Finite Group Databasebeta

← C113×#25139 #43293159

Subgroups — C113×#25139 #43293159

Order 28928.

1194 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#449×C113C211yesmaximal, characteristic, complemented
3C2×#436×C113C211yesmaximal, characteristic, complemented
4C2×#417×C113C211yesmaximal, characteristic, complemented
5C113×#2416C211yesmaximal, characteristic, complemented
6C113×#2407C211yesmaximal, characteristic, complemented
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2036C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1970C211yesmaximal, characteristic, complemented
12C113×#1933C211yesmaximal, characteristic, complemented
13C113×#1895C211yesmaximal, characteristic, complemented
14C113×#1895C211yesmaximal, characteristic, complemented
15C113×#1852C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×D8×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×#121×C113—21no—
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#121×C113C2211yescharacteristic
26C2×C4×D4×C113C2211yescharacteristic
27C22×C4⋊C4×C113C2211yescharacteristic
28#468×C113—24no—
29#449×C113—24no—
30#436×C113—24no—
31C2×#107×C113C2211yescharacteristic
32C2×#107×C113C2211yescharacteristic
33C2×C4⋊C8×C113C2211yescharacteristic
34#417×C113—24no—
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#103×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45C2×C4×C8×C113C2211yescharacteristic
46#396×C113—21no—
47#394×C113—21no—
48#394×C113—21no—
49#392×C113—21no—
50#391×C113C2211yescharacteristic
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#389×C113C2211yescharacteristic
54#386×C113—21no—
55#386×C113—21no—
56#385×C113—21no—
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—41no—
68C2×#41×C113—41no—
69C22×Q8×C113C2311yescharacteristic
70C22×D4×C113—21no—
71C22×D4×C113—21no—
72C22×D4×C113—21no—
73C22×D4×C113—21no—
74C22×D4×C113D411yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C23×C4×C113—21no—
78C23×C4×C113—21no—
79C23×C4×C113C2311yescharacteristic
80C23×C4×C113C2311yescharacteristic
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—41no—
84C2×D8×C113—22no—
85C2×D8×C113—22no—
86C2×D8×C113—41no—
87C2×M16×C113—22no—
88C2×M16×C113—22no—
89C2×M16×C113—22no—
90C2×M16×C113—22no—
91C2×M16×C113—41no—
92C2×M16×C113—41no—
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—41no—
99#121×C113—22no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—22no—
103#121×C113—41no—
104#121×C113—41no—
105#121×C113—44no—
106C4×D4×C113—22no—
107C4×D4×C113—22no—
108C2×C4⋊C4×C113—22no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113—41no—
113C2×C4⋊C4×C113D411yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C4⋊C4×C113C2311yescharacteristic
118C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113D411yescharacteristic
130C2×C22⋊C4×C113D411yescharacteristic
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133#107×C113—41no—
134C4⋊C8×C113—22no—
135#103×C113—22no—
136#103×C113—22no—
137#103×C113D414yescomplemented
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113—41no—
143C22⋊C8×C113—22no—
144C22⋊C8×C113D414yescomplemented
145C4×C8×C113—22no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113—21no—
150#95×C113—21no—
151C24×C113—21no—
152C24×C113—21no—
153C24×C113C2×D411yescharacteristic
154C24×C113C2×D411yescharacteristic
155#41×C113—28no—
156#41×C113—44no—
157#41×C113—44no—
158#41×C113—44no—
159C2×Q8×C113—21no—
160C2×Q8×C113—21no—
161C2×Q8×C113—21no—
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113C2×D412yes—
165C2×D4×C113—22no—
166C2×D4×C113—22no—
167C2×D4×C113—21no—
168C2×D4×C113—21no—
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—41no—
179C2×D4×C113—42no—
180C2×D4×C113—42no—
181C2×D4×C113—42no—
182C2×D4×C113—42no—
183C2×D4×C113—42no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—42no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—81no—
190C2×D4×C113—81no—
191C2×D4×C113#4112yes—
192C22×C4×C113—21no—
193C22×C4×C113—21no—
194C22×C4×C113—21no—
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—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—42no—
209C22×C4×C113—42no—
210C22×C4×C113—42no—
211C22×C4×C113—42no—
212C22×C4×C113—42no—
213C22×C4×C113—81no—
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D411yescharacteristic
216C22×C4×C113C2×D411yescharacteristic
217C22×C4×C113C2×D412yes—
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113#4112yes—
220C22×C4×C113C2411yescharacteristic
221SD16×C113—44no—
222D8×C113—44no—
223M16×C113—44no—
224M16×C113—44no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113—21no—
233C2×C8×C113—21no—
234C2×C8×C113C2×D412yes—
235C2×C8×C113C2×D412yes—
236C2×C8×C113C2×D412yes—
237C4⋊C4×C113—22no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—21no—
245C4⋊C4×C113—21no—
246C4⋊C4×C113—21no—
247C4⋊C4×C113—42no—
248C4⋊C4×C113—42no—
249C4⋊C4×C113—42no—
250C4⋊C4×C113C2×D412yes—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—42no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—42no—
259C22⋊C4×C113—42no—
260C22⋊C4×C113—81no—
261C22⋊C4×C113—81no—
262C22⋊C4×C113—81no—
263C42×C113—21no—
264C42×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—22no—
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
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—41no—
292C23×C113#12112yes—
293C23×C113C22×D411yescharacteristic
294Q8×C113—22no—
295Q8×C113—22no—
296Q8×C113—41no—
297Q8×C113—41no—
298D4×C113—22no—
299D4×C113—22no—
300D4×C113—44no—
301D4×C113—48no—
302D4×C113—41no—
303D4×C113—41no—
304D4×C113—41no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113—41no—
308D4×C113—84no—
309D4×C113—84no—
310D4×C113—84no—
311C2×C4×C113—21no—
312C2×C4×C113—21no—
313C2×C4×C113—21no—
314C2×C4×C113—21no—
315C2×C4×C113—22no—
316C2×C4×C113—22no—
317C2×C4×C113—22no—
318C2×C4×C113—22no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—22no—
323C2×C4×C113—22no—
324C2×C4×C113—21no—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—48no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—41no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
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—84no—
349C2×C4×C113#12112yes—
350C2×C4×C113AGL(1,ℤ/8)12yes—
351C2×C4×C113C22×D411yescharacteristic
352C2×C4×C113C22×D411yescharacteristic
353C2×C4×C113C2×#4111yescharacteristic
354C2×C4×C113C2×#4111yescharacteristic
355C2×C4×C113H(5,𝔽2)11yescharacteristic
356C2×C4×C113H(5,𝔽2)11yescharacteristic
357C8×C113—22no—
358C8×C113—22no—
359C8×C113—22no—
360C8×C113—41no—
361C22×C113—22no—
362C22×C113—22no—
363C22×C113—22no—
364C22×C113—41no—
365C22×C113—41no—
366C22×C113—41no—
367C22×C113—41no—
368C22×C113—41no—
369C22×C113—42no—
370C22×C113—42no—
371C22×C113—41no—
372C22×C113—41no—
373C22×C113—41no—
374C22×C113—41no—
375C22×C113—41no—
376C22×C113—41no—
377C22×C113—42no—
378C22×C113—81no—
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×C113C2×#12111yescharacteristic
390C22×C113D4211yescharacteristic
391C22×C113#54611yescharacteristic
392C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C113#57511yescharacteristic
394C22×C113#57611yescharacteristic
395C22×C113#57811yescharacteristic
396C4×C113—22no—
397C4×C113—22no—
398C4×C113—41no—
399C4×C113—42no—
400C4×C113—42no—
401C4×C113—41no—
402C4×C113—81no—
403C4×C113—81no—
404C4×C113—81no—
405C4×C113—81no—
406C4×C113#52511yescharacteristic
407C4×C113#53811yescharacteristic
408C4×C113D4211yescharacteristic
409C4×C113#54611yescharacteristic
410#25139C11311yesmaximal, characteristic, direct product factor, Sylow
411C2×C113—42no—
412C2×C113—81no—
413C2×C113—82no—
414C2×C113—161no—
415C2×C113#242411yescharacteristic
416C2×C113#305511yescharacteristic
417C2×C113#306111yescharacteristic
418C2×C113#327411yescharacteristic
419C2×C113#327711yescharacteristic
420C2×C113#332211yescharacteristic
421C2×C113#333011yescharacteristic
422C2×#468C2×C11311yescharacteristic, complemented
423C2×#449C2×C11311yescharacteristic, complemented
424C2×#436C2×C11311yescharacteristic, complemented
425C2×#417C2×C11311yescharacteristic, complemented
426#2416C2×C11311yescharacteristic, complemented
427#2407C2×C11311yescharacteristic, complemented
428#2067C2×C11311yescharacteristic, complemented
429#2055C2×C11311yescharacteristic, complemented
430#2036C2×C11311yescharacteristic, complemented
431#1999C2×C11311yescharacteristic, complemented
432#1970C2×C11311yescharacteristic, complemented
433#1933C2×C11311yescharacteristic, complemented
434#1895C2×C11311yescharacteristic, complemented
435#1895C2×C11311yescharacteristic, complemented
436#1852C2×C11311yescharacteristic, complemented
437C113#2513911yescharacteristic, direct product factor, Sylow
438C22×#41C22×C11311yescharacteristic
439C22×SD16C22×C11311yescharacteristic
440C22×D8C22×C11311yescharacteristic
441C22×M16C22×C11311yescharacteristic
442C22×M16C22×C11311yescharacteristic
443C2×C22⋊Q8C22×C11311yescharacteristic
444C2×#121—21no—
445C2×#121C22×C11311yescharacteristic
446C2×#121C22×C11311yescharacteristic
447C2×#121C22×C11311yescharacteristic
448C2×C4×D4C22×C11311yescharacteristic
449C22×C4⋊C4C22×C11311yescharacteristic
450#468—24no—
451#449—24no—
452#436—24no—
453C2×#107C22×C11311yescharacteristic
454C2×#107C22×C11311yescharacteristic
455C2×C4⋊C8C22×C11311yescharacteristic
456#417—24no—
457C2×#103C22×C11311yescharacteristic
458C2×#103C22×C11311yescharacteristic
459C2×#103C22×C11311yescharacteristic
460C2×#102C22×C11311yescharacteristic
461C2×#102C22×C11311yescharacteristic
462C2×#102C22×C11311yescharacteristic
463C2×#102C22×C11311yescharacteristic
464C2×#102C22×C11311yescharacteristic
465C2×C22⋊C8C22×C11311yescharacteristic
466C2×C22⋊C8C22×C11311yescharacteristic
467C2×C4×C8C22×C11311yescharacteristic
468#396—21no—
469#394—21no—
470#394—21no—
471#392—21no—
472#391C22×C11311yescharacteristic
473#390C22×C11311yescharacteristic
474#390C22×C11311yescharacteristic
475#389C22×C11311yescharacteristic
476#386—21no—
477#386—21no—
478#385—21no—
479#380C22×C11311yescharacteristic
480#380C22×C11311yescharacteristic
481#340C22×C11311yescharacteristic
482#340C22×C11311yescharacteristic
483#340C22×C11311yescharacteristic
484#340C22×C11311yescharacteristic
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—41no—
490C2×#41—41no—
491C22×Q8C23×C11311yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4D4×C11311yescharacteristic
497C22×D4C23×C11311yescharacteristic
498C22×D4C23×C11311yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4C23×C11311yescharacteristic
502C23×C4C23×C11311yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C22×C8C23×C11311yescharacteristic
516C22×C8C23×C11311yescharacteristic
517C22×C8C23×C11311yescharacteristic
518C22×C8C23×C11311yescharacteristic
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527#121—44no—
528C4×D4—22no—
529C4×D4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4D4×C11311yescharacteristic
536C2×C4⋊C4C23×C11311yescharacteristic
537C2×C4⋊C4C23×C11311yescharacteristic
538C2×C4⋊C4C23×C11311yescharacteristic
539C2×C4⋊C4C23×C11311yescharacteristic
540C2×C4⋊C4C23×C11311yescharacteristic
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⋊C4—21no—
551C2×C22⋊C4D4×C11311yescharacteristic
552C2×C22⋊C4D4×C11311yescharacteristic
553C2×C42C23×C11311yescharacteristic
554#107—22no—
555#107—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#103D4×C11314yescomplemented
560#102—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—41no—
565C22⋊C8—22no—
566C22⋊C8D4×C11314yescomplemented
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573C24—21no—
574C24—21no—
575C24C2×D4×C11311yescharacteristic
576C24C2×D4×C11311yescharacteristic
577#41—28no—
578#41—44no—
579#41—44no—
580#41—44no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C11312yes—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—41no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4#41×C11312yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
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—21no—
629C22×C4—21no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×D4×C11311yescharacteristic
637C22×C4C2×D4×C11311yescharacteristic
638C22×C4C2×D4×C11311yescharacteristic
639C22×C4C2×D4×C11312yes—
640C22×C4C2×D4×C11311yescharacteristic
641C22×C4#41×C11312yes—
642C22×C4C24×C11311yescharacteristic
643SD16—44no—
644D8—44no—
645M16—44no—
646M16—44no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8C2×D4×C11312yes—
657C2×C8C2×D4×C11312yes—
658C2×C8C2×D4×C11312yes—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C11312yes—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—81no—
683C22⋊C4—81no—
684C22⋊C4—81no—
685C42—21no—
686C42—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
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#121×C11312yes—
715C23C22×D4×C11311yescharacteristic
716Q8—22no—
717Q8—22no—
718Q8—41no—
719Q8—41no—
720D4—22no—
721D4—22no—
722D4—44no—
723D4—48no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—48no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
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—84no—
771C2×C4#121×C11312yes—
772C2×C4AGL(1,ℤ/8)×C11312yes—
773C2×C4C22×D4×C11311yescharacteristic
774C2×C4C22×D4×C11311yescharacteristic
775C2×C4C2×#41×C11311yescharacteristic
776C2×C4C2×#41×C11311yescharacteristic
777C2×C4H(5,𝔽2)×C11311yescharacteristic
778C2×C4H(5,𝔽2)×C11311yescharacteristic
779C8—22no—
780C8—22no—
781C8—22no—
782C8—41no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22C2×#121×C11311yescharacteristic
812C22D42×C11311yescharacteristic
813C22#546×C11311yescharacteristic
814C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
815C22#575×C11311yescharacteristic
816C22#576×C11311yescharacteristic
817C22#578×C11311yescharacteristic
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4#525×C11311yescharacteristic
829C4#538×C11311yescharacteristic
830C4D42×C11311yescharacteristic
831C4#546×C11311yescharacteristic
832C2—42no—
833C2—81no—
834C2—82no—
835C2—161no—
836C2C113×#242411yescharacteristic
837C2C113×#305511yescharacteristic
838C2C113×#306111yescharacteristic
839C2C113×#327411yescharacteristic
840C2C113×#327711yescharacteristic
841C2C113×#332211yescharacteristic
842C2C113×#333011yescharacteristic
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×#468×C113C2semidirect
2. C2×#449×C113C2semidirect
3. C2×#436×C113C2semidirect
4. C2×#417×C113C2semidirect
5. C113×#2416C2semidirect
6. C113×#2407C2semidirect
7. C113×#2067C2semidirect
8. C113×#2055C2semidirect
9. C113×#2036C2semidirect
10. C113×#1999C2semidirect
11. C113×#1970C2semidirect
12. C113×#1933C2semidirect
13. C113×#1895C2semidirect
14. C113×#1895C2semidirect
15. C113×#1852C2semidirect
137. #103×C113D4semidirect
144. C22⋊C8×C113D4semidirect
410. #25139C113direct (N × H)
422. C2×#468C2×C113semidirect
423. C2×#449C2×C113semidirect
424. C2×#436C2×C113semidirect
425. C2×#417C2×C113semidirect
426. #2416C2×C113semidirect
427. #2407C2×C113semidirect
428. #2067C2×C113semidirect
429. #2055C2×C113semidirect
430. #2036C2×C113semidirect
431. #1999C2×C113semidirect
432. #1970C2×C113semidirect
433. #1933C2×C113semidirect
434. #1895C2×C113semidirect
435. #1895C2×C113semidirect
436. #1852C2×C113semidirect
437. C113#25139direct (N × H)
559. #103D4×C113semidirect
566. C22⋊C8D4×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×#449×C1132
C2×#436×C1132
C2×#417×C1132
C113×#24162
C113×#24072
C113×#20672
C113×#20552
C113×#20362
C113×#19992
C113×#19702
C113×#19332
C113×#18952
C113×#18522
#25139113