Finite Group Databasebeta

← C103×#22174 #39927449

Subgroups — C103×#22174 #39927449

Order 26368.

964 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#436×C103C211yesmaximal, characteristic, complemented
2C2×#435×C103C211yesmaximal, characteristic, complemented
3C4×#121×C103C211yesmaximal, 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×#1797C211yesmaximal, characteristic, complemented
15C103×#1728C211yesmaximal, characteristic, complemented
16C22×M16×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20C2×#121×C103C411yescharacteristic
21C2×C4×D4×C103C2211yescharacteristic
22C2×C4×D4×C103C2211yescharacteristic
23C2×C4×D4×C103C2211yescharacteristic
24C22×C42×C103C2211yescharacteristic
25#436×C103—24no—
26#435×C103—24no—
27C2×C4⋊C8×C103C2211yescharacteristic
28C2×C4⋊C8×C103C2211yescharacteristic
29C2×C4⋊C8×C103C2211yescharacteristic
30C2×C4⋊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×#97×C103C2211yescharacteristic
40C2×C4×C8×C103C2211yescharacteristic
41#390×C103C411yescharacteristic
42#389×C103C411yescharacteristic
43#388×C103C411yescharacteristic
44#388×C103C411yescharacteristic
45#386×C103C411yescharacteristic
46#386×C103C411yescharacteristic
47#380×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×C103C2×C411yescharacteristic
65C23×C4×C103C2×C411yescharacteristic
66C23×C4×C103C2311yescharacteristic
67C23×C4×C103C2311yescharacteristic
68C23×C4×C103C2311yescharacteristic
69C2×M16×C103—22no—
70C2×M16×C103—22no—
71C2×M16×C103—41no—
72C2×M16×C103—41no—
73C2×M16×C103—41no—
74C2×M16×C103—41no—
75C2×M16×C103—41no—
76C2×M16×C103—41no—
77C2×M16×C103D414yescomplemented
78C22×C8×C103—22no—
79C22×C8×C103—41no—
80C22×C8×C103—41no—
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84C22×C8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89#121×C103—24no—
90C4×D4×C103—22no—
91C4×D4×C103—22no—
92C4×D4×C103—22no—
93C4×D4×C103—22no—
94C4×D4×C103—41no—
95C4×D4×C103—41no—
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×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×C22⋊C4×C103C2×C411yescharacteristic
109C2×C22⋊C4×C103C2×C411yescharacteristic
110C2×C22⋊C4×C103C2×C411yescharacteristic
111C2×C42×C103—41no—
112C2×C42×C103—41no—
113C2×C42×C103C2×C411yescharacteristic
114C2×C42×C103C2×C411yescharacteristic
115C2×C42×C103C2311yescharacteristic
116C2×C42×C103C2311yescharacteristic
117C2×C42×C103C2311yescharacteristic
118C2×C42×C103C2311yescharacteristic
119C4⋊C8×C103—22no—
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—41no—
128C22⋊C8×C103—41no—
129C22⋊C8×C103—41no—
130C22⋊C8×C103—41no—
131#97×C103—22no—
132C4×C8×C103—22no—
133#95×C103C2×C411yescharacteristic
134#95×C103C2×C411yescharacteristic
135#95×C103C2×C411yescharacteristic
136#95×C103C2×C411yescharacteristic
137#95×C103C2×C411yescharacteristic
138#95×C103C2×C411yescharacteristic
139C24×C103C22×C411yescharacteristic
140C24×C103C22×C411yescharacteristic
141C24×C103C22×C411yescharacteristic
142C2×D4×C103—22no—
143C2×D4×C103—22no—
144C2×D4×C103—22no—
145C2×D4×C103—22no—
146C2×D4×C103—22no—
147C2×D4×C103—22no—
148C2×D4×C103—41no—
149C2×D4×C103—41no—
150C2×D4×C103—41no—
151C22×C4×C103—21no—
152C22×C4×C103—21no—
153C22×C4×C103—21no—
154C22×C4×C103—21no—
155C22×C4×C103—22no—
156C22×C4×C103—22no—
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—21no—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—41no—
170C22×C4×C103—41no—
171C22×C4×C103—41no—
172C22×C4×C103—41no—
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×C103C22×C411yescharacteristic
181C22×C4×C103C22×C411yescharacteristic
182C22×C4×C103C22×C411yescharacteristic
183C22×C4×C103C22×C411yescharacteristic
184C22×C4×C103C2×D412yes—
185C22×C4×C103#4112yes—
186C22×C4×C103C2411yescharacteristic
187M16×C103—44no—
188M16×C103—44no—
189M16×C103—44no—
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—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103—44no—
213C2×C8×C103C2×D412yes—
214C2×C8×C103C2×D412yes—
215C4⋊C4×C103—22no—
216C4⋊C4×C103—22no—
217C4⋊C4×C103—22no—
218C4⋊C4×C103—22no—
219C4⋊C4×C103—41no—
220C22⋊C4×C103—22no—
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×C103M1614yescomplemented
230C42×C103—21no—
231C42×C103—21no—
232C42×C103—21no—
233C42×C103—21no—
234C42×C103—21no—
235C42×C103—21no—
236C42×C103—21no—
237C42×C103—21no—
238C42×C103—41no—
239C42×C103—41no—
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×C103—21no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103C4×D412yes—
260C23×C103C2×M1612yes—
261C23×C103C23×C411yescharacteristic
262D4×C103—44no—
263D4×C103—44no—
264D4×C103—44no—
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—22no—
274C2×C4×C103—22no—
275C2×C4×C103—22no—
276C2×C4×C103—22no—
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—21no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—44no—
299C2×C4×C103—44no—
300C2×C4×C103—41no—
301C2×C4×C103—41no—
302C2×C4×C103—41no—
303C2×C4×C103—41no—
304C2×C4×C103—41no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103C4×D412yes—
309C2×C4×C103C2×M1612yes—
310C2×C4×C103C2×M1612yes—
311C2×C4×C103#13112yes—
312C2×C4×C103C22×D411yescharacteristic
313C2×C4×C103C2×#4111yescharacteristic
314C2×C4×C103H(5,𝔽2)11yescharacteristic
315C2×C4×C103H(5,𝔽2)11yescharacteristic
316C2×C4×C103H(5,𝔽2)11yescharacteristic
317C2×C4×C1032−1+411yescharacteristic
318C8×C103—22no—
319C8×C103—22no—
320C8×C103—41no—
321C8×C103—41no—
322C8×C103—41no—
323C8×C103—41no—
324C8×C103—41no—
325C8×C103—41no—
326C22×C103—22no—
327C22×C103—22no—
328C22×C103—22no—
329C22×C103—22no—
330C22×C103—22no—
331C22×C103—22no—
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×C103—41no—
341C22×C103—41no—
342C22×C103—41no—
343C22×C103—41no—
344C22×C103—41no—
345C22×C103—41no—
346C22×C103—41no—
347C22×C103C2×C4×D411yescharacteristic
348C22×C103#51811yescharacteristic
349C22×C103#52011yescharacteristic
350C22×C103C22×M1611yescharacteristic
351C22×C103C2×#13111yescharacteristic
352C22×C103#56811yescharacteristic
353C22×C103#56811yescharacteristic
354C4×C103—22no—
355C4×C103—22no—
356C4×C103—22no—
357C4×C103—22no—
358C4×C103—41no—
359C4×C103—41no—
360C4×C103—41no—
361C4×C103—41no—
362C4×C103—41no—
363C4×C103—41no—
364C4×C103—41no—
365C4×C103#53411yescharacteristic
366C4×C103#53711yescharacteristic
367C4×C103#53811yescharacteristic
368C4×C103#53911yescharacteristic
369#22174C10311yesmaximal, characteristic, direct product factor, Sylow
370C2×C103—42no—
371C2×C103—42no—
372C2×C103—81no—
373C2×C103#232511yescharacteristic
374C2×C103D4×M1611yescharacteristic
375C2×C103#293511yescharacteristic
376C2×C103#297411yescharacteristic
377C2×C103#297811yescharacteristic
378C2×C103#298911yescharacteristic
379C2×C103#299311yescharacteristic
380C2×#436C2×C10311yescharacteristic, complemented
381C2×#435C2×C10311yescharacteristic, complemented
382C4×#121C2×C10311yescharacteristic
383#1924C2×C10311yescharacteristic, complemented
384#1923C2×C10311yescharacteristic, complemented
385#1917C2×C10311yescharacteristic, complemented
386#1916C2×C10311yescharacteristic, complemented
387#1870C2×C10311yescharacteristic, complemented
388#1870C2×C10311yescharacteristic, complemented
389#1870C2×C10311yescharacteristic, complemented
390#1869C2×C10311yescharacteristic, complemented
391#1851C2×C10311yescharacteristic, complemented
392#1850C2×C10311yescharacteristic, complemented
393#1797C2×C10311yescharacteristic, complemented
394#1728C2×C10311yescharacteristic, complemented
395C103#2217411yescharacteristic, direct product factor, Sylow
396C22×M16C22×C10311yescharacteristic
397C22×M16C22×C10311yescharacteristic
398C22×M16C22×C10311yescharacteristic
399C23×C8C22×C10311yescharacteristic
400C2×#121C4×C10311yescharacteristic
401C2×C4×D4C22×C10311yescharacteristic
402C2×C4×D4C22×C10311yescharacteristic
403C2×C4×D4C22×C10311yescharacteristic
404C22×C42C22×C10311yescharacteristic
405#436—24no—
406#435—24no—
407C2×C4⋊C8C22×C10311yescharacteristic
408C2×C4⋊C8C22×C10311yescharacteristic
409C2×C4⋊C8C22×C10311yescharacteristic
410C2×C4⋊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
421#390C4×C10311yescharacteristic
422#389C4×C10311yescharacteristic
423#388C4×C10311yescharacteristic
424#388C4×C10311yescharacteristic
425#386C4×C10311yescharacteristic
426#386C4×C10311yescharacteristic
427#380C4×C10311yescharacteristic
428C4×C4⋊C4C22×C10311yescharacteristic
429C4×C22⋊C4C22×C10311yescharacteristic
430C4×C22⋊C4C22×C10311yescharacteristic
431#336C22×C10311yescharacteristic
432#336C22×C10311yescharacteristic
433#336C22×C10311yescharacteristic
434#336C22×C10311yescharacteristic
435#336C22×C10311yescharacteristic
436#336C22×C10311yescharacteristic
437#336C22×C10311yescharacteristic
438#336C22×C10311yescharacteristic
439#336C22×C10311yescharacteristic
440#336C22×C10311yescharacteristic
441C22×D4C2×C4×C10311yescharacteristic
442C22×D4C2×C4×C10311yescharacteristic
443C22×D4C2×C4×C10311yescharacteristic
444C23×C4C2×C4×C10311yescharacteristic
445C23×C4C2×C4×C10311yescharacteristic
446C23×C4C23×C10311yescharacteristic
447C23×C4C23×C10311yescharacteristic
448C23×C4C23×C10311yescharacteristic
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C2×M16—41no—
453C2×M16—41no—
454C2×M16—41no—
455C2×M16—41no—
456C2×M16—41no—
457C2×M16D4×C10314yescomplemented
458C22×C8—22no—
459C22×C8—41no—
460C22×C8—41no—
461C22×C8C23×C10311yescharacteristic
462C22×C8C23×C10311yescharacteristic
463C22×C8C23×C10311yescharacteristic
464C22×C8C23×C10311yescharacteristic
465C22×C8C23×C10311yescharacteristic
466C22×C8C23×C10311yescharacteristic
467C22×C8C23×C10311yescharacteristic
468C22×C8C23×C10311yescharacteristic
469#121—24no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—22no—
474C4×D4—41no—
475C4×D4—41no—
476C2×C4⋊C4C2×C4×C10311yescharacteristic
477C2×C4⋊C4C2×C4×C10311yescharacteristic
478C2×C4⋊C4C2×C4×C10311yescharacteristic
479C2×C4⋊C4C2×C4×C10311yescharacteristic
480C2×C4⋊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×C22⋊C4C2×C4×C10311yescharacteristic
488C2×C22⋊C4C2×C4×C10311yescharacteristic
489C2×C22⋊C4C2×C4×C10311yescharacteristic
490C2×C22⋊C4C2×C4×C10311yescharacteristic
491C2×C42—41no—
492C2×C42—41no—
493C2×C42C2×C4×C10311yescharacteristic
494C2×C42C2×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—41no—
508C22⋊C8—41no—
509C22⋊C8—41no—
510C22⋊C8—41no—
511#97—22no—
512C4×C8—22no—
513#95C2×C4×C10311yescharacteristic
514#95C2×C4×C10311yescharacteristic
515#95C2×C4×C10311yescharacteristic
516#95C2×C4×C10311yescharacteristic
517#95C2×C4×C10311yescharacteristic
518#95C2×C4×C10311yescharacteristic
519C24C22×C4×C10311yescharacteristic
520C24C22×C4×C10311yescharacteristic
521C24C22×C4×C10311yescharacteristic
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
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—21no—
548C22×C4—21no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4C22×C4×C10311yescharacteristic
554C22×C4C22×C4×C10311yescharacteristic
555C22×C4C22×C4×C10311yescharacteristic
556C22×C4C22×C4×C10311yescharacteristic
557C22×C4C22×C4×C10311yescharacteristic
558C22×C4C22×C4×C10311yescharacteristic
559C22×C4C22×C4×C10311yescharacteristic
560C22×C4C22×C4×C10311yescharacteristic
561C22×C4C22×C4×C10311yescharacteristic
562C22×C4C22×C4×C10311yescharacteristic
563C22×C4C22×C4×C10311yescharacteristic
564C22×C4C2×D4×C10312yes—
565C22×C4#41×C10312yes—
566C22×C4C24×C10311yescharacteristic
567M16—44no—
568M16—44no—
569M16—44no—
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—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—44no—
593C2×C8C2×D4×C10312yes—
594C2×C8C2×D4×C10312yes—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—41no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—41no—
609C22⋊C4M16×C10314yescomplemented
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—41no—
619C42—41no—
620C23—21no—
621C23—21no—
622C23—21no—
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—
639C23C4×D4×C10312yes—
640C23C2×M16×C10312yes—
641C23C23×C4×C10311yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
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—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
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—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—44no—
679C2×C4—44no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4C4×D4×C10312yes—
689C2×C4C2×M16×C10312yes—
690C2×C4C2×M16×C10312yes—
691C2×C4#131×C10312yes—
692C2×C4C22×D4×C10311yescharacteristic
693C2×C4C2×#41×C10311yescharacteristic
694C2×C4H(5,𝔽2)×C10311yescharacteristic
695C2×C4H(5,𝔽2)×C10311yescharacteristic
696C2×C4H(5,𝔽2)×C10311yescharacteristic
697C2×C42−1+4×C10311yescharacteristic
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×C4×D4×C10311yescharacteristic
728C22#518×C10311yescharacteristic
729C22#520×C10311yescharacteristic
730C22C22×M16×C10311yescharacteristic
731C22C2×#131×C10311yescharacteristic
732C22#568×C10311yescharacteristic
733C22#568×C10311yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4#534×C10311yescharacteristic
746C4#537×C10311yescharacteristic
747C4#538×C10311yescharacteristic
748C4#539×C10311yescharacteristic
749C2—42no—
750C2—42no—
751C2—81no—
752C2C103×#232511yescharacteristic
753C2D4×M16×C10311yescharacteristic
754C2C103×#293511yescharacteristic
755C2C103×#297411yescharacteristic
756C2C103×#297811yescharacteristic
757C2C103×#298911yescharacteristic
758C2C103×#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
1. C2×#436×C103C2semidirect
2. C2×#435×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×#1797C2semidirect
15. C103×#1728C2semidirect
77. C2×M16×C103D4semidirect
229. C22⋊C4×C103M16semidirect
369. #22174C103direct (N × H)
380. C2×#436C2×C103semidirect
381. C2×#435C2×C103semidirect
383. #1924C2×C103semidirect
384. #1923C2×C103semidirect
385. #1917C2×C103semidirect
386. #1916C2×C103semidirect
387. #1870C2×C103semidirect
388. #1870C2×C103semidirect
389. #1870C2×C103semidirect
390. #1869C2×C103semidirect
391. #1851C2×C103semidirect
392. #1850C2×C103semidirect
393. #1797C2×C103semidirect
394. #1728C2×C103semidirect
395. C103#22174direct (N × H)
457. C2×M16D4×C103semidirect
609. C22⋊C4M16×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#436×C1032
C2×#435×C1032
C4×#121×C1032
C103×#19242
C103×#19232
C103×#19172
C103×#19162
C103×#18702
C103×#18692
C103×#18512
C103×#18502
C103×#17972
C103×#17282
#22174103