Finite Group Databasebeta

← C113×#25099 #43293119

Subgroups — C113×#25099 #43293119

Order 28928.

1104 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic
2C2×#461×C113C211yesmaximal, characteristic, complemented
3C2×#448×C113C211yesmaximal, characteristic
4C2×#419×C113C211yesmaximal, characteristic, complemented
5C113×#2434C211yesmaximal, characteristic, complemented
6C113×#2363C211yesmaximal, characteristic
7C113×#2068C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2043C211yesmaximal, characteristic, complemented
10C113×#2013C211yesmaximal, characteristic, complemented
11C113×#1981C211yesmaximal, characteristic, complemented
12C113×#1928C211yesmaximal, characteristic, complemented
13C113×#1877C211yesmaximal, characteristic, complemented
14C113×#1873C211yesmaximal, characteristic, complemented
15C113×#1851C211yesmaximal, characteristic, complemented
16C23×Q8×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic
21C2×C4⋊Q8×C113C2211yescharacteristic
22C2×C4⋊Q8×C113C2211yescharacteristic
23C2×C22⋊Q8×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×C4×D4×C113C2211yescharacteristic
26C2×#117×C113C2211yescharacteristic
27#468×C113—24no—
28#461×C113—24no—
29#448×C113—24no—
30C2×#107×C113C2211yescharacteristic
31C2×C4⋊C8×C113C2211yescharacteristic
32C2×C4⋊C8×C113C2211yescharacteristic
33#419×C113—24no—
34C2×#103×C113C2211yescharacteristic
35C2×#103×C113C2211yescharacteristic
36C2×#103×C113C2211yescharacteristic
37C2×#103×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#103×C113C2211yescharacteristic
40C2×#103×C113C2211yescharacteristic
41C2×#103×C113C2211yescharacteristic
42C2×#103×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic
45#395×C113—21no—
46#395×C113—21no—
47#391×C113C2211yescharacteristic
48#391×C113C2211yescharacteristic
49#390×C113—21no—
50#390×C113C2211yescharacteristic
51#389×C113C2211yescharacteristic
52#388×C113—21no—
53#386×C113—21no—
54#385×C113—21no—
55#385×C113—21no—
56C4×C4⋊C4×C113C2211yescharacteristic
57C4×C22⋊C4×C113—21no—
58C4×C22⋊C4×C113C2211yescharacteristic
59#340×C113C2211yescharacteristic
60#340×C113C2211yescharacteristic
61#336×C113C2211yescharacteristic
62#336×C113C2211yescharacteristic
63C22×Q8×C113—21no—
64C22×Q8×C113—22no—
65C22×Q8×C113—22no—
66C22×Q8×C113—22no—
67C22×Q8×C113—22no—
68C22×Q8×C113—41no—
69C22×Q8×C113—41no—
70C22×Q8×C113C2311yescharacteristic
71C22×Q8×C113C2311yescharacteristic
72C22×Q8×C113C2311yescharacteristic
73C22×D4×C113—21no—
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—41no—
85C2×SD16×C113—41no—
86C2×SD16×C113—41no—
87C2×M16×C113—22no—
88C2×M16×C113—22no—
89C2×M16×C113—41no—
90C22×C8×C113C2311yescharacteristic
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C4⋊Q8×C113—22no—
95C4⋊Q8×C113—22no—
96C4⋊Q8×C113—41no—
97C4⋊Q8×C113—41no—
98C22⋊Q8×C113—22no—
99C22⋊Q8×C113—22no—
100#121×C113—22no—
101#121×C113D414yes—
102C4×D4×C113—22no—
103C4×D4×C113—41no—
104#117×C113—22no—
105#117×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×C113D411yescharacteristic
123C2×C22⋊C4×C113D411yescharacteristic
124C2×C42×C113—21no—
125C2×C42×C113—21no—
126C2×C42×C113C2311yescharacteristic
127C2×C42×C113C2311yescharacteristic
128#107×C113—22no—
129C4⋊C8×C113—22no—
130C4⋊C8×C113—41no—
131#103×C113—22no—
132#103×C113—22no—
133#103×C113—22no—
134#103×C113—22no—
135#103×C113—22no—
136#103×C113—22no—
137#103×C113—22no—
138#103×C113—41no—
139#103×C113D414yescomplemented
140#102×C113—22no—
141C22⋊C8×C113—22no—
142#95×C113—21no—
143#95×C113—21no—
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×C113C2×D411yescharacteristic
152C2×Q8×C113—21no—
153C2×Q8×C113—21no—
154C2×Q8×C113—28no—
155C2×Q8×C113—21no—
156C2×Q8×C113—21no—
157C2×Q8×C113—21no—
158C2×Q8×C113—21no—
159C2×Q8×C113—21no—
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—42no—
170C2×Q8×C113—42no—
171C2×Q8×C113—44no—
172C2×Q8×C113—44no—
173C2×Q8×C113—44no—
174C2×Q8×C113—42no—
175C2×Q8×C113C2×D412yes—
176C2×Q8×C113#4112yes—
177C2×D4×C113—24no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—21no—
182C2×D4×C113—21no—
183C2×D4×C113—81no—
184C2×D4×C113—81no—
185C2×D4×C113C2×D412yes—
186C22×C4×C113—21no—
187C22×C4×C113—21no—
188C22×C4×C113—21no—
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—42no—
198C22×C4×C113—42no—
199C22×C4×C113—42no—
200C22×C4×C113—42no—
201C22×C4×C113—42no—
202C22×C4×C113—81no—
203C22×C4×C113C2×D411yescharacteristic
204C22×C4×C113C2×D411yescharacteristic
205C22×C4×C113C2×D411yescharacteristic
206C22×C4×C113C2×D412yes—
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D411yescharacteristic
209C22×C4×C113#4112yes—
210C22×C4×C113C2411yescharacteristic
211SD16×C113—44no—
212SD16×C113—44no—
213SD16×C113—44no—
214M16×C113—44no—
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×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113C2×D412yes—
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—42no—
234C4⋊C4×C113—42no—
235C4⋊C4×C113—42no—
236C4⋊C4×C113—42no—
237C4⋊C4×C113—42no—
238C4⋊C4×C113—81no—
239C4⋊C4×C113C2×D412yes—
240C4⋊C4×C113C2×D412yes—
241C22⋊C4×C113—24no—
242C22⋊C4×C113—22no—
243C22⋊C4×C113—22no—
244C22⋊C4×C113—42no—
245C22⋊C4×C113—42no—
246C22⋊C4×C113—42no—
247C22⋊C4×C113—42no—
248C22⋊C4×C113—81no—
249C42×C113—21no—
250C42×C113—21no—
251C42×C113—21no—
252C42×C113—21no—
253C42×C113—42no—
254C42×C113—81no—
255C23×C113—21no—
256C23×C113—21no—
257C23×C113—21no—
258C23×C113—21no—
259C23×C113—21no—
260C23×C113—21no—
261C23×C113—22no—
262C23×C113—41no—
263C23×C113—41no—
264C23×C113—41no—
265C23×C113—41no—
266C23×C113—41no—
267C23×C113—41no—
268C23×C113#12112yes—
269C23×C113C22×D411yescharacteristic
270Q8×C113—22no—
271Q8×C113—22no—
272Q8×C113—22no—
273Q8×C113—22no—
274Q8×C113—48no—
275Q8×C113—41no—
276Q8×C113—41no—
277Q8×C113—41no—
278Q8×C113—41no—
279Q8×C113—41no—
280Q8×C113—41no—
281Q8×C113—41no—
282Q8×C113—41no—
283D4×C113—22no—
284D4×C113—22no—
285D4×C113—41no—
286D4×C113—41no—
287D4×C113—84no—
288C2×C4×C113—21no—
289C2×C4×C113—21no—
290C2×C4×C113—21no—
291C2×C4×C113—21no—
292C2×C4×C113—21no—
293C2×C4×C113—21no—
294C2×C4×C113—22no—
295C2×C4×C113—22no—
296C2×C4×C113—22no—
297C2×C4×C113—22no—
298C2×C4×C113—22no—
299C2×C4×C113—21no—
300C2×C4×C113—22no—
301C2×C4×C113—22no—
302C2×C4×C113—21no—
303C2×C4×C113—22no—
304C2×C4×C113—21no—
305C2×C4×C113—21no—
306C2×C4×C113—21no—
307C2×C4×C113—21no—
308C2×C4×C113—48no—
309C2×C4×C113—41no—
310C2×C4×C113—41no—
311C2×C4×C113—41no—
312C2×C4×C113—41no—
313C2×C4×C113—41no—
314C2×C4×C113—41no—
315C2×C4×C113—41no—
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—84no—
327C2×C4×C113#12112yes—
328C2×C4×C113#13712yes—
329C2×C4×C113#13712yes—
330C2×C4×C113C22×D411yescharacteristic
331C2×C4×C113C22×D411yescharacteristic
332C2×C4×C113C2×#4111yescharacteristic
333C2×C4×C113C2×#4111yescharacteristic
334C2×C4×C113H(5,𝔽2)11yescharacteristic
335C2×C4×C113H(5,𝔽2)11yescharacteristic
336C8×C113—22no—
337C8×C113—41no—
338C8×C113—41no—
339C8×C113—41no—
340C22×C113—22no—
341C22×C113—22no—
342C22×C113—22no—
343C22×C113—41no—
344C22×C113—41no—
345C22×C113—41no—
346C22×C113—41no—
347C22×C113—42no—
348C22×C113—42no—
349C22×C113—42no—
350C22×C113—81no—
351C22×C113—81no—
352C22×C113—81no—
353C22×C113—81no—
354C22×C113C2×#12111yescharacteristic
355C22×C113D4211yescharacteristic
356C22×C113#54611yescharacteristic
357C22×C113C2×#13711yescharacteristic
358C22×C113C2×#13711yescharacteristic
359C22×C113#57711yescharacteristic
360C22×C113#57711yescharacteristic
361C4×C113—22no—
362C4×C113—22no—
363C4×C113—22no—
364C4×C113—41no—
365C4×C113—42no—
366C4×C113—42no—
367C4×C113—42no—
368C4×C113—41no—
369C4×C113—42no—
370C4×C113—81no—
371C4×C113—81no—
372C4×C113—81no—
373C4×C113#52511yescharacteristic
374C4×C113#53811yescharacteristic
375C4×C113D4211yescharacteristic
376C4×C113#54611yescharacteristic
377#25099C11311yesmaximal, characteristic, direct product factor, Sylow
378C2×C113—42no—
379C2×C113—82no—
380C2×C113#242411yescharacteristic
381C2×C113#303911yescharacteristic
382C2×C113#304211yescharacteristic
383C2×C113#326611yescharacteristic
384C2×C113#327811yescharacteristic
385C2×C113#332011yescharacteristic
386C2×C113#332911yescharacteristic
387C2×#468C2×C11311yescharacteristic
388C2×#461C2×C11311yescharacteristic, complemented
389C2×#448C2×C11311yescharacteristic
390C2×#419C2×C11311yescharacteristic, complemented
391#2434C2×C11311yescharacteristic, complemented
392#2363C2×C11311yescharacteristic
393#2068C2×C11311yescharacteristic, complemented
394#2055C2×C11311yescharacteristic, complemented
395#2043C2×C11311yescharacteristic, complemented
396#2013C2×C11311yescharacteristic, complemented
397#1981C2×C11311yescharacteristic, complemented
398#1928C2×C11311yescharacteristic, complemented
399#1877C2×C11311yescharacteristic, complemented
400#1873C2×C11311yescharacteristic, complemented
401#1851C2×C11311yescharacteristic, complemented
402C113#2509911yescharacteristic, direct product factor, Sylow
403C23×Q8C22×C11311yescharacteristic
404C22×SD16C22×C11311yescharacteristic
405C22×SD16C22×C11311yescharacteristic
406C22×SD16C22×C11311yescharacteristic
407C22×M16C22×C11311yescharacteristic
408C2×C4⋊Q8C22×C11311yescharacteristic
409C2×C4⋊Q8C22×C11311yescharacteristic
410C2×C22⋊Q8C22×C11311yescharacteristic
411C2×#121C22×C11311yescharacteristic
412C2×C4×D4C22×C11311yescharacteristic
413C2×#117C22×C11311yescharacteristic
414#468—24no—
415#461—24no—
416#448—24no—
417C2×#107C22×C11311yescharacteristic
418C2×C4⋊C8C22×C11311yescharacteristic
419C2×C4⋊C8C22×C11311yescharacteristic
420#419—24no—
421C2×#103C22×C11311yescharacteristic
422C2×#103C22×C11311yescharacteristic
423C2×#103C22×C11311yescharacteristic
424C2×#103C22×C11311yescharacteristic
425C2×#103C22×C11311yescharacteristic
426C2×#103C22×C11311yescharacteristic
427C2×#103C22×C11311yescharacteristic
428C2×#103C22×C11311yescharacteristic
429C2×#103C22×C11311yescharacteristic
430C2×#102C22×C11311yescharacteristic
431C2×C22⋊C8C22×C11311yescharacteristic
432#395—21no—
433#395—21no—
434#391C22×C11311yescharacteristic
435#391C22×C11311yescharacteristic
436#390—21no—
437#390C22×C11311yescharacteristic
438#389C22×C11311yescharacteristic
439#388—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443C4×C4⋊C4C22×C11311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4C22×C11311yescharacteristic
446#340C22×C11311yescharacteristic
447#340C22×C11311yescharacteristic
448#336C22×C11311yescharacteristic
449#336C22×C11311yescharacteristic
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—41no—
456C22×Q8—41no—
457C22×Q8C23×C11311yescharacteristic
458C22×Q8C23×C11311yescharacteristic
459C22×Q8C23×C11311yescharacteristic
460C22×D4—21no—
461C22×D4C23×C11311yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C11311yescharacteristic
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—41no—
472C2×SD16—41no—
473C2×SD16—41no—
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—41no—
477C22×C8C23×C11311yescharacteristic
478C22×C8C23×C11311yescharacteristic
479C22×C8C23×C11311yescharacteristic
480C22×C8C23×C11311yescharacteristic
481C4⋊Q8—22no—
482C4⋊Q8—22no—
483C4⋊Q8—41no—
484C4⋊Q8—41no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487#121—22no—
488#121D4×C11314yes—
489C4×D4—22no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4C23×C11311yescharacteristic
500C2×C4⋊C4C23×C11311yescharacteristic
501C2×C4⋊C4C23×C11311yescharacteristic
502C2×C4⋊C4C23×C11311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4D4×C11311yescharacteristic
510C2×C22⋊C4D4×C11311yescharacteristic
511C2×C42—21no—
512C2×C42—21no—
513C2×C42C23×C11311yescharacteristic
514C2×C42C23×C11311yescharacteristic
515#107—22no—
516C4⋊C8—22no—
517C4⋊C8—41no—
518#103—22no—
519#103—22no—
520#103—22no—
521#103—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#103—41no—
526#103D4×C11314yescomplemented
527#102—22no—
528C22⋊C8—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95D4×C11311yescharacteristic
536#95D4×C11311yescharacteristic
537C24—21no—
538C24C2×D4×C11311yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—28no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—42no—
557C2×Q8—42no—
558C2×Q8—44no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—42no—
562C2×Q8C2×D4×C11312yes—
563C2×Q8#41×C11312yes—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4C2×D4×C11312yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—81no—
590C22×C4C2×D4×C11311yescharacteristic
591C22×C4C2×D4×C11311yescharacteristic
592C22×C4C2×D4×C11311yescharacteristic
593C22×C4C2×D4×C11312yes—
594C22×C4C2×D4×C11311yescharacteristic
595C22×C4C2×D4×C11311yescharacteristic
596C22×C4#41×C11312yes—
597C22×C4C24×C11311yescharacteristic
598SD16—44no—
599SD16—44no—
600SD16—44no—
601M16—44no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8C2×D4×C11312yes—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C11312yes—
627C4⋊C4C2×D4×C11312yes—
628C22⋊C4—24no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—42no—
641C42—81no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23#121×C11312yes—
656C23C22×D4×C11311yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—48no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667Q8—41no—
668Q8—41no—
669Q8—41no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—84no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—48no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—84no—
714C2×C4#121×C11312yes—
715C2×C4#137×C11312yes—
716C2×C4#137×C11312yes—
717C2×C4C22×D4×C11311yescharacteristic
718C2×C4C22×D4×C11311yescharacteristic
719C2×C4C2×#41×C11311yescharacteristic
720C2×C4C2×#41×C11311yescharacteristic
721C2×C4H(5,𝔽2)×C11311yescharacteristic
722C2×C4H(5,𝔽2)×C11311yescharacteristic
723C8—22no—
724C8—41no—
725C8—41no—
726C8—41no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22C2×#121×C11311yescharacteristic
742C22D42×C11311yescharacteristic
743C22#546×C11311yescharacteristic
744C22C2×#137×C11311yescharacteristic
745C22C2×#137×C11311yescharacteristic
746C22#577×C11311yescharacteristic
747C22#577×C11311yescharacteristic
748C4—22no—
749C4—22no—
750C4—22no—
751C4—41no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—41no—
756C4—42no—
757C4—81no—
758C4—81no—
759C4—81no—
760C4#525×C11311yescharacteristic
761C4#538×C11311yescharacteristic
762C4D42×C11311yescharacteristic
763C4#546×C11311yescharacteristic
764C2—42no—
765C2—82no—
766C2C113×#242411yescharacteristic
767C2C113×#303911yescharacteristic
768C2C113×#304211yescharacteristic
769C2C113×#326611yescharacteristic
770C2C113×#327811yescharacteristic
771C2C113×#332011yescharacteristic
772C2C113×#332911yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#121×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
2. C2×#461×C113C2semidirect
4. C2×#419×C113C2semidirect
5. C113×#2434C2semidirect
7. C113×#2068C2semidirect
8. C113×#2055C2semidirect
9. C113×#2043C2semidirect
10. C113×#2013C2semidirect
11. C113×#1981C2semidirect
12. C113×#1928C2semidirect
13. C113×#1877C2semidirect
14. C113×#1873C2semidirect
15. C113×#1851C2semidirect
139. #103×C113D4semidirect
377. #25099C113direct (N × H)
388. C2×#461C2×C113semidirect
390. C2×#419C2×C113semidirect
391. #2434C2×C113semidirect
393. #2068C2×C113semidirect
394. #2055C2×C113semidirect
395. #2043C2×C113semidirect
396. #2013C2×C113semidirect
397. #1981C2×C113semidirect
398. #1928C2×C113semidirect
399. #1877C2×C113semidirect
400. #1873C2×C113semidirect
401. #1851C2×C113semidirect
402. C113#25099direct (N × H)
526. #103D4×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×#461×C1132
C2×#448×C1132
C2×#419×C1132
C113×#24342
C113×#23632
C113×#20682
C113×#20552
C113×#20432
C113×#20132
C113×#19812
C113×#19282
C113×#18772
C113×#18732
C113×#18512
#25099113