Finite Group Databasebeta

← C103×#25508 #39930783

Subgroups — C103×#25508 #39930783

Order 26368.

1198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C103C211yesmaximal, characteristic, complemented
2C2×#469×C103C211yesmaximal, characteristic, complemented
3C2×#466×C103C211yesmaximal, characteristic, complemented
4C103×#2624C211yesmaximal, characteristic, complemented
5C103×#2059C211yesmaximal, characteristic, complemented
6C103×#2041C211yesmaximal, characteristic, complemented
7C103×#2025C211yesmaximal, characteristic, complemented
8C103×#2011C211yesmaximal, characteristic, complemented
9C103×#1895C211yesmaximal, characteristic, complemented
10C103×#1893C211yesmaximal, characteristic, complemented
11C103×#1879C211yesmaximal, characteristic, complemented
12C103×#1879C211yesmaximal, characteristic, complemented
13C103×#1864C211yesmaximal, characteristic, complemented
14C103×#1862C211yesmaximal, characteristic, complemented
15C103×#1729C211yesmaximal, characteristic, complemented
16C22×D8×C103C2211yescharacteristic
17C22×D8×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20#540×C103—24no—
21#540×C103—24no—
22C2×#127×C103C2211yescharacteristic
23C2×#125×C103C2211yescharacteristic
24C2×#123×C103—21no—
25C2×#123×C103—21no—
26C2×#121×C103—21no—
27C2×#121×C103—21no—
28C2×#121×C103C2211yescharacteristic
29C2×#121×C103C2211yescharacteristic
30C2×#121×C103C2211yescharacteristic
31C2×C4×D4×C103C2211yescharacteristic
32C2×C4×D4×C103C2211yescharacteristic
33C2×#117×C103C2211yescharacteristic
34#469×C103—24no—
35#466×C103—24no—
36C2×#107×C103C2211yescharacteristic
37C2×#106×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46#399×C103—21no—
47#397×C103—21no—
48#394×C103—21no—
49#394×C103—21no—
50#390×C103C2211yescharacteristic
51#390×C103C2211yescharacteristic
52#389×C103C2211yescharacteristic
53#389×C103C2211yescharacteristic
54#380×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60#336×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×D4×C103—21no—
64C22×D4×C103—21no—
65C22×D4×C103—21no—
66C22×D4×C103—21no—
67C22×D4×C103—21no—
68C22×D4×C103C2311yescharacteristic
69C22×D4×C103C2311yescharacteristic
70C22×D4×C103C2311yescharacteristic
71C23×C4×C103—21no—
72C23×C4×C103—21no—
73C23×C4×C103C2311yescharacteristic
74C2×D8×C103—22no—
75C2×D8×C103—22no—
76C2×D8×C103—22no—
77C2×D8×C103—22no—
78C2×D8×C103—41no—
79C2×D8×C103—41no—
80C2×M16×C103—22no—
81C2×M16×C103—22no—
82C2×M16×C103—41no—
83C22×C8×C103—22no—
84C22×C8×C103—22no—
85C22×C8×C103—41no—
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90#127×C103—22no—
91#127×C103—22no—
92#125×C103—22no—
93#125×C103—22no—
94#123×C103—28no—
95#123×C103—28no—
96#121×C103—28no—
97#121×C103—28no—
98#121×C103—22no—
99#121×C103—22no—
100#121×C103—22no—
101#121×C103—22no—
102#121×C103D414yes—
103#121×C103D414yes—
104C4×D4×C103—22no—
105C4×D4×C103—22no—
106C4×D4×C103—22no—
107C4×D4×C103—22no—
108#117×C103—22no—
109#117×C103—22no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—21no—
113C2×C4⋊C4×C103—21no—
114C2×C4⋊C4×C103D411yescharacteristic
115C2×C4⋊C4×C103D411yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
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×C103—21no—
131C2×C22⋊C4×C103D411yescharacteristic
132C2×C22⋊C4×C103D411yescharacteristic
133C2×C42×C103C2311yescharacteristic
134C2×C42×C103C2311yescharacteristic
135#107×C103—22no—
136#106×C103—22no—
137#102×C103—22no—
138#102×C103—22no—
139#102×C103—22no—
140#102×C103—22no—
141#102×C103—22no—
142#102×C103—22no—
143#102×C103—41no—
144#102×C103—41no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148C24×C103—21no—
149C24×C103—21no—
150C24×C103—21no—
151C24×C103C2×D411yescharacteristic
152C2×D4×C103—24no—
153C2×D4×C103—24no—
154C2×D4×C103—24no—
155C2×D4×C103—24no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
161C2×D4×C103—21no—
162C2×D4×C103—21no—
163C2×D4×C103—21no—
164C2×D4×C103—21no—
165C2×D4×C103—21no—
166C2×D4×C103—21no—
167C2×D4×C103—21no—
168C2×D4×C103—21no—
169C2×D4×C103—21no—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—42no—
173C2×D4×C103—81no—
174C2×D4×C103—81no—
175C2×D4×C103—81no—
176C2×D4×C103—81no—
177C2×D4×C103—81no—
178C2×D4×C103—81no—
179C2×D4×C103—81no—
180C2×D4×C103—81no—
181C2×D4×C103—81no—
182C2×D4×C103—81no—
183C2×D4×C103C2×D412yes—
184C2×D4×C103C2×D412yes—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—21no—
191C22×C4×C103—24no—
192C22×C4×C103—24no—
193C22×C4×C103—21no—
194C22×C4×C103—21no—
195C22×C4×C103—21no—
196C22×C4×C103—81no—
197C22×C4×C103—81no—
198C22×C4×C103—81no—
199C22×C4×C103—81no—
200C22×C4×C103C2×D411yescharacteristic
201C22×C4×C103C2×D411yescharacteristic
202C22×C4×C103C2×D411yescharacteristic
203C22×C4×C103C2×D411yescharacteristic
204C22×C4×C103C2×D411yescharacteristic
205C22×C4×C103C2×D412yes—
206C22×C4×C103C2×D412yes—
207C22×C4×C103C2411yescharacteristic
208D8×C103—44no—
209D8×C103—44no—
210M16×C103—44no—
211C2×C8×C103—21no—
212C2×C8×C103—21no—
213C2×C8×C103—21no—
214C2×C8×C103—21no—
215C2×C8×C103—21no—
216C2×C8×C103—21no—
217C2×C8×C103—21no—
218C2×C8×C103—21no—
219C2×C8×C103—21no—
220C2×C8×C103—21no—
221C2×C8×C103—44no—
222C2×C8×C103#4112yes—
223C2×C8×C103#4112yes—
224C4⋊C4×C103—24no—
225C4⋊C4×C103—24no—
226C4⋊C4×C103—22no—
227C4⋊C4×C103—22no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—21no—
233C4⋊C4×C103—21no—
234C4⋊C4×C103—21no—
235C4⋊C4×C103—21no—
236C4⋊C4×C103—81no—
237C4⋊C4×C103—81no—
238C4⋊C4×C103C2×D412yes—
239C4⋊C4×C103C2×D412yes—
240C22⋊C4×C103—24no—
241C22⋊C4×C103—24no—
242C22⋊C4×C103—22no—
243C22⋊C4×C103—22no—
244C22⋊C4×C103—24no—
245C22⋊C4×C103—24no—
246C22⋊C4×C103—42no—
247C22⋊C4×C103—81no—
248C22⋊C4×C103—81no—
249C22⋊C4×C103—81no—
250C22⋊C4×C103—81no—
251C22⋊C4×C103—81no—
252C42×C103—21no—
253C42×C103—21no—
254C42×C103—21no—
255C42×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—21no—
262C23×C103—22no—
263C23×C103—22no—
264C23×C103—41no—
265C23×C103—41no—
266C23×C103—41no—
267C23×C103—41no—
268C23×C103—41no—
269C23×C103—41no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103—41no—
273C23×C103—41no—
274C23×C103—41no—
275C23×C103—41no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103—41no—
279C23×C103—41no—
280C23×C103—41no—
281C23×C103—41no—
282C23×C103—41no—
283C23×C103#12012yes—
284C23×C103C22×D411yescharacteristic
285D4×C103—22no—
286D4×C103—22no—
287D4×C103—22no—
288D4×C103—22no—
289D4×C103—41no—
290D4×C103—41no—
291D4×C103—41no—
292D4×C103—41no—
293D4×C103—41no—
294D4×C103—41no—
295D4×C103—41no—
296D4×C103—41no—
297D4×C103—84no—
298D4×C103—84no—
299D4×C103—84no—
300D4×C103—84no—
301D4×C103—84no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—22no—
305C2×C4×C103—22no—
306C2×C4×C103—22no—
307C2×C4×C103—22no—
308C2×C4×C103—21no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
311C2×C4×C103—21no—
312C2×C4×C103—22no—
313C2×C4×C103—22no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
319C2×C4×C103—21no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—41no—
323C2×C4×C103—41no—
324C2×C4×C103—41no—
325C2×C4×C103—41no—
326C2×C4×C103—41no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—41no—
331C2×C4×C103—41no—
332C2×C4×C103—41no—
333C2×C4×C103—41no—
334C2×C4×C103—41no—
335C2×C4×C103—84no—
336C2×C4×C103—84no—
337C2×C4×C103#12012yes—
338C2×C4×C103C22×D411yescharacteristic
339C2×C4×C103C22×D411yescharacteristic
340C2×C4×C103C2×#4111yescharacteristic
341C2×C4×C103C2×#4111yescharacteristic
342C2×C4×C103H(5,𝔽2)11yescharacteristic
343C2×C4×C1032−1+411yescharacteristic
344C8×C103—22no—
345C8×C103—22no—
346C8×C103—41no—
347C8×C103—41no—
348C22×C103—22no—
349C22×C103—22no—
350C22×C103—22no—
351C22×C103—41no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—42no—
356C22×C103—42no—
357C22×C103—42no—
358C22×C103—42no—
359C22×C103—42no—
360C22×C103—42no—
361C22×C103—81no—
362C22×C103—81no—
363C22×C103—81no—
364C22×C103—81no—
365C22×C103—81no—
366C22×C103—81no—
367C22×C103—81no—
368C22×C103—81no—
369C22×C103—81no—
370C22×C103—81no—
371C22×C103—81no—
372C22×C103—81no—
373C22×C103—81no—
374C22×C103—81no—
375C22×C103—81no—
376C22×C103C2×#12011yescharacteristic
377C22×C103#53211yescharacteristic
378C22×C103#53711yescharacteristic
379C22×C103#57611yescharacteristic
380C22×C103#57611yescharacteristic
381C22×C103#57611yescharacteristic
382C22×C103#57711yescharacteristic
383C4×C103—22no—
384C4×C103—41no—
385C4×C103—41no—
386C4×C103—42no—
387C4×C103—41no—
388C4×C103—41no—
389C4×C103—42no—
390C4×C103—81no—
391C4×C103—81no—
392C4×C103—81no—
393C4×C103#54611yescharacteristic
394C4×C103#54611yescharacteristic
395C4×C103#54711yescharacteristic
396C4×C103#54711yescharacteristic
397#25508C10311yesmaximal, characteristic, direct product factor, Sylow
398C2×C103—42no—
399C2×C103—82no—
400C2×C103—82no—
401C2×C103—161no—
402C2×C103#243011yescharacteristic
403C2×C103#300811yescharacteristic
404C2×C103#301211yescharacteristic
405C2×C103#317611yescharacteristic
406C2×C103#317911yescharacteristic
407C2×C103#325711yescharacteristic
408C2×C103#325911yescharacteristic
409C2×#540C2×C10311yescharacteristic, complemented
410C2×#469C2×C10311yescharacteristic, complemented
411C2×#466C2×C10311yescharacteristic, complemented
412#2624C2×C10311yescharacteristic, complemented
413#2059C2×C10311yescharacteristic, complemented
414#2041C2×C10311yescharacteristic, complemented
415#2025C2×C10311yescharacteristic, complemented
416#2011C2×C10311yescharacteristic, complemented
417#1895C2×C10311yescharacteristic, complemented
418#1893C2×C10311yescharacteristic, complemented
419#1879C2×C10311yescharacteristic, complemented
420#1879C2×C10311yescharacteristic, complemented
421#1864C2×C10311yescharacteristic, complemented
422#1862C2×C10311yescharacteristic, complemented
423#1729C2×C10311yescharacteristic, complemented
424C103#2550811yescharacteristic, direct product factor, Sylow
425C22×D8C22×C10311yescharacteristic
426C22×D8C22×C10311yescharacteristic
427C22×M16C22×C10311yescharacteristic
428C23×C8C22×C10311yescharacteristic
429#540—24no—
430#540—24no—
431C2×#127C22×C10311yescharacteristic
432C2×#125C22×C10311yescharacteristic
433C2×#123—21no—
434C2×#123—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C10311yescharacteristic
438C2×#121C22×C10311yescharacteristic
439C2×#121C22×C10311yescharacteristic
440C2×C4×D4C22×C10311yescharacteristic
441C2×C4×D4C22×C10311yescharacteristic
442C2×#117C22×C10311yescharacteristic
443#469—24no—
444#466—24no—
445C2×#107C22×C10311yescharacteristic
446C2×#106C22×C10311yescharacteristic
447C2×#102C22×C10311yescharacteristic
448C2×#102C22×C10311yescharacteristic
449C2×#102C22×C10311yescharacteristic
450C2×#102C22×C10311yescharacteristic
451C2×#102C22×C10311yescharacteristic
452C2×#102C22×C10311yescharacteristic
453C2×#102C22×C10311yescharacteristic
454C2×#102C22×C10311yescharacteristic
455#399—21no—
456#397—21no—
457#394—21no—
458#394—21no—
459#390C22×C10311yescharacteristic
460#390C22×C10311yescharacteristic
461#389C22×C10311yescharacteristic
462#389C22×C10311yescharacteristic
463#380C22×C10311yescharacteristic
464#340C22×C10311yescharacteristic
465#340C22×C10311yescharacteristic
466#340C22×C10311yescharacteristic
467#340C22×C10311yescharacteristic
468#336C22×C10311yescharacteristic
469#336C22×C10311yescharacteristic
470#336C22×C10311yescharacteristic
471#336C22×C10311yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C10311yescharacteristic
478C22×D4C23×C10311yescharacteristic
479C22×D4C23×C10311yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C10311yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8C23×C10311yescharacteristic
496C22×C8C23×C10311yescharacteristic
497C22×C8C23×C10311yescharacteristic
498C22×C8C23×C10311yescharacteristic
499#127—22no—
500#127—22no—
501#125—22no—
502#125—22no—
503#123—28no—
504#123—28no—
505#121—28no—
506#121—28no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121D4×C10314yes—
512#121D4×C10314yes—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C10311yescharacteristic
524C2×C4⋊C4D4×C10311yescharacteristic
525C2×C4⋊C4C23×C10311yescharacteristic
526C2×C4⋊C4C23×C10311yescharacteristic
527C2×C4⋊C4C23×C10311yescharacteristic
528C2×C4⋊C4C23×C10311yescharacteristic
529C2×C4⋊C4C23×C10311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4D4×C10311yescharacteristic
541C2×C22⋊C4D4×C10311yescharacteristic
542C2×C42C23×C10311yescharacteristic
543C2×C42C23×C10311yescharacteristic
544#107—22no—
545#106—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C10311yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C10312yes—
593C2×D4C2×D4×C10312yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C10311yescharacteristic
610C22×C4C2×D4×C10311yescharacteristic
611C22×C4C2×D4×C10311yescharacteristic
612C22×C4C2×D4×C10311yescharacteristic
613C22×C4C2×D4×C10311yescharacteristic
614C22×C4C2×D4×C10312yes—
615C22×C4C2×D4×C10312yes—
616C22×C4C24×C10311yescharacteristic
617D8—44no—
618D8—44no—
619M16—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—44no—
631C2×C8#41×C10312yes—
632C2×C8#41×C10312yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C10312yes—
648C4⋊C4C2×D4×C10312yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23#120×C10312yes—
693C23C22×D4×C10311yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#120×C10312yes—
747C2×C4C22×D4×C10311yescharacteristic
748C2×C4C22×D4×C10311yescharacteristic
749C2×C4C2×#41×C10311yescharacteristic
750C2×C4C2×#41×C10311yescharacteristic
751C2×C4H(5,𝔽2)×C10311yescharacteristic
752C2×C42−1+4×C10311yescharacteristic
753C8—22no—
754C8—22no—
755C8—41no—
756C8—41no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C10311yescharacteristic
786C22#532×C10311yescharacteristic
787C22#537×C10311yescharacteristic
788C22#576×C10311yescharacteristic
789C22#576×C10311yescharacteristic
790C22#576×C10311yescharacteristic
791C22#577×C10311yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C10311yescharacteristic
803C4#546×C10311yescharacteristic
804C4#547×C10311yescharacteristic
805C4#547×C10311yescharacteristic
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2C103×#243011yescharacteristic
811C2C103×#300811yescharacteristic
812C2C103×#301211yescharacteristic
813C2C103×#317611yescharacteristic
814C2C103×#317911yescharacteristic
815C2C103×#325711yescharacteristic
816C2C103×#325911yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C103C2semidirect
2. C2×#469×C103C2semidirect
3. C2×#466×C103C2semidirect
4. C103×#2624C2semidirect
5. C103×#2059C2semidirect
6. C103×#2041C2semidirect
7. C103×#2025C2semidirect
8. C103×#2011C2semidirect
9. C103×#1895C2semidirect
10. C103×#1893C2semidirect
11. C103×#1879C2semidirect
12. C103×#1879C2semidirect
13. C103×#1864C2semidirect
14. C103×#1862C2semidirect
15. C103×#1729C2semidirect
397. #25508C103direct (N × H)
409. C2×#540C2×C103semidirect
410. C2×#469C2×C103semidirect
411. C2×#466C2×C103semidirect
412. #2624C2×C103semidirect
413. #2059C2×C103semidirect
414. #2041C2×C103semidirect
415. #2025C2×C103semidirect
416. #2011C2×C103semidirect
417. #1895C2×C103semidirect
418. #1893C2×C103semidirect
419. #1879C2×C103semidirect
420. #1879C2×C103semidirect
421. #1864C2×C103semidirect
422. #1862C2×C103semidirect
423. #1729C2×C103semidirect
424. C103#25508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#540×C1032
C2×#469×C1032
C2×#466×C1032
C103×#26242
C103×#20592
C103×#20412
C103×#20252
C103×#20112
C103×#18952
C103×#18932
C103×#18792
C103×#18642
C103×#18622
C103×#17292
#25508103