Finite Group Databasebeta

← C113×#25101 #43293121

Subgroups — C113×#25101 #43293121

Order 28928.

1248 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#447×C113C211yesmaximal, characteristic
4C2×#418×C113C211yesmaximal, characteristic, complemented
5C113×#2435C211yesmaximal, characteristic, complemented
6C113×#2363C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2054C211yesmaximal, characteristic, complemented
9C113×#2042C211yesmaximal, characteristic, complemented
10C113×#2012C211yesmaximal, characteristic, complemented
11C113×#1983C211yesmaximal, characteristic, complemented
12C113×#1925C211yesmaximal, characteristic, complemented
13C113×#1879C211yesmaximal, characteristic, complemented
14C113×#1873C211yesmaximal, characteristic, complemented
15C113×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic, complemented
18C22×D8×C113C2211yescharacteristic
19C22×D8×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic
21C2×#124×C113C2211yescharacteristic
22C2×#124×C113C2211yescharacteristic
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×C4×D4×C113C2211yescharacteristic, complemented
26C2×#117×C113C2211yescharacteristic
27#468×C113—24no—
28#463×C113—24no—
29#447×C113—24no—
30C2×#107×C113C2211yescharacteristic, complemented
31C2×C4⋊C8×C113C2211yescharacteristic, complemented
32C2×C4⋊C8×C113C2211yescharacteristic, complemented
33#418×C113—24no—
34C2×#103×C113C2211yescharacteristic, complemented
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic, complemented
44C2×C22⋊C8×C113C2211yescharacteristic
45#394×C113—21no—
46#394×C113—21no—
47#390×C113—21no—
48#390×C113C2211yescharacteristic
49#390×C113C2211yescharacteristic
50#390×C113C2211yescharacteristic, complemented
51#389×C113C2211yescharacteristic, complemented
52#388×C113—21no—
53#386×C113—21no—
54#379×C113—21no—
55#379×C113—21no—
56C4×C4⋊C4×C113C2211yescharacteristic, complemented
57C4×C22⋊C4×C113—21no—
58C4×C22⋊C4×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#336×C113C2211yescharacteristic, complemented
62#336×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C22×Q8×C113C2311yescharacteristic
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—21no—
68C22×D4×C113—22no—
69C22×D4×C113—21no—
70C22×D4×C113—22no—
71C22×D4×C113—41no—
72C22×D4×C113—41no—
73C22×D4×C113C2311yescharacteristic
74C22×D4×C113C2311yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C23×C4×C113—21no—
77C23×C4×C113C2311yescharacteristic
78C2×SD16×C113—22no—
79C2×SD16×C113—22no—
80C2×SD16×C113—41no—
81C2×D8×C113—22no—
82C2×D8×C113—22no—
83C2×D8×C113—22no—
84C2×D8×C113—22no—
85C2×D8×C113—41no—
86C2×D8×C113—41no—
87C2×M16×C113—22no—
88C2×M16×C113—22no—
89C2×M16×C113—41no—
90C22×C8×C113C2311yescharacteristic
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94#124×C113—22no—
95#124×C113—22no—
96#124×C113—41no—
97#124×C113—41no—
98C22⋊Q8×C113—22no—
99C22⋊Q8×C113—22no—
100#121×C113—22no—
101#121×C113D414yes—
102C4×D4×C113—22no—
103C4×D4×C113—41no—
104#117×C113—22no—
105#117×C113—41no—
106C2×C4⋊C4×C113—21no—
107C2×C4⋊C4×C113—21no—
108C2×C4⋊C4×C113C2311yescharacteristic
109C2×C4⋊C4×C113C2311yescharacteristic
110C2×C4⋊C4×C113C2311yescharacteristic
111C2×C4⋊C4×C113C2311yescharacteristic
112C2×C22⋊C4×C113—21no—
113C2×C22⋊C4×C113—21no—
114C2×C22⋊C4×C113—21no—
115C2×C22⋊C4×C113—21no—
116C2×C22⋊C4×C113—21no—
117C2×C22⋊C4×C113—21no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113D411yescharacteristic
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C42×C113—21no—
129C2×C42×C113—21no—
130C2×C42×C113C2311yescharacteristic
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133C4⋊C8×C113—22no—
134C4⋊C8×C113—41no—
135#103×C113—22no—
136#103×C113—22no—
137#103×C113—41no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—22no—
143#102×C113—22no—
144#102×C113D414yescomplemented
145C22⋊C8×C113—22no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113D411yescharacteristic
149#95×C113D411yescharacteristic
150C24×C113—21no—
151C24×C113—21no—
152C24×C113—21no—
153C24×C113—42no—
154C24×C113—42no—
155C24×C113—42no—
156C24×C113—42no—
157C24×C113—42no—
158C24×C113—81no—
159C24×C113—81no—
160C24×C113C2×D411yescharacteristic
161C2×Q8×C113—21no—
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×D4×C113—28no—
168C2×D4×C113—24no—
169C2×D4×C113—21no—
170C2×D4×C113—21no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—21no—
174C2×D4×C113—21no—
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—44no—
185C2×D4×C113—44no—
186C2×D4×C113—42no—
187C2×D4×C113—42no—
188C2×D4×C113—44no—
189C2×D4×C113—42no—
190C2×D4×C113—81no—
191C2×D4×C113—81no—
192C2×D4×C113C2×D412yes—
193C2×D4×C113C2×D412yes—
194C2×D4×C113#4112yes—
195C22×C4×C113—21no—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—42no—
205C22×C4×C113—42no—
206C22×C4×C113—81no—
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D411yescharacteristic
209C22×C4×C113C2×D411yescharacteristic
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D412yes—
213C22×C4×C113#4112yes—
214C22×C4×C113C2411yescharacteristic
215SD16×C113—44no—
216D8×C113—44no—
217D8×C113—44no—
218M16×C113—44no—
219C2×C8×C113—21no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113C2×D412yes—
231C4⋊C4×C113—21no—
232C4⋊C4×C113—21no—
233C4⋊C4×C113—21no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—42no—
238C4⋊C4×C113—81no—
239C4⋊C4×C113C2×D412yes—
240C4⋊C4×C113C2×D412yes—
241C22⋊C4×C113—24no—
242C22⋊C4×C113—41no—
243C22⋊C4×C113—41no—
244C22⋊C4×C113—42no—
245C22⋊C4×C113—42no—
246C22⋊C4×C113—42no—
247C22⋊C4×C113—42no—
248C22⋊C4×C113—42no—
249C22⋊C4×C113—42no—
250C22⋊C4×C113—42no—
251C22⋊C4×C113—42no—
252C22⋊C4×C113—81no—
253C22⋊C4×C113—81no—
254C22⋊C4×C113—81no—
255C22⋊C4×C113—81no—
256C22⋊C4×C113—81no—
257C42×C113—21no—
258C42×C113—21no—
259C42×C113—21no—
260C42×C113—21no—
261C42×C113—42no—
262C42×C113—81no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—22no—
270C23×C113—22no—
271C23×C113—22no—
272C23×C113—48no—
273C23×C113—41no—
274C23×C113—41no—
275C23×C113—41no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113—41no—
279C23×C113—41no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—84no—
292C23×C113—84no—
293C23×C113—84no—
294C23×C113—84no—
295C23×C113—84no—
296C23×C113—84no—
297C23×C113#12112yes—
298C23×C113C22×D411yescharacteristic
299Q8×C113—41no—
300Q8×C113—41no—
301Q8×C113—41no—
302Q8×C113—41no—
303D4×C113—22no—
304D4×C113—22no—
305D4×C113—22no—
306D4×C113—22no—
307D4×C113—22no—
308D4×C113—22no—
309D4×C113—48no—
310D4×C113—41no—
311D4×C113—41no—
312D4×C113—41no—
313D4×C113—41no—
314D4×C113—41no—
315D4×C113—41no—
316D4×C113—84no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—22no—
320C2×C4×C113—22no—
321C2×C4×C113—22no—
322C2×C4×C113—22no—
323C2×C4×C113—22no—
324C2×C4×C113—21no—
325C2×C4×C113—21no—
326C2×C4×C113—22no—
327C2×C4×C113—21no—
328C2×C4×C113—21no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—21no—
333C2×C4×C113—21no—
334C2×C4×C113—21no—
335C2×C4×C113—21no—
336C2×C4×C113—21no—
337C2×C4×C113—41no—
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—84no—
351C2×C4×C113#12112yes—
352C2×C4×C113C22×D411yescharacteristic
353C2×C4×C113C22×D411yescharacteristic
354C2×C4×C113C2×#4111yescharacteristic
355C2×C4×C113C2×#4111yescharacteristic
356C2×C4×C113H(5,𝔽2)11yescharacteristic
357C2×C4×C113H(5,𝔽2)11yescharacteristic
358C8×C113—22no—
359C8×C113—41no—
360C8×C113—41no—
361C8×C113—41no—
362C22×C113—22no—
363C22×C113—22no—
364C22×C113—22no—
365C22×C113—41no—
366C22×C113—41no—
367C22×C113—41no—
368C22×C113—41no—
369C22×C113—42no—
370C22×C113—42no—
371C22×C113—42no—
372C22×C113—42no—
373C22×C113—42no—
374C22×C113—42no—
375C22×C113—42no—
376C22×C113—42no—
377C22×C113—42no—
378C22×C113—816no—
379C22×C113—81no—
380C22×C113—81no—
381C22×C113—81no—
382C22×C113—81no—
383C22×C113—81no—
384C22×C113—81no—
385C22×C113—81no—
386C22×C113—81no—
387C22×C113—81no—
388C22×C113—81no—
389C22×C113—81no—
390C22×C113—81no—
391C22×C113C2×#12111yescharacteristic
392C22×C113D4211yescharacteristic
393C22×C113#54611yescharacteristic
394C22×C113#57511yescharacteristic
395C22×C113#57511yescharacteristic
396C22×C113#57611yescharacteristic
397C22×C113#57611yescharacteristic
398C4×C113—22no—
399C4×C113—41no—
400C4×C113—41no—
401C4×C113—42no—
402C4×C113—42no—
403C4×C113—41no—
404C4×C113—41no—
405C4×C113—81no—
406C4×C113—81no—
407C4×C113—81no—
408C4×C113#52511yescharacteristic
409C4×C113#53811yescharacteristic
410C4×C113D4211yescharacteristic
411C4×C113#54611yescharacteristic
412#25101C11311yesmaximal, characteristic, direct product factor, Sylow
413C2×C113—42no—
414C2×C113—82no—
415C2×C113—82no—
416C2×C113—82no—
417C2×C113#242411yescharacteristic
418C2×C113#304011yescharacteristic
419C2×C113#304111yescharacteristic
420C2×C113#326811yescharacteristic
421C2×C113#327311yescharacteristic
422C2×C113#331911yescharacteristic
423C2×C113#332211yescharacteristic
424C2×#468C2×C11311yescharacteristic, complemented
425C2×#463C2×C11311yescharacteristic, complemented
426C2×#447C2×C11311yescharacteristic
427C2×#418C2×C11311yescharacteristic, complemented
428#2435C2×C11311yescharacteristic, complemented
429#2363C2×C11311yescharacteristic, complemented
430#2067C2×C11311yescharacteristic, complemented
431#2054C2×C11311yescharacteristic, complemented
432#2042C2×C11311yescharacteristic, complemented
433#2012C2×C11311yescharacteristic, complemented
434#1983C2×C11311yescharacteristic, complemented
435#1925C2×C11311yescharacteristic, complemented
436#1879C2×C11311yescharacteristic, complemented
437#1873C2×C11311yescharacteristic, complemented
438#1851C2×C11311yescharacteristic, complemented
439C113#2510111yescharacteristic, direct product factor, Sylow
440C23×D4C22×C11311yescharacteristic
441C22×SD16C22×C11311yescharacteristic, complemented
442C22×D8C22×C11311yescharacteristic
443C22×D8C22×C11311yescharacteristic
444C22×M16C22×C11311yescharacteristic
445C2×#124C22×C11311yescharacteristic
446C2×#124C22×C11311yescharacteristic
447C2×C22⋊Q8C22×C11311yescharacteristic
448C2×#121C22×C11311yescharacteristic
449C2×C4×D4C22×C11311yescharacteristic, complemented
450C2×#117C22×C11311yescharacteristic
451#468—24no—
452#463—24no—
453#447—24no—
454C2×#107C22×C11311yescharacteristic, complemented
455C2×C4⋊C8C22×C11311yescharacteristic, complemented
456C2×C4⋊C8C22×C11311yescharacteristic, complemented
457#418—24no—
458C2×#103C22×C11311yescharacteristic, complemented
459C2×#103C22×C11311yescharacteristic, complemented
460C2×#103C22×C11311yescharacteristic, complemented
461C2×#102C22×C11311yescharacteristic
462C2×#102C22×C11311yescharacteristic
463C2×#102C22×C11311yescharacteristic
464C2×#102C22×C11311yescharacteristic
465C2×#102C22×C11311yescharacteristic
466C2×#102C22×C11311yescharacteristic
467C2×#102C22×C11311yescharacteristic, complemented
468C2×C22⋊C8C22×C11311yescharacteristic
469#394—21no—
470#394—21no—
471#390—21no—
472#390C22×C11311yescharacteristic
473#390C22×C11311yescharacteristic
474#390C22×C11311yescharacteristic, complemented
475#389C22×C11311yescharacteristic, complemented
476#388—21no—
477#386—21no—
478#379—21no—
479#379—21no—
480C4×C4⋊C4C22×C11311yescharacteristic, complemented
481C4×C22⋊C4—21no—
482C4×C22⋊C4C22×C11311yescharacteristic
483#340C22×C11311yescharacteristic, complemented
484#340C22×C11311yescharacteristic, complemented
485#336C22×C11311yescharacteristic, complemented
486#336C22×C11311yescharacteristic, complemented
487C25—21no—
488C22×Q8C23×C11311yescharacteristic
489C22×D4—22no—
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C23×C11311yescharacteristic
498C22×D4C23×C11311yescharacteristic
499C22×D4C23×C11311yescharacteristic
500C23×C4—21no—
501C23×C4C23×C11311yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C22×C8C23×C11311yescharacteristic
515C22×C8C23×C11311yescharacteristic
516C22×C8C23×C11311yescharacteristic
517C22×C8C23×C11311yescharacteristic
518#124—22no—
519#124—22no—
520#124—41no—
521#124—41no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524#121—22no—
525#121D4×C11314yes—
526C4×D4—22no—
527C4×D4—41no—
528#117—22no—
529#117—41no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C11311yescharacteristic
533C2×C4⋊C4C23×C11311yescharacteristic
534C2×C4⋊C4C23×C11311yescharacteristic
535C2×C4⋊C4C23×C11311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C11311yescharacteristic
551C2×C22⋊C4D4×C11311yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C11311yescharacteristic
555C2×C42C23×C11311yescharacteristic
556#107—22no—
557C4⋊C8—22no—
558C4⋊C8—41no—
559#103—22no—
560#103—22no—
561#103—41no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102D4×C11314yescomplemented
569C22⋊C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C11311yescharacteristic
573#95D4×C11311yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24—42no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—81no—
583C24—81no—
584C24C2×D4×C11311yescharacteristic
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×D4—28no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4C2×D4×C11312yes—
617C2×D4C2×D4×C11312yes—
618C2×D4#41×C11312yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4C2×D4×C11311yescharacteristic
632C22×C4C2×D4×C11311yescharacteristic
633C22×C4C2×D4×C11311yescharacteristic
634C22×C4C2×D4×C11311yescharacteristic
635C22×C4C2×D4×C11311yescharacteristic
636C22×C4C2×D4×C11312yes—
637C22×C4#41×C11312yes—
638C22×C4C24×C11311yescharacteristic
639SD16—44no—
640D8—44no—
641D8—44no—
642M16—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8C2×D4×C11312yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C11312yes—
664C4⋊C4C2×D4×C11312yes—
665C22⋊C4—24no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—42no—
686C42—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—48no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23#121×C11312yes—
722C23C22×D4×C11311yescharacteristic
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—22no—
733D4—48no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—84no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4#121×C11312yes—
776C2×C4C22×D4×C11311yescharacteristic
777C2×C4C22×D4×C11311yescharacteristic
778C2×C4C2×#41×C11311yescharacteristic
779C2×C4C2×#41×C11311yescharacteristic
780C2×C4H(5,𝔽2)×C11311yescharacteristic
781C2×C4H(5,𝔽2)×C11311yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—816no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C11311yescharacteristic
816C22D42×C11311yescharacteristic
817C22#546×C11311yescharacteristic
818C22#575×C11311yescharacteristic
819C22#575×C11311yescharacteristic
820C22#576×C11311yescharacteristic
821C22#576×C11311yescharacteristic
822C4—22no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4#525×C11311yescharacteristic
833C4#538×C11311yescharacteristic
834C4D42×C11311yescharacteristic
835C4#546×C11311yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—82no—
840C2C113×#242411yescharacteristic
841C2C113×#304011yescharacteristic
842C2C113×#304111yescharacteristic
843C2C113×#326811yescharacteristic
844C2C113×#327311yescharacteristic
845C2C113×#331911yescharacteristic
846C2C113×#332211yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#447×C113C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C113C2semidirect
2. C2×#463×C113C2semidirect
4. C2×#418×C113C2semidirect
5. C113×#2435C2semidirect
6. C113×#2363C2semidirect
7. C113×#2067C2semidirect
8. C113×#2054C2semidirect
9. C113×#2042C2semidirect
10. C113×#2012C2semidirect
11. C113×#1983C2semidirect
12. C113×#1925C2semidirect
13. C113×#1879C2semidirect
14. C113×#1873C2semidirect
15. C113×#1851C2semidirect
17. C22×SD16×C113C22semidirect
25. C2×C4×D4×C113C22semidirect
30. C2×#107×C113C22semidirect
31. C2×C4⋊C8×C113C22semidirect
32. C2×C4⋊C8×C113C22semidirect
34. C2×#103×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
43. C2×#102×C113C22semidirect
50. #390×C113C22semidirect
51. #389×C113C22semidirect
56. C4×C4⋊C4×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
144. #102×C113D4semidirect
412. #25101C113direct (N × H)
424. C2×#468C2×C113semidirect
425. C2×#463C2×C113semidirect
427. C2×#418C2×C113semidirect
428. #2435C2×C113semidirect
429. #2363C2×C113semidirect
430. #2067C2×C113semidirect
431. #2054C2×C113semidirect
432. #2042C2×C113semidirect
433. #2012C2×C113semidirect
434. #1983C2×C113semidirect
435. #1925C2×C113semidirect
436. #1879C2×C113semidirect
437. #1873C2×C113semidirect
438. #1851C2×C113semidirect
439. C113#25101direct (N × H)
441. C22×SD16C22×C113semidirect
449. C2×C4×D4C22×C113semidirect
454. C2×#107C22×C113semidirect
455. C2×C4⋊C8C22×C113semidirect
456. C2×C4⋊C8C22×C113semidirect
458. C2×#103C22×C113semidirect
459. C2×#103C22×C113semidirect
460. C2×#103C22×C113semidirect
467. C2×#102C22×C113semidirect
474. #390C22×C113semidirect
475. #389C22×C113semidirect
480. C4×C4⋊C4C22×C113semidirect
483. #340C22×C113semidirect
484. #340C22×C113semidirect
485. #336C22×C113semidirect
486. #336C22×C113semidirect
568. #102D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1132
C2×#463×C1132
C2×#447×C1132
C2×#418×C1132
C113×#24352
C113×#23632
C113×#20672
C113×#20542
C113×#20422
C113×#20122
C113×#19832
C113×#19252
C113×#18792
C113×#18732
C113×#18512
#25101113