Finite Group Databasebeta

← C113×#24394 #43292414

Subgroups — C113×#24394 #43292414

Order 28928.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C113C211yesmaximal, characteristic
2C2×#468×C113C211yesmaximal, characteristic, complemented
3C2×#465×C113C211yesmaximal, characteristic, complemented
4C2×#450×C113C211yesmaximal, characteristic, complemented
5C2×#408×C113C211yesmaximal, characteristic, complemented
6C113×#2616C211yesmaximal, characteristic, complemented
7C113×#2034C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1895C211yesmaximal, characteristic, complemented
12C113×#1893C211yesmaximal, characteristic, complemented
13C113×#1873C211yesmaximal, characteristic, complemented
14C113×#1854C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic, complemented
21C23×C8×C113C2211yescharacteristic, complemented
22#535×C113—24no—
23#535×C113—24no—
24C2×#127×C113—21no—
25C2×#124×C113—21no—
26C2×C22⋊Q8×C113C2211yescharacteristic
27C2×C22⋊Q8×C113C2211yescharacteristic, complemented
28C2×C22⋊Q8×C113C2211yescharacteristic, complemented
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×#121×C113C2211yescharacteristic
32C2×#121×C113C2211yescharacteristic
33C2×#120×C113—21no—
34C2×#120×C113—21no—
35C2×#117×C113C2211yescharacteristic
36#468×C113—24no—
37#465×C113—24no—
38#450×C113—24no—
39C2×#107×C113C2211yescharacteristic, complemented
40C2×#106×C113C2211yescharacteristic, complemented
41C2×#103×C113C2211yescharacteristic, complemented
42C2×#103×C113C2211yescharacteristic, complemented
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49#408×C113—24no—
50C2×C22⋊C8×C113C2211yescharacteristic
51C2×C22⋊C8×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic, complemented
53C2×C22⋊C8×C113C2211yescharacteristic, complemented
54#395×C113—21no—
55#394×C113—21no—
56#394×C113—21no—
57#394×C113—21no—
58#380×C113C2211yescharacteristic
59#380×C113C2211yescharacteristic, complemented
60#380×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#340×C113C2211yescharacteristic, complemented
63#340×C113C2211yescharacteristic, complemented
64#340×C113C2211yescharacteristic, complemented
65C25×C113—21no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—41no—
71C2×#41×C113—41no—
72C22×Q8×C113D411yescharacteristic
73C22×Q8×C113C2311yescharacteristic
74C22×D4×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—22no—
79C22×D4×C113—22no—
80C22×D4×C113—21no—
81C22×D4×C113—22no—
82C22×D4×C113—22no—
83C22×D4×C113—41no—
84C22×D4×C113—41no—
85C22×D4×C113D411yescharacteristic
86C22×D4×C113D411yescharacteristic
87C22×D4×C113D411yescharacteristic
88C22×D4×C113C2311yescharacteristic
89C22×D4×C113C2311yescharacteristic
90C23×C4×C113C2311yescharacteristic
91C23×C4×C113C2311yescharacteristic
92C23×C4×C113C2311yescharacteristic
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—41no—
98C2×SD16×C113—41no—
99C2×M16×C113—22no—
100C2×M16×C113—22no—
101C2×M16×C113—41no—
102C22×C8×C113—22no—
103C22×C8×C113—22no—
104C22×C8×C113—41no—
105C22×C8×C113C2311yescharacteristic
106C22×C8×C113C2311yescharacteristic
107C22×C8×C113C2311yescharacteristic
108C22×C8×C113C2311yescharacteristic
109#127×C113—28no—
110#124×C113—28no—
111C22⋊Q8×C113—22no—
112C22⋊Q8×C113—22no—
113C22⋊Q8×C113—22no—
114C22⋊Q8×C113—22no—
115C22⋊Q8×C113—41no—
116C22⋊Q8×C113—41no—
117#121×C113—22no—
118#121×C113—22no—
119#121×C113—22no—
120#121×C113—22no—
121#121×C113—22no—
122#121×C113—22no—
123#121×C113D414yes—
124#121×C113D414yes—
125#120×C113—28no—
126#120×C113—28no—
127#117×C113—22no—
128#117×C113—22no—
129C2×C4⋊C4×C113—21no—
130C2×C4⋊C4×C113—21no—
131C2×C4⋊C4×C113—21no—
132C2×C4⋊C4×C113C2311yescharacteristic
133C2×C4⋊C4×C113C2311yescharacteristic
134C2×C4⋊C4×C113C2311yescharacteristic
135C2×C4⋊C4×C113C2311yescharacteristic
136C2×C4⋊C4×C113C2311yescharacteristic
137C2×C22⋊C4×C113—21no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113—21no—
144C2×C22⋊C4×C113—21no—
145C2×C22⋊C4×C113—21no—
146C2×C22⋊C4×C113—21no—
147C2×C22⋊C4×C113—21no—
148C2×C42×C113—21no—
149#107×C113—22no—
150#106×C113—22no—
151#103×C113—22no—
152#103×C113—22no—
153#102×C113—22no—
154#102×C113—22no—
155#102×C113—22no—
156#102×C113—22no—
157#102×C113—41no—
158#102×C113—41no—
159C22⋊C8×C113—22no—
160C22⋊C8×C113—22no—
161C22⋊C8×C113—22no—
162C22⋊C8×C113D414yescomplemented
163#95×C113—21no—
164#95×C113—21no—
165#95×C113—21no—
166C24×C113—24no—
167C24×C113—21no—
168C24×C113—21no—
169C24×C113—42no—
170C24×C113—42no—
171C24×C113—81no—
172C24×C113—81no—
173C24×C113—81no—
174C24×C113—81no—
175C24×C113C2×D411yescharacteristic
176C24×C113C2×D411yescharacteristic
177C24×C113C2×D411yescharacteristic
178#41×C113—44no—
179#41×C113—44no—
180#41×C113—44no—
181#41×C113—44no—
182C2×Q8×C113—22no—
183C2×Q8×C113—22no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113—21no—
188C2×Q8×C113—21no—
189C2×Q8×C113—21no—
190C2×Q8×C113—41no—
191C2×D4×C113—24no—
192C2×D4×C113—22no—
193C2×D4×C113—22no—
194C2×D4×C113—22no—
195C2×D4×C113—22no—
196C2×D4×C113—24no—
197C2×D4×C113—24no—
198C2×D4×C113—24no—
199C2×D4×C113—24no—
200C2×D4×C113—22no—
201C2×D4×C113—22no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—21no—
207C2×D4×C113—21no—
208C2×D4×C113—21no—
209C2×D4×C113—21no—
210C2×D4×C113—21no—
211C2×D4×C113—21no—
212C2×D4×C113—44no—
213C2×D4×C113—44no—
214C2×D4×C113—44no—
215C2×D4×C113—44no—
216C2×D4×C113—41no—
217C2×D4×C113—41no—
218C2×D4×C113—41no—
219C2×D4×C113—42no—
220C2×D4×C113—42no—
221C2×D4×C113—81no—
222C2×D4×C113—81no—
223C2×D4×C113—81no—
224C2×D4×C113—81no—
225C2×D4×C113—81no—
226C2×D4×C113—81no—
227C2×D4×C113—81no—
228C2×D4×C113—81no—
229C2×D4×C113C2×D412yes—
230C2×D4×C113C2×D412yes—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—21no—
241C22×C4×C113—21no—
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—21no—
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—21no—
249C22×C4×C113—21no—
250C22×C4×C113—21no—
251C22×C4×C113C2×D411yescharacteristic
252C22×C4×C113C2×D411yescharacteristic
253C22×C4×C113C2×D412yes—
254C22×C4×C113C2×D412yes—
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2×D412yes—
257C22×C4×C113#4112yes—
258C22×C4×C113C2411yescharacteristic
259SD16×C113—44no—
260SD16×C113—44no—
261M16×C113—44no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C2×C8×C113—21no—
272C2×C8×C113—44no—
273C2×C8×C113C2×D412yes—
274C2×C8×C113C2×D412yes—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—42no—
284C4⋊C4×C113—42no—
285C4⋊C4×C113—42no—
286C4⋊C4×C113C2×D412yes—
287C4⋊C4×C113C2×D412yes—
288C22⋊C4×C113—24no—
289C22⋊C4×C113—24no—
290C22⋊C4×C113—24no—
291C22⋊C4×C113—24no—
292C22⋊C4×C113—24no—
293C22⋊C4×C113—42no—
294C22⋊C4×C113—42no—
295C22⋊C4×C113—42no—
296C22⋊C4×C113—81no—
297C22⋊C4×C113—81no—
298C22⋊C4×C113—81no—
299C42×C113—24no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—21no—
303C23×C113—21no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—21no—
308C23×C113—21no—
309C23×C113—21no—
310C23×C113—21no—
311C23×C113—21no—
312C23×C113—22no—
313C23×C113—22no—
314C23×C113—21no—
315C23×C113—21no—
316C23×C113—21no—
317C23×C113—21no—
318C23×C113—21no—
319C23×C113—21no—
320C23×C113—21no—
321C23×C113—48no—
322C23×C113—41no—
323C23×C113—41no—
324C23×C113—41no—
325C23×C113—41no—
326C23×C113—41no—
327C23×C113—41no—
328C23×C113—41no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—41no—
333C23×C113—41no—
334C23×C113—84no—
335C23×C113—84no—
336C23×C113—84no—
337C23×C113—84no—
338C23×C113—84no—
339C23×C113—84no—
340C23×C113#12012yes—
341C23×C113#12112yes—
342C23×C113C22×D411yescharacteristic
343Q8×C113—44no—
344Q8×C113—41no—
345Q8×C113—41no—
346Q8×C113—41no—
347Q8×C113—41no—
348D4×C113—22no—
349D4×C113—22no—
350D4×C113—22no—
351D4×C113—22no—
352D4×C113—44no—
353D4×C113—44no—
354D4×C113—48no—
355D4×C113—44no—
356D4×C113—41no—
357D4×C113—41no—
358D4×C113—41no—
359D4×C113—41no—
360D4×C113—84no—
361D4×C113—84no—
362D4×C113—84no—
363D4×C113—84no—
364C2×C4×C113—21no—
365C2×C4×C113—21no—
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—22no—
369C2×C4×C113—22no—
370C2×C4×C113—22no—
371C2×C4×C113—22no—
372C2×C4×C113—22no—
373C2×C4×C113—22no—
374C2×C4×C113—22no—
375C2×C4×C113—22no—
376C2×C4×C113—22no—
377C2×C4×C113—22no—
378C2×C4×C113—21no—
379C2×C4×C113—21no—
380C2×C4×C113—21no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113—41no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—41no—
396C2×C4×C113—41no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113#12012yes—
402C2×C4×C113#12112yes—
403C2×C4×C113C22×D411yescharacteristic
404C2×C4×C113C22×D411yescharacteristic
405C2×C4×C113C22×D411yescharacteristic
406C2×C4×C113C2×#4111yescharacteristic
407C2×C4×C113H(5,𝔽2)11yescharacteristic
408C2×C4×C113H(5,𝔽2)11yescharacteristic
409C8×C113—22no—
410C8×C113—22no—
411C8×C113—41no—
412C8×C113—41no—
413C22×C113—22no—
414C22×C113—22no—
415C22×C113—22no—
416C22×C113—22no—
417C22×C113—22no—
418C22×C113—22no—
419C22×C113—41no—
420C22×C113—41no—
421C22×C113—41no—
422C22×C113—41no—
423C22×C113—41no—
424C22×C113—41no—
425C22×C113—41no—
426C22×C113—41no—
427C22×C113—41no—
428C22×C113—42no—
429C22×C113—42no—
430C22×C113—41no—
431C22×C113—41no—
432C22×C113—41no—
433C22×C113—42no—
434C22×C113—42no—
435C22×C113—41no—
436C22×C113—42no—
437C22×C113—42no—
438C22×C113—41no—
439C22×C113—41no—
440C22×C113—816no—
441C22×C113—81no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113—81no—
445C22×C113—81no—
446C22×C113—81no—
447C22×C113—81no—
448C22×C113—81no—
449C22×C113C2×#12011yescharacteristic
450C22×C113C2×#12111yescharacteristic
451C22×C113#53411yescharacteristic
452C22×C113#57611yescharacteristic
453C22×C113#57711yescharacteristic
454C22×C113#57711yescharacteristic
455C22×C113#57711yescharacteristic
456C4×C113—22no—
457C4×C113—22no—
458C4×C113—41no—
459C4×C113—42no—
460C4×C113—42no—
461C4×C113—81no—
462C4×C113—81no—
463C4×C113—81no—
464C4×C113—81no—
465C4×C113D4211yescharacteristic
466C4×C113D4211yescharacteristic
467C4×C113#54611yescharacteristic
468C4×C113#54611yescharacteristic
469#24394C11311yesmaximal, characteristic, direct product factor, Sylow
470C2×C113—42no—
471C2×C113—42no—
472C2×C113—81no—
473C2×C113—82no—
474C2×C113—82no—
475C2×C113#241011yescharacteristic
476C2×C113#300911yescharacteristic
477C2×C113#301211yescharacteristic
478C2×C113#305711yescharacteristic
479C2×C113#306211yescharacteristic
480C2×C113#319811yescharacteristic
481C2×C113#320011yescharacteristic
482C2×#535C2×C11311yescharacteristic
483C2×#468C2×C11311yescharacteristic, complemented
484C2×#465C2×C11311yescharacteristic, complemented
485C2×#450C2×C11311yescharacteristic, complemented
486C2×#408C2×C11311yescharacteristic, complemented
487#2616C2×C11311yescharacteristic, complemented
488#2034C2×C11311yescharacteristic, complemented
489#2033C2×C11311yescharacteristic, complemented
490#2000C2×C11311yescharacteristic, complemented
491#2000C2×C11311yescharacteristic, complemented
492#1895C2×C11311yescharacteristic, complemented
493#1893C2×C11311yescharacteristic, complemented
494#1873C2×C11311yescharacteristic, complemented
495#1854C2×C11311yescharacteristic, complemented
496#1786C2×C11311yescharacteristic, complemented
497C113#2439411yescharacteristic, direct product factor, Sylow
498C22×#41C22×C11311yescharacteristic
499C23×D4C22×C11311yescharacteristic
500C22×SD16C22×C11311yescharacteristic
501C22×SD16C22×C11311yescharacteristic
502C22×M16C22×C11311yescharacteristic, complemented
503C23×C8C22×C11311yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127—21no—
507C2×#124—21no—
508C2×C22⋊Q8C22×C11311yescharacteristic
509C2×C22⋊Q8C22×C11311yescharacteristic, complemented
510C2×C22⋊Q8C22×C11311yescharacteristic, complemented
511C2×#121C22×C11311yescharacteristic
512C2×#121C22×C11311yescharacteristic
513C2×#121C22×C11311yescharacteristic
514C2×#121C22×C11311yescharacteristic
515C2×#120—21no—
516C2×#120—21no—
517C2×#117C22×C11311yescharacteristic
518#468—24no—
519#465—24no—
520#450—24no—
521C2×#107C22×C11311yescharacteristic, complemented
522C2×#106C22×C11311yescharacteristic, complemented
523C2×#103C22×C11311yescharacteristic, complemented
524C2×#103C22×C11311yescharacteristic, complemented
525C2×#102C22×C11311yescharacteristic
526C2×#102C22×C11311yescharacteristic
527C2×#102C22×C11311yescharacteristic
528C2×#102C22×C11311yescharacteristic
529C2×#102C22×C11311yescharacteristic
530C2×#102C22×C11311yescharacteristic
531#408—24no—
532C2×C22⋊C8C22×C11311yescharacteristic
533C2×C22⋊C8C22×C11311yescharacteristic
534C2×C22⋊C8C22×C11311yescharacteristic, complemented
535C2×C22⋊C8C22×C11311yescharacteristic, complemented
536#395—21no—
537#394—21no—
538#394—21no—
539#394—21no—
540#380C22×C11311yescharacteristic
541#380C22×C11311yescharacteristic, complemented
542#380C22×C11311yescharacteristic, complemented
543#340C22×C11311yescharacteristic, complemented
544#340C22×C11311yescharacteristic, complemented
545#340C22×C11311yescharacteristic, complemented
546#340C22×C11311yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C11311yescharacteristic
555C22×Q8C23×C11311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C11311yescharacteristic
568C22×D4D4×C11311yescharacteristic
569C22×D4D4×C11311yescharacteristic
570C22×D4C23×C11311yescharacteristic
571C22×D4C23×C11311yescharacteristic
572C23×C4C23×C11311yescharacteristic
573C23×C4C23×C11311yescharacteristic
574C23×C4C23×C11311yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C11311yescharacteristic
588C22×C8C23×C11311yescharacteristic
589C22×C8C23×C11311yescharacteristic
590C22×C8C23×C11311yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C11314yes—
606#121D4×C11314yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C11311yescharacteristic
615C2×C4⋊C4C23×C11311yescharacteristic
616C2×C4⋊C4C23×C11311yescharacteristic
617C2×C4⋊C4C23×C11311yescharacteristic
618C2×C4⋊C4C23×C11311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C11314yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C11311yescharacteristic
658C24C2×D4×C11311yescharacteristic
659C24C2×D4×C11311yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C11312yes—
712C2×D4C2×D4×C11312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C11311yescharacteristic
734C22×C4C2×D4×C11311yescharacteristic
735C22×C4C2×D4×C11312yes—
736C22×C4C2×D4×C11312yes—
737C22×C4C2×D4×C11311yescharacteristic
738C22×C4C2×D4×C11312yes—
739C22×C4#41×C11312yes—
740C22×C4C24×C11311yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C11312yes—
756C2×C8C2×D4×C11312yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C11312yes—
769C4⋊C4C2×D4×C11312yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C11312yes—
823C23#121×C11312yes—
824C23C22×D4×C11311yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C11312yes—
884C2×C4#121×C11312yes—
885C2×C4C22×D4×C11311yescharacteristic
886C2×C4C22×D4×C11311yescharacteristic
887C2×C4C22×D4×C11311yescharacteristic
888C2×C4C2×#41×C11311yescharacteristic
889C2×C4H(5,𝔽2)×C11311yescharacteristic
890C2×C4H(5,𝔽2)×C11311yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C11311yescharacteristic
932C22C2×#121×C11311yescharacteristic
933C22#534×C11311yescharacteristic
934C22#576×C11311yescharacteristic
935C22#577×C11311yescharacteristic
936C22#577×C11311yescharacteristic
937C22#577×C11311yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C11311yescharacteristic
948C4D42×C11311yescharacteristic
949C4#546×C11311yescharacteristic
950C4#546×C11311yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C113×#241011yescharacteristic
957C2C113×#300911yescharacteristic
958C2C113×#301211yescharacteristic
959C2C113×#305711yescharacteristic
960C2C113×#306211yescharacteristic
961C2C113×#319811yescharacteristic
962C2C113×#320011yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#535×C113C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×#41×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#468×C113C2semidirect
3. C2×#465×C113C2semidirect
4. C2×#450×C113C2semidirect
5. C2×#408×C113C2semidirect
6. C113×#2616C2semidirect
7. C113×#2034C2semidirect
8. C113×#2033C2semidirect
9. C113×#2000C2semidirect
10. C113×#2000C2semidirect
11. C113×#1895C2semidirect
12. C113×#1893C2semidirect
13. C113×#1873C2semidirect
14. C113×#1854C2semidirect
15. C113×#1786C2semidirect
20. C22×M16×C113C22semidirect
21. C23×C8×C113C22semidirect
27. C2×C22⋊Q8×C113C22semidirect
28. C2×C22⋊Q8×C113C22semidirect
39. C2×#107×C113C22semidirect
40. C2×#106×C113C22semidirect
41. C2×#103×C113C22semidirect
42. C2×#103×C113C22semidirect
52. C2×C22⋊C8×C113C22semidirect
53. C2×C22⋊C8×C113C22semidirect
59. #380×C113C22semidirect
60. #380×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
63. #340×C113C22semidirect
64. #340×C113C22semidirect
162. C22⋊C8×C113D4semidirect
469. #24394C113direct (N × H)
483. C2×#468C2×C113semidirect
484. C2×#465C2×C113semidirect
485. C2×#450C2×C113semidirect
486. C2×#408C2×C113semidirect
487. #2616C2×C113semidirect
488. #2034C2×C113semidirect
489. #2033C2×C113semidirect
490. #2000C2×C113semidirect
491. #2000C2×C113semidirect
492. #1895C2×C113semidirect
493. #1893C2×C113semidirect
494. #1873C2×C113semidirect
495. #1854C2×C113semidirect
496. #1786C2×C113semidirect
497. C113#24394direct (N × H)
502. C22×M16C22×C113semidirect
503. C23×C8C22×C113semidirect
509. C2×C22⋊Q8C22×C113semidirect
510. C2×C22⋊Q8C22×C113semidirect
521. C2×#107C22×C113semidirect
522. C2×#106C22×C113semidirect
523. C2×#103C22×C113semidirect
524. C2×#103C22×C113semidirect
534. C2×C22⋊C8C22×C113semidirect
535. C2×C22⋊C8C22×C113semidirect
541. #380C22×C113semidirect
542. #380C22×C113semidirect
543. #340C22×C113semidirect
544. #340C22×C113semidirect
545. #340C22×C113semidirect
546. #340C22×C113semidirect
644. C22⋊C8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1132
C2×#468×C1132
C2×#465×C1132
C2×#450×C1132
C2×#408×C1132
C113×#26162
C113×#20342
C113×#20332
C113×#20002
C113×#18952
C113×#18932
C113×#18732
C113×#18542
C113×#17862
#24394113