Finite Group Databasebeta

← C2×#21435192 #29460046

Subgroups — C2×#21435192 #29460046

Order 15104.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838023C211yesmaximal, characteristic, complemented
2C2×#16837971C211yesmaximal, characteristic, complemented
3#21435192C2116yesmaximal, direct product factor
4C2×#16837791C211yesmaximal, characteristic, complemented
5C2×#16837786C211yesmaximal, characteristic, complemented
6C2×#16837762C211yesmaximal, characteristic, complemented
7C2×#16837749C211yesmaximal, characteristic, complemented
8C2×#16837625C211yesmaximal, characteristic, complemented
9C2×#16837603C211yesmaximal, characteristic, complemented
10C2×#16837618C211yesmaximal, characteristic, complemented
11C2×#16837598C211yesmaximal, characteristic, complemented
12C2×#16837566C211yesmaximal, characteristic, complemented
13C2×#16837549C211yesmaximal, characteristic, complemented
14C2×#16837555C211yesmaximal, characteristic, complemented
15C2×#16837538C211yesmaximal, characteristic, complemented
16C2×C59×#433C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C23×D236C2211yescharacteristic
19C22×Dic236C2211yescharacteristic, complemented
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×#11745660C2211yescharacteristic, complemented
23C22×#11745660C2211yescharacteristic, complemented
24C22×D472C2211yescharacteristic
25C22×D472C2211yescharacteristic
26C22×D472C2211yescharacteristic, complemented
27#16838023—24no—
28#16838023C2218yescomplemented
29#16837971—24no—
30#16837971C2218yescomplemented
31C2×#14273727C2211yescharacteristic, complemented
32C2×#14273724C2211yescharacteristic
33C2×#14273724C2211yescharacteristic
34C2×#14273722—21no—
35C2×#14273715C2211yescharacteristic
36C2×#14273715C2211yescharacteristic
37C2×#14273715C2211yescharacteristic, complemented
38C2×#14273713—21no—
39C2×#14273709—21no—
40C2×#14273706C2211yescharacteristic
41C2×#14273705—21no—
42C2×#14273702—21no—
43C2×#14273702—21no—
44C2×#14273701C2211yescharacteristic
45C2×#14273697—21no—
46C2×#14273697—21no—
47C2×C4×Dic118C2211yescharacteristic, complemented
48C2×C4×D236C2211yescharacteristic, complemented
49#16837791C2218yescomplemented
50#16837786C2218yescomplemented
51#16837762C2218yescomplemented
52#16837749C2218yescomplemented
53#16837625C2218yescomplemented
54#16837618C2218yescomplemented
55#16837603C2218yescomplemented
56#16837598C2218yescomplemented
57#16837566C2218yescomplemented
58#16837555C2218yescomplemented
59#16837549C2218yescomplemented
60#16837538C2218yescomplemented
61C2×#14273652C2211yescharacteristic, complemented
62C2×#14273652C2211yescharacteristic, complemented
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273649C2211yescharacteristic
66C2×#14273649C2211yescharacteristic
67C2×#14273649C2211yescharacteristic, complemented
68C2×#14273649C2211yescharacteristic, complemented
69C2×#117×C59C2211yescharacteristic
70C59×#433C2218yescomplemented
71C2×C4⋊C8×C59C2211yescharacteristic, complemented
72C2×C4⋊C8×C59C2211yescharacteristic, complemented
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×#97×C59C2211yescharacteristic, complemented
76C2×C4×C8×C59C2211yescharacteristic, complemented
77C24×D59—21no—
78C2×#11745685—22no—
79C2×#11745685—42no—
80C2×#11745685—42no—
81C2×#11745685C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C22×Dic118C2311yescharacteristic
85C22×D236—21no—
86C22×D236—22no—
87C22×D236—21no—
88C22×D236—21no—
89C22×D236—21no—
90C22×D236—21no—
91C22×D236—42no—
92C22×D236—42no—
93C22×D236C2311yescharacteristic
94C22×D236C2311yescharacteristic
95C22×D236C2311yescharacteristic
96C22×D236C2311yescharacteristic
97C22×D236C2314yes—
98C22×C22⋊D59—21no—
99C22×C22⋊D59—21no—
100C22×C4×D59—21no—
101C22×C4×D59—21no—
102C2×Dic236—42no—
103C2×Dic236C2314yescomplemented
104C2×#11745660—42no—
105C2×#11745660—42no—
106C2×#11745660—42no—
107C2×#11745660—42no—
108C2×#11745660C2314yes—
109C2×#11745660C2314yes—
110C2×#11745660C2314yescomplemented
111C2×#11745660C2314yescomplemented
112C2×D472—42no—
113C2×D472—42no—
114C2×D472—42no—
115C2×D472C2314yes—
116C2×D472C2314yes—
117C2×D472C2314yescomplemented
118#14273727—22no—
119#14273727C2314yescomplemented
120#14273724—22no—
121#14273724—22no—
122#14273724C2314yes—
123#14273724C2314yes—
124#14273722—28no—
125#14273715—22no—
126#14273715—22no—
127#14273715—22no—
128#14273715C2314yes—
129#14273715C2314yes—
130#14273715C2314yescomplemented
131#14273713—28no—
132#14273709—28no—
133#14273706—22no—
134#14273706C2314yes—
135#14273705—28no—
136#14273702—28no—
137#14273702—28no—
138#14273701—22no—
139#14273701C2314yes—
140#14273697—28no—
141#14273697—28no—
142C4×Dic118—22no—
143C4×Dic118C2314yescomplemented
144C4×D236—22no—
145C4×D236C2314yescomplemented
146C2×C4⋊Dic59—21no—
147C2×C4⋊Dic59C2311yescharacteristic
148C2×C4⋊Dic59C2311yescharacteristic
149C2×Dic59⋊C4—21no—
150C2×Dic59⋊C4—21no—
151C2×C22⋊Dic59—21no—
152C2×(C2×D59)⋊C4—21no—
153C2×(C2×D59)⋊C4—21no—
154C2×(C2×D59)⋊C4—21no—
155C2×(C2×D59)⋊C4—21no—
156C2×(C2×D59)⋊C4—21no—
157C2×(C2×D59)⋊C4—21no—
158C2×(C2×D59)⋊C4—21no—
159C2×(C2×D59)⋊C4—21no—
160C2×C4×Dic59—21no—
161#14273652C2314yescomplemented
162#14273652C2314yescomplemented
163#14273649C2314yes—
164#14273649C2314yes—
165#14273649C2314yes—
166#14273649C2314yes—
167#14273649C2314yescomplemented
168#14273649C2314yescomplemented
169C23×C4×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174#117×C59D414yes—
175#117×C59C2314yes—
176C2×C4⋊C4×C59D411yescharacteristic
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C22⋊C4×C59D411yescharacteristic
179C2×C22⋊C4×C59D411yescharacteristic
180C2×C42×C59C2311yescharacteristic
181C2×C42×C59C2311yescharacteristic
182C4⋊C8×C59C2314yescomplemented
183C4⋊C8×C59C2314yescomplemented
184C22⋊C8×C59C2314yes—
185C22⋊C8×C59C2314yes—
186#97×C59C2314yescomplemented
187C4×C8×C59C2314yescomplemented
188C24×C59C2×D411yescharacteristic
189C23×D59—21no—
190C23×D59—21no—
191C23×D59—21no—
192C23×D59—21no—
193C23×D59—24no—
194C23×D59—44no—
195C23×D59—82no—
196C23×D59—82no—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D412yes—
205C22×C4×C59C2412yes—
206C22×C4×C59C2411yescharacteristic
207C2×C22⋊D59—24no—
208C2×C22⋊D59—24no—
209C2×C22⋊D59—44no—
210C2×C22⋊D59—82no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215#11745685—44no—
216#11745685—44no—
217#11745685—48no—
218C2×D236—22no—
219C2×D236—22no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—22no—
223C2×D236—22no—
224C2×D236—22no—
225C2×D236—22no—
226C2×D236—21no—
227C2×D236—24no—
228C2×D236—21no—
229C2×D236—21no—
230C2×D236—21no—
231C2×D236—24no—
232C2×D236—24no—
233C2×D236—24no—
234C2×D236—24no—
235C2×D236—44no—
236C2×D236—44no—
237C2×D236—44no—
238C2×D236—48no—
239C2×D236—82no—
240C2×D236—82no—
241C2×D236—82no—
242C2×D236—82no—
243C2×D236C2412yes—
244C2×D236C2412yes—
245C2×D236C2412yes—
246C2×D236C2412yes—
247C2×C4×D59—24no—
248C2×C4×D59—24no—
249C2×C4×D59—44no—
250C2×C4×D59—82no—
251C2×Dic118—22no—
252C2×Dic118—22no—
253C2×Dic118—22no—
254C2×Dic118—22no—
255C2×Dic118—21no—
256C2×Dic118—21no—
257C2×Dic118—24no—
258C2×Dic118—82no—
259C2×Dic118C2412yes—
260C2×Dic118C2412yes—
261C2×C8×C59—22no—
262C2×C8×C59—22no—
263C2×C8×C59—22no—
264C2×C8×C59—22no—
265C2×C8×C59C2412yes—
266C2×C8×C59C2412yes—
267C2×C8×C59C2412yes—
268C2×C8×C59C2412yes—
269C4⋊C4×C59C2×D414yes—
270C4⋊C4×C59C2×D414yes—
271C22⋊C4×C59C2×D414yes—
272C22⋊C4×C59C2×D414yes—
273C42×C59C2×D412yes—
274C42×C59C2×D412yes—
275C42×C59C2412yes—
276C42×C59C2412yes—
277C22⋊Dic59—24no—
278(C2×D59)⋊C4—24no—
279(C2×D59)⋊C4—24no—
280(C2×D59)⋊C4—24no—
281(C2×D59)⋊C4—24no—
282(C2×D59)⋊C4—24no—
283(C2×D59)⋊C4—24no—
284(C2×D59)⋊C4—24no—
285(C2×D59)⋊C4—24no—
286C4⋊Dic59—24no—
287C4⋊Dic59—21no—
288C4⋊Dic59—21no—
289C4⋊Dic59C2412yes—
290C4⋊Dic59C2412yes—
291Dic59⋊C4—24no—
292Dic59⋊C4—24no—
293C4×Dic59—24no—
294Dic236—44no—
295D472—44no—
296D472—44no—
297D472—44no—
298#11745660—44no—
299#11745660—44no—
300#11745660—44no—
301#11745660—44no—
302C23×C59—22no—
303C23×C59—22no—
304C23×C59—22no—
305C23×C59C22×D412yes—
306C23×C59C22×D411yescharacteristic
307C22×D59—22no—
308C22×D59—22no—
309C22×D59—22no—
310C22×D59—22no—
311C22×D59—48no—
312C22×D59—42no—
313C22×D59—42no—
314C22×D59—42no—
315C22×D59—42no—
316C22×D59—42no—
317C22×D59—42no—
318C22×D59—42no—
319C22×D59—42no—
320C22×D59—42no—
321C22×D59—42no—
322C22×D59—42no—
323C22×D59—42no—
324C22×D59—84no—
325C22×D59—84no—
326C22×D59—816no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59—22no—
330C2×C4×C59—22no—
331C2×C4×C59—22no—
332C2×C4×C59—24no—
333C2×C4×C59—22no—
334C2×C4×C59—22no—
335C2×C4×C59C22×D412yes—
336C2×C4×C59C22×D412yes—
337C2×C4×C59C22×D412yes—
338C2×C4×C59C22×D412yes—
339C2×C4×C59C22×D412yes—
340C2×C4×C59C22×D411yescharacteristic
341C2×C4×C59H(5,𝔽2)12yes—
342C2×C4×C59H(5,𝔽2)12yes—
343C2×C4×C59C2511yescharacteristic
344C22⋊D59—48no—
345C22⋊D59—84no—
346C2×Dic59—22no—
347C2×Dic59—22no—
348C2×Dic59—22no—
349C2×Dic59—22no—
350C2×Dic59—42no—
351C2×Dic59—42no—
352C2×Dic59—42no—
353C2×Dic59—42no—
354D236—22no—
355D236—22no—
356D236—22no—
357D236—22no—
358D236—22no—
359D236—22no—
360D236—22no—
361D236—22no—
362D236—48no—
363D236—42no—
364D236—42no—
365D236—42no—
366D236—42no—
367D236—84no—
368D236—84no—
369D236—84no—
370D236—84no—
371C4×D59—48no—
372C4×D59—84no—
373Dic118—22no—
374Dic118—22no—
375Dic118—22no—
376Dic118—22no—
377Dic118—42no—
378Dic118—42no—
379Dic118—84no—
380C8×C59—22no—
381C8×C59—22no—
382C8×C59—22no—
383C8×C59—22no—
384C2×#3224—591nomaximal, Sylow
385C22×C59—22no—
386C22×C59—22no—
387C22×C59—22no—
388C22×C59—44no—
389C22×C59#53512yes—
390C22×C59#57612yes—
391C22×C59#57712yes—
392C22×C59C23×D411yescharacteristic
393C2×D59—42no—
394C2×D59—42no—
395C2×D59—42no—
396C2×D59—42no—
397C2×D59—42no—
398C2×D59—42no—
399C2×D59—42no—
400C2×D59—42no—
401C2×D59—42no—
402C2×D59—42no—
403C2×D59—42no—
404C2×D59—42no—
405C2×D59—816no—
406C2×D59—84no—
407C2×D59—84no—
408C2×D59—84no—
409C2×D59—84no—
410C4×C59—22no—
411C4×C59—22no—
412C4×C59—22no—
413C4×C59—22no—
414C4×C59—22no—
415C4×C59#53512yes—
416C4×C59C2×H(5,𝔽2)11yescharacteristic
417C4×C59C2×H(5,𝔽2)11yescharacteristic
418Dic59—42no—
419Dic59—42no—
420Dic59—42no—
421Dic59—42no—
422C2×#542—591no—
423C2×#535—591no—
424#3224—5916no—
425C2×#496—591no—
426C2×#495—591no—
427C2×#489—591no—
428C2×#486—591no—
429C2×#464—591no—
430C2×#460—591no—
431C2×#463—591no—
432C2×#459—591no—
433C2×#452—591no—
434C2×#449—591no—
435C2×#450—591no—
436C2×#447—591no—
437C2×#433D5911yescharacteristic, complemented
438C2×C59—42no—
439C2×C59#322414yescomplemented
440C2×C59C2×#53511yescharacteristic
441C2×C59C2×#57611yescharacteristic
442C2×C59C2×#57711yescharacteristic
443D59—82no—
444D59—82no—
445D59—82no—
446D59—82no—
447C22×#41—591no—
448C23×D4—591no—
449C22×Q16—591no—
450C22×SD16—591no—
451C22×SD16—591no—
452C22×SD16—591no—
453C22×SD16—591no—
454C22×D8—591no—
455C22×D8—591no—
456C22×D8—591no—
457#542—598no—
458#542—1184no—
459#535—598no—
460#535—1184no—
461C2×C4⋊Q8—591no—
462C2×#127—591no—
463C2×#127—591no—
464C2×#126—1181no—
465C2×#124—591no—
466C2×#124—591no—
467C2×#124—591no—
468C2×#124—1181no—
469C2×#123—1181no—
470C2×C22⋊Q8—591no—
471C2×C22⋊Q8—1181no—
472C2×#121—591no—
473C2×#121—1181no—
474C2×#121—1181no—
475C2×#120—1181no—
476C2×#120—1181no—
477C2×C4×Q8—591no—
478C2×C4×D4—591no—
479C2×#117C2×D5911yescharacteristic
480#496—598no—
481#495—598no—
482#489—598no—
483#486—598no—
484#464—598no—
485#463—598no—
486#460—598no—
487#459—598no—
488#452—598no—
489#450—598no—
490#449—598no—
491#447—598no—
492#433C2×D5918yescomplemented
493C2×C4⋊C8C2×D5911yescharacteristic, complemented
494C2×C4⋊C8C2×D5911yescharacteristic, complemented
495C2×#103—591no—
496C2×#103—591no—
497C2×#102—591no—
498C2×#102—591no—
499C2×#102—591no—
500C2×#102—591no—
501C2×#102—591no—
502C2×#102—591no—
503C2×C22⋊C8C2×D5911yescharacteristic
504C2×C22⋊C8C2×D5911yescharacteristic
505C2×#97C2×D5911yescharacteristic, complemented
506C2×C4×C8C2×D5911yescharacteristic, complemented
507C59C2×#322411yescharacteristic, complemented, Sylow
508C25—1181no—
509C2×#41—594no—
510C2×#41—1182no—
511C2×#41—2362no—
512C2×#41—2362no—
513C22×Q8—591no—
514C22×Q8—591no—
515C22×Q8—1181no—
516C22×D4—591no—
517C22×D4—591no—
518C22×D4—591no—
519C22×D4—591no—
520C22×D4—594no—
521C22×D4—1181no—
522C22×D4—1181no—
523C22×D4—1181no—
524C22×D4—1181no—
525C22×D4—1181no—
526C22×D4—1181no—
527C22×D4—1181no—
528C22×D4—1182no—
529C22×D4—2362no—
530C22×D4—2362no—
531C23×C4—1181no—
532C23×C4—1181no—
533C23×C4C22×D5911yescharacteristic
534C2×Q16—594no—
535C2×Q16—2362no—
536C2×SD16—594no—
537C2×SD16—594no—
538C2×SD16—594no—
539C2×SD16—594no—
540C2×SD16—2362no—
541C2×SD16—2362no—
542C2×SD16—2362no—
543C2×SD16—2362no—
544C2×D8—594no—
545C2×D8—594no—
546C2×D8—594no—
547C2×D8—2362no—
548C2×D8—2362no—
549C2×D8—2362no—
550C22×C8C22×D5911yescharacteristic
551C22×C8C22×D5911yescharacteristic
552C22×C8C22×D5911yescharacteristic
553C22×C8C22×D5911yescharacteristic
554C4⋊Q8—594no—
555C4⋊Q8—1182no—
556#127—594no—
557#127—594no—
558#127—1182no—
559#127—1182no—
560#126—1188no—
561#124—594no—
562#124—594no—
563#124—594no—
564#124—1188no—
565#124—1182no—
566#124—1182no—
567#124—1182no—
568#123—1188no—
569C22⋊Q8—594no—
570C22⋊Q8—1182no—
571C22⋊Q8—1188no—
572#121—594no—
573#121—1182no—
574#121—1188no—
575#121—1188no—
576#120—1188no—
577#120—1188no—
578C4×Q8—594no—
579C4×Q8—1182no—
580C4×D4—594no—
581C4×D4—1182no—
582#117D23614yes—
583#117C22×D5914yes—
584C2×C4⋊C4—591no—
585C2×C4⋊C4—591no—
586C2×C4⋊C4—1181no—
587C2×C4⋊C4—1181no—
588C2×C4⋊C4—1181no—
589C2×C4⋊C4D23611yescharacteristic
590C2×C4⋊C4D23611yescharacteristic
591C2×C22⋊C4—1181no—
592C2×C22⋊C4—1181no—
593C2×C22⋊C4—1181no—
594C2×C22⋊C4—1181no—
595C2×C22⋊C4—1181no—
596C2×C22⋊C4—1181no—
597C2×C22⋊C4—1181no—
598C2×C22⋊C4—1181no—
599C2×C22⋊C4—1181no—
600C2×C22⋊C4D23611yescharacteristic
601C2×C22⋊C4D23611yescharacteristic
602C2×C42—1181no—
603C2×C42C22×D5911yescharacteristic
604C2×C42C22×D5911yescharacteristic
605C4⋊C8C22×D5914yescomplemented
606C4⋊C8C22×D5914yescomplemented
607#103—594no—
608#103—594no—
609#102—594no—
610#102—594no—
611#102—594no—
612#102—594no—
613#102—594no—
614#102—594no—
615C22⋊C8C22×D5914yes—
616C22⋊C8C22×D5914yes—
617#97C22×D5914yescomplemented
618C4×C8C22×D5914yescomplemented
619C24—1184no—
620C24—1181no—
621C24—1181no—
622C24—1181no—
623C24—1181no—
624C24—4722no—
625C24—4722no—
626C24—2364no—
627C24C2×D23611yescharacteristic
628#41—2364no—
629#41—2364no—
630#41—2368no—
631C2×Q8—592no—
632C2×Q8—592no—
633C2×Q8—1184no—
634C2×Q8—1181no—
635C2×Q8—1181no—
636C2×Q8—1182no—
637C2×Q8—1182no—
638C2×Q8—1182no—
639C2×Q8—1182no—
640C2×Q8—4722no—
641C2×D4—592no—
642C2×D4—592no—
643C2×D4—592no—
644C2×D4—592no—
645C2×D4—1184no—
646C2×D4—1184no—
647C2×D4—1184no—
648C2×D4—1184no—
649C2×D4—1184no—
650C2×D4—1184no—
651C2×D4—1181no—
652C2×D4—1184no—
653C2×D4—1181no—
654C2×D4—1181no—
655C2×D4—1181no—
656C2×D4—1182no—
657C2×D4—1182no—
658C2×D4—1182no—
659C2×D4—1182no—
660C2×D4—1182no—
661C2×D4—1182no—
662C2×D4—1182no—
663C2×D4—1182no—
664C2×D4—4722no—
665C2×D4—4722no—
666C2×D4—4722no—
667C2×D4—4722no—
668C2×D4—4722no—
669C2×D4—2364no—
670C2×D4—2364no—
671C2×D4—2364no—
672C2×D4—2368no—
673C2×D4—2364no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—1181no—
677C22×C4—1181no—
678C22×C4—1181no—
679C22×C4—1181no—
680C22×C4—1184no—
681C22×C4—1184no—
682C22×C4—4722no—
683C22×C4—2364no—
684C22×C4C2×D23612yes—
685C22×C4C2×D23611yescharacteristic
686C22×C4C2×D23611yescharacteristic
687C22×C4C2×D23611yescharacteristic
688C22×C4C2×D23611yescharacteristic
689C22×C4C2×D23611yescharacteristic
690C22×C4C23×D5912yes—
691C22×C4C23×D5911yescharacteristic
692Q16—2364no—
693SD16—2364no—
694SD16—2364no—
695SD16—2364no—
696SD16—2364no—
697D8—2364no—
698D8—2364no—
699D8—2364no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—22no—
703C2×C8—22no—
704C2×C8C23×D5912yes—
705C2×C8C23×D5912yes—
706C2×C8C23×D5912yes—
707C2×C8C23×D5912yes—
708C4⋊C4—592no—
709C4⋊C4—592no—
710C4⋊C4—1181no—
711C4⋊C4—1181no—
712C4⋊C4—1184no—
713C4⋊C4—1184no—
714C4⋊C4—1184no—
715C4⋊C4C2×D23614yes—
716C4⋊C4C2×D23614yes—
717C22⋊C4—1184no—
718C22⋊C4—1184no—
719C22⋊C4—1184no—
720C22⋊C4—1184no—
721C22⋊C4—1184no—
722C22⋊C4—1184no—
723C22⋊C4—1184no—
724C22⋊C4—1184no—
725C22⋊C4—1184no—
726C22⋊C4C2×D23614yes—
727C22⋊C4C2×D23614yes—
728C42—1184no—
729C42C2×D23612yes—
730C42C2×D23612yes—
731C42C23×D5912yes—
732C42C23×D5912yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—1182no—
737C23—1182no—
738C23—1182no—
739C23—1182no—
740C23—4724no—
741C23—4724no—
742C23—47216no—
743C23—2368no—
744C23—2362no—
745C23—2362no—
746C23—2362no—
747C23—2362no—
748C23—2362no—
749C23—2362no—
750C23—2362no—
751C23—2362no—
752C23—2362no—
753C23—2362no—
754C23—2362no—
755C23—2362no—
756C23C22×D23612yes—
757C23C22×D23611yescharacteristic
758Q8—1182no—
759Q8—1182no—
760Q8—1182no—
761Q8—1182no—
762Q8—4724no—
763Q8—2362no—
764Q8—2362no—
765D4—1182no—
766D4—1182no—
767D4—1182no—
768D4—1182no—
769D4—1182no—
770D4—1182no—
771D4—1182no—
772D4—1182no—
773D4—4724no—
774D4—4724no—
775D4—4724no—
776D4—4724no—
777D4—4724no—
778D4—2368no—
779D4—2368no—
780D4—2362no—
781D4—2362no—
782D4—2362no—
783D4—2362no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—1182no—
793C2×C4—1182no—
794C2×C4—1182no—
795C2×C4—1182no—
796C2×C4—4724no—
797C2×C4—2368no—
798C2×C4—2362no—
799C2×C4—2362no—
800C2×C4—2362no—
801C2×C4—2362no—
802C2×C4C22×D23612yes—
803C2×C4C22×D23612yes—
804C2×C4C22×D23612yes—
805C2×C4C22×D23612yes—
806C2×C4C22×D23612yes—
807C2×C4C22×D23611yescharacteristic
808C2×C4#1427377312yes—
809C2×C4#1427377312yes—
810C2×C4C24×D5911yescharacteristic
811C8—22no—
812C8—22no—
813C8—22no—
814C8—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—47216no—
820C22—4724no—
821C22—4724no—
822C22—4724no—
823C22—4724no—
824C22—2362no—
825C22—2362no—
826C22—2362no—
827C22—2362no—
828C22—2362no—
829C22—2362no—
830C22—2362no—
831C22—2362no—
832C22—2362no—
833C22—2362no—
834C22—2362no—
835C22—2362no—
836C22#1683797112yes—
837C22#1683820712yes—
838C22#1683821412yes—
839C22C23×D23611yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—2362no—
846C4—2362no—
847C4—2362no—
848C4—2362no—
849C4#1683797112yes—
850C4C2×#1427377311yescharacteristic
851C4C2×#1427377311yescharacteristic
852C2—42no—
853C2—4722no—
854C2—4722no—
855C2—4722no—
856C2—4722no—
857C2#2143519214yesdirect product factor
858C2C2×#1683797111yescharacteristic
859C2C2×#1683820711yescharacteristic
860C2C2×#1683821411yescharacteristic
subgroupG/H
centerC23C22×D236
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#433C2
socleC23×C59C22×D4
hypercenterC2×#433D59
hypocenterC59C2×#3224
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16838023C2semidirect
2. C2×#16837971C2semidirect
3. #21435192C2direct (N × H)
4. C2×#16837791C2semidirect
5. C2×#16837786C2semidirect
6. C2×#16837762C2semidirect
7. C2×#16837749C2semidirect
8. C2×#16837625C2semidirect
9. C2×#16837603C2semidirect
10. C2×#16837618C2semidirect
11. C2×#16837598C2semidirect
12. C2×#16837566C2semidirect
13. C2×#16837549C2semidirect
14. C2×#16837555C2semidirect
15. C2×#16837538C2semidirect
16. C2×C59×#433C2semidirect
19. C22×Dic236C22semidirect
22. C22×#11745660C22semidirect
23. C22×#11745660C22semidirect
26. C22×D472C22semidirect
28. #16838023C22semidirect
30. #16837971C22semidirect
31. C2×#14273727C22semidirect
37. C2×#14273715C22semidirect
47. C2×C4×Dic118C22semidirect
48. C2×C4×D236C22semidirect
49. #16837791C22semidirect
50. #16837786C22semidirect
51. #16837762C22semidirect
52. #16837749C22semidirect
53. #16837625C22semidirect
54. #16837618C22semidirect
55. #16837603C22semidirect
56. #16837598C22semidirect
57. #16837566C22semidirect
58. #16837555C22semidirect
59. #16837549C22semidirect
60. #16837538C22semidirect
61. C2×#14273652C22semidirect
62. C2×#14273652C22semidirect
67. C2×#14273649C22semidirect
68. C2×#14273649C22semidirect
70. C59×#433C22semidirect
71. C2×C4⋊C8×C59C22semidirect
72. C2×C4⋊C8×C59C22semidirect
75. C2×#97×C59C22semidirect
76. C2×C4×C8×C59C22semidirect
103. C2×Dic236C23semidirect
110. C2×#11745660C23semidirect
111. C2×#11745660C23semidirect
117. C2×D472C23semidirect
119. #14273727C23semidirect
130. #14273715C23semidirect
143. C4×Dic118C23semidirect
145. C4×D236C23semidirect
161. #14273652C23semidirect
162. #14273652C23semidirect
167. #14273649C23semidirect
168. #14273649C23semidirect
182. C4⋊C8×C59C23semidirect
183. C4⋊C8×C59C23semidirect
186. #97×C59C23semidirect
187. C4×C8×C59C23semidirect
437. C2×#433D59semidirect
439. C2×C59#3224semidirect
492. #433C2×D59semidirect
493. C2×C4⋊C8C2×D59semidirect
494. C2×C4⋊C8C2×D59semidirect
505. C2×#97C2×D59semidirect
506. C2×C4×C8C2×D59semidirect
507. C59C2×#3224semidirect
605. C4⋊C8C22×D59semidirect
606. C4⋊C8C22×D59semidirect
617. #97C22×D59semidirect
618. C4×C8C22×D59semidirect
857. C2#21435192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380232
C2×#168379712
#214351922
C2×#168377912
C2×#168377862
C2×#168377622
C2×#168377492
C2×#168376252
C2×#168376032
C2×#168376182
C2×#168375982
C2×#168375662
C2×#168375492
C2×#168375552
C2×#168375382
C2×C59×#4332
C2×#322459