Finite Group Databasebeta

← C113×#24017 #43292037

Subgroups — C113×#24017 #43292037

Order 28928.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C113C211yesmaximal, characteristic
2C2×#485×C113C211yesmaximal, characteristic, complemented
3C2×#482×C113C211yesmaximal, characteristic, complemented
4C113×#2311C211yesmaximal, characteristic, complemented
5C113×#2036C211yesmaximal, characteristic, complemented
6C113×#2035C211yesmaximal, characteristic, complemented
7C113×#2034C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#1874C211yesmaximal, characteristic, complemented
10C113×#1872C211yesmaximal, characteristic, complemented
11C113×#1853C211yesmaximal, characteristic, complemented
12C113×#1852C211yesmaximal, characteristic, complemented
13C113×#1788C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18#537×C113—24no—
19#537×C113—24no—
20C2×C22⋊Q8×C113—21no—
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×C22⋊Q8×C113C2211yescharacteristic
23C2×#121×C113—21no—
24C2×#121×C113—21no—
25C2×#121×C113—21no—
26C2×#121×C113C2211yescharacteristic
27C2×#121×C113C2211yescharacteristic
28C2×#117×C113C2211yescharacteristic
29C22×C4⋊C4×C113C2211yescharacteristic
30C22×C4⋊C4×C113C2211yescharacteristic
31#485×C113—24no—
32#482×C113—24no—
33C2×#107×C113C2211yescharacteristic
34C2×#107×C113C2211yescharacteristic
35C2×#106×C113C2211yescharacteristic
36C2×#106×C113C2211yescharacteristic
37C2×#103×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#103×C113C2211yescharacteristic
40C2×#103×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
48C2×C22⋊C8×C113C2211yescharacteristic
49C2×C22⋊C8×C113C2211yescharacteristic
50C2×C22⋊C8×C113C2211yescharacteristic
51#391×C113—21no—
52#390×C113—21no—
53#386×C113—21no—
54#386×C113—21no—
55#380×C113C2211yescharacteristic
56#380×C113C2211yescharacteristic
57#380×C113C2211yescharacteristic
58#380×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63C2×#41×C113—22no—
64C2×#41×C113—22no—
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—41no—
72C2×#41×C113—41no—
73C2×#41×C113—41no—
74C2×#41×C113—41no—
75C22×Q8×C113D411yescharacteristic
76C22×Q8×C113C2311yescharacteristic
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113D411yescharacteristic
81C22×D4×C113D411yescharacteristic
82C22×D4×C113D411yescharacteristic
83C22×D4×C113C2311yescharacteristic
84C23×C4×C113—21no—
85C23×C4×C113—21no—
86C23×C4×C113—21no—
87C23×C4×C113C2311yescharacteristic
88C23×C4×C113C2311yescharacteristic
89C23×C4×C113C2311yescharacteristic
90C22×C8×C113C2311yescharacteristic
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22⋊Q8×C113—28no—
95C22⋊Q8×C113—22no—
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113D414yes—
99#121×C113—28no—
100#121×C113—28no—
101#121×C113—28no—
102#121×C113—22no—
103#121×C113—22no—
104#121×C113—22no—
105#121×C113D414yes—
106#117×C113—22no—
107#117×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—22no—
112C2×C4⋊C4×C113—22no—
113C2×C4⋊C4×C113—21no—
114C2×C4⋊C4×C113—41no—
115C2×C4⋊C4×C113—41no—
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
119C2×C4⋊C4×C113C2311yescharacteristic
120C2×C4⋊C4×C113C2311yescharacteristic
121C2×C4⋊C4×C113C2311yescharacteristic
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
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×C42×C113—21no—
132#107×C113—22no—
133#107×C113—22no—
134#106×C113—22no—
135#106×C113—22no—
136#103×C113—22no—
137#103×C113—22no—
138#103×C113—41no—
139#103×C113—41no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—41no—
143#102×C113—41no—
144C22⋊C8×C113—22no—
145C22⋊C8×C113—22no—
146C22⋊C8×C113—22no—
147C22⋊C8×C113—22no—
148C22⋊C8×C113—41no—
149C22⋊C8×C113—41no—
150#95×C113—21no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—21no—
154C24×C113—21no—
155C24×C113C2×D411yescharacteristic
156C24×C113C2×D411yescharacteristic
157C24×C113C2×D411yescharacteristic
158#41×C113—44no—
159#41×C113—44no—
160#41×C113—44no—
161#41×C113—44no—
162#41×C113—44no—
163#41×C113—44no—
164#41×C113—44no—
165#41×C113—44no—
166C2×Q8×C113—22no—
167C2×Q8×C113—22no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—21no—
171C2×Q8×C113—21no—
172C2×Q8×C113—21no—
173C2×Q8×C113—41no—
174C2×Q8×C113C2×D412yes—
175C2×D4×C113—24no—
176C2×D4×C113—22no—
177C2×D4×C113—22no—
178C2×D4×C113—22no—
179C2×D4×C113—22no—
180C2×D4×C113—24no—
181C2×D4×C113—24no—
182C2×D4×C113—22no—
183C2×D4×C113—22no—
184C2×D4×C113—21no—
185C2×D4×C113—21no—
186C2×D4×C113—21no—
187C2×D4×C113—21no—
188C2×D4×C113—21no—
189C2×D4×C113—41no—
190C2×D4×C113—41no—
191C2×D4×C113—41no—
192C2×D4×C113—42no—
193C2×D4×C113—42no—
194C2×D4×C113—81no—
195C2×D4×C113—81no—
196C2×D4×C113—81no—
197C2×D4×C113—81no—
198C2×D4×C113C2×D412yes—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—24no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—24no—
212C22×C4×C113—21no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—42no—
223C22×C4×C113—42no—
224C22×C4×C113—42no—
225C22×C4×C113—81no—
226C22×C4×C113—81no—
227C22×C4×C113—81no—
228C22×C4×C113—81no—
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113C2×D411yescharacteristic
231C22×C4×C113C2×D412yes—
232C22×C4×C113C2×D412yes—
233C22×C4×C113C2×D411yescharacteristic
234C22×C4×C113#4112yes—
235C22×C4×C113#4112yes—
236C22×C4×C113C2411yescharacteristic
237C2×C8×C113—21no—
238C2×C8×C113—21no—
239C2×C8×C113—21no—
240C2×C8×C113—21no—
241C2×C8×C113—21no—
242C2×C8×C113—21no—
243C2×C8×C113—21no—
244C2×C8×C113—21no—
245C2×C8×C113—21no—
246C2×C8×C113—21no—
247C2×C8×C113—21no—
248C2×C8×C113—21no—
249C4⋊C4×C113—24no—
250C4⋊C4×C113—24no—
251C4⋊C4×C113—24no—
252C4⋊C4×C113—21no—
253C4⋊C4×C113—21no—
254C4⋊C4×C113—21no—
255C4⋊C4×C113—21no—
256C4⋊C4×C113—21no—
257C4⋊C4×C113—21no—
258C4⋊C4×C113—21no—
259C4⋊C4×C113—21no—
260C4⋊C4×C113—21no—
261C4⋊C4×C113—21no—
262C4⋊C4×C113—42no—
263C4⋊C4×C113C2×D412yes—
264C4⋊C4×C113C2×D412yes—
265C22⋊C4×C113—24no—
266C22⋊C4×C113—24no—
267C22⋊C4×C113—24no—
268C22⋊C4×C113—24no—
269C22⋊C4×C113—42no—
270C22⋊C4×C113—81no—
271C22⋊C4×C113—81no—
272C22⋊C4×C113—81no—
273C22⋊C4×C113—81no—
274C42×C113—42no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—21no—
281C23×C113—21no—
282C23×C113—21no—
283C23×C113—21no—
284C23×C113—21no—
285C23×C113—21no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—22no—
289C23×C113—21no—
290C23×C113—21no—
291C23×C113—21no—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—41no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113#12012yes—
302C23×C113#12312yes—
303C23×C113C22×D411yescharacteristic
304Q8×C113—22no—
305Q8×C113—22no—
306Q8×C113—44no—
307Q8×C113—41no—
308Q8×C113—41no—
309D4×C113—22no—
310D4×C113—22no—
311D4×C113—44no—
312D4×C113—44no—
313D4×C113—44no—
314D4×C113—48no—
315D4×C113—41no—
316D4×C113—41no—
317D4×C113—84no—
318D4×C113—84no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—22no—
324C2×C4×C113—22no—
325C2×C4×C113—22no—
326C2×C4×C113—22no—
327C2×C4×C113—22no—
328C2×C4×C113—22no—
329C2×C4×C113—22no—
330C2×C4×C113—22no—
331C2×C4×C113—22no—
332C2×C4×C113—22no—
333C2×C4×C113—22no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
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—41no—
357C2×C4×C113—41no—
358C2×C4×C113—41no—
359C2×C4×C113—41no—
360C2×C4×C113—84no—
361C2×C4×C113—84no—
362C2×C4×C113#12012yes—
363C2×C4×C113#12312yes—
364C2×C4×C113C22×D411yescharacteristic
365C2×C4×C113C22×D411yescharacteristic
366C2×C4×C113C2×#4111yescharacteristic
367C2×C4×C113C2×#4111yescharacteristic
368C2×C4×C113H(5,𝔽2)11yescharacteristic
369C2×C4×C113H(5,𝔽2)11yescharacteristic
370C8×C113—41no—
371C8×C113—41no—
372C8×C113—41no—
373C8×C113—41no—
374C22×C113—22no—
375C22×C113—22no—
376C22×C113—22no—
377C22×C113—22no—
378C22×C113—22no—
379C22×C113—22no—
380C22×C113—41no—
381C22×C113—41no—
382C22×C113—41no—
383C22×C113—41no—
384C22×C113—41no—
385C22×C113—41no—
386C22×C113—41no—
387C22×C113—41no—
388C22×C113—41no—
389C22×C113—41no—
390C22×C113—42no—
391C22×C113—41no—
392C22×C113—41no—
393C22×C113—41no—
394C22×C113—41no—
395C22×C113—42no—
396C22×C113—41no—
397C22×C113—42no—
398C22×C113—81no—
399C22×C113—81no—
400C22×C113—81no—
401C22×C113—81no—
402C22×C113C2×#12011yescharacteristic
403C22×C113C2×#12311yescharacteristic
404C22×C113#53411yescharacteristic
405C22×C113#57611yescharacteristic
406C22×C113#57711yescharacteristic
407C22×C113#57711yescharacteristic
408C22×C113#57811yescharacteristic
409C4×C113—22no—
410C4×C113—22no—
411C4×C113—41no—
412C4×C113—42no—
413C4×C113—42no—
414C4×C113—42no—
415C4×C113—81no—
416C4×C113—81no—
417C4×C113—81no—
418C4×C113—81no—
419C4×C113#54611yescharacteristic
420C4×C113#54611yescharacteristic
421C4×C113#54611yescharacteristic
422C4×C113#54611yescharacteristic
423#24017C11311yesmaximal, characteristic, direct product factor, Sylow
424C2×C113—42no—
425C2×C113—42no—
426C2×C113—81no—
427C2×C113—82no—
428C2×C113#240511yescharacteristic
429C2×C113#301211yescharacteristic
430C2×C113#301311yescharacteristic
431C2×C113#309811yescharacteristic
432C2×C113#309911yescharacteristic
433C2×C113#319811yescharacteristic
434C2×C113#320111yescharacteristic
435C2×#537C2×C11311yescharacteristic
436C2×#485C2×C11311yescharacteristic, complemented
437C2×#482C2×C11311yescharacteristic, complemented
438#2311C2×C11311yescharacteristic, complemented
439#2036C2×C11311yescharacteristic, complemented
440#2035C2×C11311yescharacteristic, complemented
441#2034C2×C11311yescharacteristic, complemented
442#2033C2×C11311yescharacteristic, complemented
443#1874C2×C11311yescharacteristic, complemented
444#1872C2×C11311yescharacteristic, complemented
445#1853C2×C11311yescharacteristic, complemented
446#1852C2×C11311yescharacteristic, complemented
447#1788C2×C11311yescharacteristic, complemented
448#1788C2×C11311yescharacteristic, complemented
449#1780C2×C11311yescharacteristic, complemented
450C113#2401711yescharacteristic, direct product factor, Sylow
451C22×#41C22×C11311yescharacteristic
452C22×#41C22×C11311yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C11311yescharacteristic
457C2×C22⋊Q8C22×C11311yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C11311yescharacteristic
462C2×#121C22×C11311yescharacteristic
463C2×#117C22×C11311yescharacteristic
464C22×C4⋊C4C22×C11311yescharacteristic
465C22×C4⋊C4C22×C11311yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C11311yescharacteristic
469C2×#107C22×C11311yescharacteristic
470C2×#106C22×C11311yescharacteristic
471C2×#106C22×C11311yescharacteristic
472C2×#103C22×C11311yescharacteristic
473C2×#103C22×C11311yescharacteristic
474C2×#103C22×C11311yescharacteristic
475C2×#103C22×C11311yescharacteristic
476C2×#102C22×C11311yescharacteristic
477C2×#102C22×C11311yescharacteristic
478C2×#102C22×C11311yescharacteristic
479C2×#102C22×C11311yescharacteristic
480C2×C22⋊C8C22×C11311yescharacteristic
481C2×C22⋊C8C22×C11311yescharacteristic
482C2×C22⋊C8C22×C11311yescharacteristic
483C2×C22⋊C8C22×C11311yescharacteristic
484C2×C22⋊C8C22×C11311yescharacteristic
485C2×C22⋊C8C22×C11311yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C11311yescharacteristic
491#380C22×C11311yescharacteristic
492#380C22×C11311yescharacteristic
493#380C22×C11311yescharacteristic
494#340C22×C11311yescharacteristic
495#340C22×C11311yescharacteristic
496#340C22×C11311yescharacteristic
497#340C22×C11311yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C11311yescharacteristic
511C22×Q8C23×C11311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C11311yescharacteristic
516C22×D4D4×C11311yescharacteristic
517C22×D4D4×C11311yescharacteristic
518C22×D4C23×C11311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C11311yescharacteristic
523C23×C4C23×C11311yescharacteristic
524C23×C4C23×C11311yescharacteristic
525C22×C8C23×C11311yescharacteristic
526C22×C8C23×C11311yescharacteristic
527C22×C8C23×C11311yescharacteristic
528C22×C8C23×C11311yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C11314yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C11314yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C11311yescharacteristic
552C2×C4⋊C4C23×C11311yescharacteristic
553C2×C4⋊C4C23×C11311yescharacteristic
554C2×C4⋊C4C23×C11311yescharacteristic
555C2×C4⋊C4C23×C11311yescharacteristic
556C2×C4⋊C4C23×C11311yescharacteristic
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⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C11311yescharacteristic
591C24C2×D4×C11311yescharacteristic
592C24C2×D4×C11311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C11312yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C11312yes—
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—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C11311yescharacteristic
665C22×C4C2×D4×C11311yescharacteristic
666C22×C4C2×D4×C11312yes—
667C22×C4C2×D4×C11312yes—
668C22×C4C2×D4×C11311yescharacteristic
669C22×C4#41×C11312yes—
670C22×C4#41×C11312yes—
671C22×C4C24×C11311yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C11312yes—
699C4⋊C4C2×D4×C11312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C11312yes—
737C23#123×C11312yes—
738C23C22×D4×C11311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
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—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4#120×C11312yes—
798C2×C4#123×C11312yes—
799C2×C4C22×D4×C11311yescharacteristic
800C2×C4C22×D4×C11311yescharacteristic
801C2×C4C2×#41×C11311yescharacteristic
802C2×C4C2×#41×C11311yescharacteristic
803C2×C4H(5,𝔽2)×C11311yescharacteristic
804C2×C4H(5,𝔽2)×C11311yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C11311yescharacteristic
838C22C2×#123×C11311yescharacteristic
839C22#534×C11311yescharacteristic
840C22#576×C11311yescharacteristic
841C22#577×C11311yescharacteristic
842C22#577×C11311yescharacteristic
843C22#578×C11311yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C11311yescharacteristic
855C4#546×C11311yescharacteristic
856C4#546×C11311yescharacteristic
857C4#546×C11311yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C113×#240511yescharacteristic
863C2C113×#301211yescharacteristic
864C2C113×#301311yescharacteristic
865C2C113×#309811yescharacteristic
866C2C113×#309911yescharacteristic
867C2C113×#319811yescharacteristic
868C2C113×#320111yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#537×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×#485×C113C2semidirect
3. C2×#482×C113C2semidirect
4. C113×#2311C2semidirect
5. C113×#2036C2semidirect
6. C113×#2035C2semidirect
7. C113×#2034C2semidirect
8. C113×#2033C2semidirect
9. C113×#1874C2semidirect
10. C113×#1872C2semidirect
11. C113×#1853C2semidirect
12. C113×#1852C2semidirect
13. C113×#1788C2semidirect
14. C113×#1788C2semidirect
15. C113×#1780C2semidirect
423. #24017C113direct (N × H)
436. C2×#485C2×C113semidirect
437. C2×#482C2×C113semidirect
438. #2311C2×C113semidirect
439. #2036C2×C113semidirect
440. #2035C2×C113semidirect
441. #2034C2×C113semidirect
442. #2033C2×C113semidirect
443. #1874C2×C113semidirect
444. #1872C2×C113semidirect
445. #1853C2×C113semidirect
446. #1852C2×C113semidirect
447. #1788C2×C113semidirect
448. #1788C2×C113semidirect
449. #1780C2×C113semidirect
450. C113#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#537×C1132
C2×#485×C1132
C2×#482×C1132
C113×#23112
C113×#20362
C113×#20352
C113×#20342
C113×#20332
C113×#18742
C113×#18722
C113×#18532
C113×#18522
C113×#17882
C113×#17802
#24017113