Finite Group Databasebeta

← C103×#24364 #39929639

Subgroups — C103×#24364 #39929639

Order 26368.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C103C211yesmaximal, characteristic, complemented
2C2×#463×C103C211yesmaximal, characteristic, complemented
3C2×#459×C103C211yesmaximal, characteristic, complemented
4C2×#449×C103C211yesmaximal, characteristic, complemented
5C103×#2431C211yesmaximal, characteristic, complemented
6C103×#2339C211yesmaximal, characteristic, complemented
7C103×#2056C211yesmaximal, characteristic, complemented
8C103×#2055C211yesmaximal, characteristic, complemented
9C103×#2015C211yesmaximal, characteristic, complemented
10C103×#2014C211yesmaximal, characteristic, complemented
11C103×#1893C211yesmaximal, characteristic, complemented
12C103×#1879C211yesmaximal, characteristic, complemented
13C103×#1877C211yesmaximal, characteristic, complemented
14C103×#1850C211yesmaximal, characteristic, complemented
15C103×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C2×#135×C103—24no—
19C2×#135×C103—24no—
20C2×#135×C103—24no—
21C22×Q16×C103C2211yescharacteristic
22C22×SD16×C103C2211yescharacteristic
23C22×SD16×C103C2211yescharacteristic
24C22×SD16×C103C2211yescharacteristic
25C22×D8×C103C2211yescharacteristic
26C22×D8×C103C2211yescharacteristic
27C23×C8×C103C2211yescharacteristic
28C2×#127×C103C2211yescharacteristic
29C2×#124×C103C2211yescharacteristic
30C2×#121×C103C2211yescharacteristic
31C2×C4×D4×C103C2211yescharacteristic
32C2×C4×D4×C103C2211yescharacteristic
33#463×C103—24no—
34#459×C103—24no—
35#449×C103—24no—
36C2×C4⋊C8×C103C2211yescharacteristic
37C2×C4⋊C8×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#102×C103C2211yescharacteristic
45C2×#102×C103C2211yescharacteristic
46C2×C22⋊C8×C103C2211yescharacteristic
47#392×C103—21no—
48#392×C103—21no—
49#391×C103C2211yescharacteristic
50#391×C103C2211yescharacteristic
51#391×C103C2211yescharacteristic
52#390×C103C2211yescharacteristic
53#386×C103—21no—
54#386×C103—21no—
55#386×C103—21no—
56#386×C103—21no—
57#381×C103—21no—
58#380×C103C2211yescharacteristic
59C4×C22⋊C4×C103C2211yescharacteristic
60C2×#95×C103—21no—
61#340×C103C2211yescharacteristic
62#340×C103C2211yescharacteristic
63#336×C103C2211yescharacteristic
64#336×C103C2211yescharacteristic
65C2×#41×C103—22no—
66C2×#41×C103—22no—
67C2×#41×C103—22no—
68C2×#41×C103—22no—
69C2×#41×C103—22no—
70C2×#41×C103—22no—
71C2×#41×C103—22no—
72C2×#41×C103—41no—
73C2×#41×C103—41no—
74C2×#41×C103—41no—
75C2×#41×C103—41no—
76C2×#41×C103D414yescomplemented
77C22×Q8×C103C2311yescharacteristic
78C22×Q8×C103C2311yescharacteristic
79C22×D4×C103—21no—
80C22×D4×C103—21no—
81C22×D4×C103—21no—
82C22×D4×C103—21no—
83C22×D4×C103—21no—
84C22×D4×C103C2311yescharacteristic
85C22×D4×C103C2311yescharacteristic
86C22×D4×C103C2311yescharacteristic
87C23×C4×C103—21no—
88C23×C4×C103—21no—
89C23×C4×C103—21no—
90C23×C4×C103—21no—
91C23×C4×C103C2311yescharacteristic
92#135×C103—232no—
93C2×Q16×C103—22no—
94C2×Q16×C103—22no—
95C2×Q16×C103—22no—
96C2×SD16×C103—22no—
97C2×SD16×C103—22no—
98C2×SD16×C103—22no—
99C2×SD16×C103—22no—
100C2×SD16×C103—22no—
101C2×SD16×C103—22no—
102C2×SD16×C103—41no—
103C2×SD16×C103—41no—
104C2×SD16×C103D414yescomplemented
105C2×D8×C103—22no—
106C2×D8×C103—22no—
107C2×D8×C103—22no—
108C2×D8×C103—22no—
109C2×D8×C103—22no—
110C2×D8×C103D414yescomplemented
111C22×C8×C103—22no—
112C22×C8×C103—22no—
113C22×C8×C103—22no—
114C22×C8×C103C2311yescharacteristic
115C22×C8×C103C2311yescharacteristic
116C22×C8×C103C2311yescharacteristic
117C22×C8×C103C2311yescharacteristic
118#127×C103—22no—
119#127×C103—41no—
120#124×C103—22no—
121#124×C103—41no—
122#121×C103—22no—
123#121×C103—22no—
124C4×D4×C103—22no—
125C4×D4×C103—22no—
126C4×D4×C103—41no—
127C4×D4×C103—41no—
128C2×C4⋊C4×C103C2311yescharacteristic
129C2×C4⋊C4×C103C2311yescharacteristic
130C2×C4⋊C4×C103C2311yescharacteristic
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103—21no—
135C2×C22⋊C4×C103—21no—
136C2×C22⋊C4×C103—21no—
137C2×C22⋊C4×C103—21no—
138C2×C22⋊C4×C103—21no—
139C2×C22⋊C4×C103D411yescharacteristic
140C2×C22⋊C4×C103D411yescharacteristic
141C2×C42×C103C2311yescharacteristic
142C2×C42×C103C2311yescharacteristic
143C4⋊C8×C103—22no—
144C4⋊C8×C103—22no—
145#103×C103—22no—
146#103×C103—22no—
147#103×C103—41no—
148#102×C103—22no—
149#102×C103—22no—
150#102×C103—22no—
151#102×C103—22no—
152#102×C103—41no—
153C22⋊C8×C103—22no—
154#95×C103—21no—
155#95×C103—21no—
156#95×C103—21no—
157#95×C103—21no—
158#95×C103—21no—
159#95×C103—21no—
160#95×C103—21no—
161#95×C103D411yescharacteristic
162#95×C103D411yescharacteristic
163C24×C103—21no—
164C24×C103—21no—
165C24×C103—21no—
166C24×C103C2×D411yescharacteristic
167#41×C103—28no—
168#41×C103—28no—
169#41×C103—44no—
170#41×C103—44no—
171#41×C103—44no—
172#41×C103—44no—
173#41×C103—44no—
174#41×C103—44no—
175C2×Q8×C103—21no—
176C2×Q8×C103—21no—
177C2×Q8×C103—21no—
178C2×Q8×C103—21no—
179C2×Q8×C103—21no—
180C2×Q8×C103—21no—
181C2×Q8×C103—21no—
182C2×Q8×C103—21no—
183C2×Q8×C103—21no—
184C2×Q8×C103—21no—
185C2×Q8×C103C2×D412yes—
186C2×Q8×C103C2×D412yes—
187C2×D4×C103—24no—
188C2×D4×C103—21no—
189C2×D4×C103—21no—
190C2×D4×C103—21no—
191C2×D4×C103—21no—
192C2×D4×C103—21no—
193C2×D4×C103—21no—
194C2×D4×C103—21no—
195C2×D4×C103—21no—
196C2×D4×C103—21no—
197C2×D4×C103—21no—
198C2×D4×C103—21no—
199C2×D4×C103—21no—
200C2×D4×C103—21no—
201C2×D4×C103—21no—
202C2×D4×C103—42no—
203C2×D4×C103—42no—
204C2×D4×C103—42no—
205C2×D4×C103—42no—
206C2×D4×C103—42no—
207C2×D4×C103—42no—
208C2×D4×C103—42no—
209C2×D4×C103—42no—
210C2×D4×C103—42no—
211C2×D4×C103—42no—
212C2×D4×C103—81no—
213C2×D4×C103—81no—
214C2×D4×C103—81no—
215C2×D4×C103—81no—
216C2×D4×C103C2×D412yes—
217C2×D4×C103C2×D412yes—
218C2×D4×C103C2×D412yes—
219C2×D4×C103C2×D412yes—
220C22×C4×C103—21no—
221C22×C4×C103—21no—
222C22×C4×C103—21no—
223C22×C4×C103—21no—
224C22×C4×C103—21no—
225C22×C4×C103—21no—
226C22×C4×C103—24no—
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×C103—42no—
235C22×C4×C103—42no—
236C22×C4×C103—42no—
237C22×C4×C103—42no—
238C22×C4×C103—42no—
239C22×C4×C103—81no—
240C22×C4×C103—81no—
241C22×C4×C103C2×D411yescharacteristic
242C22×C4×C103C2×D411yescharacteristic
243C22×C4×C103C2×D411yescharacteristic
244C22×C4×C103C2×D411yescharacteristic
245C22×C4×C103C2×D412yes—
246C22×C4×C103C2×D411yescharacteristic
247C22×C4×C103#4112yes—
248C22×C4×C103C2411yescharacteristic
249Q16×C103—28no—
250SD16×C103—28no—
251SD16×C103—28no—
252SD16×C103—44no—
253D8×C103—28no—
254D8×C103—44no—
255C2×C8×C103—28no—
256C2×C8×C103—21no—
257C2×C8×C103—21no—
258C2×C8×C103—21no—
259C2×C8×C103—21no—
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×C103C2×D412yes—
267C2×C8×C103C2×D412yes—
268C4⋊C4×C103—21no—
269C4⋊C4×C103—21no—
270C4⋊C4×C103—21no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103—21no—
273C4⋊C4×C103—21no—
274C22⋊C4×C103—22no—
275C22⋊C4×C103—41no—
276C22⋊C4×C103—42no—
277C22⋊C4×C103—42no—
278C22⋊C4×C103—42no—
279C22⋊C4×C103—42no—
280C22⋊C4×C103—42no—
281C22⋊C4×C103—81no—
282C22⋊C4×C103—81no—
283C22⋊C4×C103—81no—
284C42×C103—21no—
285C42×C103—21no—
286C42×C103—21no—
287C42×C103—21no—
288C23×C103—22no—
289C23×C103—22no—
290C23×C103—22no—
291C23×C103—21no—
292C23×C103—21no—
293C23×C103—21no—
294C23×C103—21no—
295C23×C103—21no—
296C23×C103—21no—
297C23×C103—22no—
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—41no—
312C23×C103—41no—
313C23×C103—41no—
314C23×C103—41no—
315C23×C103#12112yes—
316C23×C103C22×D411yescharacteristic
317Q8×C103—22no—
318Q8×C103—22no—
319Q8×C103—22no—
320Q8×C103—22no—
321Q8×C103—41no—
322Q8×C103—41no—
323Q8×C103—41no—
324Q8×C103—41no—
325D4×C103—22no—
326D4×C103—22no—
327D4×C103—22no—
328D4×C103—22no—
329D4×C103—22no—
330D4×C103—48no—
331D4×C103—48no—
332D4×C103—41no—
333D4×C103—41no—
334D4×C103—41no—
335D4×C103—41no—
336D4×C103—41no—
337D4×C103—41no—
338D4×C103—84no—
339D4×C103—84no—
340D4×C103—84no—
341D4×C103#12014yes—
342C2×C4×C103—21no—
343C2×C4×C103—21no—
344C2×C4×C103—21no—
345C2×C4×C103—21no—
346C2×C4×C103—22no—
347C2×C4×C103—22no—
348C2×C4×C103—22no—
349C2×C4×C103—22no—
350C2×C4×C103—22no—
351C2×C4×C103—21no—
352C2×C4×C103—21no—
353C2×C4×C103—21no—
354C2×C4×C103—22no—
355C2×C4×C103—21no—
356C2×C4×C103—21no—
357C2×C4×C103—21no—
358C2×C4×C103—21no—
359C2×C4×C103—21no—
360C2×C4×C103—21no—
361C2×C4×C103—48no—
362C2×C4×C103—48no—
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—41no—
373C2×C4×C103—41no—
374C2×C4×C103—41no—
375C2×C4×C103—41no—
376C2×C4×C103—84no—
377C2×C4×C103—84no—
378C2×C4×C103#12112yes—
379C2×C4×C103#13512yescomplemented
380C2×C4×C103C22×D411yescharacteristic
381C2×C4×C103C22×D411yescharacteristic
382C2×C4×C103C22×D411yescharacteristic
383C2×C4×C103C2×#4111yescharacteristic
384C2×C4×C103H(5,𝔽2)11yescharacteristic
385C2×C4×C103H(5,𝔽2)11yescharacteristic
386C8×C103—22no—
387C8×C103—22no—
388C8×C103—41no—
389C8×C103—41no—
390C22×C103—22no—
391C22×C103—24no—
392C22×C103—22no—
393C22×C103—22no—
394C22×C103—41no—
395C22×C103—42no—
396C22×C103—42no—
397C22×C103—41no—
398C22×C103—42no—
399C22×C103—41no—
400C22×C103—41no—
401C22×C103—42no—
402C22×C103—42no—
403C22×C103—42no—
404C22×C103—42no—
405C22×C103—42no—
406C22×C103—42no—
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×C103C2×#12111yescharacteristic
419C22×C103D4211yescharacteristic
420C22×C103D4211yescharacteristic
421C22×C103C2×#13511yescharacteristic
422C22×C103#57511yescharacteristic
423C22×C103#57611yescharacteristic
424C22×C103#57711yescharacteristic
425C4×C103—22no—
426C4×C103—22no—
427C4×C103—42no—
428C4×C103—42no—
429C4×C103—41no—
430C4×C103—41no—
431C4×C103—41no—
432C4×C103—81no—
433C4×C103—81no—
434C4×C103—81no—
435C4×C103C2×#12011yescharacteristic
436C4×C103#53411yescharacteristic
437C4×C103#54611yescharacteristic
438C4×C103#54611yescharacteristic
439#24364C10311yesmaximal, characteristic, direct product factor, Sylow
440C2×C103—42no—
441C2×C103—44no—
442C2×C103—82no—
443C2×C103—161no—
444C2×C103#241011yescharacteristic
445C2×C103#303511yescharacteristic
446C2×C103#304511yescharacteristic
447C2×C103#326711yescharacteristic
448C2×C103#326811yescharacteristic
449C2×C103#328011yescharacteristic
450C2×C103#328411yescharacteristic
451C22×#135C2×C10311yescharacteristic, complemented
452C2×#463C2×C10311yescharacteristic, complemented
453C2×#459C2×C10311yescharacteristic, complemented
454C2×#449C2×C10311yescharacteristic, complemented
455#2431C2×C10311yescharacteristic, complemented
456#2339C2×C10311yescharacteristic, complemented
457#2056C2×C10311yescharacteristic, complemented
458#2055C2×C10311yescharacteristic, complemented
459#2015C2×C10311yescharacteristic, complemented
460#2014C2×C10311yescharacteristic, complemented
461#1893C2×C10311yescharacteristic, complemented
462#1879C2×C10311yescharacteristic, complemented
463#1877C2×C10311yescharacteristic, complemented
464#1850C2×C10311yescharacteristic, complemented
465#1788C2×C10311yescharacteristic, complemented
466C103#2436411yescharacteristic, direct product factor, Sylow
467C22×#41C22×C10311yescharacteristic
468C22×#41C22×C10311yescharacteristic
469C2×#135—24no—
470C2×#135—24no—
471C2×#135—24no—
472C22×Q16C22×C10311yescharacteristic
473C22×SD16C22×C10311yescharacteristic
474C22×SD16C22×C10311yescharacteristic
475C22×SD16C22×C10311yescharacteristic
476C22×D8C22×C10311yescharacteristic
477C22×D8C22×C10311yescharacteristic
478C23×C8C22×C10311yescharacteristic
479C2×#127C22×C10311yescharacteristic
480C2×#124C22×C10311yescharacteristic
481C2×#121C22×C10311yescharacteristic
482C2×C4×D4C22×C10311yescharacteristic
483C2×C4×D4C22×C10311yescharacteristic
484#463—24no—
485#459—24no—
486#449—24no—
487C2×C4⋊C8C22×C10311yescharacteristic
488C2×C4⋊C8C22×C10311yescharacteristic
489C2×#103C22×C10311yescharacteristic
490C2×#103C22×C10311yescharacteristic
491C2×#103C22×C10311yescharacteristic
492C2×#102C22×C10311yescharacteristic
493C2×#102C22×C10311yescharacteristic
494C2×#102C22×C10311yescharacteristic
495C2×#102C22×C10311yescharacteristic
496C2×#102C22×C10311yescharacteristic
497C2×C22⋊C8C22×C10311yescharacteristic
498#392—21no—
499#392—21no—
500#391C22×C10311yescharacteristic
501#391C22×C10311yescharacteristic
502#391C22×C10311yescharacteristic
503#390C22×C10311yescharacteristic
504#386—21no—
505#386—21no—
506#386—21no—
507#386—21no—
508#381—21no—
509#380C22×C10311yescharacteristic
510C4×C22⋊C4C22×C10311yescharacteristic
511C2×#95—21no—
512#340C22×C10311yescharacteristic
513#340C22×C10311yescharacteristic
514#336C22×C10311yescharacteristic
515#336C22×C10311yescharacteristic
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41D4×C10314yescomplemented
528C22×Q8C23×C10311yescharacteristic
529C22×Q8C23×C10311yescharacteristic
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4C23×C10311yescharacteristic
536C22×D4C23×C10311yescharacteristic
537C22×D4C23×C10311yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C23×C10311yescharacteristic
543#135—232no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16D4×C10314yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8D4×C10314yescomplemented
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8C23×C10311yescharacteristic
566C22×C8C23×C10311yescharacteristic
567C22×C8C23×C10311yescharacteristic
568C22×C8C23×C10311yescharacteristic
569#127—22no—
570#127—41no—
571#124—22no—
572#124—41no—
573#121—22no—
574#121—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C2×C4⋊C4C23×C10311yescharacteristic
580C2×C4⋊C4C23×C10311yescharacteristic
581C2×C4⋊C4C23×C10311yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C10311yescharacteristic
591C2×C22⋊C4D4×C10311yescharacteristic
592C2×C42C23×C10311yescharacteristic
593C2×C42C23×C10311yescharacteristic
594C4⋊C8—22no—
595C4⋊C8—22no—
596#103—22no—
597#103—22no—
598#103—41no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95D4×C10311yescharacteristic
613#95D4×C10311yescharacteristic
614C24—21no—
615C24—21no—
616C24—21no—
617C24C2×D4×C10311yescharacteristic
618#41—28no—
619#41—28no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×D4×C10312yes—
637C2×Q8C2×D4×C10312yes—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
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×D4C2×D4×C10312yes—
670C2×D4C2×D4×C10312yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—81no—
691C22×C4—81no—
692C22×C4C2×D4×C10311yescharacteristic
693C22×C4C2×D4×C10311yescharacteristic
694C22×C4C2×D4×C10311yescharacteristic
695C22×C4C2×D4×C10311yescharacteristic
696C22×C4C2×D4×C10312yes—
697C22×C4C2×D4×C10311yescharacteristic
698C22×C4#41×C10312yes—
699C22×C4C24×C10311yescharacteristic
700Q16—28no—
701SD16—28no—
702SD16—28no—
703SD16—44no—
704D8—28no—
705D8—44no—
706C2×C8—28no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8C2×D4×C10312yes—
718C2×C8C2×D4×C10312yes—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—41no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—81no—
733C22⋊C4—81no—
734C22⋊C4—81no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
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#121×C10312yes—
767C23C22×D4×C10311yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4#120×C10314yes—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
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—84no—
828C2×C4—84no—
829C2×C4#121×C10312yes—
830C2×C4#135×C10312yescomplemented
831C2×C4C22×D4×C10311yescharacteristic
832C2×C4C22×D4×C10311yescharacteristic
833C2×C4C22×D4×C10311yescharacteristic
834C2×C4C2×#41×C10311yescharacteristic
835C2×C4H(5,𝔽2)×C10311yescharacteristic
836C2×C4H(5,𝔽2)×C10311yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—24no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×#121×C10311yescharacteristic
870C22D42×C10311yescharacteristic
871C22D42×C10311yescharacteristic
872C22C2×#135×C10311yescharacteristic
873C22#575×C10311yescharacteristic
874C22#576×C10311yescharacteristic
875C22#577×C10311yescharacteristic
876C4—22no—
877C4—22no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—42no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4C2×#120×C10311yescharacteristic
887C4#534×C10311yescharacteristic
888C4#546×C10311yescharacteristic
889C4#546×C10311yescharacteristic
890C2—42no—
891C2—44no—
892C2—82no—
893C2—161no—
894C2C103×#241011yescharacteristic
895C2C103×#303511yescharacteristic
896C2C103×#304511yescharacteristic
897C2C103×#326711yescharacteristic
898C2C103×#326811yescharacteristic
899C2C103×#328011yescharacteristic
900C2C103×#328411yescharacteristic
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. C22×#135×C103C2semidirect
2. C2×#463×C103C2semidirect
3. C2×#459×C103C2semidirect
4. C2×#449×C103C2semidirect
5. C103×#2431C2semidirect
6. C103×#2339C2semidirect
7. C103×#2056C2semidirect
8. C103×#2055C2semidirect
9. C103×#2015C2semidirect
10. C103×#2014C2semidirect
11. C103×#1893C2semidirect
12. C103×#1879C2semidirect
13. C103×#1877C2semidirect
14. C103×#1850C2semidirect
15. C103×#1788C2semidirect
76. C2×#41×C103D4semidirect
104. C2×SD16×C103D4semidirect
110. C2×D8×C103D4semidirect
379. C2×C4×C103#135semidirect
439. #24364C103direct (N × H)
451. C22×#135C2×C103semidirect
452. C2×#463C2×C103semidirect
453. C2×#459C2×C103semidirect
454. C2×#449C2×C103semidirect
455. #2431C2×C103semidirect
456. #2339C2×C103semidirect
457. #2056C2×C103semidirect
458. #2055C2×C103semidirect
459. #2015C2×C103semidirect
460. #2014C2×C103semidirect
461. #1893C2×C103semidirect
462. #1879C2×C103semidirect
463. #1877C2×C103semidirect
464. #1850C2×C103semidirect
465. #1788C2×C103semidirect
466. C103#24364direct (N × H)
527. C2×#41D4×C103semidirect
555. C2×SD16D4×C103semidirect
561. C2×D8D4×C103semidirect
830. C2×C4#135×C103semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1032
C2×#463×C1032
C2×#459×C1032
C2×#449×C1032
C103×#24312
C103×#23392
C103×#20562
C103×#20552
C103×#20152
C103×#20142
C103×#18932
C103×#18792
C103×#18772
C103×#18502
C103×#17882
#24364103