Finite Group Databasebeta

← C2×#21434954 #29459348

Subgroups — C2×#21434954 #29459348

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×#16837982C211yesmaximal, characteristic, complemented
2C2×#16837971C211yesmaximal, characteristic, complemented
3#21434954C2116yesmaximal, direct product factor
4C2×#16837722C211yesmaximal, characteristic, complemented
5C2×#16837726C211yesmaximal, characteristic, complemented
6C2×#16837717C211yesmaximal, characteristic, complemented
7C2×#16837656C211yesmaximal, characteristic, complemented
8C2×#16837651C211yesmaximal, characteristic, complemented
9C2×#16837639C211yesmaximal, characteristic, complemented
10C2×#16837634C211yesmaximal, characteristic, complemented
11C2×#16837550C211yesmaximal, characteristic, complemented
12C2×#16837550C211yesmaximal, characteristic, complemented
13C2×#16837552C211yesmaximal, characteristic, complemented
14C2×#16837538C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#485C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic, complemented
18C22×#11745685C2211yescharacteristic
19C23×D236C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22C22×D472C2211yescharacteristic
23C22×D472C2211yescharacteristic
24C22×#11745659C2211yescharacteristic, complemented
25C22×C8×D59C2211yescharacteristic, complemented
26#16837982—24no—
27#16837982C2218yescomplemented
28#16837971—24no—
29#16837971C2218yescomplemented
30C2×#14273724—21no—
31C2×#14273715—21no—
32C2×#14273705—21no—
33C2×#14273703C2211yescharacteristic, complemented
34C2×#14273702—21no—
35C2×#14273702C2211yescharacteristic
36C2×#14273702C2211yescharacteristic
37C2×#14273702C2211yescharacteristic
38C2×#14273702C2211yescharacteristic
39C2×#14273702C2211yescharacteristic, complemented
40C2×#14273701C2211yescharacteristic
41C2×#14273700—21no—
42C2×#14273700—21no—
43C2×#14273697—21no—
44C2×#14273697—21no—
45C2×C4⋊C4×D59C2211yescharacteristic, complemented
46#16837726C2218yescomplemented
47#16837722C2218yescomplemented
48#16837717C2218yescomplemented
49#16837656C2218yescomplemented
50#16837651C2218yescomplemented
51#16837639C2218yescomplemented
52#16837634C2218yescomplemented
53#16837552C2218yescomplemented
54#16837550C2218yescomplemented
55#16837550C2218yescomplemented
56#16837538C2218yescomplemented
57C2×#14273660C2211yescharacteristic, complemented
58C2×#14273658C2211yescharacteristic, complemented
59C2×#14273649C2211yescharacteristic
60C2×#14273649C2211yescharacteristic
61C2×#14273647C2211yescharacteristic
62C2×#14273647C2211yescharacteristic
63C2×#14273647C2211yescharacteristic, complemented
64C2×#14273647C2211yescharacteristic, complemented
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D59)⋊C8C2211yescharacteristic, complemented
69C2×C22⋊Q8×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#485C2218yescomplemented
72C2×#107×C59C2211yescharacteristic, complemented
73C2×#106×C59C2211yescharacteristic, complemented
74C2×#103×C59C2211yescharacteristic, complemented
75C2×#103×C59C2211yescharacteristic, complemented
76C2×C22⋊C8×C59C2211yescharacteristic
77C24×D59—21no—
78C2×#11745689—22no—
79C2×#11745689—42no—
80C2×#11745689—42no—
81C2×#11745689C2314yescomplemented
82C2×#11745685—42no—
83C2×#11745685—42no—
84C2×#11745685D414yes—
85C2×#11745685C2314yes—
86C22×Dic118D411yescharacteristic
87C22×D236—21no—
88C22×D236—21no—
89C22×D236—22no—
90C22×D236—21no—
91C22×D236—21no—
92C22×D236—21no—
93C22×D236—21no—
94C22×D236—21no—
95C22×D236—42no—
96C22×D236—42no—
97C22×D236D411yescharacteristic
98C22×D236C2311yescharacteristic
99C22×D236C2311yescharacteristic
100C22×D236C2311yescharacteristic
101C22×D236C2314yes—
102C22×C22⋊D59—21no—
103C22×C22⋊D59D411yescharacteristic
104C22×C22⋊D59D411yescharacteristic
105C22×C4×D59—21no—
106C22×C4×D59—21no—
107C22×C4×D59C2311yescharacteristic
108C22×C4×D59C2311yescharacteristic
109C2×#11745671—42no—
110C2×#11745671—42no—
111C2×#11745671C2314yes—
112C2×#11745671C2314yes—
113C2×D472—42no—
114C2×D472—42no—
115C2×D472C2314yes—
116C2×D472C2314yes—
117C2×#11745659—42no—
118C2×#11745659C2314yescomplemented
119C22×C59⋊C8C2311yescharacteristic
120C22×C59⋊C8C2311yescharacteristic
121C2×C8×D59—42no—
122C2×C8×D59C2314yescomplemented
123#14273724—28no—
124#14273715—28no—
125#14273705—28no—
126#14273703—22no—
127#14273703C2314yescomplemented
128#14273702—28no—
129#14273702—22no—
130#14273702—22no—
131#14273702—22no—
132#14273702—22no—
133#14273702—22no—
134#14273702C2314yes—
135#14273702C2314yes—
136#14273702C2314yes—
137#14273702C2314yes—
138#14273702C2314yescomplemented
139#14273701—22no—
140#14273701C2314yes—
141#14273700—28no—
142#14273700—28no—
143#14273697—28no—
144#14273697—28no—
145C2×C4⋊Dic59C2311yescharacteristic
146C2×Dic59⋊C4—21no—
147C2×Dic59⋊C4—21no—
148C4⋊C4×D59—22no—
149C4⋊C4×D59C2314yescomplemented
150C2×(C2×D59)⋊C4—21no—
151C2×(C2×D59)⋊C4—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#14273649C2314yes—
160#14273649C2314yes—
161#14273647C2314yes—
162#14273647C2314yes—
163#14273647C2314yescomplemented
164#14273647C2314yescomplemented
165C22⋊(C59⋊C8)C2314yes—
166(C2×D59)⋊C8C2314yescomplemented
167(C2×D59)⋊C8C2314yescomplemented
168C22×Q8×C59C2311yescharacteristic
169C23×C4×C59C2311yescharacteristic
170C22×C8×C59C2311yescharacteristic
171C22×C8×C59C2311yescharacteristic
172C22⋊Q8×C59—22no—
173C22⋊Q8×C59C2314yes—
174#117×C59—22no—
175#117×C59C2314yes—
176C2×C4⋊C4×C59—21no—
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#103×C59C2314yescomplemented
186#103×C59C2314yescomplemented
187C22⋊C8×C59C2314yes—
188C24×C59C2×D411yescharacteristic
189C23×D59—21no—
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×Q8×C59—21no—
199C2×Q8×C59—22no—
200C2×Q8×C59—22no—
201C2×Q8×C59C2412yes—
202C22×C4×C59—22no—
203C22×C4×C59—22no—
204C22×C4×C59—21no—
205C22×C4×C59—21no—
206C22×C4×C59—21no—
207C22×C4×C59—21no—
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C2×C22⋊D59—24no—
213C2×C22⋊D59—42no—
214C2×C22⋊D59—42no—
215C2×C22⋊D59—82no—
216C2×C22⋊D59C2×D414yes—
217C2×C22⋊D59C2×D414yes—
218C22×Dic59—21no—
219C22×Dic59C2×D411yescharacteristic
220C22×Dic59C2×D411yescharacteristic
221#11745689—44no—
222#11745689—44no—
223#11745689—48no—
224#11745685—48no—
225#11745685—44no—
226#11745685—44no—
227C2×D236—22no—
228C2×D236—22no—
229C2×D236—22no—
230C2×D236—22no—
231C2×D236—22no—
232C2×D236—22no—
233C2×D236—24no—
234C2×D236—21no—
235C2×D236—21no—
236C2×D236—21no—
237C2×D236—24no—
238C2×D236—24no—
239C2×D236—24no—
240C2×D236—24no—
241C2×D236—24no—
242C2×D236—24no—
243C2×D236—44no—
244C2×D236—44no—
245C2×D236—42no—
246C2×D236—44no—
247C2×D236—48no—
248C2×D236—44no—
249C2×D236—82no—
250C2×D236—82no—
251C2×D236—82no—
252C2×D236—82no—
253C2×D236—82no—
254C2×D236C2×D414yes—
255C2×D236C2412yes—
256C2×D236C2412yes—
257C2×D236C2412yes—
258C2×C4×D59—22no—
259C2×C4×D59—22no—
260C2×C4×D59—22no—
261C2×C4×D59—22no—
262C2×C4×D59—24no—
263C2×C4×D59—24no—
264C2×C4×D59—44no—
265C2×C4×D59—82no—
266C2×C4×D59C2×D412yes—
267C2×C4×D59C2×D412yes—
268C2×C4×D59C2412yes—
269C2×C4×D59C2412yes—
270C2×Dic118—42no—
271C2×Dic118C2×D414yes—
272C2×C8×C59—22no—
273C2×C8×C59—22no—
274C2×C8×C59C2412yes—
275C2×C8×C59C2412yes—
276C4⋊C4×C59—24no—
277C4⋊C4×C59—21no—
278C4⋊C4×C59—21no—
279C4⋊C4×C59—21no—
280C4⋊C4×C59C2412yes—
281C4⋊C4×C59C2412yes—
282C4⋊C4×C59C2412yes—
283C22⋊C4×C59—24no—
284C22⋊C4×C59—24no—
285C42×C59—24no—
286#11745671—44no—
287#11745671—44no—
288(C2×D59)⋊C4—24no—
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—
294(C2×D59)⋊C4—24no—
295C4⋊Dic59—21no—
296C4⋊Dic59C2412yes—
297Dic59⋊C4—24no—
298Dic59⋊C4—24no—
299C2×C59⋊C8—22no—
300C2×C59⋊C8—22no—
301C2×C59⋊C8C2412yes—
302C2×C59⋊C8C2412yes—
303D472—44no—
304D472—44no—
305#11745659—44no—
306C8×D59—44no—
307C23×C59—22no—
308C23×C59—22no—
309C23×C59—22no—
310C23×C59C22×D412yes—
311C23×C59C22×D411yescharacteristic
312C22×D59—22no—
313C22×D59—22no—
314C22×D59—22no—
315C22×D59—22no—
316C22×D59—22no—
317C22×D59—22no—
318C22×D59—22no—
319C22×D59—22no—
320C22×D59—22no—
321C22×D59—48no—
322C22×D59—42no—
323C22×D59—42no—
324C22×D59—42no—
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—
336Q8×C59—22no—
337Q8×C59—22no—
338Q8×C59—42no—
339C2×C4×C59—22no—
340C2×C4×C59—24no—
341C2×C4×C59—22no—
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×C59—42no—
351C2×C4×C59C22×D412yes—
352C2×C4×C59C22×D411yescharacteristic
353C2×C4×C59H(5,𝔽2)12yes—
354C2×C4×C59H(5,𝔽2)12yes—
355C2×C4×C59C2511yescharacteristic
356C22⋊D59—44no—
357C22⋊D59—44no—
358C22⋊D59—84no—
359C2×Dic59—22no—
360C2×Dic59—22no—
361C2×Dic59—22no—
362C2×Dic59—42no—
363C2×Dic59C22×D412yes—
364C2×Dic59C22×D412yes—
365D236—22no—
366D236—22no—
367D236—22no—
368D236—22no—
369D236—22no—
370D236—22no—
371D236—44no—
372D236—48no—
373D236—48no—
374D236—42no—
375D236—42no—
376D236—42no—
377D236—84no—
378D236—84no—
379D236—84no—
380D236—84no—
381D236—84no—
382C4×D59—24no—
383C4×D59—24no—
384C4×D59—22no—
385C4×D59—22no—
386C4×D59—22no—
387C4×D59—22no—
388C4×D59—48no—
389C4×D59—84no—
390Dic118—44no—
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#53412yes—
401C22×C59#57612yes—
402C22×C59#57712yes—
403C22×C59C23×D411yescharacteristic
404C2×D59—22no—
405C2×D59—22no—
406C2×D59—22no—
407C2×D59—22no—
408C2×D59—22no—
409C2×D59—22no—
410C2×D59—44no—
411C2×D59—44no—
412C2×D59—42no—
413C2×D59—42no—
414C2×D59—42no—
415C2×D59—42no—
416C2×D59—42no—
417C2×D59—42no—
418C2×D59—42no—
419C2×D59—42no—
420C2×D59—42no—
421C2×D59—816no—
422C2×D59—84no—
423C2×D59—84no—
424C2×D59—84no—
425C4×C59—22no—
426C4×C59—42no—
427C4×C59—42no—
428C4×C59—42no—
429C4×C59—42no—
430C4×C59#53412yes—
431C4×C59C2×H(5,𝔽2)11yescharacteristic
432C4×C59C2×H(5,𝔽2)11yescharacteristic
433Dic59—22no—
434Dic59—22no—
435Dic59—42no—
436C2×#537—591no—
437C2×#535—591no—
438#3198—5916no—
439C2×#481—591no—
440C2×#485D5911yescharacteristic, complemented
441C2×#482—591no—
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#319814yescomplemented
454C2×C59C2×#53411yescharacteristic
455C2×C59C2×#57611yescharacteristic
456C2×C59C2×#57711yescharacteristic
457D59—42no—
458D59—42no—
459D59—82no—
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—1181no—
479C2×C22⋊Q8C2×D5911yescharacteristic
480C2×#121—591no—
481C2×#121—591no—
482C2×#121—591no—
483C2×#121—591no—
484C2×#121—591no—
485C2×#121—591no—
486C2×#121—1181no—
487C2×#121—1181no—
488C2×#121—1181no—
489C2×#120—1181no—
490C2×#120—1181no—
491C2×#117C2×D5911yescharacteristic
492C22×C4⋊C4—591no—
493#485C2×D5918yescomplemented
494#482—598no—
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×#103C2×D5911yescharacteristic, complemented
510C2×#103C2×D5911yescharacteristic, complemented
511C2×#102—591no—
512C2×#102—591no—
513C2×#102—591no—
514C2×#102—591no—
515C2×#102—591no—
516C2×#102—591no—
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×Q8C22×D5911yescharacteristic
534C22×D4—591no—
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—1181no—
549C22×D4—1182no—
550C22×D4—2362no—
551C22×D4—2362no—
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—22no—
576C22⋊Q8—594no—
577C22⋊Q8—1188no—
578C22⋊Q8—1182no—
579C22⋊Q8C22×D5914yes—
580#121—594no—
581#121—594no—
582#121—594no—
583#121—594no—
584#121—594no—
585#121—594no—
586#121—1188no—
587#121—1188no—
588#121—1182no—
589#121—1182no—
590#121—1182no—
591#121—1182no—
592#121—1182no—
593#121—1188no—
594#121—1182no—
595#120—1188no—
596#120—1188no—
597#117—22no—
598#117C22×D5914yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—591no—
601C2×C4⋊C4—594no—
602C2×C4⋊C4—1182no—
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#103C22×D5914yescomplemented
623#103C22×D5914yescomplemented
624#102—594no—
625#102—594no—
626#102—594no—
627#102—594no—
628#102—594no—
629#102—594no—
630C22⋊C8—594no—
631C22⋊C8—594no—
632C22⋊C8—594no—
633C22⋊C8C22×D5914yes—
634C24—591no—
635C24—591no—
636C24—1184no—
637C24—1181no—
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—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—594no—
654C2×Q8—2362no—
655C2×Q8C23×D5912yes—
656C2×D4—594no—
657C2×D4—594no—
658C2×D4—594no—
659C2×D4—592no—
660C2×D4—592no—
661C2×D4—592no—
662C2×D4—1184no—
663C2×D4—1184no—
664C2×D4—1184no—
665C2×D4—1184no—
666C2×D4—1184no—
667C2×D4—1184no—
668C2×D4—1184no—
669C2×D4—1181no—
670C2×D4—1181no—
671C2×D4—1181no—
672C2×D4—1184no—
673C2×D4—1182no—
674C2×D4—1182no—
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—4722no—
685C2×D4—2364no—
686C2×D4—2364no—
687C2×D4—2362no—
688C2×D4—2364no—
689C2×D4—2368no—
690C2×D4—2364no—
691C2×D4—2362no—
692C2×D4—2362no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—591no—
700C22×C4—591no—
701C22×C4—592no—
702C22×C4—592no—
703C22×C4—592no—
704C22×C4—592no—
705C22×C4—1184no—
706C22×C4—1184no—
707C22×C4—1182no—
708C22×C4—1182no—
709C22×C4—1182no—
710C22×C4—1182no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—592no—
737C4⋊C4—1184no—
738C4⋊C4—1184no—
739C4⋊C4—1181no—
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—592no—
757C23—592no—
758C23—1182no—
759C23—1182no—
760C23—1182no—
761C23—1182no—
762C23—1182no—
763C23—1182no—
764C23—1182no—
765C23—1182no—
766C23—1182no—
767C23—4724no—
768C23—4724no—
769C23—47216no—
770C23—2368no—
771C23—2362no—
772C23—2362no—
773C23—2362no—
774C23—2362no—
775C23—2362no—
776C23—2362no—
777C23—2362no—
778C23—2362no—
779C23—2362no—
780C23C2×D4×D5912yes—
781C23C2×D4×D5911yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—2364no—
786D4—1182no—
787D4—1182no—
788D4—1182no—
789D4—1182no—
790D4—1182no—
791D4—1182no—
792D4—4724no—
793D4—4724no—
794D4—4724no—
795D4—4724no—
796D4—4724no—
797D4—4724no—
798D4—2364no—
799D4—2368no—
800D4—2368no—
801D4—2364no—
802D4—2364no—
803D4—2362no—
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—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—592no—
819C2×C4—592no—
820C2×C4—1182no—
821C2×C4—1182no—
822C2×C4—1184no—
823C2×C4—1184no—
824C2×C4—1182no—
825C2×C4—1182no—
826C2×C4—1182no—
827C2×C4—1182no—
828C2×C4—1182no—
829C2×C4—4724no—
830C2×C4—2368no—
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—1182no—
846C22—1182no—
847C22—1182no—
848C22—1182no—
849C22—1182no—
850C22—1182no—
851C22—47216no—
852C22—4724no—
853C22—4724no—
854C22—4724no—
855C22—2362no—
856C22—2362no—
857C22—2362no—
858C22—2362no—
859C22—2362no—
860C22—2362no—
861C22—2362no—
862C22—2362no—
863C22—2362no—
864C22—2364no—
865C22—2364no—
866C22#1683796312yes—
867C22#1683820412yes—
868C22#1683821112yes—
869C22C22×D4×D5911yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—1182no—
876C4—1182no—
877C4—2362no—
878C4#1683796312yes—
879C4C2×#1427377311yescharacteristic
880C4C2×#1427377311yescharacteristic
881C2—42no—
882C2—4722no—
883C2—4722no—
884C2—4722no—
885C2—2362no—
886C2—2362no—
887C2#2143495414yesdirect product factor
888C2C2×#1683796311yescharacteristic
889C2C2×#1683820411yescharacteristic
890C2C2×#1683821111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#485C2
socleC23×C59C22×D4
hypercenterC2×#485D59
hypocenterC59C2×#3198
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16837982C2semidirect
2. C2×#16837971C2semidirect
3. #21434954C2direct (N × H)
4. C2×#16837722C2semidirect
5. C2×#16837726C2semidirect
6. C2×#16837717C2semidirect
7. C2×#16837656C2semidirect
8. C2×#16837651C2semidirect
9. C2×#16837639C2semidirect
10. C2×#16837634C2semidirect
11. C2×#16837550C2semidirect
12. C2×#16837550C2semidirect
13. C2×#16837552C2semidirect
14. C2×#16837538C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#485C2semidirect
17. C22×#11745689C22semidirect
24. C22×#11745659C22semidirect
25. C22×C8×D59C22semidirect
27. #16837982C22semidirect
29. #16837971C22semidirect
33. C2×#14273703C22semidirect
39. C2×#14273702C22semidirect
45. C2×C4⋊C4×D59C22semidirect
46. #16837726C22semidirect
47. #16837722C22semidirect
48. #16837717C22semidirect
49. #16837656C22semidirect
50. #16837651C22semidirect
51. #16837639C22semidirect
52. #16837634C22semidirect
53. #16837552C22semidirect
54. #16837550C22semidirect
55. #16837550C22semidirect
56. #16837538C22semidirect
57. C2×#14273660C22semidirect
58. C2×#14273658C22semidirect
63. C2×#14273647C22semidirect
64. C2×#14273647C22semidirect
65. #16837367C22semidirect
67. C2×(C2×D59)⋊C8C22semidirect
68. C2×(C2×D59)⋊C8C22semidirect
71. C59×#485C22semidirect
72. C2×#107×C59C22semidirect
73. C2×#106×C59C22semidirect
74. C2×#103×C59C22semidirect
75. C2×#103×C59C22semidirect
81. C2×#11745689C23semidirect
118. C2×#11745659C23semidirect
122. C2×C8×D59C23semidirect
127. #14273703C23semidirect
138. #14273702C23semidirect
149. C4⋊C4×D59C23semidirect
157. #14273660C23semidirect
158. #14273658C23semidirect
163. #14273647C23semidirect
164. #14273647C23semidirect
166. (C2×D59)⋊C8C23semidirect
167. (C2×D59)⋊C8C23semidirect
183. #107×C59C23semidirect
184. #106×C59C23semidirect
185. #103×C59C23semidirect
186. #103×C59C23semidirect
440. C2×#485D59semidirect
453. C2×C59#3198semidirect
493. #485C2×D59semidirect
506. C2×#107C2×D59semidirect
508. C2×#106C2×D59semidirect
509. C2×#103C2×D59semidirect
510. C2×#103C2×D59semidirect
522. C59C2×#3198semidirect
619. #107C22×D59semidirect
621. #106C22×D59semidirect
622. #103C22×D59semidirect
623. #103C22×D59semidirect
887. C2#21434954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379822
C2×#168379712
#214349542
C2×#168377222
C2×#168377262
C2×#168377172
C2×#168376562
C2×#168376512
C2×#168376392
C2×#168376342
C2×#168375502
C2×#168375522
C2×#168375382
C2×#168373672
C2×C59×#4852
C2×#319859