Finite Group Databasebeta

← C113×#23853 #43291873

Subgroups — C113×#23853 #43291873

Order 28928.

1800 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C113C211yesmaximal, characteristic, complemented
2C2×#547×C113C211yesmaximal, characteristic, complemented
3C2×#452×C113C211yesmaximal, characteristic, complemented
4C2×#452×C113C211yesmaximal, characteristic, complemented
5C2×#449×C113C211yesmaximal, characteristic, complemented
6C113×#2407C211yesmaximal, characteristic, complemented
7C113×#2016C211yesmaximal, characteristic, complemented
8C113×#2013C211yesmaximal, characteristic, complemented
9C113×#2001C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1892C211yesmaximal, characteristic, complemented
12C113×#1879C211yesmaximal, characteristic, complemented
13C113×#1877C211yesmaximal, characteristic, complemented
14C113×#1869C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×#41×C113C2211yescharacteristic
19C2×#135×C113—24no—
20C2×#135×C113—24no—
21C2×#135×C113—24no—
22C22×Q16×C113C2211yescharacteristic
23C22×Q16×C113C2211yescharacteristic
24C22×SD16×C113C2211yescharacteristic
25C22×SD16×C113C2211yescharacteristic
26C22×SD16×C113C2211yescharacteristic
27C22×D8×C113C2211yescharacteristic
28C23×C8×C113C2211yescharacteristic
29#547×C113—24no—
30#547×C113—24no—
31C2×C4⋊Q8×C113C2211yescharacteristic
32C2×#123×C113—21no—
33C2×#123×C113—21no—
34C2×C22⋊Q8×C113C2211yescharacteristic
35C2×C22⋊Q8×C113C2211yescharacteristic
36C2×C22⋊Q8×C113C2211yescharacteristic
37C2×#121×C113—21no—
38C2×#121×C113C2211yescharacteristic
39C2×C4×D4×C113C2211yescharacteristic
40C2×C4×D4×C113C2211yescharacteristic
41C22×C4⋊C4×C113—21no—
42#452×C113—24no—
43#452×C113—24no—
44#449×C113—24no—
45C2×#103×C113C2211yescharacteristic
46C2×#103×C113C2211yescharacteristic
47C2×#103×C113C2211yescharacteristic
48C2×#103×C113C2211yescharacteristic
49C2×#103×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic
52C2×#102×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic
55C2×C22⋊C8×C113C2211yescharacteristic
56#394×C113—21no—
57#392×C113—21no—
58#391×C113C2211yescharacteristic
59#390×C113C2211yescharacteristic
60#386×C113—21no—
61#385×C113—21no—
62#380×C113C2211yescharacteristic
63#340×C113C2211yescharacteristic
64#340×C113C2211yescharacteristic
65#336×C113C2211yescharacteristic
66#336×C113C2211yescharacteristic
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—22no—
72C2×#41×C113—22no—
73C2×#41×C113—22no—
74C2×#41×C113—22no—
75C2×#41×C113—22no—
76C2×#41×C113—22no—
77C2×#41×C113—22no—
78C2×#41×C113—41no—
79C2×#41×C113—41no—
80C2×#41×C113—41no—
81C2×#41×C113—41no—
82C2×#41×C113—41no—
83C2×#41×C113—41no—
84C2×#41×C113D414yescomplemented
85C22×Q8×C113C2311yescharacteristic
86C22×Q8×C113C2311yescharacteristic
87C22×Q8×C113C2311yescharacteristic
88C22×D4×C113—21no—
89C22×D4×C113—21no—
90C22×D4×C113—21no—
91C22×D4×C113—21no—
92C22×D4×C113D411yescharacteristic
93C22×D4×C113C2311yescharacteristic
94C22×D4×C113C2311yescharacteristic
95C23×C4×C113—21no—
96C23×C4×C113—21no—
97C23×C4×C113—21no—
98C23×C4×C113—21no—
99C23×C4×C113C2311yescharacteristic
100C23×C4×C113C2311yescharacteristic
101#135×C113—232no—
102C2×Q16×C113—22no—
103C2×Q16×C113—22no—
104C2×Q16×C113—22no—
105C2×Q16×C113—22no—
106C2×Q16×C113—22no—
107C2×Q16×C113—41no—
108C2×SD16×C113—22no—
109C2×SD16×C113—22no—
110C2×SD16×C113—22no—
111C2×SD16×C113—22no—
112C2×SD16×C113—22no—
113C2×SD16×C113—22no—
114C2×SD16×C113—22no—
115C2×SD16×C113—41no—
116C2×SD16×C113D414yescomplemented
117C2×D8×C113—22no—
118C2×D8×C113—22no—
119C2×D8×C113D414yescomplemented
120C22×C8×C113—22no—
121C22×C8×C113—22no—
122C22×C8×C113—22no—
123C22×C8×C113C2311yescharacteristic
124C22×C8×C113C2311yescharacteristic
125C22×C8×C113C2311yescharacteristic
126C22×C8×C113C2311yescharacteristic
127C4⋊Q8×C113—22no—
128C4⋊Q8×C113—22no—
129#123×C113—28no—
130#123×C113—28no—
131C22⋊Q8×C113—22no—
132C22⋊Q8×C113—22no—
133C22⋊Q8×C113—22no—
134C22⋊Q8×C113—22no—
135C22⋊Q8×C113—41no—
136C22⋊Q8×C113D414yescomplemented
137#121×C113—28no—
138#121×C113—22no—
139#121×C113—41no—
140C4×D4×C113—22no—
141C4×D4×C113—22no—
142C4×D4×C113—22no—
143C4×D4×C113—22no—
144C2×C4⋊C4×C113—28no—
145C2×C4⋊C4×C113—21no—
146C2×C4⋊C4×C113—21no—
147C2×C4⋊C4×C113—21no—
148C2×C4⋊C4×C113—21no—
149C2×C4⋊C4×C113—21no—
150C2×C4⋊C4×C113D411yescharacteristic
151C2×C4⋊C4×C113C2311yescharacteristic
152C2×C4⋊C4×C113C2311yescharacteristic
153C2×C4⋊C4×C113C2311yescharacteristic
154C2×C22⋊C4×C113—21no—
155C2×C22⋊C4×C113—21no—
156C2×C22⋊C4×C113—21no—
157C2×C22⋊C4×C113—21no—
158C2×C22⋊C4×C113—21no—
159C2×C22⋊C4×C113—21no—
160C2×C22⋊C4×C113—21no—
161C2×C22⋊C4×C113—21no—
162C2×C22⋊C4×C113D411yescharacteristic
163C2×C22⋊C4×C113D411yescharacteristic
164C2×C42×C113C2311yescharacteristic
165#103×C113—22no—
166#103×C113—22no—
167#103×C113—22no—
168#103×C113—41no—
169#103×C113—41no—
170#102×C113—22no—
171#102×C113—22no—
172#102×C113—22no—
173C22⋊C8×C113—22no—
174C22⋊C8×C113—22no—
175C22⋊C8×C113—22no—
176#95×C113—21no—
177#95×C113—21no—
178#95×C113—21no—
179C24×C113—21no—
180C24×C113—21no—
181C24×C113C2×D411yescharacteristic
182C24×C113C2×D411yescharacteristic
183#41×C113—28no—
184#41×C113—28no—
185#41×C113—44no—
186#41×C113—44no—
187#41×C113—44no—
188#41×C113—44no—
189#41×C113—44no—
190#41×C113—44no—
191#41×C113—44no—
192#41×C113—44no—
193#41×C113—44no—
194#41×C113—44no—
195C2×Q8×C113—21no—
196C2×Q8×C113—21no—
197C2×Q8×C113—21no—
198C2×Q8×C113—21no—
199C2×Q8×C113—21no—
200C2×Q8×C113—21no—
201C2×Q8×C113—21no—
202C2×Q8×C113—21no—
203C2×Q8×C113—21no—
204C2×Q8×C113—21no—
205C2×Q8×C113—21no—
206C2×Q8×C113—21no—
207C2×Q8×C113—21no—
208C2×Q8×C113—21no—
209C2×Q8×C113—21no—
210C2×Q8×C113C2×D412yes—
211C2×Q8×C113C2×D412yes—
212C2×Q8×C113C2×D412yes—
213C2×D4×C113—24no—
214C2×D4×C113—22no—
215C2×D4×C113—24no—
216C2×D4×C113—22no—
217C2×D4×C113—21no—
218C2×D4×C113—21no—
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—21no—
225C2×D4×C113—41no—
226C2×D4×C113—42no—
227C2×D4×C113—42no—
228C2×D4×C113—42no—
229C2×D4×C113—42no—
230C2×D4×C113—42no—
231C2×D4×C113—42no—
232C2×D4×C113—42no—
233C2×D4×C113—42no—
234C2×D4×C113—42no—
235C2×D4×C113—81no—
236C2×D4×C113C2×D412yes—
237C2×D4×C113C2×D412yes—
238C2×D4×C113C2×D412yes—
239C2×D4×C113C2×D412yes—
240C22×C4×C113—21no—
241C22×C4×C113—21no—
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—24no—
245C22×C4×C113—24no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—21no—
249C22×C4×C113—21no—
250C22×C4×C113—24no—
251C22×C4×C113—21no—
252C22×C4×C113—21no—
253C22×C4×C113—21no—
254C22×C4×C113—21no—
255C22×C4×C113—21no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—21no—
259C22×C4×C113—42no—
260C22×C4×C113—42no—
261C22×C4×C113—42no—
262C22×C4×C113—42no—
263C22×C4×C113—42no—
264C22×C4×C113—42no—
265C22×C4×C113—42no—
266C22×C4×C113—42no—
267C22×C4×C113—42no—
268C22×C4×C113C2×D411yescharacteristic
269C22×C4×C113C2×D411yescharacteristic
270C22×C4×C113C2×D411yescharacteristic
271C22×C4×C113C2×D412yes—
272C22×C4×C113C2×D412yes—
273C22×C4×C113C2×D411yescharacteristic
274C22×C4×C113C2411yescharacteristic
275Q16×C113—28no—
276Q16×C113—44no—
277SD16×C113—28no—
278SD16×C113—28no—
279SD16×C113—44no—
280D8×C113—28no—
281C2×C8×C113—28no—
282C2×C8×C113—21no—
283C2×C8×C113—21no—
284C2×C8×C113—21no—
285C2×C8×C113—21no—
286C2×C8×C113—21no—
287C2×C8×C113—21no—
288C2×C8×C113—21no—
289C2×C8×C113—21no—
290C2×C8×C113—21no—
291C2×C8×C113—21no—
292C2×C8×C113C2×D412yes—
293C2×C8×C113C2×D412yes—
294C4⋊C4×C113—24no—
295C4⋊C4×C113—24no—
296C4⋊C4×C113—24no—
297C4⋊C4×C113—22no—
298C4⋊C4×C113—24no—
299C4⋊C4×C113—21no—
300C4⋊C4×C113—21no—
301C4⋊C4×C113—21no—
302C4⋊C4×C113—21no—
303C4⋊C4×C113—21no—
304C4⋊C4×C113—42no—
305C4⋊C4×C113C2×D412yes—
306C22⋊C4×C113—24no—
307C22⋊C4×C113—24no—
308C22⋊C4×C113—24no—
309C22⋊C4×C113—22no—
310C22⋊C4×C113—22no—
311C22⋊C4×C113—42no—
312C22⋊C4×C113—42no—
313C22⋊C4×C113—42no—
314C22⋊C4×C113—81no—
315C22⋊C4×C113—81no—
316C42×C113—21no—
317C42×C113—21no—
318C23×C113—22no—
319C23×C113—21no—
320C23×C113—21no—
321C23×C113—22no—
322C23×C113—22no—
323C23×C113—21no—
324C23×C113—21no—
325C23×C113—21no—
326C23×C113—21no—
327C23×C113—21no—
328C23×C113—21no—
329C23×C113—22no—
330C23×C113—21no—
331C23×C113—21no—
332C23×C113—21no—
333C23×C113—21no—
334C23×C113—21no—
335C23×C113—41no—
336C23×C113—41no—
337C23×C113—41no—
338C23×C113—41no—
339C23×C113—41no—
340C23×C113—41no—
341C23×C113—41no—
342C23×C113—41no—
343C23×C113—41no—
344C23×C113—41no—
345C23×C113#12012yes—
346C23×C113C22×D411yescharacteristic
347Q8×C113—22no—
348Q8×C113—22no—
349Q8×C113—22no—
350Q8×C113—22no—
351Q8×C113—22no—
352Q8×C113—22no—
353Q8×C113—41no—
354Q8×C113—41no—
355Q8×C113—41no—
356Q8×C113—41no—
357Q8×C113—41no—
358Q8×C113—41no—
359D4×C113—22no—
360D4×C113—22no—
361D4×C113—22no—
362D4×C113—22no—
363D4×C113—22no—
364D4×C113—44no—
365D4×C113—48no—
366D4×C113—48no—
367D4×C113—48no—
368D4×C113—41no—
369D4×C113—41no—
370D4×C113—84no—
371D4×C113#12014yes—
372C2×C4×C113—21no—
373C2×C4×C113—21no—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—22no—
377C2×C4×C113—22no—
378C2×C4×C113—22no—
379C2×C4×C113—22no—
380C2×C4×C113—21no—
381C2×C4×C113—22no—
382C2×C4×C113—21no—
383C2×C4×C113—22no—
384C2×C4×C113—22no—
385C2×C4×C113—21no—
386C2×C4×C113—22no—
387C2×C4×C113—21no—
388C2×C4×C113—21no—
389C2×C4×C113—21no—
390C2×C4×C113—48no—
391C2×C4×C113—48no—
392C2×C4×C113—48no—
393C2×C4×C113—48no—
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—41no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—41no—
405C2×C4×C113—41no—
406C2×C4×C113—41no—
407C2×C4×C113—41no—
408C2×C4×C113—41no—
409C2×C4×C113—41no—
410C2×C4×C113—41no—
411C2×C4×C113—41no—
412C2×C4×C113#12012yes—
413C2×C4×C113#13512yescomplemented
414C2×C4×C113C22×D411yescharacteristic
415C2×C4×C113C22×D411yescharacteristic
416C2×C4×C113C22×D411yescharacteristic
417C2×C4×C113C22×D411yescharacteristic
418C2×C4×C113H(5,𝔽2)11yescharacteristic
419C2×C4×C113H(5,𝔽2)11yescharacteristic
420C8×C113—22no—
421C8×C113—22no—
422C8×C113—41no—
423C8×C113—41no—
424C22×C113—22no—
425C22×C113—24no—
426C22×C113—22no—
427C22×C113—22no—
428C22×C113—42no—
429C22×C113—41no—
430C22×C113—42no—
431C22×C113—42no—
432C22×C113—41no—
433C22×C113—42no—
434C22×C113—41no—
435C22×C113—42no—
436C22×C113—41no—
437C22×C113—42no—
438C22×C113—42no—
439C22×C113—41no—
440C22×C113—41no—
441C22×C113—41no—
442C22×C113—42no—
443C22×C113—41no—
444C22×C113—41no—
445C22×C113—41no—
446C22×C113—42no—
447C22×C113—41no—
448C22×C113—81no—
449C22×C113—81no—
450C22×C113—81no—
451C22×C113—81no—
452C22×C113C2×#12011yescharacteristic
453C22×C113D4211yescharacteristic
454C22×C113D4211yescharacteristic
455C22×C113C2×#13511yescharacteristic
456C22×C113#57511yescharacteristic
457C22×C113#57711yescharacteristic
458C22×C113#57811yescharacteristic
459C4×C113—22no—
460C4×C113—22no—
461C4×C113—41no—
462C4×C113—42no—
463C4×C113—42no—
464C4×C113—42no—
465C4×C113—42no—
466C4×C113—41no—
467C4×C113—81no—
468C4×C113—81no—
469C4×C113C2×#12011yescharacteristic
470C4×C113#53411yescharacteristic
471C4×C113D4211yescharacteristic
472C4×C113D4211yescharacteristic
473#23853C11311yesmaximal, characteristic, direct product factor, Sylow
474C2×C113—42no—
475C2×C113—44no—
476C2×C113—81no—
477C2×C113—82no—
478C2×C113#240311yescharacteristic
479C2×C113#300211yescharacteristic
480C2×C113#301311yescharacteristic
481C2×C113#326711yescharacteristic
482C2×C113#326911yescharacteristic
483C2×C113#328311yescharacteristic
484C2×C113#328411yescharacteristic
485C22×#135C2×C11311yescharacteristic, complemented
486C2×#547C2×C11311yescharacteristic, complemented
487C2×#452C2×C11311yescharacteristic, complemented
488C2×#452C2×C11311yescharacteristic, complemented
489C2×#449C2×C11311yescharacteristic, complemented
490#2407C2×C11311yescharacteristic, complemented
491#2016C2×C11311yescharacteristic, complemented
492#2013C2×C11311yescharacteristic, complemented
493#2001C2×C11311yescharacteristic, complemented
494#2000C2×C11311yescharacteristic, complemented
495#1892C2×C11311yescharacteristic, complemented
496#1879C2×C11311yescharacteristic, complemented
497#1877C2×C11311yescharacteristic, complemented
498#1869C2×C11311yescharacteristic, complemented
499#1788C2×C11311yescharacteristic, complemented
500C113#2385311yescharacteristic, direct product factor, Sylow
501C22×#41C22×C11311yescharacteristic
502C22×#41C22×C11311yescharacteristic
503C22×#41C22×C11311yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C11311yescharacteristic
508C22×Q16C22×C11311yescharacteristic
509C22×SD16C22×C11311yescharacteristic
510C22×SD16C22×C11311yescharacteristic
511C22×SD16C22×C11311yescharacteristic
512C22×D8C22×C11311yescharacteristic
513C23×C8C22×C11311yescharacteristic
514#547—24no—
515#547—24no—
516C2×C4⋊Q8C22×C11311yescharacteristic
517C2×#123—21no—
518C2×#123—21no—
519C2×C22⋊Q8C22×C11311yescharacteristic
520C2×C22⋊Q8C22×C11311yescharacteristic
521C2×C22⋊Q8C22×C11311yescharacteristic
522C2×#121—21no—
523C2×#121C22×C11311yescharacteristic
524C2×C4×D4C22×C11311yescharacteristic
525C2×C4×D4C22×C11311yescharacteristic
526C22×C4⋊C4—21no—
527#452—24no—
528#452—24no—
529#449—24no—
530C2×#103C22×C11311yescharacteristic
531C2×#103C22×C11311yescharacteristic
532C2×#103C22×C11311yescharacteristic
533C2×#103C22×C11311yescharacteristic
534C2×#103C22×C11311yescharacteristic
535C2×#102C22×C11311yescharacteristic
536C2×#102C22×C11311yescharacteristic
537C2×#102C22×C11311yescharacteristic
538C2×C22⋊C8C22×C11311yescharacteristic
539C2×C22⋊C8C22×C11311yescharacteristic
540C2×C22⋊C8C22×C11311yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C11311yescharacteristic
544#390C22×C11311yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C11311yescharacteristic
548#340C22×C11311yescharacteristic
549#340C22×C11311yescharacteristic
550#336C22×C11311yescharacteristic
551#336C22×C11311yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—41no—
564C2×#41—41no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C11314yescomplemented
570C22×Q8C23×C11311yescharacteristic
571C22×Q8C23×C11311yescharacteristic
572C22×Q8C23×C11311yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C11311yescharacteristic
578C22×D4C23×C11311yescharacteristic
579C22×D4C23×C11311yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C11311yescharacteristic
585C23×C4C23×C11311yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16—41no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C11314yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8D4×C11314yescomplemented
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C11311yescharacteristic
609C22×C8C23×C11311yescharacteristic
610C22×C8C23×C11311yescharacteristic
611C22×C8C23×C11311yescharacteristic
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614#123—28no—
615#123—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—41no—
621C22⋊Q8D4×C11314yescomplemented
622#121—28no—
623#121—22no—
624#121—41no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4D4×C11311yescharacteristic
636C2×C4⋊C4C23×C11311yescharacteristic
637C2×C4⋊C4C23×C11311yescharacteristic
638C2×C4⋊C4C23×C11311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4D4×C11311yescharacteristic
648C2×C22⋊C4D4×C11311yescharacteristic
649C2×C42C23×C11311yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C11311yescharacteristic
667C24C2×D4×C11311yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676#41—44no—
677#41—44no—
678#41—44no—
679#41—44no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8C2×D4×C11312yes—
696C2×Q8C2×D4×C11312yes—
697C2×Q8C2×D4×C11312yes—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—22no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—41no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—81no—
721C2×D4C2×D4×C11312yes—
722C2×D4C2×D4×C11312yes—
723C2×D4C2×D4×C11312yes—
724C2×D4C2×D4×C11312yes—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C11311yescharacteristic
754C22×C4C2×D4×C11311yescharacteristic
755C22×C4C2×D4×C11311yescharacteristic
756C22×C4C2×D4×C11312yes—
757C22×C4C2×D4×C11312yes—
758C22×C4C2×D4×C11311yescharacteristic
759C22×C4C24×C11311yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C11312yes—
778C2×C8C2×D4×C11312yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—24no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—42no—
790C4⋊C4C2×D4×C11312yes—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—42no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C42—21no—
802C42—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—22no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23#120×C11312yes—
831C23C22×D4×C11311yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844D4—22no—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—44no—
850D4—48no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—84no—
856D4#120×C11314yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4#120×C11312yes—
898C2×C4#135×C11312yescomplemented
899C2×C4C22×D4×C11311yescharacteristic
900C2×C4C22×D4×C11311yescharacteristic
901C2×C4C22×D4×C11311yescharacteristic
902C2×C4C22×D4×C11311yescharacteristic
903C2×C4H(5,𝔽2)×C11311yescharacteristic
904C2×C4H(5,𝔽2)×C11311yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—24no—
911C22—22no—
912C22—22no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C11311yescharacteristic
938C22D42×C11311yescharacteristic
939C22D42×C11311yescharacteristic
940C22C2×#135×C11311yescharacteristic
941C22#575×C11311yescharacteristic
942C22#577×C11311yescharacteristic
943C22#578×C11311yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C11311yescharacteristic
955C4#534×C11311yescharacteristic
956C4D42×C11311yescharacteristic
957C4D42×C11311yescharacteristic
958C2—42no—
959C2—44no—
960C2—81no—
961C2—82no—
962C2C113×#240311yescharacteristic
963C2C113×#300211yescharacteristic
964C2C113×#301311yescharacteristic
965C2C113×#326711yescharacteristic
966C2C113×#326911yescharacteristic
967C2C113×#328311yescharacteristic
968C2C113×#328411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C113C2semidirect
2. C2×#547×C113C2semidirect
3. C2×#452×C113C2semidirect
4. C2×#452×C113C2semidirect
5. C2×#449×C113C2semidirect
6. C113×#2407C2semidirect
7. C113×#2016C2semidirect
8. C113×#2013C2semidirect
9. C113×#2001C2semidirect
10. C113×#2000C2semidirect
11. C113×#1892C2semidirect
12. C113×#1879C2semidirect
13. C113×#1877C2semidirect
14. C113×#1869C2semidirect
15. C113×#1788C2semidirect
84. C2×#41×C113D4semidirect
116. C2×SD16×C113D4semidirect
119. C2×D8×C113D4semidirect
136. C22⋊Q8×C113D4semidirect
413. C2×C4×C113#135semidirect
473. #23853C113direct (N × H)
485. C22×#135C2×C113semidirect
486. C2×#547C2×C113semidirect
487. C2×#452C2×C113semidirect
488. C2×#452C2×C113semidirect
489. C2×#449C2×C113semidirect
490. #2407C2×C113semidirect
491. #2016C2×C113semidirect
492. #2013C2×C113semidirect
493. #2001C2×C113semidirect
494. #2000C2×C113semidirect
495. #1892C2×C113semidirect
496. #1879C2×C113semidirect
497. #1877C2×C113semidirect
498. #1869C2×C113semidirect
499. #1788C2×C113semidirect
500. C113#23853direct (N × H)
569. C2×#41D4×C113semidirect
601. C2×SD16D4×C113semidirect
604. C2×D8D4×C113semidirect
621. C22⋊Q8D4×C113semidirect
898. C2×C4#135×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1132
C2×#547×C1132
C2×#452×C1132
C2×#449×C1132
C113×#24072
C113×#20162
C113×#20132
C113×#20012
C113×#20002
C113×#18922
C113×#18792
C113×#18772
C113×#18692
C113×#17882
#23853113