Finite Group Databasebeta

← C103×#22888 #39928163

Subgroups — C103×#22888 #39928163

Order 26368.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3002C211yesmaximal, characteristic
2C2×#443×C103C211yesmaximal, characteristic, complemented
3C103×#2933C211yesmaximal, characteristic, complemented
4C22×#104×C103C211yesmaximal, characteristic, complemented
5C103×#2880C211yesmaximal, characteristic, complemented
6C103×#1974C211yesmaximal, characteristic, complemented
7C103×#1937C211yesmaximal, characteristic, complemented
8C103×#1929C211yesmaximal, characteristic, complemented
9C103×#1896C211yesmaximal, characteristic, complemented
10C103×#1876C211yesmaximal, characteristic, complemented
11C103×#1876C211yesmaximal, characteristic, complemented
12C103×#1866C211yesmaximal, characteristic, complemented
13C103×#1855C211yesmaximal, characteristic, complemented
14C103×#1764C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C103C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C2×#135×C103C2211yescharacteristic
18C2×#135×C103C2211yescharacteristic
19C2×#131×C103C2211yescharacteristic
20C2×#131×C103C2211yescharacteristic
21C2×#131×C103C2211yescharacteristic, complemented
22C22×M16×C103C2211yescharacteristic
23#525×C103C2211yescharacteristic
24C22×C42×C103C2211yescharacteristic
25#452×C103C411yescharacteristic, complemented
26#452×C103C411yescharacteristic, complemented
27#451×C103C411yescharacteristic, complemented
28#450×C103C411yescharacteristic, complemented
29#449×C103C411yescharacteristic, complemented
30#449×C103C411yescharacteristic, complemented
31#448×C103C411yescharacteristic, complemented
32#447×C103C411yescharacteristic, complemented
33#443×C103—24no—
34#436×C103—21no—
35#435×C103—21no—
36#435×C103—21no—
37C8×D4×C103—21no—
38C2×#108×C103C2211yescharacteristic, complemented
39C2×#108×C103C2211yescharacteristic, complemented
40#424×C103C2211yescharacteristic, complemented
41C2×#104×C103—24no—
42C2×#104×C103C2211yescharacteristic
43C2×#104×C103C2211yescharacteristic
44C2×#104×C103C2211yescharacteristic
45C2×#104×C103C2211yescharacteristic
46C2×#104×C103C2211yescharacteristic, complemented
47C2×#104×C103C2211yescharacteristic, complemented
48#416×C103C2211yescharacteristic
49#416×C103C2211yescharacteristic
50#408×C103—21no—
51#408×C103—21no—
52#408×C103C2211yescharacteristic
53#408×C103C2211yescharacteristic
54#408×C103C2211yescharacteristic, complemented
55#407×C103—21no—
56#407×C103C2211yescharacteristic
57C2×C22⋊C8×C103—21no—
58C2×C22⋊C8×C103C2211yescharacteristic
59C2×C22⋊C8×C103C2211yescharacteristic
60#405×C103C2211yescharacteristic, complemented
61C2×C4×C8×C103C2211yescharacteristic, complemented
62C2×C4×C8×C103C2211yescharacteristic, complemented
63#341×C103C2211yescharacteristic, complemented
64#341×C103C2211yescharacteristic, complemented
65#339×C103C2211yescharacteristic, complemented
66#339×C103C2211yescharacteristic, complemented
67#336×C103C2211yescharacteristic, complemented
68#336×C103C2211yescharacteristic, complemented
69C2×#41×C103—21no—
70C2×#41×C103—21no—
71C2×#41×C103—22no—
72C2×#41×C103—22no—
73C2×#41×C103—41no—
74C2×#41×C103—41no—
75C2×#41×C103C2×C411yescharacteristic
76C2×#41×C103C2×C411yescharacteristic
77C2×#41×C103C2311yescharacteristic
78C2×#41×C103C2311yescharacteristic
79C2×#41×C103C2311yescharacteristic
80C22×Q8×C103C2×C411yescharacteristic
81C22×D4×C103—21no—
82C22×D4×C103C2×C411yescharacteristic
83C23×C4×C103—21no—
84C23×C4×C103—21no—
85C23×C4×C103C2311yescharacteristic
86#135×C103—22no—
87#135×C103—22no—
88#135×C103—41no—
89#135×C103—41no—
90C2×Q16×C103C2×C411yescharacteristic, complemented
91C2×Q16×C103C2×C411yescharacteristic, complemented
92C2×SD16×C103C2×C411yescharacteristic, complemented
93C2×SD16×C103C2×C411yescharacteristic, complemented
94C2×SD16×C103C2×C411yescharacteristic, complemented
95C2×SD16×C103C2×C411yescharacteristic, complemented
96C2×D8×C103C2×C411yescharacteristic, complemented
97C2×D8×C103C2×C411yescharacteristic, complemented
98#131×C103—22no—
99#131×C103—22no—
100#131×C103—22no—
101#131×C103—41no—
102#131×C103—41no—
103#131×C103—41no—
104C2×M16×C103—21no—
105C2×M16×C103—21no—
106C2×M16×C103—21no—
107C2×M16×C103—21no—
108C2×M16×C103—22no—
109C2×M16×C103—41no—
110C2×M16×C103C2311yescharacteristic
111C2×M16×C103C2311yescharacteristic
112C2×M16×C103C2311yescharacteristic
113C2×M16×C103C2311yescharacteristic
114C22×C8×C103—21no—
115C22×C8×C103—21no—
116C22×C8×C103—21no—
117C22×C8×C103—21no—
118C22×C8×C103C2311yescharacteristic
119C22×C8×C103C2311yescharacteristic
120C22×C8×C103C2311yescharacteristic
121C22×C8×C103C2311yescharacteristic
122#123×C103—21no—
123C22⋊Q8×C103C2×C411yescharacteristic
124C22⋊Q8×C103C2×C411yescharacteristic
125#121×C103C2×C411yescharacteristic
126#121×C103C2×C411yescharacteristic
127#120×C103—21no—
128C4×D4×C103—21no—
129C4×D4×C103—21no—
130#117×C103C2311yescharacteristic
131C2×C42×C103—22no—
132C2×C42×C103—21no—
133C2×C42×C103—41no—
134C2×C42×C103C2311yescharacteristic
135C2×C42×C103C2311yescharacteristic
136#108×C103—22no—
137#108×C103—41no—
138C4⋊C8×C103—21no—
139C4⋊C8×C103—21no—
140#104×C103—22no—
141#104×C103—22no—
142#104×C103—22no—
143#104×C103—22no—
144#104×C103—41no—
145#104×C103D414yescomplemented
146#103×C103C2×C411yescharacteristic, complemented
147#103×C103C2×C411yescharacteristic, complemented
148#103×C103C2×C411yescharacteristic, complemented
149#103×C103C2×C411yescharacteristic, complemented
150#102×C103C2×C411yescharacteristic, complemented
151#102×C103C2×C411yescharacteristic, complemented
152#102×C103C2×C411yescharacteristic, complemented
153#102×C103C2×C411yescharacteristic, complemented
154C22⋊C8×C103—21no—
155C22⋊C8×C103—21no—
156C22⋊C8×C103—21no—
157C22⋊C8×C103—21no—
158C22⋊C8×C103—21no—
159C22⋊C8×C103—21no—
160C22⋊C8×C103—21no—
161C22⋊C8×C103—21no—
162C22⋊C8×C103C2×C411yescharacteristic
163C22⋊C8×C103C2×C411yescharacteristic
164C22⋊C8×C103C2×C411yescharacteristic
165C22⋊C8×C103C2×C411yescharacteristic
166C22⋊C8×C103D411yescharacteristic
167C22⋊C8×C103D411yescharacteristic
168C22⋊C8×C103D411yescharacteristic
169C22⋊C8×C103D411yescharacteristic
170#97×C103—21no—
171C4×C8×C103—21no—
172C4×C8×C103—22no—
173C4×C8×C103—41no—
174C24×C103—21no—
175C24×C103#4111yescharacteristic
176#41×C103—21no—
177#41×C103—21no—
178#41×C103—22no—
179#41×C103—22no—
180#41×C103—21no—
181#41×C103—21no—
182#41×C103—21no—
183#41×C103—21no—
184#41×C103—21no—
185#41×C103—21no—
186#41×C103—21no—
187#41×C103—21no—
188#41×C103—42no—
189#41×C103—42no—
190#41×C103—41no—
191#41×C103—41no—
192#41×C103—42no—
193#41×C103—42no—
194#41×C103C2×D412yes—
195#41×C103#4112yes—
196C2×Q8×C103—21no—
197C2×Q8×C103—22no—
198C2×Q8×C103—41no—
199C2×Q8×C103C22×C411yescharacteristic
200C2×Q8×C103C22×C411yescharacteristic
201C2×Q8×C103C22×C411yescharacteristic
202C2×D4×C103—21no—
203C2×D4×C103—22no—
204C2×D4×C103—21no—
205C2×D4×C103—21no—
206C2×D4×C103—21no—
207C2×D4×C103—21no—
208C2×D4×C103—21no—
209C2×D4×C103—21no—
210C2×D4×C103—21no—
211C2×D4×C103—41no—
212C2×D4×C103—42no—
213C2×D4×C103—42no—
214C2×D4×C103C22×C411yescharacteristic
215C2×D4×C103C22×C411yescharacteristic
216C2×D4×C103C22×C411yescharacteristic
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—21no—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—24no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—21no—
227C22×C4×C103—21no—
228C22×C4×C103—21no—
229C22×C4×C103—21no—
230C22×C4×C103—42no—
231C22×C4×C103—42no—
232C22×C4×C103—42no—
233C22×C4×C103—42no—
234C22×C4×C103C22×C411yescharacteristic
235C22×C4×C103C22×C411yescharacteristic
236C22×C4×C103C2×D411yescharacteristic
237C22×C4×C103C2×D411yescharacteristic
238C22×C4×C103#4111yescharacteristic
239C22×C4×C103C2411yescharacteristic
240Q16×C103—22no—
241Q16×C103—41no—
242SD16×C103—22no—
243SD16×C103—22no—
244SD16×C103—41no—
245SD16×C103—41no—
246D8×C103—22no—
247D8×C103—41no—
248M16×C103—21no—
249M16×C103—21no—
250M16×C103—21no—
251M16×C103—21no—
252M16×C103—21no—
253M16×C103—21no—
254M16×C103—21no—
255M16×C103—42no—
256M16×C103—42no—
257M16×C103—42no—
258M16×C103—42no—
259M16×C103C2×D412yes—
260C2×C8×C103—21no—
261C2×C8×C103—21no—
262C2×C8×C103—21no—
263C2×C8×C103—21no—
264C2×C8×C103—21no—
265C2×C8×C103—21no—
266C2×C8×C103—21no—
267C2×C8×C103—21no—
268C2×C8×C103—21no—
269C2×C8×C103—21no—
270C2×C8×C103—21no—
271C2×C8×C103—21no—
272C2×C8×C103—42no—
273C2×C8×C103—42no—
274C2×C8×C103—42no—
275C2×C8×C103—42no—
276C2×C8×C103C22×C411yescharacteristic
277C2×C8×C103C22×C411yescharacteristic
278C2×C8×C103C22×C411yescharacteristic
279C2×C8×C103C22×C411yescharacteristic
280C2×C8×C103C2×D411yescharacteristic
281C2×C8×C103C2×D411yescharacteristic
282C2×C8×C103C2×D411yescharacteristic
283C2×C8×C103C2×D411yescharacteristic
284C4⋊C4×C103—21no—
285C4⋊C4×C103—21no—
286C4⋊C4×C103C22×C411yescharacteristic
287C4⋊C4×C103C22×C411yescharacteristic
288C22⋊C4×C103—21no—
289C22⋊C4×C103—21no—
290C22⋊C4×C103—21no—
291C22⋊C4×C103—21no—
292C22⋊C4×C103—21no—
293C42×C103—21no—
294C42×C103—21no—
295C42×C103—21no—
296C42×C103—21no—
297C42×C103—42no—
298C42×C103C2×D412yes—
299C23×C103—21no—
300C23×C103—21no—
301C23×C103—21no—
302C23×C103—22no—
303C23×C103—21no—
304C23×C103—21no—
305C23×C103—41no—
306C23×C103—42no—
307C23×C103—42no—
308C23×C103—81no—
309C23×C103C4×D411yescharacteristic
310C23×C103C4×D411yescharacteristic
311C23×C103C2×#4111yescharacteristic
312Q8×C103—21no—
313Q8×C103—21no—
314Q8×C103—21no—
315Q8×C103—21no—
316Q8×C103—21no—
317Q8×C103—42no—
318Q8×C103C4×D412yes—
319D4×C103—22no—
320D4×C103—22no—
321D4×C103—21no—
322D4×C103—21no—
323D4×C103—21no—
324D4×C103—21no—
325D4×C103—21no—
326D4×C103—42no—
327D4×C103—42no—
328D4×C103—42no—
329D4×C103—41no—
330D4×C103—41no—
331D4×C103—41no—
332D4×C103—41no—
333D4×C103—42no—
334D4×C103—81no—
335D4×C103C4×D412yes—
336C2×C4×C103—22no—
337C2×C4×C103—22no—
338C2×C4×C103—21no—
339C2×C4×C103—22no—
340C2×C4×C103—21no—
341C2×C4×C103—21no—
342C2×C4×C103—21no—
343C2×C4×C103—21no—
344C2×C4×C103—21no—
345C2×C4×C103—21no—
346C2×C4×C103—21no—
347C2×C4×C103—22no—
348C2×C4×C103—21no—
349C2×C4×C103—22no—
350C2×C4×C103—21no—
351C2×C4×C103—21no—
352C2×C4×C103—22no—
353C2×C4×C103—21no—
354C2×C4×C103—21no—
355C2×C4×C103—21no—
356C2×C4×C103—21no—
357C2×C4×C103—42no—
358C2×C4×C103—42no—
359C2×C4×C103—42no—
360C2×C4×C103—48no—
361C2×C4×C103—41no—
362C2×C4×C103—41no—
363C2×C4×C103—41no—
364C2×C4×C103—41no—
365C2×C4×C103—41no—
366C2×C4×C103—41no—
367C2×C4×C103C4×D411yescharacteristic
368C2×C4×C103C4×D411yescharacteristic
369C2×C4×C103C23×C411yescharacteristic
370C2×C4×C103C22×D411yescharacteristic
371C2×C4×C103C22×D411yescharacteristic
372C2×C4×C103C2×#4111yescharacteristic
373C2×C4×C103H(5,𝔽2)11yescharacteristic
374C2×C4×C103H(5,𝔽2)11yescharacteristic
375C8×C103—21no—
376C8×C103—21no—
377C8×C103—21no—
378C8×C103—21no—
379C8×C103—21no—
380C8×C103—21no—
381C8×C103—22no—
382C8×C103—21no—
383C8×C103—21no—
384C8×C103—41no—
385C8×C103—41no—
386C8×C103—41no—
387C22×C103—21no—
388C22×C103—21no—
389C22×C103—21no—
390C22×C103—21no—
391C22×C103—21no—
392C22×C103—22no—
393C22×C103—21no—
394C22×C103—21no—
395C22×C103—42no—
396C22×C103—42no—
397C22×C103—41no—
398C22×C103—41no—
399C22×C103—41no—
400C22×C103—41no—
401C22×C103—41no—
402C22×C103—41no—
403C22×C103—41no—
404C22×C103—41no—
405C22×C103—84no—
406C22×C103#44312yescomplemented
407C22×C103C2×C4×D411yescharacteristic
408C22×C103#54611yescharacteristic
409C22×C103#55111yescharacteristic
410C4×C103—24no—
411C4×C103—21no—
412C4×C103—21no—
413C4×C103—22no—
414C4×C103—42no—
415C4×C103—41no—
416C4×C103—41no—
417C4×C103—41no—
418C4×C103—41no—
419C4×C103C2×C4×D411yescharacteristic
420C4×C103#51811yescharacteristic
421C4×C103D4211yescharacteristic
422C4×C103#54611yescharacteristic
423#22888C10311yesmaximal, characteristic, direct product factor, Sylow
424C2×C103—21no—
425C2×C103—22no—
426C2×C103—21no—
427C2×C103—41no—
428C2×C103—42no—
429C2×C103—81no—
430C2×C103—81no—
431C2×C103#235811yescharacteristic
432C2×C103C2×#44311yescharacteristic
433C2×C103#295611yescharacteristic
434#3002C2×C10311yescharacteristic
435C2×#443C2×C10311yescharacteristic, complemented
436#2933C2×C10311yescharacteristic, complemented
437C22×#104C2×C10311yescharacteristic, complemented
438#2880C2×C10311yescharacteristic, complemented
439#1974C2×C10311yescharacteristic, complemented
440#1937C2×C10311yescharacteristic, complemented
441#1929C2×C10311yescharacteristic, complemented
442#1896C2×C10311yescharacteristic, complemented
443#1876C2×C10311yescharacteristic, complemented
444#1876C2×C10311yescharacteristic, complemented
445#1866C2×C10311yescharacteristic, complemented
446#1855C2×C10311yescharacteristic, complemented
447#1764C2×C10311yescharacteristic, complemented
448C4×C22⋊C8C2×C10311yescharacteristic, complemented
449C103#2288811yescharacteristic, direct product factor, Sylow
450C22×#41C22×C10311yescharacteristic
451C2×#135C22×C10311yescharacteristic
452C2×#135C22×C10311yescharacteristic
453C2×#131C22×C10311yescharacteristic
454C2×#131C22×C10311yescharacteristic
455C2×#131C22×C10311yescharacteristic, complemented
456C22×M16C22×C10311yescharacteristic
457#525C22×C10311yescharacteristic
458C22×C42C22×C10311yescharacteristic
459#452C4×C10311yescharacteristic, complemented
460#452C4×C10311yescharacteristic, complemented
461#451C4×C10311yescharacteristic, complemented
462#450C4×C10311yescharacteristic, complemented
463#449C4×C10311yescharacteristic, complemented
464#449C4×C10311yescharacteristic, complemented
465#448C4×C10311yescharacteristic, complemented
466#447C4×C10311yescharacteristic, complemented
467#443—24no—
468#436—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108C22×C10311yescharacteristic, complemented
473C2×#108C22×C10311yescharacteristic, complemented
474#424C22×C10311yescharacteristic, complemented
475C2×#104—24no—
476C2×#104C22×C10311yescharacteristic
477C2×#104C22×C10311yescharacteristic
478C2×#104C22×C10311yescharacteristic
479C2×#104C22×C10311yescharacteristic
480C2×#104C22×C10311yescharacteristic, complemented
481C2×#104C22×C10311yescharacteristic, complemented
482#416C22×C10311yescharacteristic
483#416C22×C10311yescharacteristic
484#408—21no—
485#408—21no—
486#408C22×C10311yescharacteristic
487#408C22×C10311yescharacteristic
488#408C22×C10311yescharacteristic, complemented
489#407—21no—
490#407C22×C10311yescharacteristic
491C2×C22⋊C8—21no—
492C2×C22⋊C8C22×C10311yescharacteristic
493C2×C22⋊C8C22×C10311yescharacteristic
494#405C22×C10311yescharacteristic, complemented
495C2×C4×C8C22×C10311yescharacteristic, complemented
496C2×C4×C8C22×C10311yescharacteristic, complemented
497#341C22×C10311yescharacteristic, complemented
498#341C22×C10311yescharacteristic, complemented
499#339C22×C10311yescharacteristic, complemented
500#339C22×C10311yescharacteristic, complemented
501#336C22×C10311yescharacteristic, complemented
502#336C22×C10311yescharacteristic, complemented
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×C4×C10311yescharacteristic
510C2×#41C2×C4×C10311yescharacteristic
511C2×#41C23×C10311yescharacteristic
512C2×#41C23×C10311yescharacteristic
513C2×#41C23×C10311yescharacteristic
514C22×Q8C2×C4×C10311yescharacteristic
515C22×D4—21no—
516C22×D4C2×C4×C10311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C10311yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×C4×C10311yescharacteristic, complemented
525C2×Q16C2×C4×C10311yescharacteristic, complemented
526C2×SD16C2×C4×C10311yescharacteristic, complemented
527C2×SD16C2×C4×C10311yescharacteristic, complemented
528C2×SD16C2×C4×C10311yescharacteristic, complemented
529C2×SD16C2×C4×C10311yescharacteristic, complemented
530C2×D8C2×C4×C10311yescharacteristic, complemented
531C2×D8C2×C4×C10311yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—22no—
535#131—41no—
536#131—41no—
537#131—41no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16C23×C10311yescharacteristic
545C2×M16C23×C10311yescharacteristic
546C2×M16C23×C10311yescharacteristic
547C2×M16C23×C10311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8—21no—
552C22×C8C23×C10311yescharacteristic
553C22×C8C23×C10311yescharacteristic
554C22×C8C23×C10311yescharacteristic
555C22×C8C23×C10311yescharacteristic
556#123—21no—
557C22⋊Q8C2×C4×C10311yescharacteristic
558C22⋊Q8C2×C4×C10311yescharacteristic
559#121C2×C4×C10311yescharacteristic
560#121C2×C4×C10311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C23×C10311yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C23×C10311yescharacteristic
569C2×C42C23×C10311yescharacteristic
570#108—22no—
571#108—41no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—22no—
578#104—41no—
579#104D4×C10314yescomplemented
580#103C2×C4×C10311yescharacteristic, complemented
581#103C2×C4×C10311yescharacteristic, complemented
582#103C2×C4×C10311yescharacteristic, complemented
583#103C2×C4×C10311yescharacteristic, complemented
584#102C2×C4×C10311yescharacteristic, complemented
585#102C2×C4×C10311yescharacteristic, complemented
586#102C2×C4×C10311yescharacteristic, complemented
587#102C2×C4×C10311yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8C2×C4×C10311yescharacteristic
597C22⋊C8C2×C4×C10311yescharacteristic
598C22⋊C8C2×C4×C10311yescharacteristic
599C22⋊C8C2×C4×C10311yescharacteristic
600C22⋊C8D4×C10311yescharacteristic
601C22⋊C8D4×C10311yescharacteristic
602C22⋊C8D4×C10311yescharacteristic
603C22⋊C8D4×C10311yescharacteristic
604#97—21no—
605C4×C8—21no—
606C4×C8—22no—
607C4×C8—41no—
608C24—21no—
609C24#41×C10311yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C10312yes—
629#41#41×C10312yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C10311yescharacteristic
634C2×Q8C22×C4×C10311yescharacteristic
635C2×Q8C22×C4×C10311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C10311yescharacteristic
649C2×D4C22×C4×C10311yescharacteristic
650C2×D4C22×C4×C10311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C10311yescharacteristic
669C22×C4C22×C4×C10311yescharacteristic
670C22×C4C2×D4×C10311yescharacteristic
671C22×C4C2×D4×C10311yescharacteristic
672C22×C4#41×C10311yescharacteristic
673C22×C4C24×C10311yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C10312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C10311yescharacteristic
711C2×C8C22×C4×C10311yescharacteristic
712C2×C8C22×C4×C10311yescharacteristic
713C2×C8C22×C4×C10311yescharacteristic
714C2×C8C2×D4×C10311yescharacteristic
715C2×C8C2×D4×C10311yescharacteristic
716C2×C8C2×D4×C10311yescharacteristic
717C2×C8C2×D4×C10311yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C10311yescharacteristic
721C4⋊C4C22×C4×C10311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C10312yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C10311yescharacteristic
744C23C4×D4×C10311yescharacteristic
745C23C2×#41×C10311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C10312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4C4×D4×C10312yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—48no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C10311yescharacteristic
802C2×C4C4×D4×C10311yescharacteristic
803C2×C4C23×C4×C10311yescharacteristic
804C2×C4C22×D4×C10311yescharacteristic
805C2×C4C22×D4×C10311yescharacteristic
806C2×C4C2×#41×C10311yescharacteristic
807C2×C4H(5,𝔽2)×C10311yescharacteristic
808C2×C4H(5,𝔽2)×C10311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#443×C10312yescomplemented
841C22C2×C4×D4×C10311yescharacteristic
842C22#546×C10311yescharacteristic
843C22#551×C10311yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C10311yescharacteristic
854C4#518×C10311yescharacteristic
855C4D42×C10311yescharacteristic
856C4#546×C10311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2C103×#235811yescharacteristic
865C2C2×#443×C10311yescharacteristic
866C2C103×#295611yescharacteristic
subgroupG/H
centerC2×C4×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC22×C103C2×C4×D4
prime radicalC103×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C22⋊C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#443×C103C2semidirect
3. C103×#2933C2semidirect
4. C22×#104×C103C2semidirect
5. C103×#2880C2semidirect
6. C103×#1974C2semidirect
7. C103×#1937C2semidirect
8. C103×#1929C2semidirect
9. C103×#1896C2semidirect
10. C103×#1876C2semidirect
11. C103×#1876C2semidirect
12. C103×#1866C2semidirect
13. C103×#1855C2semidirect
14. C103×#1764C2semidirect
15. C4×C22⋊C8×C103C2semidirect
21. C2×#131×C103C22semidirect
25. #452×C103C4semidirect
26. #452×C103C4semidirect
27. #451×C103C4semidirect
28. #450×C103C4semidirect
29. #449×C103C4semidirect
30. #449×C103C4semidirect
31. #448×C103C4semidirect
32. #447×C103C4semidirect
38. C2×#108×C103C22semidirect
39. C2×#108×C103C22semidirect
40. #424×C103C22semidirect
46. C2×#104×C103C22semidirect
47. C2×#104×C103C22semidirect
54. #408×C103C22semidirect
60. #405×C103C22semidirect
61. C2×C4×C8×C103C22semidirect
62. C2×C4×C8×C103C22semidirect
63. #341×C103C22semidirect
64. #341×C103C22semidirect
65. #339×C103C22semidirect
66. #339×C103C22semidirect
67. #336×C103C22semidirect
68. #336×C103C22semidirect
90. C2×Q16×C103C2×C4semidirect
91. C2×Q16×C103C2×C4semidirect
92. C2×SD16×C103C2×C4semidirect
93. C2×SD16×C103C2×C4semidirect
94. C2×SD16×C103C2×C4semidirect
95. C2×SD16×C103C2×C4semidirect
96. C2×D8×C103C2×C4semidirect
97. C2×D8×C103C2×C4semidirect
145. #104×C103D4semidirect
146. #103×C103C2×C4semidirect
147. #103×C103C2×C4semidirect
148. #103×C103C2×C4semidirect
149. #103×C103C2×C4semidirect
150. #102×C103C2×C4semidirect
151. #102×C103C2×C4semidirect
152. #102×C103C2×C4semidirect
153. #102×C103C2×C4semidirect
406. C22×C103#443semidirect
423. #22888C103direct (N × H)
435. C2×#443C2×C103semidirect
436. #2933C2×C103semidirect
437. C22×#104C2×C103semidirect
438. #2880C2×C103semidirect
439. #1974C2×C103semidirect
440. #1937C2×C103semidirect
441. #1929C2×C103semidirect
442. #1896C2×C103semidirect
443. #1876C2×C103semidirect
444. #1876C2×C103semidirect
445. #1866C2×C103semidirect
446. #1855C2×C103semidirect
447. #1764C2×C103semidirect
448. C4×C22⋊C8C2×C103semidirect
449. C103#22888direct (N × H)
455. C2×#131C22×C103semidirect
459. #452C4×C103semidirect
460. #452C4×C103semidirect
461. #451C4×C103semidirect
462. #450C4×C103semidirect
463. #449C4×C103semidirect
464. #449C4×C103semidirect
465. #448C4×C103semidirect
466. #447C4×C103semidirect
472. C2×#108C22×C103semidirect
473. C2×#108C22×C103semidirect
474. #424C22×C103semidirect
480. C2×#104C22×C103semidirect
481. C2×#104C22×C103semidirect
488. #408C22×C103semidirect
494. #405C22×C103semidirect
495. C2×C4×C8C22×C103semidirect
496. C2×C4×C8C22×C103semidirect
497. #341C22×C103semidirect
498. #341C22×C103semidirect
499. #339C22×C103semidirect
500. #339C22×C103semidirect
501. #336C22×C103semidirect
502. #336C22×C103semidirect
524. C2×Q16C2×C4×C103semidirect
525. C2×Q16C2×C4×C103semidirect
526. C2×SD16C2×C4×C103semidirect
527. C2×SD16C2×C4×C103semidirect
528. C2×SD16C2×C4×C103semidirect
529. C2×SD16C2×C4×C103semidirect
530. C2×D8C2×C4×C103semidirect
531. C2×D8C2×C4×C103semidirect
579. #104D4×C103semidirect
580. #103C2×C4×C103semidirect
581. #103C2×C4×C103semidirect
582. #103C2×C4×C103semidirect
583. #103C2×C4×C103semidirect
584. #102C2×C4×C103semidirect
585. #102C2×C4×C103semidirect
586. #102C2×C4×C103semidirect
587. #102C2×C4×C103semidirect
840. C22#443×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30022
C2×#443×C1032
C103×#29332
C22×#104×C1032
C103×#28802
C103×#19742
C103×#19372
C103×#19292
C103×#18962
C103×#18762
C103×#18662
C103×#18552
C103×#17642
C4×C22⋊C8×C1032
#22888103