Finite Group Databasebeta

← C113×#25553 #43293573

Subgroups — C113×#25553 #43293573

Order 28928.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C113C211yesmaximal, characteristic, complemented
2C2×#480×C113C211yesmaximal, characteristic, complemented
3C2×#469×C113C211yesmaximal, characteristic, complemented
4C113×#2414C211yesmaximal, characteristic, complemented
5C113×#2059C211yesmaximal, characteristic, complemented
6C113×#2033C211yesmaximal, characteristic, complemented
7C113×#2025C211yesmaximal, characteristic, complemented
8C113×#1999C211yesmaximal, characteristic, complemented
9C113×#1879C211yesmaximal, characteristic, complemented
10C113×#1875C211yesmaximal, characteristic, complemented
11C113×#1875C211yesmaximal, characteristic, complemented
12C113×#1870C211yesmaximal, characteristic, complemented
13C113×#1862C211yesmaximal, characteristic, complemented
14C113×#1854C211yesmaximal, characteristic, complemented
15C113×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C113C2211yescharacteristic
17C22×M16×C113C2211yescharacteristic
18#553×C113—24no—
19#553×C113—24no—
20C2×#126×C113—21no—
21C2×#125×C113C2211yescharacteristic
22C2×#123×C113—21no—
23C2×#121×C113—21no—
24C2×#121×C113C2211yescharacteristic
25C2×#121×C113C2211yescharacteristic
26C2×#121×C113C2211yescharacteristic
27C2×#121×C113C2211yescharacteristic
28C2×C4×D4×C113—21no—
29C2×C4×D4×C113C2211yescharacteristic
30C2×C4×D4×C113C2211yescharacteristic
31C2×#117×C113C2211yescharacteristic
32C2×#117×C113C2211yescharacteristic
33C22×C4⋊C4×C113C2211yescharacteristic
34#480×C113—24no—
35#469×C113—24no—
36C2×#107×C113C2211yescharacteristic
37C2×#107×C113C2211yescharacteristic
38C2×#106×C113C2211yescharacteristic
39C2×#102×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#390×C113—21no—
51#390×C113C2211yescharacteristic
52#389×C113C2211yescharacteristic
53#388×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
63C22×D4×C113—21no—
64C22×D4×C113—21no—
65C22×D4×C113—21no—
66C22×D4×C113—21no—
67C22×D4×C113D411yescharacteristic
68C22×D4×C113C2311yescharacteristic
69C22×D4×C113C2311yescharacteristic
70C23×C4×C113—21no—
71C23×C4×C113—21no—
72C23×C4×C113C2311yescharacteristic
73C23×C4×C113C2311yescharacteristic
74C2×D8×C113—22no—
75C2×D8×C113—22no—
76C2×D8×C113—41no—
77C2×M16×C113—22no—
78C2×M16×C113—22no—
79C2×M16×C113—41no—
80C22×C8×C113C2311yescharacteristic
81C22×C8×C113C2311yescharacteristic
82C22×C8×C113C2311yescharacteristic
83C22×C8×C113C2311yescharacteristic
84#126×C113—28no—
85#125×C113—22no—
86#125×C113—22no—
87#123×C113—28no—
88#121×C113—28no—
89#121×C113—22no—
90#121×C113—22no—
91#121×C113—22no—
92#121×C113—22no—
93#121×C113—22no—
94#121×C113—22no—
95#121×C113—41no—
96#121×C113D414yescomplemented
97C4×D4×C113—28no—
98C4×D4×C113—22no—
99C4×D4×C113—22no—
100C4×D4×C113—22no—
101C4×D4×C113—22no—
102#117×C113—22no—
103#117×C113—22no—
104#117×C113—22no—
105#117×C113—41no—
106C2×C4⋊C4×C113—21no—
107C2×C4⋊C4×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113D411yescharacteristic
112C2×C4⋊C4×C113D414yescomplemented
113C2×C4⋊C4×C113C2311yescharacteristic
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×C113—21no—
132C2×C42×C113—21no—
133C2×C42×C113C2311yescharacteristic
134#107×C113—22no—
135#107×C113—22no—
136#106×C113—22no—
137#102×C113—22no—
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×C113—22no—
145C22⋊C8×C113—41no—
146#95×C113—21no—
147#95×C113—21no—
148C24×C113—21no—
149C24×C113—21no—
150C24×C113C2×D411yescharacteristic
151C24×C113C2×D411yescharacteristic
152C2×D4×C113—22no—
153C2×D4×C113—24no—
154C2×D4×C113—24no—
155C2×D4×C113—21no—
156C2×D4×C113—21no—
157C2×D4×C113—21no—
158C2×D4×C113—21no—
159C2×D4×C113—21no—
160C2×D4×C113—21no—
161C2×D4×C113—21no—
162C2×D4×C113—21no—
163C2×D4×C113—21no—
164C2×D4×C113—21no—
165C2×D4×C113—21no—
166C2×D4×C113—41no—
167C2×D4×C113—41no—
168C2×D4×C113—42no—
169C2×D4×C113—42no—
170C2×D4×C113—42no—
171C2×D4×C113—42no—
172C2×D4×C113—42no—
173C2×D4×C113—81no—
174C2×D4×C113—81no—
175C2×D4×C113—81no—
176C2×D4×C113—81no—
177C2×D4×C113—81no—
178C2×D4×C113C2×D412yes—
179C22×C4×C113—21no—
180C22×C4×C113—21no—
181C22×C4×C113—21no—
182C22×C4×C113—21no—
183C22×C4×C113—21no—
184C22×C4×C113—21no—
185C22×C4×C113—21no—
186C22×C4×C113—21no—
187C22×C4×C113—24no—
188C22×C4×C113—24no—
189C22×C4×C113—21no—
190C22×C4×C113—21no—
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—81no—
198C22×C4×C113—81no—
199C22×C4×C113—81no—
200C22×C4×C113—81no—
201C22×C4×C113C2×D411yescharacteristic
202C22×C4×C113C2×D411yescharacteristic
203C22×C4×C113C2×D411yescharacteristic
204C22×C4×C113C2×D411yescharacteristic
205C22×C4×C113C2×D412yes—
206C22×C4×C113C2×D412yes—
207C22×C4×C113C2411yescharacteristic
208D8×C113—44no—
209M16×C113—44no—
210C2×C8×C113—21no—
211C2×C8×C113—21no—
212C2×C8×C113—21no—
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#4112yes—
222C4⋊C4×C113—24no—
223C4⋊C4×C113—24no—
224C4⋊C4×C113—24no—
225C4⋊C4×C113—22no—
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—21no—
233C4⋊C4×C113—21no—
234C4⋊C4×C113—81no—
235C4⋊C4×C113C2×D412yes—
236C4⋊C4×C113C2×D412yes—
237C4⋊C4×C113C2×D412yes—
238C4⋊C4×C113#4112yes—
239C22⋊C4×C113—24no—
240C22⋊C4×C113—24no—
241C22⋊C4×C113—24no—
242C22⋊C4×C113—22no—
243C22⋊C4×C113—24no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—42no—
246C22⋊C4×C113—42no—
247C22⋊C4×C113—42no—
248C22⋊C4×C113—42no—
249C22⋊C4×C113—81no—
250C22⋊C4×C113—81no—
251C42×C113—24no—
252C42×C113—21no—
253C42×C113—21no—
254C42×C113—42no—
255C23×C113—21no—
256C23×C113—21no—
257C23×C113—21no—
258C23×C113—21no—
259C23×C113—21no—
260C23×C113—21no—
261C23×C113—21no—
262C23×C113—22no—
263C23×C113—21no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
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—41no—
279C23×C113—41no—
280C23×C113—41no—
281C23×C113—41no—
282C23×C113#12012yes—
283C23×C113C22×D411yescharacteristic
284D4×C113—22no—
285D4×C113—22no—
286D4×C113—44no—
287D4×C113—48no—
288D4×C113—41no—
289D4×C113—41no—
290D4×C113—41no—
291D4×C113—41no—
292D4×C113—41no—
293D4×C113—41no—
294D4×C113—84no—
295D4×C113—84no—
296D4×C113—84no—
297C2×C4×C113—21no—
298C2×C4×C113—21no—
299C2×C4×C113—22no—
300C2×C4×C113—22no—
301C2×C4×C113—22no—
302C2×C4×C113—22no—
303C2×C4×C113—21no—
304C2×C4×C113—21no—
305C2×C4×C113—22no—
306C2×C4×C113—21no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—22no—
310C2×C4×C113—21no—
311C2×C4×C113—21no—
312C2×C4×C113—21no—
313C2×C4×C113—21no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—41no—
317C2×C4×C113—41no—
318C2×C4×C113—41no—
319C2×C4×C113—41no—
320C2×C4×C113—41no—
321C2×C4×C113—41no—
322C2×C4×C113—41no—
323C2×C4×C113—41no—
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—84no—
335C2×C4×C113—84no—
336C2×C4×C113#12012yes—
337C2×C4×C113C22×D411yescharacteristic
338C2×C4×C113C22×D411yescharacteristic
339C2×C4×C113C2×#4111yescharacteristic
340C2×C4×C113C2×#4111yescharacteristic
341C2×C4×C113H(5,𝔽2)11yescharacteristic
342C2×C4×C1132−1+411yescharacteristic
343C8×C113—22no—
344C8×C113—41no—
345C8×C113—41no—
346C8×C113—41no—
347C22×C113—22no—
348C22×C113—22no—
349C22×C113—22no—
350C22×C113—41no—
351C22×C113—41no—
352C22×C113—41no—
353C22×C113—41no—
354C22×C113—41no—
355C22×C113—41no—
356C22×C113—41no—
357C22×C113—42no—
358C22×C113—41no—
359C22×C113—42no—
360C22×C113—42no—
361C22×C113—41no—
362C22×C113—41no—
363C22×C113—41no—
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×C113—81no—
373C22×C113—81no—
374C22×C113—81no—
375C22×C113C2×#12011yescharacteristic
376C22×C113#54611yescharacteristic
377C22×C113#54711yescharacteristic
378C22×C113#57511yescharacteristic
379C22×C113#57511yescharacteristic
380C22×C113#57611yescharacteristic
381C22×C113#57611yescharacteristic
382C4×C113—22no—
383C4×C113—41no—
384C4×C113—41no—
385C4×C113—42no—
386C4×C113—41no—
387C4×C113—42no—
388C4×C113—42no—
389C4×C113—42no—
390C4×C113—81no—
391C4×C113—81no—
392C4×C113#53211yescharacteristic
393C4×C113#53711yescharacteristic
394C4×C113#54611yescharacteristic
395C4×C113#54711yescharacteristic
396#25553C11311yesmaximal, characteristic, direct product factor, Sylow
397C2×C113—42no—
398C2×C113—81no—
399C2×C113—82no—
400C2×C113—161no—
401C2×C113#243011yescharacteristic
402C2×C113#300511yescharacteristic
403C2×C113#300811yescharacteristic
404C2×C113#330911yescharacteristic
405C2×C113#332211yescharacteristic
406C2×C113#334711yescharacteristic
407C2×C113#335511yescharacteristic
408C2×#553C2×C11311yescharacteristic, complemented
409C2×#480C2×C11311yescharacteristic, complemented
410C2×#469C2×C11311yescharacteristic, complemented
411#2414C2×C11311yescharacteristic, complemented
412#2059C2×C11311yescharacteristic, complemented
413#2033C2×C11311yescharacteristic, complemented
414#2025C2×C11311yescharacteristic, complemented
415#1999C2×C11311yescharacteristic, complemented
416#1879C2×C11311yescharacteristic, complemented
417#1875C2×C11311yescharacteristic, complemented
418#1875C2×C11311yescharacteristic, complemented
419#1870C2×C11311yescharacteristic, complemented
420#1862C2×C11311yescharacteristic, complemented
421#1854C2×C11311yescharacteristic, complemented
422#1736C2×C11311yescharacteristic, complemented
423C113#2555311yescharacteristic, direct product factor, Sylow
424C22×D8C22×C11311yescharacteristic
425C22×M16C22×C11311yescharacteristic
426#553—24no—
427#553—24no—
428C2×#126—21no—
429C2×#125C22×C11311yescharacteristic
430C2×#123—21no—
431C2×#121—21no—
432C2×#121C22×C11311yescharacteristic
433C2×#121C22×C11311yescharacteristic
434C2×#121C22×C11311yescharacteristic
435C2×#121C22×C11311yescharacteristic
436C2×C4×D4—21no—
437C2×C4×D4C22×C11311yescharacteristic
438C2×C4×D4C22×C11311yescharacteristic
439C2×#117C22×C11311yescharacteristic
440C2×#117C22×C11311yescharacteristic
441C22×C4⋊C4C22×C11311yescharacteristic
442#480—24no—
443#469—24no—
444C2×#107C22×C11311yescharacteristic
445C2×#107C22×C11311yescharacteristic
446C2×#106C22×C11311yescharacteristic
447C2×#102C22×C11311yescharacteristic
448C2×#102C22×C11311yescharacteristic
449C2×#102C22×C11311yescharacteristic
450C2×#102C22×C11311yescharacteristic
451C2×#102C22×C11311yescharacteristic
452C2×#102C22×C11311yescharacteristic
453C2×C22⋊C8C22×C11311yescharacteristic
454C2×C22⋊C8C22×C11311yescharacteristic
455C2×C22⋊C8C22×C11311yescharacteristic
456#394—21no—
457#392—21no—
458#390—21no—
459#390C22×C11311yescharacteristic
460#389C22×C11311yescharacteristic
461#388—21no—
462#380C22×C11311yescharacteristic
463#340C22×C11311yescharacteristic
464#340C22×C11311yescharacteristic
465#340C22×C11311yescharacteristic
466#340C22×C11311yescharacteristic
467#340C22×C11311yescharacteristic
468#340C22×C11311yescharacteristic
469#336C22×C11311yescharacteristic
470#336C22×C11311yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C11311yescharacteristic
476C22×D4C23×C11311yescharacteristic
477C22×D4C23×C11311yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C11311yescharacteristic
481C23×C4C23×C11311yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—41no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8C23×C11311yescharacteristic
489C22×C8C23×C11311yescharacteristic
490C22×C8C23×C11311yescharacteristic
491C22×C8C23×C11311yescharacteristic
492#126—28no—
493#125—22no—
494#125—22no—
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121D4×C11314yescomplemented
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C11311yescharacteristic
520C2×C4⋊C4D4×C11314yescomplemented
521C2×C4⋊C4C23×C11311yescharacteristic
522C2×C4⋊C4C23×C11311yescharacteristic
523C2×C4⋊C4C23×C11311yescharacteristic
524C2×C4⋊C4C23×C11311yescharacteristic
525C2×C4⋊C4C23×C11311yescharacteristic
526C2×C4⋊C4C23×C11311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4D4×C11311yescharacteristic
538C2×C22⋊C4D4×C11311yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C11311yescharacteristic
542#107—22no—
543#107—22no—
544#106—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C11311yescharacteristic
559C24C2×D4×C11311yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C11312yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
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—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C11311yescharacteristic
610C22×C4C2×D4×C11311yescharacteristic
611C22×C4C2×D4×C11311yescharacteristic
612C22×C4C2×D4×C11311yescharacteristic
613C22×C4C2×D4×C11312yes—
614C22×C4C2×D4×C11312yes—
615C22×C4C24×C11311yescharacteristic
616D8—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×C8#41×C11312yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4C2×D4×C11312yes—
644C4⋊C4C2×D4×C11312yes—
645C4⋊C4C2×D4×C11312yes—
646C4⋊C4#41×C11312yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23#120×C11312yes—
691C23C22×D4×C11311yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
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—84no—
743C2×C4—84no—
744C2×C4#120×C11312yes—
745C2×C4C22×D4×C11311yescharacteristic
746C2×C4C22×D4×C11311yescharacteristic
747C2×C4C2×#41×C11311yescharacteristic
748C2×C4C2×#41×C11311yescharacteristic
749C2×C4H(5,𝔽2)×C11311yescharacteristic
750C2×C42−1+4×C11311yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C11311yescharacteristic
784C22#546×C11311yescharacteristic
785C22#547×C11311yescharacteristic
786C22#575×C11311yescharacteristic
787C22#575×C11311yescharacteristic
788C22#576×C11311yescharacteristic
789C22#576×C11311yescharacteristic
790C4—22no—
791C4—42no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4#532×C11311yescharacteristic
801C4#537×C11311yescharacteristic
802C4#546×C11311yescharacteristic
803C4#547×C11311yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2C113×#243011yescharacteristic
809C2C113×#300511yescharacteristic
810C2C113×#300811yescharacteristic
811C2C113×#330911yescharacteristic
812C2C113×#332211yescharacteristic
813C2C113×#334711yescharacteristic
814C2C113×#335511yescharacteristic
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×#553×C113C2semidirect
2. C2×#480×C113C2semidirect
3. C2×#469×C113C2semidirect
4. C113×#2414C2semidirect
5. C113×#2059C2semidirect
6. C113×#2033C2semidirect
7. C113×#2025C2semidirect
8. C113×#1999C2semidirect
9. C113×#1879C2semidirect
10. C113×#1875C2semidirect
11. C113×#1875C2semidirect
12. C113×#1870C2semidirect
13. C113×#1862C2semidirect
14. C113×#1854C2semidirect
15. C113×#1736C2semidirect
96. #121×C113D4semidirect
112. C2×C4⋊C4×C113D4semidirect
396. #25553C113direct (N × H)
408. C2×#553C2×C113semidirect
409. C2×#480C2×C113semidirect
410. C2×#469C2×C113semidirect
411. #2414C2×C113semidirect
412. #2059C2×C113semidirect
413. #2033C2×C113semidirect
414. #2025C2×C113semidirect
415. #1999C2×C113semidirect
416. #1879C2×C113semidirect
417. #1875C2×C113semidirect
418. #1875C2×C113semidirect
419. #1870C2×C113semidirect
420. #1862C2×C113semidirect
421. #1854C2×C113semidirect
422. #1736C2×C113semidirect
423. C113#25553direct (N × H)
504. #121D4×C113semidirect
520. C2×C4⋊C4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1132
C2×#480×C1132
C2×#469×C1132
C113×#24142
C113×#20592
C113×#20332
C113×#20252
C113×#19992
C113×#18792
C113×#18752
C113×#18702
C113×#18622
C113×#18542
C113×#17362
#25553113