic
743C2C103×#299211yescharacteristic
744C2C103×#299311yescharacteristic
subgroupG/H
centerC22×C4×C103C24
commutatorC23C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC23×C103C23×C4
prime radical#392×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×C8×D4×C103C2semidirect
4. C103×#1924C2semidirect
5. C103×#1923C2semidirect
6. C103×#1917C2semidirect
7. C103×#1916C2semidirect
8. C103×#1870C2semidirect
9. C103×#1870C2semidirect
10. C103×#1870C2semidirect
11. C103×#1869C2semidirect
12. C103×#1851C2semidirect
13. C103×#1850C2semidirect
14. C103×#1798C2semidirect
15. C103×#1729C2semidirect
78. C22×C8×C103D4semidirect
362. #22173C103direct (N × H)
373. C2×#435C2×C103semidirect
374. C2×C8×D4C2×C103semidirect
376. #1924C2×C103semidirect
377. #1923C2×C103semidirect
378. #1917C2×C103semidirect
379. #1916C2×C103semidirect
380. #1870C2×C103semidirect
381. #1870C2×C103semidirect
382. #1870C2×C103semidirect
383. #1869C2×C103semidirect
384. #1851C2×C103semidirect
385. #1850C2×C103semidirect
386. #1798C2×C103semidirect
387. #1729C2×C103semidirect
388. C103#22173direct (N × H)
451. C22×C8D4×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×C8×D4×C1032
C103×#23922
C103×#19242
C103×#19232
C103×#19172
C103×#19162
C103×#18702
C103×#18692
C103×#18512
C103×#18502
C103×#17982
C103×#17292
#22173103