Finite Group Databasebeta

← C113×#23965 #43291985

Subgroups — C113×#23965 #43291985

Order 28928.

1332 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C113C211yesmaximal, characteristic, complemented
2C2×#449×C113C211yesmaximal, characteristic, complemented
3C2×#416×C113C211yesmaximal, characteristic, complemented
4C113×#2407C211yesmaximal, characteristic, complemented
5C113×#2024C211yesmaximal, characteristic, complemented
6C113×#2023C211yesmaximal, characteristic, complemented
7C113×#2000C211yesmaximal, characteristic, complemented
8C113×#1999C211yesmaximal, characteristic, complemented
9C113×#1893C211yesmaximal, characteristic, complemented
10C113×#1879C211yesmaximal, characteristic, complemented
11C113×#1877C211yesmaximal, characteristic, complemented
12C113×#1875C211yesmaximal, characteristic, complemented
13C113×#1873C211yesmaximal, characteristic, complemented
14C113×#1869C211yesmaximal, characteristic, complemented
15C113×#1825C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×D8×C113C2211yescharacteristic
19C23×C8×C113C2211yescharacteristic
20#555×C113—24no—
21#555×C113—24no—
22C2×C4⋊Q8×C113C2211yescharacteristic
23C2×#124×C113—21no—
24C2×#124×C113—21no—
25C2×C22⋊Q8×C113C2211yescharacteristic
26C2×#121×C113—21no—
27C2×#121×C113C2211yescharacteristic
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30C2×C4×D4×C113C2211yescharacteristic
31C2×C4×D4×C113C2211yescharacteristic
32C2×#117×C113—21no—
33C2×#117×C113C2211yescharacteristic
34C2×#117×C113C2211yescharacteristic
35#449×C113—24no—
36#416×C113—24no—
37C2×#103×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#103×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×C22⋊C8×C113C2211yescharacteristic
46C2×C22⋊C8×C113C2211yescharacteristic
47C2×C22⋊C8×C113C2211yescharacteristic
48#394×C113—21no—
49#392×C113—21no—
50#391×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic
52#386×C113—21no—
53#385×C113—21no—
54#380×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×C113C2211yescharacteristic
63C2×#41×C113—22no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—41no—
68C2×#41×C113—41no—
69C22×Q8×C113—21no—
70C22×Q8×C113C2311yescharacteristic
71C22×D4×C113—21no—
72C22×D4×C113—21no—
73C22×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113D411yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C22×D4×C113C2311yescharacteristic
78C23×C4×C113—21no—
79C23×C4×C113—21no—
80C23×C4×C113C2311yescharacteristic
81C23×C4×C113C2311yescharacteristic
82C2×SD16×C113—22no—
83C2×SD16×C113—22no—
84C2×SD16×C113—41no—
85C2×D8×C113—22no—
86C2×D8×C113—22no—
87C2×D8×C113—41no—
88C22×C8×C113—22no—
89C22×C8×C113—41no—
90C22×C8×C113—41no—
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C4⋊Q8×C113—22no—
96C4⋊Q8×C113—22no—
97#124×C113—28no—
98#124×C113—28no—
99C22⋊Q8×C113—22no—
100C22⋊Q8×C113—41no—
101#121×C113—28no—
102#121×C113—22no—
103#121×C113—22no—
104#121×C113—22no—
105#121×C113—22no—
106#121×C113—41no—
107#121×C113D414yescomplemented
108C4×D4×C113—22no—
109C4×D4×C113—22no—
110C4×D4×C113—22no—
111C4×D4×C113—22no—
112#117×C113—28no—
113#117×C113—22no—
114#117×C113—22no—
115#117×C113—22no—
116#117×C113D414yescomplemented
117C2×C4⋊C4×C113—21no—
118C2×C4⋊C4×C113—21no—
119C2×C4⋊C4×C113D411yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
121C2×C4⋊C4×C113C2311yescharacteristic
122C2×C4⋊C4×C113C2311yescharacteristic
123C2×C4⋊C4×C113C2311yescharacteristic
124C2×C4⋊C4×C113C2311yescharacteristic
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113D411yescharacteristic
136C2×C22⋊C4×C113D411yescharacteristic
137C2×C42×C113—21no—
138C2×C42×C113—21no—
139C2×C42×C113C2311yescharacteristic
140#103×C113—22no—
141#103×C113—22no—
142#103×C113—22no—
143#102×C113—22no—
144#102×C113—22no—
145#102×C113—22no—
146#102×C113—41no—
147#102×C113—41no—
148C22⋊C8×C113—22no—
149C22⋊C8×C113—41no—
150C22⋊C8×C113—41no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—21no—
154C24×C113—21no—
155C24×C113—21no—
156C24×C113C2×D411yescharacteristic
157C24×C113C2×D411yescharacteristic
158#41×C113—28no—
159#41×C113—44no—
160#41×C113—44no—
161#41×C113—44no—
162C2×Q8×C113—24no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×Q8×C113—81no—
169C2×Q8×C113—81no—
170C2×Q8×C113#4112yes—
171C2×D4×C113—22no—
172C2×D4×C113—24no—
173C2×D4×C113—24no—
174C2×D4×C113—22no—
175C2×D4×C113—21no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—21no—
184C2×D4×C113—21no—
185C2×D4×C113—41no—
186C2×D4×C113—42no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—42no—
190C2×D4×C113—42no—
191C2×D4×C113—81no—
192C2×D4×C113—81no—
193C2×D4×C113—81no—
194C2×D4×C113—81no—
195C2×D4×C113—81no—
196C2×D4×C113C2×D412yes—
197C2×D4×C113#4112yes—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—24no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—42no—
216C22×C4×C113—42no—
217C22×C4×C113—42no—
218C22×C4×C113—42no—
219C22×C4×C113—42no—
220C22×C4×C113C2×D411yescharacteristic
221C22×C4×C113C2×D411yescharacteristic
222C22×C4×C113C2×D411yescharacteristic
223C22×C4×C113C2×D412yes—
224C22×C4×C113C2×D412yes—
225C22×C4×C113C2×D411yescharacteristic
226C22×C4×C113C2411yescharacteristic
227SD16×C113—44no—
228D8×C113—44no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113—21no—
235C2×C8×C113—21no—
236C2×C8×C113—21no—
237C2×C8×C113—21no—
238C2×C8×C113—21no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113—44no—
242C4⋊C4×C113—24no—
243C4⋊C4×C113—22no—
244C4⋊C4×C113—21no—
245C4⋊C4×C113—21no—
246C4⋊C4×C113—21no—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—21no—
249C4⋊C4×C113—21no—
250C4⋊C4×C113—21no—
251C4⋊C4×C113—42no—
252C4⋊C4×C113C2×D412yes—
253C4⋊C4×C113C2×D412yes—
254C4⋊C4×C113C2×D412yes—
255C22⋊C4×C113—24no—
256C22⋊C4×C113—24no—
257C22⋊C4×C113—24no—
258C22⋊C4×C113—24no—
259C22⋊C4×C113—22no—
260C22⋊C4×C113—24no—
261C22⋊C4×C113—22no—
262C22⋊C4×C113—42no—
263C22⋊C4×C113—42no—
264C22⋊C4×C113—42no—
265C22⋊C4×C113—81no—
266C22⋊C4×C113—81no—
267C42×C113—24no—
268C42×C113—24no—
269C42×C113—21no—
270C42×C113—21no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—21no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—22no—
279C23×C113—21no—
280C23×C113—22no—
281C23×C113—21no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—41no—
294C23×C113—41no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—41no—
298C23×C113#12012yes—
299C23×C113C22×D411yescharacteristic
300Q8×C113—22no—
301Q8×C113—22no—
302Q8×C113—41no—
303Q8×C113—41no—
304Q8×C113—84no—
305D4×C113—22no—
306D4×C113—22no—
307D4×C113—22no—
308D4×C113—22no—
309D4×C113—44no—
310D4×C113—48no—
311D4×C113—41no—
312D4×C113—41no—
313D4×C113—41no—
314D4×C113—41no—
315D4×C113—84no—
316D4×C113—84no—
317D4×C113—84no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—22no—
323C2×C4×C113—22no—
324C2×C4×C113—22no—
325C2×C4×C113—22no—
326C2×C4×C113—21no—
327C2×C4×C113—22no—
328C2×C4×C113—21no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—21no—
332C2×C4×C113—22no—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—48no—
337C2×C4×C113—48no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—41no—
341C2×C4×C113—41no—
342C2×C4×C113—41no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113—41no—
354C2×C4×C113—41no—
355C2×C4×C113—41no—
356C2×C4×C113#12012yes—
357C2×C4×C113#13512yes—
358C2×C4×C113C22×D411yescharacteristic
359C2×C4×C113C22×D411yescharacteristic
360C2×C4×C113C2×#4111yescharacteristic
361C2×C4×C113C2×#4111yescharacteristic
362C2×C4×C113H(5,𝔽2)11yescharacteristic
363C2×C4×C113H(5,𝔽2)11yescharacteristic
364C8×C113—41no—
365C8×C113—41no—
366C8×C113—41no—
367C8×C113—41no—
368C22×C113—22no—
369C22×C113—22no—
370C22×C113—22no—
371C22×C113—41no—
372C22×C113—41no—
373C22×C113—41no—
374C22×C113—41no—
375C22×C113—42no—
376C22×C113—41no—
377C22×C113—42no—
378C22×C113—42no—
379C22×C113—41no—
380C22×C113—41no—
381C22×C113—42no—
382C22×C113—41no—
383C22×C113—42no—
384C22×C113—41no—
385C22×C113—41no—
386C22×C113—42no—
387C22×C113—41no—
388C22×C113—81no—
389C22×C113—81no—
390C22×C113—81no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113—81no—
395C22×C113—81no—
396C22×C113C2×#12011yescharacteristic
397C22×C113#54611yescharacteristic
398C22×C113#54611yescharacteristic
399C22×C113C2×#13511yescharacteristic
400C22×C113#57511yescharacteristic
401C22×C113#57611yescharacteristic
402C22×C113#57711yescharacteristic
403C4×C113—22no—
404C4×C113—22no—
405C4×C113—41no—
406C4×C113—42no—
407C4×C113—42no—
408C4×C113—41no—
409C4×C113—42no—
410C4×C113—42no—
411C4×C113—81no—
412C4×C113—81no—
413C4×C113#52511yescharacteristic
414C4×C113#53511yescharacteristic
415C4×C113#54611yescharacteristic
416C4×C113#54611yescharacteristic
417#23965C11311yesmaximal, characteristic, direct product factor, Sylow
418C2×C113—42no—
419C2×C113—81no—
420C2×C113—82no—
421C2×C113—82no—
422C2×C113#240411yescharacteristic
423C2×C113#300211yescharacteristic
424C2×C113#301211yescharacteristic
425C2×C113#330311yescharacteristic
426C2×C113#330511yescharacteristic
427C2×C113#331911yescharacteristic
428C2×C113#332111yescharacteristic
429C2×#555C2×C11311yescharacteristic, complemented
430C2×#449C2×C11311yescharacteristic, complemented
431C2×#416C2×C11311yescharacteristic, complemented
432#2407C2×C11311yescharacteristic, complemented
433#2024C2×C11311yescharacteristic, complemented
434#2023C2×C11311yescharacteristic, complemented
435#2000C2×C11311yescharacteristic, complemented
436#1999C2×C11311yescharacteristic, complemented
437#1893C2×C11311yescharacteristic, complemented
438#1879C2×C11311yescharacteristic, complemented
439#1877C2×C11311yescharacteristic, complemented
440#1875C2×C11311yescharacteristic, complemented
441#1873C2×C11311yescharacteristic, complemented
442#1869C2×C11311yescharacteristic, complemented
443#1825C2×C11311yescharacteristic, complemented
444C113#2396511yescharacteristic, direct product factor, Sylow
445C22×#41C22×C11311yescharacteristic
446C22×SD16C22×C11311yescharacteristic
447C22×D8C22×C11311yescharacteristic
448C23×C8C22×C11311yescharacteristic
449#555—24no—
450#555—24no—
451C2×C4⋊Q8C22×C11311yescharacteristic
452C2×#124—21no—
453C2×#124—21no—
454C2×C22⋊Q8C22×C11311yescharacteristic
455C2×#121—21no—
456C2×#121C22×C11311yescharacteristic
457C2×#121C22×C11311yescharacteristic
458C2×#121C22×C11311yescharacteristic
459C2×C4×D4C22×C11311yescharacteristic
460C2×C4×D4C22×C11311yescharacteristic
461C2×#117—21no—
462C2×#117C22×C11311yescharacteristic
463C2×#117C22×C11311yescharacteristic
464#449—24no—
465#416—24no—
466C2×#103C22×C11311yescharacteristic
467C2×#103C22×C11311yescharacteristic
468C2×#103C22×C11311yescharacteristic
469C2×#102C22×C11311yescharacteristic
470C2×#102C22×C11311yescharacteristic
471C2×#102C22×C11311yescharacteristic
472C2×#102C22×C11311yescharacteristic
473C2×#102C22×C11311yescharacteristic
474C2×C22⋊C8C22×C11311yescharacteristic
475C2×C22⋊C8C22×C11311yescharacteristic
476C2×C22⋊C8C22×C11311yescharacteristic
477#394—21no—
478#392—21no—
479#391C22×C11311yescharacteristic
480#390C22×C11311yescharacteristic
481#386—21no—
482#385—21no—
483#380C22×C11311yescharacteristic
484#340C22×C11311yescharacteristic
485#340C22×C11311yescharacteristic
486#340C22×C11311yescharacteristic
487#340C22×C11311yescharacteristic
488#340C22×C11311yescharacteristic
489#340C22×C11311yescharacteristic
490#336C22×C11311yescharacteristic
491#336C22×C11311yescharacteristic
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8—21no—
499C22×Q8C23×C11311yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4D4×C11311yescharacteristic
505C22×D4C23×C11311yescharacteristic
506C22×D4C23×C11311yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C11311yescharacteristic
510C23×C4C23×C11311yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8C23×C11311yescharacteristic
521C22×C8C23×C11311yescharacteristic
522C22×C8C23×C11311yescharacteristic
523C22×C8C23×C11311yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526#124—28no—
527#124—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C11314yescomplemented
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541#117—28no—
542#117—22no—
543#117—22no—
544#117—22no—
545#117D4×C11314yescomplemented
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4D4×C11311yescharacteristic
549C2×C4⋊C4C23×C11311yescharacteristic
550C2×C4⋊C4C23×C11311yescharacteristic
551C2×C4⋊C4C23×C11311yescharacteristic
552C2×C4⋊C4C23×C11311yescharacteristic
553C2×C4⋊C4C23×C11311yescharacteristic
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4D4×C11311yescharacteristic
565C2×C22⋊C4D4×C11311yescharacteristic
566C2×C42—21no—
567C2×C42—21no—
568C2×C42C23×C11311yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C11311yescharacteristic
586C24C2×D4×C11311yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—24no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—81no—
598C2×Q8—81no—
599C2×Q8#41×C11312yes—
600C2×D4—22no—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—22no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4C2×D4×C11312yes—
626C2×D4#41×C11312yes—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C2×D4×C11311yescharacteristic
650C22×C4C2×D4×C11311yescharacteristic
651C22×C4C2×D4×C11311yescharacteristic
652C22×C4C2×D4×C11312yes—
653C22×C4C2×D4×C11312yes—
654C22×C4C2×D4×C11311yescharacteristic
655C22×C4C24×C11311yescharacteristic
656SD16—44no—
657D8—44no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—44no—
671C4⋊C4—24no—
672C4⋊C4—22no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—42no—
681C4⋊C4C2×D4×C11312yes—
682C4⋊C4C2×D4×C11312yes—
683C4⋊C4C2×D4×C11312yes—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—22no—
689C22⋊C4—24no—
690C22⋊C4—22no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C42—24no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C11312yes—
728C23C22×D4×C11311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733Q8—84no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—44no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746D4—84no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4#120×C11312yes—
786C2×C4#135×C11312yes—
787C2×C4C22×D4×C11311yescharacteristic
788C2×C4C22×D4×C11311yescharacteristic
789C2×C4C2×#41×C11311yescharacteristic
790C2×C4C2×#41×C11311yescharacteristic
791C2×C4H(5,𝔽2)×C11311yescharacteristic
792C2×C4H(5,𝔽2)×C11311yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—42no—
814C22—41no—
815C22—41no—
816C22—42no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C11311yescharacteristic
826C22#546×C11311yescharacteristic
827C22#546×C11311yescharacteristic
828C22C2×#135×C11311yescharacteristic
829C22#575×C11311yescharacteristic
830C22#576×C11311yescharacteristic
831C22#577×C11311yescharacteristic
832C4—22no—
833C4—22no—
834C4—41no—
835C4—42no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4#525×C11311yescharacteristic
843C4#535×C11311yescharacteristic
844C4#546×C11311yescharacteristic
845C4#546×C11311yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C113×#240411yescharacteristic
851C2C113×#300211yescharacteristic
852C2C113×#301211yescharacteristic
853C2C113×#330311yescharacteristic
854C2C113×#330511yescharacteristic
855C2C113×#331911yescharacteristic
856C2C113×#332111yescharacteristic
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. C2×#555×C113C2semidirect
2. C2×#449×C113C2semidirect
3. C2×#416×C113C2semidirect
4. C113×#2407C2semidirect
5. C113×#2024C2semidirect
6. C113×#2023C2semidirect
7. C113×#2000C2semidirect
8. C113×#1999C2semidirect
9. C113×#1893C2semidirect
10. C113×#1879C2semidirect
11. C113×#1877C2semidirect
12. C113×#1875C2semidirect
13. C113×#1873C2semidirect
14. C113×#1869C2semidirect
15. C113×#1825C2semidirect
107. #121×C113D4semidirect
116. #117×C113D4semidirect
417. #23965C113direct (N × H)
429. C2×#555C2×C113semidirect
430. C2×#449C2×C113semidirect
431. C2×#416C2×C113semidirect
432. #2407C2×C113semidirect
433. #2024C2×C113semidirect
434. #2023C2×C113semidirect
435. #2000C2×C113semidirect
436. #1999C2×C113semidirect
437. #1893C2×C113semidirect
438. #1879C2×C113semidirect
439. #1877C2×C113semidirect
440. #1875C2×C113semidirect
441. #1873C2×C113semidirect
442. #1869C2×C113semidirect
443. #1825C2×C113semidirect
444. C113#23965direct (N × H)
536. #121D4×C113semidirect
545. #117D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1132
C2×#449×C1132
C2×#416×C1132
C113×#24072
C113×#20242
C113×#20232
C113×#20002
C113×#19992
C113×#18932
C113×#18792
C113×#18772
C113×#18752
C113×#18732
C113×#18692
C113×#18252
#23965113