Finite Group Databasebeta

← C113×#21772 #43289792

Subgroups — C113×#21772 #43289792

Order 28928.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C113C211yesmaximal, characteristic
2C2×#408×C113C211yesmaximal, characteristic, complemented
3C113×#2311C211yesmaximal, characteristic, complemented
4C113×#1895C211yesmaximal, characteristic, complemented
5C113×#1894C211yesmaximal, characteristic, complemented
6C113×#1893C211yesmaximal, characteristic, complemented
7C113×#1892C211yesmaximal, characteristic, complemented
8C113×#1875C211yesmaximal, characteristic, complemented
9C113×#1874C211yesmaximal, characteristic, complemented
10C113×#1873C211yesmaximal, characteristic, complemented
11C113×#1872C211yesmaximal, characteristic, complemented
12C113×#1824C211yesmaximal, characteristic, complemented
13C113×#1823C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C22×M16×C113C2211yescharacteristic
19C23×C8×C113C2211yescharacteristic
20#537×C113—24no—
21#537×C113C418yescomplemented
22C2×C22⋊Q8×C113—21no—
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×C22⋊Q8×C113C2211yescharacteristic
25C2×#121×C113—21no—
26C2×#121×C113—21no—
27C2×#121×C113—21no—
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30C2×#117×C113C2211yescharacteristic
31C22×C4⋊C4×C113C2211yescharacteristic
32C22×C4⋊C4×C113C2211yescharacteristic
33C2×#103×C113C2211yescharacteristic
34C2×#103×C113C2211yescharacteristic
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41#408×C113—24no—
42C2×C22⋊C8×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45C2×C22⋊C8×C113C2211yescharacteristic
46#391×C113—21no—
47#390×C113—21no—
48#386×C113—21no—
49#386×C113—21no—
50#380×C113C2211yescharacteristic
51#380×C113C2211yescharacteristic
52#380×C113C2211yescharacteristic
53#380×C113C2211yescharacteristic
54#340×C113C2211yescharacteristic
55#340×C113C2211yescharacteristic
56#340×C113C2211yescharacteristic
57#340×C113C2211yescharacteristic
58#340×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic
62C2×#41×C113—22no—
63C2×#41×C113—41no—
64C2×#41×C113—41no—
65C2×#41×C113—41no—
66C2×#41×C113—41no—
67C2×#41×C113—41no—
68C2×#41×C113—41no—
69C2×#41×C113—41no—
70C2×#41×C113—41no—
71C2×#41×C113C2×C414yes—
72C2×#41×C113C2×C414yescomplemented
73C2×#41×C113D414yes—
74C22×Q8×C113D411yescharacteristic
75C22×Q8×C113C2311yescharacteristic
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—21no—
79C22×D4×C113D411yescharacteristic
80C22×D4×C113D411yescharacteristic
81C22×D4×C113D411yescharacteristic
82C22×D4×C113C2311yescharacteristic
83C23×C4×C113—21no—
84C23×C4×C113—21no—
85C23×C4×C113—21no—
86C23×C4×C113C2311yescharacteristic
87C23×C4×C113C2311yescharacteristic
88C23×C4×C113C2311yescharacteristic
89C2×M16×C113—22no—
90C2×M16×C113—41no—
91C2×M16×C113—41no—
92C22×C8×C113—22no—
93C22×C8×C113—41no—
94C22×C8×C113—41no—
95C22×C8×C113C2311yescharacteristic
96C22×C8×C113C2311yescharacteristic
97C22×C8×C113C2311yescharacteristic
98C22×C8×C113C2311yescharacteristic
99C22⋊Q8×C113—28no—
100C22⋊Q8×C113—22no—
101C22⋊Q8×C113—22no—
102C22⋊Q8×C113C2×C414yes—
103C22⋊Q8×C113C2×C414yescomplemented
104#121×C113—28no—
105#121×C113—28no—
106#121×C113—28no—
107#121×C113—22no—
108#121×C113—22no—
109#121×C113C2×C414yes—
110#121×C113C2×C414yescomplemented
111#117×C113—41no—
112#117×C113—41no—
113C2×C4⋊C4×C113—21no—
114C2×C4⋊C4×C113—22no—
115C2×C4⋊C4×C113—21no—
116C2×C4⋊C4×C113—21no—
117C2×C4⋊C4×C113—21no—
118C2×C4⋊C4×C113—41no—
119C2×C4⋊C4×C113—41no—
120C2×C4⋊C4×C113C2×C414yescomplemented
121C2×C4⋊C4×C113C2311yescharacteristic
122C2×C4⋊C4×C113C2311yescharacteristic
123C2×C4⋊C4×C113C2311yescharacteristic
124C2×C4⋊C4×C113C2311yescharacteristic
125C2×C4⋊C4×C113C2311yescharacteristic
126C2×C4⋊C4×C113C2311yescharacteristic
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—21no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113—21no—
136C2×C42×C113—21no—
137#103×C113—41no—
138#103×C113—41no—
139#103×C113—41no—
140#103×C113—41no—
141#102×C113—41no—
142#102×C113—41no—
143#102×C113—41no—
144#102×C113—41no—
145C22⋊C8×C113—22no—
146C22⋊C8×C113—22no—
147C22⋊C8×C113—22no—
148C22⋊C8×C113—22no—
149#95×C113—21no—
150#95×C113—21no—
151#95×C113—21no—
152#95×C113—21no—
153C24×C113—21no—
154C24×C113C2×D411yescharacteristic
155C24×C113C2×D411yescharacteristic
156C24×C113C2×D411yescharacteristic
157#41×C113—44no—
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—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—41no—
171C2×Q8×C113—41no—
172C2×Q8×C113C22⋊C414yes—
173C2×Q8×C113C22×C412yes—
174C2×D4×C113—24no—
175C2×D4×C113—24no—
176C2×D4×C113—24no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—41no—
183C2×D4×C113—41no—
184C2×D4×C113—41no—
185C2×D4×C113—41no—
186C2×D4×C113—41no—
187C2×D4×C113—41no—
188C2×D4×C113—42no—
189C2×D4×C113—42no—
190C2×D4×C113—81no—
191C2×D4×C113—81no—
192C2×D4×C113—81no—
193C2×D4×C113—81no—
194C2×D4×C113C22⋊C414yes—
195C2×D4×C113C22⋊C414yes—
196C2×D4×C113C22⋊C414yes—
197C2×D4×C113C22×C412yes—
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—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113—21no—
213C22×C4×C113—24no—
214C22×C4×C113—24no—
215C22×C4×C113—21no—
216C22×C4×C113—21no—
217C22×C4×C113—21no—
218C22×C4×C113—21no—
219C22×C4×C113—42no—
220C22×C4×C113—42no—
221C22×C4×C113—42no—
222C22×C4×C113—81no—
223C22×C4×C113—81no—
224C22×C4×C113—81no—
225C22×C4×C113—81no—
226C22×C4×C113C22×C412yes—
227C22×C4×C113C22×C412yes—
228C22×C4×C113C22×C412yes—
229C22×C4×C113C2×D411yescharacteristic
230C22×C4×C113C2×D411yescharacteristic
231C22×C4×C113C2×D411yescharacteristic
232C22×C4×C113C2×D412yes—
233C22×C4×C113C2×D412yes—
234C22×C4×C113C2×D412yes—
235C22×C4×C113C2411yescharacteristic
236M16×C113—44no—
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—
249C2×C8×C113—44no—
250C4⋊C4×C113—24no—
251C4⋊C4×C113—24no—
252C4⋊C4×C113—24no—
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—21no—
263C4⋊C4×C113—42no—
264C4⋊C4×C113C22×C412yes—
265C4⋊C4×C113C22×C412yes—
266C22⋊C4×C113—24no—
267C22⋊C4×C113—24no—
268C22⋊C4×C113—24no—
269C22⋊C4×C113—24no—
270C22⋊C4×C113—42no—
271C22⋊C4×C113—81no—
272C22⋊C4×C113—81no—
273C22⋊C4×C113—81no—
274C22⋊C4×C113—81no—
275C42×C113—42no—
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—21no—
289C23×C113—21no—
290C23×C113—21no—
291C23×C113—21no—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—22no—
295C23×C113—41no—
296C23×C113—41no—
297C23×C113—41no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113C2×C22⋊C412yes—
302C23×C113C2×C22⋊C412yes—
303C23×C113C2×C22⋊C412yes—
304C23×C113C22×D411yescharacteristic
305Q8×C113—22no—
306Q8×C113—22no—
307Q8×C113—44no—
308Q8×C113—41no—
309Q8×C113—41no—
310D4×C113—22no—
311D4×C113—22no—
312D4×C113—44no—
313D4×C113—44no—
314D4×C113—44no—
315D4×C113—48no—
316D4×C113—41no—
317D4×C113—41no—
318D4×C113—84no—
319D4×C113—84no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
323C2×C4×C113—21no—
324C2×C4×C113—21no—
325C2×C4×C113—21no—
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—22no—
335C2×C4×C113—22no—
336C2×C4×C113—22no—
337C2×C4×C113—22no—
338C2×C4×C113—22no—
339C2×C4×C113—22no—
340C2×C4×C113—22no—
341C2×C4×C113—48no—
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×C113C2×C22⋊C412yes—
363C2×C4×C113C2×C22⋊C412yes—
364C2×C4×C113C2×C22⋊C412yes—
365C2×C4×C113C23×C411yescharacteristic
366C2×C4×C113C22×D411yescharacteristic
367C2×C4×C113H(5,𝔽2)11yescharacteristic
368C2×C4×C113H(5,𝔽2)11yescharacteristic
369C2×C4×C113H(5,𝔽2)11yescharacteristic
370C2×C4×C113H(5,𝔽2)11yescharacteristic
371C8×C113—41no—
372C8×C113—41no—
373C8×C113—41no—
374C8×C113—41no—
375C22×C113—22no—
376C22×C113—22no—
377C22×C113—22no—
378C22×C113—22no—
379C22×C113—22no—
380C22×C113—22no—
381C22×C113—22no—
382C22×C113—22no—
383C22×C113—22no—
384C22×C113—41no—
385C22×C113—41no—
386C22×C113—41no—
387C22×C113—41no—
388C22×C113—41no—
389C22×C113—41no—
390C22×C113—41no—
391C22×C113—41no—
392C22×C113—41no—
393C22×C113—41no—
394C22×C113—41no—
395C22×C113—41no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—42no—
399C22×C113—81no—
400C22×C113—81no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113C22×C22⋊C411yescharacteristic
404C22×C113#53411yescharacteristic
405C22×C113#53411yescharacteristic
406C22×C113#57611yescharacteristic
407C22×C113#57711yescharacteristic
408C22×C113#57711yescharacteristic
409C22×C113#57811yescharacteristic
410C4×C113—22no—
411C4×C113—22no—
412C4×C113—22no—
413C4×C113—42no—
414C4×C113—42no—
415C4×C113—42no—
416C4×C113—81no—
417C4×C113—81no—
418C4×C113—81no—
419C4×C113—81no—
420C4×C113#51811yescharacteristic
421C4×C113#51811yescharacteristic
422C4×C113#53411yescharacteristic
423C4×C113#53411yescharacteristic
424#21772C11311yesmaximal, characteristic, direct product factor, Sylow
425C2×C113—42no—
426C2×C113—42no—
427C2×C113—42no—
428C2×C113—82no—
429C2×C113#230811yescharacteristic
430C2×C113#289711yescharacteristic
431C2×C113#289811yescharacteristic
432C2×C113#319811yescharacteristic
433C2×C113#320111yescharacteristic
434C2×C113#320311yescharacteristic
435C2×C113#320411yescharacteristic
436C2×#537C2×C11311yescharacteristic
437C2×#408C2×C11311yescharacteristic, complemented
438#2311C2×C11311yescharacteristic, complemented
439#1895C2×C11311yescharacteristic, complemented
440#1894C2×C11311yescharacteristic, complemented
441#1893C2×C11311yescharacteristic, complemented
442#1892C2×C11311yescharacteristic, complemented
443#1875C2×C11311yescharacteristic, complemented
444#1874C2×C11311yescharacteristic, complemented
445#1873C2×C11311yescharacteristic, complemented
446#1872C2×C11311yescharacteristic, complemented
447#1824C2×C11311yescharacteristic, complemented
448#1823C2×C11311yescharacteristic, complemented
449#1788C2×C11311yescharacteristic, complemented
450#1788C2×C11311yescharacteristic, complemented
451C113#2177211yescharacteristic, direct product factor, Sylow
452C22×#41C22×C11311yescharacteristic
453C22×#41C22×C11311yescharacteristic
454C22×M16C22×C11311yescharacteristic
455C23×C8C22×C11311yescharacteristic
456#537—24no—
457#537C4×C11318yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C11311yescharacteristic
460C2×C22⋊Q8C22×C11311yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C11311yescharacteristic
465C2×#121C22×C11311yescharacteristic
466C2×#117C22×C11311yescharacteristic
467C22×C4⋊C4C22×C11311yescharacteristic
468C22×C4⋊C4C22×C11311yescharacteristic
469C2×#103C22×C11311yescharacteristic
470C2×#103C22×C11311yescharacteristic
471C2×#103C22×C11311yescharacteristic
472C2×#103C22×C11311yescharacteristic
473C2×#102C22×C11311yescharacteristic
474C2×#102C22×C11311yescharacteristic
475C2×#102C22×C11311yescharacteristic
476C2×#102C22×C11311yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C11311yescharacteristic
479C2×C22⋊C8C22×C11311yescharacteristic
480C2×C22⋊C8C22×C11311yescharacteristic
481C2×C22⋊C8C22×C11311yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C11311yescharacteristic
487#380C22×C11311yescharacteristic
488#380C22×C11311yescharacteristic
489#380C22×C11311yescharacteristic
490#340C22×C11311yescharacteristic
491#340C22×C11311yescharacteristic
492#340C22×C11311yescharacteristic
493#340C22×C11311yescharacteristic
494#340C22×C11311yescharacteristic
495#340C22×C11311yescharacteristic
496#340C22×C11311yescharacteristic
497#340C22×C11311yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C11314yes—
508C2×#41C2×C4×C11314yescomplemented
509C2×#41D4×C11314yes—
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
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C11311yescharacteristic
532C22×C8C23×C11311yescharacteristic
533C22×C8C23×C11311yescharacteristic
534C22×C8C23×C11311yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C11314yes—
539C22⋊Q8C2×C4×C11314yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C11314yes—
546#121C2×C4×C11314yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C11314yescomplemented
557C2×C4⋊C4C23×C11311yescharacteristic
558C2×C4⋊C4C23×C11311yescharacteristic
559C2×C4⋊C4C23×C11311yescharacteristic
560C2×C4⋊C4C23×C11311yescharacteristic
561C2×C4⋊C4C23×C11311yescharacteristic
562C2×C4⋊C4C23×C11311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
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—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C11314yes—
609C2×Q8C22×C4×C11312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C11314yes—
631C2×D4C22⋊C4×C11314yes—
632C2×D4C22⋊C4×C11314yes—
633C2×D4C22×C4×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—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C11312yes—
663C22×C4C22×C4×C11312yes—
664C22×C4C22×C4×C11312yes—
665C22×C4C2×D4×C11311yescharacteristic
666C22×C4C2×D4×C11311yescharacteristic
667C22×C4C2×D4×C11311yescharacteristic
668C22×C4C2×D4×C11312yes—
669C22×C4C2×D4×C11312yes—
670C22×C4C2×D4×C11312yes—
671C22×C4C24×C11311yescharacteristic
672M16—44no—
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—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
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—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C11312yes—
701C4⋊C4C22×C4×C11312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C11312yes—
738C23C2×C22⋊C4×C11312yes—
739C23C2×C22⋊C4×C11312yes—
740C23C22×D4×C11311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
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—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C11312yes—
799C2×C4C2×C22⋊C4×C11312yes—
800C2×C4C2×C22⋊C4×C11312yes—
801C2×C4C23×C4×C11311yescharacteristic
802C2×C4C22×D4×C11311yescharacteristic
803C2×C4H(5,𝔽2)×C11311yescharacteristic
804C2×C4H(5,𝔽2)×C11311yescharacteristic
805C2×C4H(5,𝔽2)×C11311yescharacteristic
806C2×C4H(5,𝔽2)×C11311yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C11311yescharacteristic
840C22#534×C11311yescharacteristic
841C22#534×C11311yescharacteristic
842C22#576×C11311yescharacteristic
843C22#577×C11311yescharacteristic
844C22#577×C11311yescharacteristic
845C22#578×C11311yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C11311yescharacteristic
857C4#518×C11311yescharacteristic
858C4#534×C11311yescharacteristic
859C4#534×C11311yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C113×#230811yescharacteristic
865C2C113×#289711yescharacteristic
866C2C113×#289811yescharacteristic
867C2C113×#319811yescharacteristic
868C2C113×#320111yescharacteristic
869C2C113×#320311yescharacteristic
870C2C113×#320411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC2×#537×C113C2
LCSG ▷ C2×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×#408×C113C2semidirect
3. C113×#2311C2semidirect
4. C113×#1895C2semidirect
5. C113×#1894C2semidirect
6. C113×#1893C2semidirect
7. C113×#1892C2semidirect
8. C113×#1875C2semidirect
9. C113×#1874C2semidirect
10. C113×#1873C2semidirect
11. C113×#1872C2semidirect
12. C113×#1824C2semidirect
13. C113×#1823C2semidirect
14. C113×#1788C2semidirect
15. C113×#1788C2semidirect
21. #537×C113C4semidirect
72. C2×#41×C113C2×C4semidirect
103. C22⋊Q8×C113C2×C4semidirect
110. #121×C113C2×C4semidirect
120. C2×C4⋊C4×C113C2×C4semidirect
424. #21772C113direct (N × H)
437. C2×#408C2×C113semidirect
438. #2311C2×C113semidirect
439. #1895C2×C113semidirect
440. #1894C2×C113semidirect
441. #1893C2×C113semidirect
442. #1892C2×C113semidirect
443. #1875C2×C113semidirect
444. #1874C2×C113semidirect
445. #1873C2×C113semidirect
446. #1872C2×C113semidirect
447. #1824C2×C113semidirect
448. #1823C2×C113semidirect
449. #1788C2×C113semidirect
450. #1788C2×C113semidirect
451. C113#21772direct (N × H)
457. #537C4×C113semidirect
508. C2×#41C2×C4×C113semidirect
539. C22⋊Q8C2×C4×C113semidirect
546. #121C2×C4×C113semidirect
556. C2×C4⋊C4C2×C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1132
C2×#408×C1132
C113×#23112
C113×#18952
C113×#18942
C113×#18932
C113×#18922
C113×#18752
C113×#18742
C113×#18732
C113×#18722
C113×#18242
C113×#18232
C113×#17882
#21772113