Finite Group Databasebeta

← C103×#25076 #39930351

Subgroups — C103×#25076 #39930351

Order 26368.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C103C211yesmaximal, characteristic, complemented
2C2×#459×C103C211yesmaximal, characteristic, complemented
3C2×#447×C103C211yesmaximal, characteristic, complemented
4C22×#102×C103C211yesmaximal, characteristic, complemented
5C103×#2433C211yesmaximal, characteristic, complemented
6C103×#2361C211yesmaximal, characteristic, complemented
7C103×#2067C211yesmaximal, characteristic, complemented
8C103×#2054C211yesmaximal, characteristic, complemented
9C103×#2041C211yesmaximal, characteristic, complemented
10C103×#2011C211yesmaximal, characteristic, complemented
11C103×#1982C211yesmaximal, characteristic, complemented
12C103×#1925C211yesmaximal, characteristic, complemented
13C103×#1879C211yesmaximal, characteristic, complemented
14C103×#1874C211yesmaximal, characteristic, complemented
15C103×#1850C211yesmaximal, characteristic, complemented
16C23×D4×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C22×D8×C103C2211yescharacteristic
19C22×D8×C103C2211yescharacteristic, complemented
20C23×C8×C103C2211yescharacteristic
21C2×#127×C103C2211yescharacteristic
22C2×#127×C103C2211yescharacteristic
23C2×#121×C103C2211yescharacteristic
24C2×#121×C103C2211yescharacteristic
25C2×#120×C103—21no—
26C2×#120×C103—21no—
27C2×C4×D4×C103—21no—
28C2×C4×D4×C103C2211yescharacteristic, complemented
29C22×C4⋊C4×C103C2211yescharacteristic
30#466×C103—24no—
31#459×C103—24no—
32#447×C103—24no—
33C2×#107×C103C2211yescharacteristic, complemented
34C2×C4⋊C8×C103C2211yescharacteristic, complemented
35C2×C4⋊C8×C103C2211yescharacteristic, complemented
36C2×#102×C103—24no—
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic, complemented
44C2×#102×C103C2211yescharacteristic, complemented
45C2×#102×C103C2211yescharacteristic, complemented
46C2×#102×C103C2211yescharacteristic, complemented
47C2×C22⋊C8×C103C2211yescharacteristic
48#392×C103—21no—
49#392×C103—21no—
50#390×C103C2211yescharacteristic
51#390×C103C2211yescharacteristic
52#390×C103C2211yescharacteristic, complemented
53#389×C103C2211yescharacteristic, complemented
54#388×C103—21no—
55#386×C103—21no—
56#385×C103—21no—
57C4×C4⋊C4×C103C2211yescharacteristic, complemented
58C4×C22⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic, complemented
60#340×C103C2211yescharacteristic, complemented
61#336×C103C2211yescharacteristic, complemented
62#336×C103C2211yescharacteristic, complemented
63C25×C103—21no—
64C22×D4×C103—22no—
65C22×D4×C103—22no—
66C22×D4×C103—21no—
67C22×D4×C103—21no—
68C22×D4×C103—22no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C22×D4×C103—21no—
72C22×D4×C103—21no—
73C22×D4×C103—21no—
74C22×D4×C103—22no—
75C22×D4×C103—41no—
76C22×D4×C103—41no—
77C22×D4×C103C2311yescharacteristic
78C22×D4×C103C2311yescharacteristic
79C22×D4×C103C2311yescharacteristic
80C22×D4×C103C2311yescharacteristic
81C23×C4×C103—21no—
82C23×C4×C103—21no—
83C23×C4×C103C2311yescharacteristic
84C2×D8×C103—22no—
85C2×D8×C103—22no—
86C2×D8×C103—22no—
87C2×D8×C103—22no—
88C2×D8×C103—22no—
89C2×D8×C103—22no—
90C2×D8×C103—41no—
91C2×D8×C103—41no—
92C2×D8×C103—41no—
93C22×C8×C103—22no—
94C22×C8×C103—22no—
95C22×C8×C103—41no—
96C22×C8×C103C2311yescharacteristic
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99C22×C8×C103C2311yescharacteristic
100#127×C103—22no—
101#127×C103—22no—
102#127×C103—41no—
103#127×C103—41no—
104#121×C103—22no—
105#121×C103—22no—
106#121×C103—22no—
107#121×C103D414yescomplemented
108#120×C103—44no—
109#120×C103—44no—
110C4×D4×C103—22no—
111C4×D4×C103—41no—
112C4×D4×C103—44no—
113C2×C4⋊C4×C103—22no—
114C2×C4⋊C4×C103—21no—
115C2×C4⋊C4×C103—21no—
116C2×C4⋊C4×C103—41no—
117C2×C4⋊C4×C103C2311yescharacteristic
118C2×C4⋊C4×C103C2311yescharacteristic
119C2×C4⋊C4×C103C2311yescharacteristic
120C2×C4⋊C4×C103C2311yescharacteristic
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103—21no—
125C2×C22⋊C4×C103—21no—
126C2×C22⋊C4×C103—21no—
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103D411yescharacteristic
131C2×C22⋊C4×C103D411yescharacteristic
132C2×C42×C103—21no—
133C2×C42×C103C2311yescharacteristic
134C2×C42×C103C2311yescharacteristic
135#107×C103—22no—
136C4⋊C8×C103—22no—
137C4⋊C8×C103—41no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—22no—
144#102×C103—22no—
145#102×C103—22no—
146#102×C103—41no—
147#102×C103D414yescomplemented
148C22⋊C8×C103—22no—
149#95×C103—21no—
150#95×C103—21no—
151#95×C103D411yescharacteristic
152#95×C103D411yescharacteristic
153C24×C103—21no—
154C24×C103—21no—
155C24×C103—21no—
156C24×C103—21no—
157C24×C103—42no—
158C24×C103—42no—
159C24×C103—42no—
160C24×C103—42no—
161C24×C103—42no—
162C24×C103—81no—
163C24×C103—81no—
164C24×C103C2×D411yescharacteristic
165C2×D4×C103—28no—
166C2×D4×C103—24no—
167C2×D4×C103—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103—21no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×C103—21no—
181C2×D4×C103—21no—
182C2×D4×C103—21no—
183C2×D4×C103—21no—
184C2×D4×C103—21no—
185C2×D4×C103—21no—
186C2×D4×C103—21no—
187C2×D4×C103—21no—
188C2×D4×C103—44no—
189C2×D4×C103—44no—
190C2×D4×C103—42no—
191C2×D4×C103—42no—
192C2×D4×C103—44no—
193C2×D4×C103—42no—
194C2×D4×C103—42no—
195C2×D4×C103—42no—
196C2×D4×C103—42no—
197C2×D4×C103—42no—
198C2×D4×C103—42no—
199C2×D4×C103—42no—
200C2×D4×C103—42no—
201C2×D4×C103—42no—
202C2×D4×C103—42no—
203C2×D4×C103—42no—
204C2×D4×C103—42no—
205C2×D4×C103—42no—
206C2×D4×C103—42no—
207C2×D4×C103—81no—
208C2×D4×C103—81no—
209C2×D4×C103—81no—
210C2×D4×C103—81no—
211C2×D4×C103C2×D412yes—
212C2×D4×C103C2×D412yes—
213C2×D4×C103#4112yes—
214C22×C4×C103—21no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—21no—
220C22×C4×C103—21no—
221C22×C4×C103—21no—
222C22×C4×C103—42no—
223C22×C4×C103—42no—
224C22×C4×C103—42no—
225C22×C4×C103—42no—
226C22×C4×C103—81no—
227C22×C4×C103—81no—
228C22×C4×C103C2×D411yescharacteristic
229C22×C4×C103C2×D411yescharacteristic
230C22×C4×C103C2×D411yescharacteristic
231C22×C4×C103C2×D412yes—
232C22×C4×C103C2×D411yescharacteristic
233C22×C4×C103C2×D411yescharacteristic
234C22×C4×C103#4112yes—
235C22×C4×C103C2411yescharacteristic
236D8×C103—44no—
237D8×C103—44no—
238D8×C103—44no—
239C2×C8×C103—21no—
240C2×C8×C103—21no—
241C2×C8×C103—21no—
242C2×C8×C103—21no—
243C2×C8×C103—21no—
244C2×C8×C103—21no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—21no—
249C2×C8×C103—21no—
250C2×C8×C103—44no—
251C2×C8×C103C2×D412yes—
252C4⋊C4×C103—21no—
253C4⋊C4×C103—21no—
254C4⋊C4×C103—21no—
255C4⋊C4×C103—21no—
256C4⋊C4×C103—21no—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—42no—
259C4⋊C4×C103—42no—
260C4⋊C4×C103C2×D412yes—
261C4⋊C4×C103C2×D412yes—
262C22⋊C4×C103—22no—
263C22⋊C4×C103—24no—
264C22⋊C4×C103—42no—
265C22⋊C4×C103—42no—
266C22⋊C4×C103—42no—
267C22⋊C4×C103—42no—
268C22⋊C4×C103—42no—
269C22⋊C4×C103—42no—
270C22⋊C4×C103—42no—
271C22⋊C4×C103—81no—
272C22⋊C4×C103D814yescomplemented
273C42×C103—21no—
274C42×C103—21no—
275C42×C103—21no—
276C42×C103—21no—
277C42×C103—42no—
278C23×C103—21no—
279C23×C103—21no—
280C23×C103—21no—
281C23×C103—21no—
282C23×C103—22no—
283C23×C103—22no—
284C23×C103—22no—
285C23×C103—48no—
286C23×C103—41no—
287C23×C103—41no—
288C23×C103—41no—
289C23×C103—41no—
290C23×C103—41no—
291C23×C103—41no—
292C23×C103—41no—
293C23×C103—41no—
294C23×C103—41no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—41no—
298C23×C103—41no—
299C23×C103—41no—
300C23×C103—41no—
301C23×C103—41no—
302C23×C103—41no—
303C23×C103—41no—
304C23×C103—41no—
305C23×C103—41no—
306C23×C103—41no—
307C23×C103—41no—
308C23×C103—41no—
309C23×C103—41no—
310C23×C103—41no—
311C23×C103—84no—
312C23×C103—84no—
313C23×C103—84no—
314C23×C103—84no—
315C23×C103—84no—
316C23×C103—84no—
317C23×C103#12112yes—
318C23×C103C2×D812yes—
319C23×C103AGL(1,ℤ/8)12yes—
320C23×C103C22×D411yescharacteristic
321D4×C103—22no—
322D4×C103—22no—
323D4×C103—22no—
324D4×C103—22no—
325D4×C103—22no—
326D4×C103—22no—
327D4×C103—48no—
328D4×C103—48no—
329D4×C103—41no—
330D4×C103—41no—
331D4×C103—41no—
332D4×C103—41no—
333D4×C103—41no—
334D4×C103—41no—
335D4×C103—41no—
336D4×C103—41no—
337D4×C103—41no—
338D4×C103—41no—
339D4×C103—84no—
340D4×C103—84no—
341D4×C103—84no—
342D4×C103—84no—
343D4×C103—84no—
344C2×C4×C103—21no—
345C2×C4×C103—21no—
346C2×C4×C103—21no—
347C2×C4×C103—21no—
348C2×C4×C103—21no—
349C2×C4×C103—21no—
350C2×C4×C103—22no—
351C2×C4×C103—22no—
352C2×C4×C103—22no—
353C2×C4×C103—22no—
354C2×C4×C103—22no—
355C2×C4×C103—21no—
356C2×C4×C103—22no—
357C2×C4×C103—21no—
358C2×C4×C103—21no—
359C2×C4×C103—21no—
360C2×C4×C103—21no—
361C2×C4×C103—21no—
362C2×C4×C103—41no—
363C2×C4×C103—41no—
364C2×C4×C103—41no—
365C2×C4×C103—41no—
366C2×C4×C103—41no—
367C2×C4×C103—41no—
368C2×C4×C103—41no—
369C2×C4×C103—41no—
370C2×C4×C103—41no—
371C2×C4×C103—41no—
372C2×C4×C103—84no—
373C2×C4×C103—84no—
374C2×C4×C103#12112yes—
375C2×C4×C103C2×D812yes—
376C2×C4×C103C2×D812yes—
377C2×C4×C103C22×D411yescharacteristic
378C2×C4×C103C22×D411yescharacteristic
379C2×C4×C103C2×#4111yescharacteristic
380C2×C4×C103C2×#4111yescharacteristic
381C2×C4×C103H(5,𝔽2)11yescharacteristic
382C2×C4×C103H(5,𝔽2)11yescharacteristic
383C8×C103—22no—
384C8×C103—41no—
385C8×C103—41no—
386C8×C103—41no—
387C22×C103—22no—
388C22×C103—22no—
389C22×C103—22no—
390C22×C103—22no—
391C22×C103—22no—
392C22×C103—22no—
393C22×C103—42no—
394C22×C103—42no—
395C22×C103—42no—
396C22×C103—42no—
397C22×C103—42no—
398C22×C103—42no—
399C22×C103—42no—
400C22×C103—42no—
401C22×C103—42no—
402C22×C103—816no—
403C22×C103—81no—
404C22×C103—81no—
405C22×C103—81no—
406C22×C103—81no—
407C22×C103—81no—
408C22×C103—81no—
409C22×C103—81no—
410C22×C103—81no—
411C22×C103—81no—
412C22×C103—81no—
413C22×C103—81no—
414C22×C103—81no—
415C22×C103—81no—
416C22×C103—81no—
417C22×C103—81no—
418C22×C103—81no—
419C22×C103—81no—
420C22×C103—81no—
421C22×C103—81no—
422C22×C103#45914yescomplemented
423C22×C103C2×#12111yescharacteristic
424C22×C103D4211yescharacteristic
425C22×C103#54611yescharacteristic
426C22×C103C22×D811yescharacteristic
427C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C103#57611yescharacteristic
429C22×C103#57711yescharacteristic
430C4×C103—22no—
431C4×C103—22no—
432C4×C103—22no—
433C4×C103—41no—
434C4×C103—42no—
435C4×C103—42no—
436C4×C103—41no—
437C4×C103—81no—
438C4×C103—81no—
439C4×C103#52511yescharacteristic
440C4×C103#53811yescharacteristic
441C4×C103D4211yescharacteristic
442C4×C103#54611yescharacteristic
443#25076C10311yesmaximal, characteristic, direct product factor, Sylow
444C2×C103—24no—
445C2×C103—82no—
446C2×C103—82no—
447C2×C103—82no—
448C2×C103—161no—
449C2×C103#242411yescharacteristic
450C2×C103C2×#45911yescharacteristic
451C2×C103#304511yescharacteristic
452C2×C103#326511yescharacteristic
453C2×C103D4×D811yescharacteristic
454C2×C103#329411yescharacteristic
455C2×C103#331811yescharacteristic
456C2×#466C2×C10311yescharacteristic, complemented
457C2×#459C2×C10311yescharacteristic, complemented
458C2×#447C2×C10311yescharacteristic, complemented
459C22×#102C2×C10311yescharacteristic, complemented
460#2433C2×C10311yescharacteristic, complemented
461#2361C2×C10311yescharacteristic, complemented
462#2067C2×C10311yescharacteristic, complemented
463#2054C2×C10311yescharacteristic, complemented
464#2041C2×C10311yescharacteristic, complemented
465#2011C2×C10311yescharacteristic, complemented
466#1982C2×C10311yescharacteristic, complemented
467#1925C2×C10311yescharacteristic, complemented
468#1879C2×C10311yescharacteristic, complemented
469#1874C2×C10311yescharacteristic, complemented
470#1850C2×C10311yescharacteristic, complemented
471C103#2507611yescharacteristic, direct product factor, Sylow
472C23×D4C22×C10311yescharacteristic
473C22×D8C22×C10311yescharacteristic
474C22×D8C22×C10311yescharacteristic
475C22×D8C22×C10311yescharacteristic, complemented
476C23×C8C22×C10311yescharacteristic
477C2×#127C22×C10311yescharacteristic
478C2×#127C22×C10311yescharacteristic
479C2×#121C22×C10311yescharacteristic
480C2×#121C22×C10311yescharacteristic
481C2×#120—21no—
482C2×#120—21no—
483C2×C4×D4—21no—
484C2×C4×D4C22×C10311yescharacteristic, complemented
485C22×C4⋊C4C22×C10311yescharacteristic
486#466—24no—
487#459—24no—
488#447—24no—
489C2×#107C22×C10311yescharacteristic, complemented
490C2×C4⋊C8C22×C10311yescharacteristic, complemented
491C2×C4⋊C8C22×C10311yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C10311yescharacteristic
494C2×#102C22×C10311yescharacteristic
495C2×#102C22×C10311yescharacteristic
496C2×#102C22×C10311yescharacteristic
497C2×#102C22×C10311yescharacteristic
498C2×#102C22×C10311yescharacteristic
499C2×#102C22×C10311yescharacteristic, complemented
500C2×#102C22×C10311yescharacteristic, complemented
501C2×#102C22×C10311yescharacteristic, complemented
502C2×#102C22×C10311yescharacteristic, complemented
503C2×C22⋊C8C22×C10311yescharacteristic
504#392—21no—
505#392—21no—
506#390C22×C10311yescharacteristic
507#390C22×C10311yescharacteristic
508#390C22×C10311yescharacteristic, complemented
509#389C22×C10311yescharacteristic, complemented
510#388—21no—
511#386—21no—
512#385—21no—
513C4×C4⋊C4C22×C10311yescharacteristic, complemented
514C4×C22⋊C4C22×C10311yescharacteristic
515#340C22×C10311yescharacteristic, complemented
516#340C22×C10311yescharacteristic, complemented
517#336C22×C10311yescharacteristic, complemented
518#336C22×C10311yescharacteristic, complemented
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C10311yescharacteristic
534C22×D4C23×C10311yescharacteristic
535C22×D4C23×C10311yescharacteristic
536C22×D4C23×C10311yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C10311yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C10311yescharacteristic
553C22×C8C23×C10311yescharacteristic
554C22×C8C23×C10311yescharacteristic
555C22×C8C23×C10311yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C10314yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C10311yescharacteristic
574C2×C4⋊C4C23×C10311yescharacteristic
575C2×C4⋊C4C23×C10311yescharacteristic
576C2×C4⋊C4C23×C10311yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C10311yescharacteristic
587C2×C22⋊C4D4×C10311yescharacteristic
588C2×C42—21no—
589C2×C42C23×C10311yescharacteristic
590C2×C42C23×C10311yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C10314yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C10311yescharacteristic
608#95D4×C10311yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C10311yescharacteristic
621C2×D4—28no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C10312yes—
668C2×D4C2×D4×C10312yes—
669C2×D4#41×C10312yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C10311yescharacteristic
685C22×C4C2×D4×C10311yescharacteristic
686C22×C4C2×D4×C10311yescharacteristic
687C22×C4C2×D4×C10312yes—
688C22×C4C2×D4×C10311yescharacteristic
689C22×C4C2×D4×C10311yescharacteristic
690C22×C4#41×C10312yes—
691C22×C4C24×C10311yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
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—44no—
707C2×C8C2×D4×C10312yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C10312yes—
717C4⋊C4C2×D4×C10312yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C10314yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C10312yes—
774C23C2×D8×C10312yes—
775C23AGL(1,ℤ/8)×C10312yes—
776C23C22×D4×C10311yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C10312yes—
831C2×C4C2×D8×C10312yes—
832C2×C4C2×D8×C10312yes—
833C2×C4C22×D4×C10311yescharacteristic
834C2×C4C22×D4×C10311yescharacteristic
835C2×C4C2×#41×C10311yescharacteristic
836C2×C4C2×#41×C10311yescharacteristic
837C2×C4H(5,𝔽2)×C10311yescharacteristic
838C2×C4H(5,𝔽2)×C10311yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22#459×C10314yescomplemented
879C22C2×#121×C10311yescharacteristic
880C22D42×C10311yescharacteristic
881C22#546×C10311yescharacteristic
882C22C22×D8×C10311yescharacteristic
883C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
884C22#576×C10311yescharacteristic
885C22#577×C10311yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4#525×C10311yescharacteristic
896C4#538×C10311yescharacteristic
897C4D42×C10311yescharacteristic
898C4#546×C10311yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2C103×#242411yescharacteristic
905C2C2×#459×C10311yescharacteristic
906C2C103×#304511yescharacteristic
907C2C103×#326511yescharacteristic
908C2D4×D8×C10311yescharacteristic
909C2C103×#329411yescharacteristic
910C2C103×#331811yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C103C2semidirect
2. C2×#459×C103C2semidirect
3. C2×#447×C103C2semidirect
4. C22×#102×C103C2semidirect
5. C103×#2433C2semidirect
6. C103×#2361C2semidirect
7. C103×#2067C2semidirect
8. C103×#2054C2semidirect
9. C103×#2041C2semidirect
10. C103×#2011C2semidirect
11. C103×#1982C2semidirect
12. C103×#1925C2semidirect
13. C103×#1879C2semidirect
14. C103×#1874C2semidirect
15. C103×#1850C2semidirect
19. C22×D8×C103C22semidirect
28. C2×C4×D4×C103C22semidirect
33. C2×#107×C103C22semidirect
34. C2×C4⋊C8×C103C22semidirect
35. C2×C4⋊C8×C103C22semidirect
43. C2×#102×C103C22semidirect
44. C2×#102×C103C22semidirect
45. C2×#102×C103C22semidirect
46. C2×#102×C103C22semidirect
52. #390×C103C22semidirect
53. #389×C103C22semidirect
57. C4×C4⋊C4×C103C22semidirect
59. #340×C103C22semidirect
60. #340×C103C22semidirect
61. #336×C103C22semidirect
62. #336×C103C22semidirect
107. #121×C103D4semidirect
147. #102×C103D4semidirect
272. C22⋊C4×C103D8semidirect
422. C22×C103#459semidirect
443. #25076C103direct (N × H)
456. C2×#466C2×C103semidirect
457. C2×#459C2×C103semidirect
458. C2×#447C2×C103semidirect
459. C22×#102C2×C103semidirect
460. #2433C2×C103semidirect
461. #2361C2×C103semidirect
462. #2067C2×C103semidirect
463. #2054C2×C103semidirect
464. #2041C2×C103semidirect
465. #2011C2×C103semidirect
466. #1982C2×C103semidirect
467. #1925C2×C103semidirect
468. #1879C2×C103semidirect
469. #1874C2×C103semidirect
470. #1850C2×C103semidirect
471. C103#25076direct (N × H)
475. C22×D8C22×C103semidirect
484. C2×C4×D4C22×C103semidirect
489. C2×#107C22×C103semidirect
490. C2×C4⋊C8C22×C103semidirect
491. C2×C4⋊C8C22×C103semidirect
499. C2×#102C22×C103semidirect
500. C2×#102C22×C103semidirect
501. C2×#102C22×C103semidirect
502. C2×#102C22×C103semidirect
508. #390C22×C103semidirect
509. #389C22×C103semidirect
513. C4×C4⋊C4C22×C103semidirect
515. #340C22×C103semidirect
516. #340C22×C103semidirect
517. #336C22×C103semidirect
518. #336C22×C103semidirect
563. #121D4×C103semidirect
603. #102D4×C103semidirect
728. C22⋊C4D8×C103semidirect
878. C22#459×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1032
C2×#459×C1032
C2×#447×C1032
C22×#102×C1032
C103×#24332
C103×#23612
C103×#20672
C103×#20542
C103×#20412
C103×#20112
C103×#19822
C103×#19252
C103×#18792
C103×#18742
C103×#18502
#25076103