Finite Group Databasebeta

← C113×#25105 #43293125

Subgroups — C113×#25105 #43293125

Order 28928.

1192 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C113C211yesmaximal, characteristic, complemented
2C2×#464×C113C211yesmaximal, characteristic, complemented
3C2×#450×C113C211yesmaximal, characteristic
4C2×#418×C113C211yesmaximal, characteristic
5C113×#2435C211yesmaximal, characteristic
6C113×#2362C211yesmaximal, characteristic, complemented
7C113×#2065C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2042C211yesmaximal, characteristic, complemented
10C113×#2015C211yesmaximal, characteristic, complemented
11C113×#1983C211yesmaximal, characteristic, complemented
12C113×#1926C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1873C211yesmaximal, characteristic, complemented
15C113×#1851C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×Q16×C113C2211yescharacteristic, complemented
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic
21C2×#124×C113C2211yescharacteristic
22C2×#124×C113C2211yescharacteristic
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×C22⋊Q8×C113C2211yescharacteristic
25C2×C4×Q8×C113C2211yescharacteristic, complemented
26C2×#117×C113C2211yescharacteristic
27#470×C113—24no—
28#464×C113—24no—
29#450×C113—24no—
30C2×#106×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×#103×C113C2211yescharacteristic, complemented
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45#394×C113—21no—
46#394×C113—21no—
47#391×C113C2211yescharacteristic, complemented
48#390×C113C2211yescharacteristic
49#390×C113C2211yescharacteristic
50#389×C113C2211yescharacteristic, complemented
51#388×C113—21no—
52#388×C113—21no—
53#387×C113—21no—
54#379×C113—21no—
55#379×C113—21no—
56C4×C4⋊C4×C113—21no—
57C4×C4⋊C4×C113C2211yescharacteristic, complemented
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×Q8×C113C2311yescharacteristic
66C22×D4×C113—22no—
67C22×D4×C113—22no—
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
75C23×C4×C113C2311yescharacteristic
76C2×Q16×C113—22no—
77C2×Q16×C113—22no—
78C2×Q16×C113—41no—
79C2×SD16×C113—22no—
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—41no—
84C2×SD16×C113—41no—
85C2×M16×C113—22no—
86C2×M16×C113—22no—
87C2×M16×C113—41no—
88C22×C8×C113C2311yescharacteristic
89C22×C8×C113C2311yescharacteristic
90C22×C8×C113C2311yescharacteristic
91C22×C8×C113C2311yescharacteristic
92#124×C113—22no—
93#124×C113—22no—
94#124×C113—41no—
95#124×C113—41no—
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—22no—
99C22⋊Q8×C113D414yes—
100C4×Q8×C113—22no—
101C4×Q8×C113—41no—
102#117×C113—22no—
103#117×C113—41no—
104C2×C4⋊C4×C113—21no—
105C2×C4⋊C4×C113—21no—
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×C113D411yescharacteristic
124C2×C22⋊C4×C113D411yescharacteristic
125C2×C42×C113—21no—
126C2×C42×C113—21no—
127C2×C42×C113—21no—
128C2×C42×C113C2311yescharacteristic
129C2×C42×C113C2311yescharacteristic
130#106×C113—22no—
131C4⋊C8×C113—22no—
132C4⋊C8×C113—41no—
133#103×C113—22no—
134#103×C113—22no—
135#103×C113—22no—
136#103×C113—41no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113D414yes—
143C22⋊C8×C113—22no—
144#95×C113—21no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113D411yescharacteristic
149#95×C113D411yescharacteristic
150C24×C113—21no—
151C24×C113—21no—
152C24×C113—42no—
153C24×C113—42no—
154C24×C113—42no—
155C24×C113—42no—
156C24×C113—42no—
157C24×C113—81no—
158C24×C113—81no—
159C24×C113C2×D411yescharacteristic
160C2×Q8×C113—21no—
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×Q8×C113—21no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—21no—
171C2×Q8×C113C2×D412yes—
172C2×D4×C113—28no—
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—44no—
184C2×D4×C113—44no—
185C2×D4×C113—42no—
186C2×D4×C113—42no—
187C2×D4×C113—44no—
188C2×D4×C113—42no—
189C2×D4×C113C2×D412yes—
190C2×D4×C113#4112yes—
191C22×C4×C113—21no—
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×C113C2×D411yescharacteristic
202C22×C4×C113C2×D411yescharacteristic
203C22×C4×C113C2×D411yescharacteristic
204C22×C4×C113C2×D411yescharacteristic
205C22×C4×C113C2×D411yescharacteristic
206C22×C4×C113C2×D412yes—
207C22×C4×C113#4112yes—
208C22×C4×C113C2411yescharacteristic
209Q16×C113—44no—
210SD16×C113—44no—
211SD16×C113—44no—
212M16×C113—44no—
213C2×C8×C113—21no—
214C2×C8×C113—21no—
215C2×C8×C113—21no—
216C2×C8×C113—21no—
217C2×C8×C113—21no—
218C2×C8×C113—21no—
219C2×C8×C113—21no—
220C2×C8×C113—21no—
221C2×C8×C113—21no—
222C2×C8×C113—21no—
223C2×C8×C113—21no—
224C2×C8×C113C2×D412yes—
225C4⋊C4×C113—24no—
226C4⋊C4×C113—21no—
227C4⋊C4×C113—21no—
228C4⋊C4×C113—21no—
229C4⋊C4×C113—21no—
230C4⋊C4×C113—21no—
231C4⋊C4×C113—21no—
232C4⋊C4×C113—42no—
233C4⋊C4×C113—42no—
234C4⋊C4×C113—42no—
235C4⋊C4×C113C2×D412yes—
236C4⋊C4×C113C2×D412yes—
237C22⋊C4×C113—24no—
238C22⋊C4×C113—41no—
239C22⋊C4×C113—41no—
240C22⋊C4×C113—42no—
241C22⋊C4×C113—42no—
242C22⋊C4×C113—42no—
243C22⋊C4×C113—42no—
244C22⋊C4×C113—42no—
245C22⋊C4×C113—42no—
246C22⋊C4×C113—81no—
247C22⋊C4×C113—81no—
248C22⋊C4×C113—81no—
249C22⋊C4×C113—81no—
250C42×C113—21no—
251C42×C113—21no—
252C42×C113—21no—
253C42×C113—21no—
254C42×C113—42no—
255C42×C113—42no—
256C42×C113—42no—
257C23×C113—21no—
258C23×C113—21no—
259C23×C113—21no—
260C23×C113—21no—
261C23×C113—21no—
262C23×C113—21no—
263C23×C113—22no—
264C23×C113—22no—
265C23×C113—48no—
266C23×C113—41no—
267C23×C113—41no—
268C23×C113—41no—
269C23×C113—41no—
270C23×C113—41no—
271C23×C113—41no—
272C23×C113—41no—
273C23×C113—41no—
274C23×C113—41no—
275C23×C113—41no—
276C23×C113—41no—
277C23×C113—41no—
278C23×C113—84no—
279C23×C113—84no—
280C23×C113—84no—
281C23×C113—84no—
282C23×C113—84no—
283C23×C113—84no—
284C23×C113#12112yes—
285C23×C113C22×D411yescharacteristic
286Q8×C113—22no—
287Q8×C113—22no—
288Q8×C113—41no—
289Q8×C113—41no—
290Q8×C113—41no—
291Q8×C113—41no—
292Q8×C113—41no—
293Q8×C113—41no—
294D4×C113—22no—
295D4×C113—22no—
296D4×C113—22no—
297D4×C113—22no—
298D4×C113—48no—
299D4×C113—41no—
300D4×C113—41no—
301D4×C113—41no—
302D4×C113—41no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—22no—
306C2×C4×C113—22no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—22no—
310C2×C4×C113—22no—
311C2×C4×C113—21no—
312C2×C4×C113—21no—
313C2×C4×C113—22no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
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#12112yes—
340C2×C4×C113C22×D411yescharacteristic
341C2×C4×C113C22×D411yescharacteristic
342C2×C4×C113C2×#4111yescharacteristic
343C2×C4×C113C2×#4111yescharacteristic
344C2×C4×C113H(5,𝔽2)11yescharacteristic
345C2×C4×C113H(5,𝔽2)11yescharacteristic
346C8×C113—22no—
347C8×C113—41no—
348C8×C113—41no—
349C8×C113—41no—
350C22×C113—22no—
351C22×C113—22no—
352C22×C113—22no—
353C22×C113—41no—
354C22×C113—41no—
355C22×C113—41no—
356C22×C113—41no—
357C22×C113—42no—
358C22×C113—42no—
359C22×C113—42no—
360C22×C113—42no—
361C22×C113—42no—
362C22×C113—42no—
363C22×C113—816no—
364C22×C113—81no—
365C22×C113—81no—
366C22×C113—81no—
367C22×C113—81no—
368C22×C113—81no—
369C22×C113—81no—
370C22×C113—81no—
371C22×C113—81no—
372C22×C113C2×#12111yescharacteristic
373C22×C113D4211yescharacteristic
374C22×C113#54611yescharacteristic
375C22×C113#57511yescharacteristic
376C22×C113#57511yescharacteristic
377C22×C113#57711yescharacteristic
378C22×C113#57711yescharacteristic
379C4×C113—22no—
380C4×C113—42no—
381C4×C113—41no—
382C4×C113—42no—
383C4×C113—41no—
384C4×C113—42no—
385C4×C113—41no—
386C4×C113—41no—
387C4×C113—81no—
388C4×C113—81no—
389C4×C113—81no—
390C4×C113#52511yescharacteristic
391C4×C113#53811yescharacteristic
392C4×C113D4211yescharacteristic
393C4×C113#54611yescharacteristic
394#25105C11311yesmaximal, characteristic, direct product factor, Sylow
395C2×C113—42no—
396C2×C113—82no—
397C2×C113—82no—
398C2×C113#242411yescharacteristic
399C2×C113#304011yescharacteristic
400C2×C113#304311yescharacteristic
401C2×C113#326711yescharacteristic
402C2×C113#327511yescharacteristic
403C2×C113#331111yescharacteristic
404C2×C113#332311yescharacteristic
405C2×#470C2×C11311yescharacteristic, complemented
406C2×#464C2×C11311yescharacteristic, complemented
407C2×#450C2×C11311yescharacteristic
408C2×#418C2×C11311yescharacteristic
409#2435C2×C11311yescharacteristic
410#2362C2×C11311yescharacteristic, complemented
411#2065C2×C11311yescharacteristic, complemented
412#2055C2×C11311yescharacteristic, complemented
413#2042C2×C11311yescharacteristic, complemented
414#2015C2×C11311yescharacteristic, complemented
415#1983C2×C11311yescharacteristic, complemented
416#1926C2×C11311yescharacteristic, complemented
417#1880C2×C11311yescharacteristic, complemented
418#1873C2×C11311yescharacteristic, complemented
419#1851C2×C11311yescharacteristic, complemented
420C113#2510511yescharacteristic, direct product factor, Sylow
421C23×D4C22×C11311yescharacteristic
422C22×Q16C22×C11311yescharacteristic, complemented
423C22×SD16C22×C11311yescharacteristic
424C22×SD16C22×C11311yescharacteristic
425C22×M16C22×C11311yescharacteristic
426C2×#124C22×C11311yescharacteristic
427C2×#124C22×C11311yescharacteristic
428C2×C22⋊Q8C22×C11311yescharacteristic
429C2×C22⋊Q8C22×C11311yescharacteristic
430C2×C4×Q8C22×C11311yescharacteristic, complemented
431C2×#117C22×C11311yescharacteristic
432#470—24no—
433#464—24no—
434#450—24no—
435C2×#106C22×C11311yescharacteristic, complemented
436C2×C4⋊C8C22×C11311yescharacteristic, complemented
437C2×C4⋊C8C22×C11311yescharacteristic, complemented
438#418—24no—
439C2×#103C22×C11311yescharacteristic, complemented
440C2×#103C22×C11311yescharacteristic, complemented
441C2×#103C22×C11311yescharacteristic, complemented
442C2×#103C22×C11311yescharacteristic, complemented
443C2×#102C22×C11311yescharacteristic
444C2×#102C22×C11311yescharacteristic
445C2×#102C22×C11311yescharacteristic
446C2×#102C22×C11311yescharacteristic
447C2×#102C22×C11311yescharacteristic
448C2×#102C22×C11311yescharacteristic
449C2×C22⋊C8C22×C11311yescharacteristic
450#394—21no—
451#394—21no—
452#391C22×C11311yescharacteristic, complemented
453#390C22×C11311yescharacteristic
454#390C22×C11311yescharacteristic
455#389C22×C11311yescharacteristic, complemented
456#388—21no—
457#388—21no—
458#387—21no—
459#379—21no—
460#379—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4C22×C11311yescharacteristic, complemented
463C4×C22⋊C4C22×C11311yescharacteristic
464#340C22×C11311yescharacteristic, complemented
465#340C22×C11311yescharacteristic, complemented
466#336C22×C11311yescharacteristic, complemented
467#336C22×C11311yescharacteristic, complemented
468C25—21no—
469C22×Q8C23×C11311yescharacteristic
470C22×Q8C23×C11311yescharacteristic
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—41no—
477C22×D4—41no—
478C22×D4C23×C11311yescharacteristic
479C22×D4C23×C11311yescharacteristic
480C23×C4C23×C11311yescharacteristic
481C2×Q16—22no—
482C2×Q16—22no—
483C2×Q16—41no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—41no—
489C2×SD16—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C11311yescharacteristic
494C22×C8C23×C11311yescharacteristic
495C22×C8C23×C11311yescharacteristic
496C22×C8C23×C11311yescharacteristic
497#124—22no—
498#124—22no—
499#124—41no—
500#124—41no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—22no—
504C22⋊Q8D4×C11314yes—
505C4×Q8—22no—
506C4×Q8—41no—
507#117—22no—
508#117—41no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4C23×C11311yescharacteristic
514C2×C4⋊C4C23×C11311yescharacteristic
515C2×C4⋊C4C23×C11311yescharacteristic
516C2×C4⋊C4C23×C11311yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4D4×C11311yescharacteristic
529C2×C22⋊C4D4×C11311yescharacteristic
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42C23×C11311yescharacteristic
534C2×C42C23×C11311yescharacteristic
535#106—22no—
536C4⋊C8—22no—
537C4⋊C8—41no—
538#103—22no—
539#103—22no—
540#103—22no—
541#103—41no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102D4×C11314yes—
548C22⋊C8—22no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95D4×C11311yescharacteristic
554#95D4×C11311yescharacteristic
555C24—21no—
556C24—21no—
557C24—42no—
558C24—42no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—81no—
563C24—81no—
564C24C2×D4×C11311yescharacteristic
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8C2×D4×C11312yes—
577C2×D4—28no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—44no—
589C2×D4—44no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4C2×D4×C11312yes—
595C2×D4#41×C11312yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4C2×D4×C11311yescharacteristic
607C22×C4C2×D4×C11311yescharacteristic
608C22×C4C2×D4×C11311yescharacteristic
609C22×C4C2×D4×C11311yescharacteristic
610C22×C4C2×D4×C11311yescharacteristic
611C22×C4C2×D4×C11312yes—
612C22×C4#41×C11312yes—
613C22×C4C24×C11311yescharacteristic
614Q16—44no—
615SD16—44no—
616SD16—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8C2×D4×C11312yes—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4C2×D4×C11312yes—
641C4⋊C4C2×D4×C11312yes—
642C22⋊C4—24no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—81no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—42no—
660C42—42no—
661C42—42no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23#121×C11312yes—
690C23C22×D4×C11311yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—41no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4#121×C11312yes—
745C2×C4C22×D4×C11311yescharacteristic
746C2×C4C22×D4×C11311yescharacteristic
747C2×C4C2×#41×C11311yescharacteristic
748C2×C4C2×#41×C11311yescharacteristic
749C2×C4H(5,𝔽2)×C11311yescharacteristic
750C2×C4H(5,𝔽2)×C11311yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#121×C11311yescharacteristic
778C22D42×C11311yescharacteristic
779C22#546×C11311yescharacteristic
780C22#575×C11311yescharacteristic
781C22#575×C11311yescharacteristic
782C22#577×C11311yescharacteristic
783C22#577×C11311yescharacteristic
784C4—22no—
785C4—41no—
786C4—41no—
787C4—42no—
788C4—41no—
789C4—42no—
790C4—41no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4#525×C11311yescharacteristic
796C4#538×C11311yescharacteristic
797C4D42×C11311yescharacteristic
798C4#546×C11311yescharacteristic
799C2—42no—
800C2—82no—
801C2—82no—
802C2C113×#242411yescharacteristic
803C2C113×#304011yescharacteristic
804C2C113×#304311yescharacteristic
805C2C113×#326711yescharacteristic
806C2C113×#327511yescharacteristic
807C2C113×#331111yescharacteristic
808C2C113×#332311yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC23×D4×C113C22
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×#470×C113C2semidirect
2. C2×#464×C113C2semidirect
6. C113×#2362C2semidirect
7. C113×#2065C2semidirect
8. C113×#2055C2semidirect
9. C113×#2042C2semidirect
10. C113×#2015C2semidirect
11. C113×#1983C2semidirect
12. C113×#1926C2semidirect
13. C113×#1880C2semidirect
14. C113×#1873C2semidirect
15. C113×#1851C2semidirect
17. C22×Q16×C113C22semidirect
25. C2×C4×Q8×C113C22semidirect
30. C2×#106×C113C22semidirect
31. C2×C4⋊C8×C113C22semidirect
32. C2×C4⋊C8×C113C22semidirect
34. C2×#103×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
37. C2×#103×C113C22semidirect
47. #391×C113C22semidirect
50. #389×C113C22semidirect
57. C4×C4⋊C4×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
394. #25105C113direct (N × H)
405. C2×#470C2×C113semidirect
406. C2×#464C2×C113semidirect
410. #2362C2×C113semidirect
411. #2065C2×C113semidirect
412. #2055C2×C113semidirect
413. #2042C2×C113semidirect
414. #2015C2×C113semidirect
415. #1983C2×C113semidirect
416. #1926C2×C113semidirect
417. #1880C2×C113semidirect
418. #1873C2×C113semidirect
419. #1851C2×C113semidirect
420. C113#25105direct (N × H)
422. C22×Q16C22×C113semidirect
430. C2×C4×Q8C22×C113semidirect
435. C2×#106C22×C113semidirect
436. C2×C4⋊C8C22×C113semidirect
437. C2×C4⋊C8C22×C113semidirect
439. C2×#103C22×C113semidirect
440. C2×#103C22×C113semidirect
441. C2×#103C22×C113semidirect
442. C2×#103C22×C113semidirect
452. #391C22×C113semidirect
455. #389C22×C113semidirect
462. C4×C4⋊C4C22×C113semidirect
464. #340C22×C113semidirect
465. #340C22×C113semidirect
466. #336C22×C113semidirect
467. #336C22×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#470×C1132
C2×#464×C1132
C2×#450×C1132
C2×#418×C1132
C113×#24352
C113×#23622
C113×#20652
C113×#20552
C113×#20422
C113×#20152
C113×#19832
C113×#19262
C113×#18802
C113×#18732
C113×#18512
#25105113