Finite Group Databasebeta

← C113×#25156 #43293176

Subgroups — C113×#25156 #43293176

Order 28928.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C113C211yesmaximal, characteristic, complemented
2C2×#450×C113C211yesmaximal, characteristic
3C2×#450×C113C211yesmaximal, characteristic
4C2×C4×SD16×C113C211yesmaximal, characteristic, complemented
5C113×#2429C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C113C211yesmaximal, characteristic
7C113×#2065C211yesmaximal, characteristic, complemented
8C113×#2035C211yesmaximal, characteristic, complemented
9C113×#2035C211yesmaximal, characteristic, complemented
10C113×#2013C211yesmaximal, characteristic, complemented
11C113×#1968C211yesmaximal, characteristic, complemented
12C113×#1923C211yesmaximal, characteristic, complemented
13C113×#1880C211yesmaximal, characteristic, complemented
14C113×#1877C211yesmaximal, characteristic, complemented
15C113×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×SD16×C113C2211yescharacteristic
21C2×C4⋊Q8×C113C2211yescharacteristic, complemented
22C2×C22⋊Q8×C113C2211yescharacteristic
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×C4×Q8×C113C2211yescharacteristic, complemented
25C2×C4×D4×C113C2211yescharacteristic
26C2×C4×D4×C113C2211yescharacteristic
27C22×C22⋊C4×C113—21no—
28#461×C113—24no—
29#450×C113—24no—
30#450×C113—24no—
31C4×SD16×C113—24no—
32C2×#106×C113C2211yescharacteristic, complemented
33C2×#106×C113C2211yescharacteristic, complemented
34C2×C4⋊C8×C113C2211yescharacteristic, complemented
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#103×C113C2211yescharacteristic, complemented
38C2×#103×C113C2211yescharacteristic, complemented
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45C2×C4×C8×C113C2211yescharacteristic, complemented
46#398×C113—21no—
47#396×C113—21no—
48#391×C113C2211yescharacteristic, complemented
49#390×C113C2211yescharacteristic
50#390×C113C2211yescharacteristic
51#389×C113—21no—
52#389×C113C2211yescharacteristic, complemented
53#388×C113—21no—
54#386×C113—21no—
55#386×C113—21no—
56#380×C113C2211yescharacteristic
57#379×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×Q8×C113C2311yescharacteristic
66C22×D4×C113—22no—
67C22×D4×C113—22no—
68C22×D4×C113—22no—
69C22×D4×C113—22no—
70C22×D4×C113—21no—
71C22×D4×C113—41no—
72C22×D4×C113—41no—
73C22×D4×C113C2311yescharacteristic
74C22×D4×C113C2311yescharacteristic
75C23×C4×C113—21no—
76C23×C4×C113—21no—
77C23×C4×C113C2311yescharacteristic
78C2×SD16×C113—22no—
79C2×SD16×C113—22no—
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—22no—
84C2×SD16×C113—22no—
85C2×SD16×C113—22no—
86C2×SD16×C113—22no—
87C2×SD16×C113—41no—
88C2×SD16×C113—41no—
89C2×SD16×C113D414yes—
90C22×C8×C113C2311yescharacteristic
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C4⋊Q8×C113—22no—
95C4⋊Q8×C113—41no—
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—41no—
99C22⋊Q8×C113—41no—
100C4×Q8×C113—22no—
101C4×Q8×C113—41no—
102C4×D4×C113—22no—
103C4×D4×C113—22no—
104C4×D4×C113—41no—
105C4×D4×C113—41no—
106C2×C4⋊C4×C113—21no—
107C2×C4⋊C4×C113—21no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113—21no—
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
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—44no—
126C2×C22⋊C4×C113D411yescharacteristic
127C2×C22⋊C4×C113D411yescharacteristic
128C2×C42×C113—21no—
129C2×C42×C113C2311yescharacteristic
130C2×C42×C113C2311yescharacteristic
131#106×C113—22no—
132#106×C113—41no—
133C4⋊C8×C113—22no—
134#103×C113—22no—
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×C113D414yes—
142C22⋊C8×C113—22no—
143C22⋊C8×C113—22no—
144C4×C8×C113—22no—
145#95×C113—21no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113D411yescharacteristic
150#95×C113D411yescharacteristic
151C24×C113—21no—
152C24×C113—24no—
153C24×C113—21no—
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×Q8×C113—21no—
168C2×Q8×C113—21no—
169C2×Q8×C113—21no—
170C2×Q8×C113—21no—
171C2×Q8×C113—21no—
172C2×Q8×C113C2×D412yes—
173C2×D4×C113—24no—
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—42no—
183C2×D4×C113—42no—
184C2×D4×C113—44no—
185C2×D4×C113—44no—
186C2×D4×C113—44no—
187C2×D4×C113—44no—
188C2×D4×C113C2×D412yes—
189C2×D4×C113C2×D412yes—
190C2×D4×C113#4112yes—
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—42no—
205C22×C4×C113—42no—
206C22×C4×C113—42no—
207C22×C4×C113—42no—
208C22×C4×C113—81no—
209C22×C4×C113—81no—
210C22×C4×C113C2×D411yescharacteristic
211C22×C4×C113C2×D411yescharacteristic
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2411yescharacteristic
216SD16×C113—28no—
217SD16×C113—44no—
218SD16×C113—44no—
219SD16×C113—44no—
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—
231C2×C8×C113C2×D412yes—
232C4⋊C4×C113—21no—
233C4⋊C4×C113—21no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—42no—
240C4⋊C4×C113—42no—
241C4⋊C4×C113—42no—
242C4⋊C4×C113—42no—
243C4⋊C4×C113—42no—
244C4⋊C4×C113—42no—
245C4⋊C4×C113C2×D412yes—
246C22⋊C4×C113—41no—
247C22⋊C4×C113—42no—
248C22⋊C4×C113—42no—
249C22⋊C4×C113—42no—
250C22⋊C4×C113—42no—
251C22⋊C4×C113—42no—
252C22⋊C4×C113—42no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—81no—
255C22⋊C4×C113—81no—
256C22⋊C4×C113SD1614yescomplemented
257C42×C113—21no—
258C42×C113—21no—
259C42×C113—21no—
260C42×C113—21no—
261C42×C113—42no—
262C23×C113—21no—
263C23×C113—22no—
264C23×C113—21no—
265C23×C113—21no—
266C23×C113—22no—
267C23×C113—22no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—22no—
272C23×C113—48no—
273C23×C113—48no—
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—84no—
285C23×C113—84no—
286C23×C113—84no—
287C23×C113—84no—
288C23×C113—84no—
289C23×C113C2×SD1612yes—
290C23×C113C22×D411yescharacteristic
291Q8×C113—22no—
292Q8×C113—22no—
293Q8×C113—41no—
294Q8×C113—41no—
295Q8×C113—41no—
296Q8×C113—41no—
297Q8×C113—41no—
298Q8×C113—41no—
299D4×C113—22no—
300D4×C113—22no—
301D4×C113—22no—
302D4×C113—22no—
303D4×C113—22no—
304D4×C113—48no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113#12114yes—
308C2×C4×C113—21no—
309C2×C4×C113—21no—
310C2×C4×C113—21no—
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—21no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—21no—
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—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—84no—
344C2×C4×C113—84no—
345C2×C4×C113C2×SD1612yes—
346C2×C4×C113C2×SD1612yes—
347C2×C4×C113C22×D411yescharacteristic
348C2×C4×C113C22×D411yescharacteristic
349C2×C4×C113C2×#4111yescharacteristic
350C2×C4×C113C2×#4111yescharacteristic
351C2×C4×C113H(5,𝔽2)11yescharacteristic
352C2×C4×C113H(5,𝔽2)11yescharacteristic
353C8×C113—22no—
354C8×C113—22no—
355C8×C113—41no—
356C8×C113—41no—
357C22×C113—22no—
358C22×C113—24no—
359C22×C113—22no—
360C22×C113—22no—
361C22×C113—42no—
362C22×C113—41no—
363C22×C113—42no—
364C22×C113—41no—
365C22×C113—41no—
366C22×C113—42no—
367C22×C113—41no—
368C22×C113—42no—
369C22×C113—42no—
370C22×C113—42no—
371C22×C113—42no—
372C22×C113—42no—
373C22×C113—42no—
374C22×C113—816no—
375C22×C113—81no—
376C22×C113—81no—
377C22×C113—81no—
378C22×C113—81no—
379C22×C113#52511yescharacteristic
380C22×C113D4211yescharacteristic
381C22×C113D4211yescharacteristic
382C22×C113C22×SD1611yescharacteristic
383C22×C113#57511yescharacteristic
384C22×C113#57711yescharacteristic
385C22×C113#57711yescharacteristic
386C4×C113—22no—
387C4×C113—22no—
388C4×C113—41no—
389C4×C113—42no—
390C4×C113—41no—
391C4×C113—42no—
392C4×C113—41no—
393C4×C113—81no—
394C4×C113—81no—
395C4×C113—81no—
396C4×C113—81no—
397C4×C113C2×#12111yescharacteristic
398C4×C113#53811yescharacteristic
399C4×C113#54611yescharacteristic
400C4×C113#54611yescharacteristic
401#25156C11311yesmaximal, characteristic, direct product factor, Sylow
402C2×C113—42no—
403C2×C113—44no—
404C2×C113—82no—
405C2×C113#242411yescharacteristic
406C2×C113#310111yescharacteristic
407C2×C113#312311yescharacteristic
408C2×C113#326711yescharacteristic
409C2×C113#327511yescharacteristic
410C2×C113D4×SD1611yescharacteristic
411C2×C113D4×SD1611yescharacteristic
412C2×#461C2×C11311yescharacteristic, complemented
413C2×#450C2×C11311yescharacteristic
414C2×#450C2×C11311yescharacteristic
415C2×C4×SD16C2×C11311yescharacteristic, complemented
416#2429C2×C11311yescharacteristic, complemented
417D4×C22⋊C4C2×C11311yescharacteristic
418#2065C2×C11311yescharacteristic, complemented
419#2035C2×C11311yescharacteristic, complemented
420#2035C2×C11311yescharacteristic, complemented
421#2013C2×C11311yescharacteristic, complemented
422#1968C2×C11311yescharacteristic, complemented
423#1923C2×C11311yescharacteristic, complemented
424#1880C2×C11311yescharacteristic, complemented
425#1877C2×C11311yescharacteristic, complemented
426#1864C2×C11311yescharacteristic, complemented
427C113#2515611yescharacteristic, direct product factor, Sylow
428C23×D4C22×C11311yescharacteristic
429C22×SD16C22×C11311yescharacteristic
430C22×SD16C22×C11311yescharacteristic
431C22×SD16C22×C11311yescharacteristic
432C22×SD16C22×C11311yescharacteristic
433C2×C4⋊Q8C22×C11311yescharacteristic, complemented
434C2×C22⋊Q8C22×C11311yescharacteristic
435C2×C22⋊Q8C22×C11311yescharacteristic
436C2×C4×Q8C22×C11311yescharacteristic, complemented
437C2×C4×D4C22×C11311yescharacteristic
438C2×C4×D4C22×C11311yescharacteristic
439C22×C22⋊C4—21no—
440#461—24no—
441#450—24no—
442#450—24no—
443C4×SD16—24no—
444C2×#106C22×C11311yescharacteristic, complemented
445C2×#106C22×C11311yescharacteristic, complemented
446C2×C4⋊C8C22×C11311yescharacteristic, complemented
447C2×#103C22×C11311yescharacteristic, complemented
448C2×#103C22×C11311yescharacteristic, complemented
449C2×#103C22×C11311yescharacteristic, complemented
450C2×#103C22×C11311yescharacteristic, complemented
451C2×#102C22×C11311yescharacteristic
452C2×#102C22×C11311yescharacteristic
453C2×#102C22×C11311yescharacteristic
454C2×#102C22×C11311yescharacteristic
455C2×C22⋊C8C22×C11311yescharacteristic
456C2×C22⋊C8C22×C11311yescharacteristic
457C2×C4×C8C22×C11311yescharacteristic, complemented
458#398—21no—
459#396—21no—
460#391C22×C11311yescharacteristic, complemented
461#390C22×C11311yescharacteristic
462#390C22×C11311yescharacteristic
463#389—21no—
464#389C22×C11311yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#380C22×C11311yescharacteristic
469#379—21no—
470C4×C22⋊C4C22×C11311yescharacteristic
471#340C22×C11311yescharacteristic, complemented
472#340C22×C11311yescharacteristic, complemented
473#336C22×C11311yescharacteristic, complemented
474#336C22×C11311yescharacteristic, complemented
475C25—21no—
476C22×Q8C23×C11311yescharacteristic
477C22×Q8C23×C11311yescharacteristic
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C23×C11311yescharacteristic
486C22×D4C23×C11311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C11311yescharacteristic
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16D4×C11314yes—
502C22×C8C23×C11311yescharacteristic
503C22×C8C23×C11311yescharacteristic
504C22×C8C23×C11311yescharacteristic
505C22×C8C23×C11311yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4C23×C11311yescharacteristic
525C2×C4⋊C4C23×C11311yescharacteristic
526C2×C4⋊C4C23×C11311yescharacteristic
527C2×C4⋊C4C23×C11311yescharacteristic
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⋊C4—44no—
538C2×C22⋊C4D4×C11311yescharacteristic
539C2×C22⋊C4D4×C11311yescharacteristic
540C2×C42—21no—
541C2×C42C23×C11311yescharacteristic
542C2×C42C23×C11311yescharacteristic
543#106—22no—
544#106—41no—
545C4⋊C8—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—41no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102D4×C11314yes—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C4×C8—22no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C11311yescharacteristic
562#95D4×C11311yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×D4×C11311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C11312yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4C2×D4×C11312yes—
601C2×D4C2×D4×C11312yes—
602C2×D4#41×C11312yes—
603C2×D4#41×C11312yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C11311yescharacteristic
623C22×C4C2×D4×C11311yescharacteristic
624C22×C4C2×D4×C11311yescharacteristic
625C22×C4C2×D4×C11311yescharacteristic
626C22×C4C2×D4×C11311yescharacteristic
627C22×C4C24×C11311yescharacteristic
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8C2×D4×C11312yes—
643C2×C8C2×D4×C11312yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C11312yes—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4SD16×C11314yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×SD16×C11312yes—
702C23C22×D4×C11311yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#121×C11314yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
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—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C2×SD16×C11312yes—
758C2×C4C2×SD16×C11312yes—
759C2×C4C22×D4×C11311yescharacteristic
760C2×C4C22×D4×C11311yescharacteristic
761C2×C4C2×#41×C11311yescharacteristic
762C2×C4C2×#41×C11311yescharacteristic
763C2×C4H(5,𝔽2)×C11311yescharacteristic
764C2×C4H(5,𝔽2)×C11311yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—41no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#525×C11311yescharacteristic
792C22D42×C11311yescharacteristic
793C22D42×C11311yescharacteristic
794C22C22×SD16×C11311yescharacteristic
795C22#575×C11311yescharacteristic
796C22#577×C11311yescharacteristic
797C22#577×C11311yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#121×C11311yescharacteristic
810C4#538×C11311yescharacteristic
811C4#546×C11311yescharacteristic
812C4#546×C11311yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2C113×#242411yescharacteristic
817C2C113×#310111yescharacteristic
818C2C113×#312311yescharacteristic
819C2C113×#326711yescharacteristic
820C2C113×#327511yescharacteristic
821C2D4×SD16×C11311yescharacteristic
822C2D4×SD16×C11311yescharacteristic
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×#461×C113C2semidirect
4. C2×C4×SD16×C113C2semidirect
5. C113×#2429C2semidirect
7. C113×#2065C2semidirect
8. C113×#2035C2semidirect
9. C113×#2035C2semidirect
10. C113×#2013C2semidirect
11. C113×#1968C2semidirect
12. C113×#1923C2semidirect
13. C113×#1880C2semidirect
14. C113×#1877C2semidirect
15. C113×#1864C2semidirect
21. C2×C4⋊Q8×C113C22semidirect
24. C2×C4×Q8×C113C22semidirect
32. C2×#106×C113C22semidirect
33. C2×#106×C113C22semidirect
34. C2×C4⋊C8×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
37. C2×#103×C113C22semidirect
38. C2×#103×C113C22semidirect
45. C2×C4×C8×C113C22semidirect
48. #391×C113C22semidirect
52. #389×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #336×C113C22semidirect
62. #336×C113C22semidirect
256. C22⋊C4×C113SD16semidirect
401. #25156C113direct (N × H)
412. C2×#461C2×C113semidirect
415. C2×C4×SD16C2×C113semidirect
416. #2429C2×C113semidirect
418. #2065C2×C113semidirect
419. #2035C2×C113semidirect
420. #2035C2×C113semidirect
421. #2013C2×C113semidirect
422. #1968C2×C113semidirect
423. #1923C2×C113semidirect
424. #1880C2×C113semidirect
425. #1877C2×C113semidirect
426. #1864C2×C113semidirect
427. C113#25156direct (N × H)
433. C2×C4⋊Q8C22×C113semidirect
436. C2×C4×Q8C22×C113semidirect
444. C2×#106C22×C113semidirect
445. C2×#106C22×C113semidirect
446. C2×C4⋊C8C22×C113semidirect
447. C2×#103C22×C113semidirect
448. C2×#103C22×C113semidirect
449. C2×#103C22×C113semidirect
450. C2×#103C22×C113semidirect
457. C2×C4×C8C22×C113semidirect
460. #391C22×C113semidirect
464. #389C22×C113semidirect
471. #340C22×C113semidirect
472. #340C22×C113semidirect
473. #336C22×C113semidirect
474. #336C22×C113semidirect
668. C22⋊C4SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1132
C2×#450×C1132
C2×C4×SD16×C1132
C113×#24292
D4×C22⋊C4×C1132
C113×#20652
C113×#20352
C113×#20132
C113×#19682
C113×#19232
C113×#18802
C113×#18772
C113×#18642
#25156113