Finite Group Databasebeta

← C2×#21434946 #29459340

Subgroups — C2×#21434946 #29459340

Order 15104.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837981C211yesmaximal, characteristic, complemented
2C2×#16837971C211yesmaximal, characteristic, complemented
3#21434946C2116yesmaximal, direct product factor
4C2×#16837722C211yesmaximal, characteristic, complemented
5C2×#16837743C211yesmaximal, characteristic, complemented
6C2×#16837717C211yesmaximal, characteristic, complemented
7C2×#16837654C211yesmaximal, characteristic, complemented
8C2×#16837649C211yesmaximal, characteristic, complemented
9C2×#16837637C211yesmaximal, characteristic, complemented
10C2×#16837632C211yesmaximal, characteristic, complemented
11C2×#16837548C211yesmaximal, characteristic, complemented
12C2×#16837548C211yesmaximal, characteristic, complemented
13C2×#16837555C211yesmaximal, characteristic, complemented
14C2×#16837535C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745687C2211yescharacteristic, complemented
19C23×D236C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745660C2211yescharacteristic
22C22×#11745669C2211yescharacteristic
23C22×#11745669C2211yescharacteristic
24C22×#11745659C2211yescharacteristic, complemented
25C22×C8×D59C2211yescharacteristic, complemented
26#16837981—24no—
27#16837981C2218yescomplemented
28#16837971—24no—
29#16837971C2218yescomplemented
30C2×#14273724—21no—
31C2×#14273715—21no—
32C2×#14273707C2211yescharacteristic, complemented
33C2×#14273706C2211yescharacteristic
34C2×#14273704—21no—
35C2×#14273702C2211yescharacteristic
36C2×#14273702C2211yescharacteristic
37C2×#14273702C2211yescharacteristic
38C2×#14273702C2211yescharacteristic
39C2×#14273700—21no—
40C2×#14273699—21no—
41C2×#14273698—21no—
42C2×#14273698C2211yescharacteristic, complemented
43C2×#14273697—21no—
44C2×#14273697—21no—
45C2×C4⋊C4×D59C2211yescharacteristic, complemented
46#16837743C2218yescomplemented
47#16837722C2218yescomplemented
48#16837717C2218yescomplemented
49#16837654C2218yescomplemented
50#16837649C2218yescomplemented
51#16837637C2218yescomplemented
52#16837632C2218yescomplemented
53#16837555C2218yescomplemented
54#16837548C2218yescomplemented
55#16837548C2218yescomplemented
56#16837535C2218yescomplemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273650C2211yescharacteristic, complemented
60C2×#14273650C2211yescharacteristic, complemented
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#102×C59C2211yescharacteristic, complemented
75C2×#102×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745685—42no—
79C2×#11745685—42no—
80C2×#11745685D414yes—
81C2×#11745685C2314yes—
82C2×#11745687—22no—
83C2×#11745687—42no—
84C2×#11745687—42no—
85C2×#11745687C2314yescomplemented
86C22×Dic118D411yescharacteristic
87C22×Dic118C2311yescharacteristic
88C22×D236—21no—
89C22×D236—22no—
90C22×D236—21no—
91C22×D236—21no—
92C22×D236—21no—
93C22×D236—21no—
94C22×D236—42no—
95C22×D236—42no—
96C22×D236D411yescharacteristic
97C22×D236C2311yescharacteristic
98C22×D236C2311yescharacteristic
99C22×D236C2314yes—
100C22×C22⋊D59—21no—
101C22×C22⋊D59—21no—
102C22×C22⋊D59D411yescharacteristic
103C22×C22⋊D59D411yescharacteristic
104C23×Dic59—21no—
105C22×C4×D59—21no—
106C22×C4×D59C2311yescharacteristic
107C22×C4×D59C2311yescharacteristic
108C2×#11745660—42no—
109C2×#11745660—42no—
110C2×#11745660C2314yes—
111C2×#11745660C2314yes—
112C2×#11745669—42no—
113C2×#11745669—42no—
114C2×#11745669C2314yes—
115C2×#11745669C2314yes—
116C2×#11745659—42no—
117C2×#11745659C2314yescomplemented
118C22×C59⋊C8C2311yescharacteristic
119C22×C59⋊C8C2311yescharacteristic
120C2×C8×D59—42no—
121C2×C8×D59C2314yescomplemented
122#14273724—28no—
123#14273715—28no—
124#14273707—22no—
125#14273707C2314yescomplemented
126#14273706—22no—
127#14273706C2314yes—
128#14273704—28no—
129#14273702—22no—
130#14273702—22no—
131#14273702—22no—
132#14273702—22no—
133#14273702C2314yes—
134#14273702C2314yes—
135#14273702C2314yes—
136#14273702C2314yes—
137#14273700—28no—
138#14273699—28no—
139#14273698—28no—
140#14273698—22no—
141#14273698C2314yescomplemented
142#14273697—28no—
143#14273697—28no—
144C2×C4⋊Dic59—21no—
145C2×C4⋊Dic59C2311yescharacteristic
146C2×Dic59⋊C4—21no—
147C2×Dic59⋊C4—21no—
148C4⋊C4×D59—22no—
149C4⋊C4×D59C2314yescomplemented
150C2×C22⋊Dic59—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—
157#14273660C2314yescomplemented
158#14273658C2314yescomplemented
159#14273650C2314yescomplemented
160#14273650C2314yescomplemented
161#14273649C2314yes—
162#14273649C2314yes—
163#14273647C2314yes—
164#14273647C2314yes—
165C22⋊(C59⋊C8)C2314yes—
166(C2×D59)⋊C8C2314yescomplemented
167(C2×D59)⋊C8C2314yescomplemented
168C22×D4×C59—21no—
169C22×D4×C59C2311yescharacteristic
170C23×C4×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173#121×C59—22no—
174#121×C59C2314yes—
175#117×C59—22no—
176#117×C59C2314yes—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C42×C59—21no—
183#107×C59C2314yescomplemented
184#106×C59C2314yescomplemented
185#102×C59C2314yescomplemented
186#102×C59C2314yescomplemented
187C22⋊C8×C59C2314yes—
188C24×C59—21no—
189C24×C59C2×D411yescharacteristic
190C23×D59—21no—
191C23×D59—21no—
192C23×D59—24no—
193C23×D59—44no—
194C23×D59—82no—
195C23×D59—82no—
196C23×D59C2×D411yescharacteristic
197C23×D59C2×D411yescharacteristic
198C2×D4×C59—24no—
199C2×D4×C59—21no—
200C2×D4×C59—22no—
201C2×D4×C59—22no—
202C2×D4×C59—82no—
203C2×D4×C59C2412yes—
204C22×C4×C59—22no—
205C22×C4×C59—22no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2412yes—
212C22×C4×C59C2411yescharacteristic
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—42no—
216C2×C22⋊D59—42no—
217C2×C22⋊D59—44no—
218C2×C22⋊D59—82no—
219C2×C22⋊D59C2×D414yes—
220C2×C22⋊D59C2×D414yes—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—24no—
224C22×Dic59—44no—
225C22×Dic59C2×D411yescharacteristic
226C22×Dic59C2×D411yescharacteristic
227#11745687—44no—
228#11745687—44no—
229#11745687—48no—
230#11745685—48no—
231#11745685—44no—
232#11745685—44no—
233C2×D236—22no—
234C2×D236—22no—
235C2×D236—22no—
236C2×D236—22no—
237C2×D236—21no—
238C2×D236—21no—
239C2×D236—24no—
240C2×D236—24no—
241C2×D236—24no—
242C2×D236—24no—
243C2×D236—24no—
244C2×D236—44no—
245C2×D236—44no—
246C2×D236—42no—
247C2×D236—44no—
248C2×D236—48no—
249C2×D236—82no—
250C2×D236—82no—
251C2×D236—82no—
252C2×D236—82no—
253C2×D236C2×D414yes—
254C2×D236C2412yes—
255C2×D236C2412yes—
256C2×C4×D59—22no—
257C2×C4×D59—22no—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—24no—
261C2×C4×D59—82no—
262C2×C4×D59C2×D412yes—
263C2×C4×D59C2×D412yes—
264C2×C4×D59C2412yes—
265C2×C4×D59C2412yes—
266C2×Dic118—22no—
267C2×Dic118—22no—
268C2×Dic118—21no—
269C2×Dic118—42no—
270C2×Dic118C2×D414yes—
271C2×Dic118C2412yes—
272C2×C8×C59—22no—
273C2×C8×C59—22no—
274C2×C8×C59C2412yes—
275C2×C8×C59C2412yes—
276C4⋊C4×C59—21no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59C2412yes—
280C4⋊C4×C59C2412yes—
281C4⋊C4×C59C2412yes—
282C22⋊C4×C59—24no—
283C22⋊C4×C59—24no—
284C42×C59—24no—
285C22⋊Dic59—24no—
286C22⋊Dic59—24no—
287#11745669—44no—
288#11745669—44no—
289(C2×D59)⋊C4—24no—
290(C2×D59)⋊C4—24no—
291(C2×D59)⋊C4—24no—
292(C2×D59)⋊C4—24no—
293(C2×D59)⋊C4—24no—
294C4⋊Dic59—21no—
295C4⋊Dic59—24no—
296C4⋊Dic59C2412yes—
297Dic59⋊C4—24no—
298Dic59⋊C4—24no—
299C2×C59⋊C8—22no—
300C2×C59⋊C8—22no—
301C2×C59⋊C8C2412yes—
302C2×C59⋊C8C2412yes—
303#11745660—44no—
304#11745660—44no—
305#11745659—44no—
306C8×D59—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59—22no—
311C23×C59—42no—
312C23×C59—42no—
313C23×C59—42no—
314C23×C59C22×D412yes—
315C23×C59C22×D411yescharacteristic
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—22no—
322C22×D59—22no—
323C22×D59—22no—
324C22×D59—48no—
325C22×D59—42no—
326C22×D59—42no—
327C22×D59—42no—
328C22×D59—42no—
329C22×D59—42no—
330C22×D59—42no—
331C22×D59—84no—
332C22×D59—84no—
333C22×D59—816no—
334C22×D59C22×D412yes—
335C22×D59C22×D412yes—
336D4×C59—22no—
337D4×C59—22no—
338D4×C59—42no—
339D4×C59—84no—
340C2×C4×C59—22no—
341C2×C4×C59—24no—
342C2×C4×C59—22no—
343C2×C4×C59—22no—
344C2×C4×C59—22no—
345C2×C4×C59—22no—
346C2×C4×C59—22no—
347C2×C4×C59—42no—
348C2×C4×C59—42no—
349C2×C4×C59—42no—
350C2×C4×C59C22×D412yes—
351C2×C4×C59C22×D411yescharacteristic
352C2×C4×C59H(5,𝔽2)12yes—
353C2×C4×C59H(5,𝔽2)12yes—
354C2×C4×C59C2511yescharacteristic
355C22⋊D59—44no—
356C22⋊D59—44no—
357C22⋊D59—48no—
358C22⋊D59—84no—
359C2×Dic59—22no—
360C2×Dic59—22no—
361C2×Dic59—22no—
362C2×Dic59—22no—
363C2×Dic59—48no—
364C2×Dic59—42no—
365C2×Dic59—42no—
366C2×Dic59C22×D412yes—
367C2×Dic59C22×D412yes—
368D236—22no—
369D236—22no—
370D236—22no—
371D236—22no—
372D236—44no—
373D236—48no—
374D236—42no—
375D236—42no—
376D236—84no—
377D236—84no—
378D236—84no—
379D236—84no—
380C4×D59—24no—
381C4×D59—24no—
382C4×D59—22no—
383C4×D59—22no—
384C4×D59—22no—
385C4×D59—22no—
386C4×D59—84no—
387Dic118—22no—
388Dic118—22no—
389Dic118—44no—
390Dic118—42no—
391C8×C59—22no—
392C8×C59—22no—
393C59⋊C8—22no—
394C59⋊C8—22no—
395C2×#3198—591nomaximal, Sylow
396C22×C59—22no—
397C22×C59—22no—
398C22×C59—22no—
399C22×C59—44no—
400C22×C59—42no—
401C22×C59—42no—
402C22×C59—42no—
403C22×C59—84no—
404C22×C59#53412yes—
405C22×C59#57612yes—
406C22×C59#57712yes—
407C22×C59C23×D411yescharacteristic
408C2×D59—22no—
409C2×D59—22no—
410C2×D59—22no—
411C2×D59—22no—
412C2×D59—22no—
413C2×D59—22no—
414C2×D59—44no—
415C2×D59—44no—
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—42no—
422C2×D59—816no—
423C2×D59—84no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—42no—
427C4×C59—42no—
428C4×C59—42no—
429C4×C59#53412yes—
430C4×C59C2×H(5,𝔽2)11yescharacteristic
431C4×C59C2×H(5,𝔽2)11yescharacteristic
432Dic59—22no—
433Dic59—22no—
434Dic59—42no—
435Dic59—42no—
436C2×#537—591no—
437C2×#535—591no—
438#3198—5916no—
439C2×#481—591no—
440C2×#485—591no—
441C2×#482D5911yescharacteristic, complemented
442C2×#480—591no—
443C2×#469—591no—
444C2×#468—591no—
445C2×#466—591no—
446C2×#465—591no—
447C2×#449—591no—
448C2×#449—591no—
449C2×#450—591no—
450C2×#447—591no—
451C2×#408—591no—
452C2×C59—42no—
453C2×C59—82no—
454C2×C59#319814yescomplemented
455C2×C59C2×#53411yescharacteristic
456C2×C59C2×#57611yescharacteristic
457C2×C59C2×#57711yescharacteristic
458D59—42no—
459D59—42no—
460D59—82no—
461D59—82no—
462C22×#41—591no—
463C22×#41—591no—
464C23×D4—591no—
465C22×SD16—591no—
466C22×SD16—591no—
467C22×D8—591no—
468C22×D8—591no—
469C22×M16—591no—
470C23×C8—591no—
471#537—598no—
472#537—1184no—
473#535—598no—
474#535—1184no—
475C2×#127—1181no—
476C2×#124—1181no—
477C2×C22⋊Q8—591no—
478C2×C22⋊Q8—591no—
479C2×C22⋊Q8—1181no—
480C2×#121—591no—
481C2×#121—591no—
482C2×#121—591no—
483C2×#121—591no—
484C2×#121—591no—
485C2×#121—1181no—
486C2×#121—1181no—
487C2×#121—1181no—
488C2×#121C2×D5911yescharacteristic
489C2×#120—1181no—
490C2×#120—1181no—
491C2×#117C2×D5911yescharacteristic
492C22×C4⋊C4—591no—
493#485—598no—
494#482C2×D5918yescomplemented
495#481—598no—
496#480—598no—
497#469—598no—
498#468—598no—
499#466—598no—
500#465—598no—
501#450—598no—
502#449—598no—
503#449—598no—
504#447—598no—
505C2×#107—591no—
506C2×#107C2×D5911yescharacteristic, complemented
507C2×#106—591no—
508C2×#106C2×D5911yescharacteristic, complemented
509C2×#103—591no—
510C2×#103—591no—
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102C2×D5911yescharacteristic, complemented
516C2×#102C2×D5911yescharacteristic, complemented
517#408—598no—
518C2×C22⋊C8—591no—
519C2×C22⋊C8—591no—
520C2×C22⋊C8—591no—
521C2×C22⋊C8C2×D5911yescharacteristic
522C59C2×#319811yescharacteristic, complemented, Sylow
523C25—1181no—
524C2×#41—594no—
525C2×#41—594no—
526C2×#41—594no—
527C2×#41—1182no—
528C2×#41—2362no—
529C2×#41—2362no—
530C2×#41—2362no—
531C2×#41—2362no—
532C22×Q8—591no—
533C22×Q8—591no—
534C22×D4—21no—
535C22×D4—591no—
536C22×D4—591no—
537C22×D4—591no—
538C22×D4—591no—
539C22×D4—591no—
540C22×D4—594no—
541C22×D4—1181no—
542C22×D4—1181no—
543C22×D4—1181no—
544C22×D4—1181no—
545C22×D4—1181no—
546C22×D4—1181no—
547C22×D4—1181no—
548C22×D4—1182no—
549C22×D4—2362no—
550C22×D4—2362no—
551C22×D4C22×D5911yescharacteristic
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—1181no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×SD16—594no—
558C2×SD16—594no—
559C2×SD16—2362no—
560C2×SD16—2362no—
561C2×D8—594no—
562C2×D8—594no—
563C2×D8—2362no—
564C2×D8—2362no—
565C2×M16—594no—
566C2×M16—2362no—
567C22×C8—591no—
568C22×C8—591no—
569C22×C8—594no—
570C22×C8—2362no—
571C22×C8C22×D5911yescharacteristic
572C22×C8C22×D5911yescharacteristic
573#127—1188no—
574#124—1188no—
575C22⋊Q8—594no—
576C22⋊Q8—594no—
577C22⋊Q8—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8—1182no—
580#121—22no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1188no—
587#121—1182no—
588#121—1182no—
589#121—1182no—
590#121—1182no—
591#121—1182no—
592#121—1188no—
593#121—1188no—
594#121C22×D5914yes—
595#120—1188no—
596#120—1188no—
597#117—22no—
598#117C22×D5914yes—
599C2×C4⋊C4—591no—
600C2×C4⋊C4—594no—
601C2×C4⋊C4—1182no—
602C2×C4⋊C4—1181no—
603C2×C4⋊C4—1181no—
604C2×C4⋊C4—1181no—
605C2×C4⋊C4C22×D5911yescharacteristic
606C2×C4⋊C4C22×D5911yescharacteristic
607C2×C4⋊C4C22×D5911yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—1181no—
611C2×C22⋊C4—1181no—
612C2×C22⋊C4—1181no—
613C2×C22⋊C4—1181no—
614C2×C22⋊C4—1181no—
615C2×C22⋊C4—1181no—
616C2×C22⋊C4—1181no—
617C2×C42—21no—
618#107—594no—
619#107C22×D5914yescomplemented
620#106—594no—
621#106C22×D5914yescomplemented
622#103—594no—
623#103—594no—
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102C22×D5914yescomplemented
629#102C22×D5914yescomplemented
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8C22×D5914yes—
634C24—21no—
635C24—591no—
636C24—591no—
637C24—1184no—
638C24—1181no—
639C24—1181no—
640C24—4722no—
641C24—4722no—
642C24—2364no—
643C24D4×D5911yescharacteristic
644#41—2368no—
645#41—2364no—
646#41—2364no—
647#41—2364no—
648#41—2364no—
649#41—2368no—
650C2×Q8—594no—
651C2×Q8—592no—
652C2×Q8—1181no—
653C2×Q8—1182no—
654C2×Q8—1182no—
655C2×Q8—2362no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—594no—
662C2×D4—594no—
663C2×D4—594no—
664C2×D4—592no—
665C2×D4—592no—
666C2×D4—1184no—
667C2×D4—1184no—
668C2×D4—1184no—
669C2×D4—1184no—
670C2×D4—1184no—
671C2×D4—1184no—
672C2×D4—1181no—
673C2×D4—1181no—
674C2×D4—1184no—
675C2×D4—1182no—
676C2×D4—1182no—
677C2×D4—1182no—
678C2×D4—1182no—
679C2×D4—4722no—
680C2×D4—4722no—
681C2×D4—4722no—
682C2×D4—4722no—
683C2×D4—4722no—
684C2×D4—2364no—
685C2×D4—2364no—
686C2×D4—2362no—
687C2×D4—2364no—
688C2×D4—2368no—
689C2×D4—2362no—
690C2×D4—2362no—
691C2×D4—2364no—
692C2×D4C23×D5912yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—591no—
699C22×C4—591no—
700C22×C4—592no—
701C22×C4—592no—
702C22×C4—592no—
703C22×C4—592no—
704C22×C4—1184no—
705C22×C4—1184no—
706C22×C4—1182no—
707C22×C4—1182no—
708C22×C4—1182no—
709C22×C4—1182no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—4722no—
713C22×C4—2364no—
714C22×C4D4×D5912yes—
715C22×C4D4×D5911yescharacteristic
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718SD16—2364no—
719SD16—2364no—
720D8—2364no—
721D8—2364no—
722M16—2364no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—592no—
726C2×C8—592no—
727C2×C8—1182no—
728C2×C8—1182no—
729C2×C8—2364no—
730C2×C8C23×D5912yes—
731C2×C8C23×D5912yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—592no—
736C4⋊C4—1184no—
737C4⋊C4—1184no—
738C4⋊C4—1181no—
739C4⋊C4—1184no—
740C4⋊C4C23×D5912yes—
741C4⋊C4C23×D5912yes—
742C4⋊C4C23×D5912yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—1184no—
746C22⋊C4—1184no—
747C22⋊C4—1184no—
748C22⋊C4—1184no—
749C22⋊C4—1184no—
750C22⋊C4—1184no—
751C22⋊C4—1184no—
752C42—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—592no—
761C23—592no—
762C23—1182no—
763C23—1182no—
764C23—1182no—
765C23—1182no—
766C23—1182no—
767C23—1182no—
768C23—1182no—
769C23—1182no—
770C23—4724no—
771C23—4724no—
772C23—47216no—
773C23—2368no—
774C23—2362no—
775C23—2362no—
776C23—2362no—
777C23—2362no—
778C23—2362no—
779C23—2362no—
780C23C2×D4×D5912yes—
781C23C2×D4×D5911yescharacteristic
782Q8—1182no—
783Q8—1182no—
784Q8—2364no—
785Q8—2362no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—1182no—
791D4—1182no—
792D4—1182no—
793D4—1182no—
794D4—4724no—
795D4—4724no—
796D4—4724no—
797D4—4724no—
798D4—4724no—
799D4—2364no—
800D4—2368no—
801D4—2364no—
802D4—2364no—
803D4—2368no—
804D4—2362no—
805D4—2362no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—592no—
817C2×C4—592no—
818C2×C4—1182no—
819C2×C4—1182no—
820C2×C4—1184no—
821C2×C4—1184no—
822C2×C4—1182no—
823C2×C4—1182no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—4724no—
829C2×C4—2368no—
830C2×C4—2362no—
831C2×C4—2362no—
832C2×C4C2×D4×D5912yes—
833C2×C4C2×D4×D5911yescharacteristic
834C2×C4#1427377312yes—
835C2×C4#1427377312yes—
836C2×C4C24×D5911yescharacteristic
837C8—22no—
838C8—22no—
839C8—1182no—
840C8—1182no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—1182no—
850C22—1182no—
851C22—1182no—
852C22—1182no—
853C22—1182no—
854C22—1182no—
855C22—47216no—
856C22—4724no—
857C22—4724no—
858C22—2362no—
859C22—2362no—
860C22—2362no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2364no—
865C22—2364no—
866C22#1683796312yes—
867C22#1683820612yes—
868C22#1683820912yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—1182no—
875C4—1182no—
876C4—2362no—
877C4—2362no—
878C4#1683796312yes—
879C4C2×#1427377311yescharacteristic
880C4C2×#1427377311yescharacteristic
881C2—42no—
882C2—82no—
883C2—4722no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143494614yesdirect product factor
888C2C2×#1683796311yescharacteristic
889C2C2×#1683820611yescharacteristic
890C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
hypercenterC2×#482D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16837981C2semidirect
2. C2×#16837971C2semidirect
3. #21434946C2direct (N × H)
4. C2×#16837722C2semidirect
5. C2×#16837743C2semidirect
6. C2×#16837717C2semidirect
7. C2×#16837654C2semidirect
8. C2×#16837649C2semidirect
9. C2×#16837637C2semidirect
10. C2×#16837632C2semidirect
11. C2×#16837548C2semidirect
12. C2×#16837548C2semidirect
13. C2×#16837555C2semidirect
14. C2×#16837535C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#482C2semidirect
18. C22×#11745687C22semidirect
24. C22×#11745659C22semidirect
25. C22×C8×D59C22semidirect
27. #16837981C22semidirect
29. #16837971C22semidirect
32. C2×#14273707C22semidirect
42. C2×#14273698C22semidirect
45. C2×C4⋊C4×D59C22semidirect
46. #16837743C22semidirect
47. #16837722C22semidirect
48. #16837717C22semidirect
49. #16837654C22semidirect
50. #16837649C22semidirect
51. #16837637C22semidirect
52. #16837632C22semidirect
53. #16837555C22semidirect
54. #16837548C22semidirect
55. #16837548C22semidirect
56. #16837535C22semidirect
57. C2×#14273660C22semidirect
58. C2×#14273658C22semidirect
59. C2×#14273650C22semidirect
60. C2×#14273650C22semidirect
65. #16837367C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
71. C59×#482C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#102×C59C22semidirect
75. C2×#102×C59C22semidirect
85. C2×#11745687C23semidirect
117. C2×#11745659C23semidirect
121. C2×C8×D59C23semidirect
125. #14273707C23semidirect
141. #14273698C23semidirect
149. C4⋊C4×D59C23semidirect
157. #14273660C23semidirect
158. #14273658C23semidirect
159. #14273650C23semidirect
160. #14273650C23semidirect
166. (C2×D59)⋊C8C23semidirect
167. (C2×D59)⋊C8C23semidirect
183. #107×C59C23semidirect
184. #106×C59C23semidirect
185. #102×C59C23semidirect
186. #102×C59C23semidirect
441. C2×#482D59semidirect
454. C2×C59#3198semidirect
494. #482C2×D59semidirect
506. C2×#107C2×D59semidirect
508. C2×#106C2×D59semidirect
515. C2×#102C2×D59semidirect
516. C2×#102C2×D59semidirect
522. C59C2×#3198semidirect
619. #107C22×D59semidirect
621. #106C22×D59semidirect
628. #102C22×D59semidirect
629. #102C22×D59semidirect
887. C2#21434946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379812
C2×#168379712
#214349462
C2×#168377222
C2×#168377432
C2×#168377172
C2×#168376542
C2×#168376492
C2×#168376372
C2×#168376322
C2×#168375482
C2×#168375552
C2×#168375352
C2×#168373672
C2×C59×#4822
C2×#319859