Finite Group Databasebeta

← C2×#21434393 #29457042

Subgroups — C2×#21434393 #29457042

Order 15104.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838010C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic
3#21434393C2116yesmaximal, direct product factor
4C2×#16837745C211yesmaximal, characteristic
5C2×#16837742C211yesmaximal, characteristic
6C2×#16837711C211yesmaximal, characteristic, complemented
7C2×#16837708C211yesmaximal, characteristic, complemented
8C2×#16837611C211yesmaximal, characteristic, complemented
9C2×#16837610C211yesmaximal, characteristic, complemented
10C2×#16837559C211yesmaximal, characteristic
11C2×#16837556C211yesmaximal, characteristic
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837507C211yesmaximal, characteristic, complemented
14C2×C4×Dic236C211yesmaximal, characteristic, complemented
15C2×#16837461C211yesmaximal, characteristic
16C2×C4×Q16×C59C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745672C2211yescharacteristic
21#16838010—24no—
22#16838010C2218yes—
23C2×#14273725C2211yescharacteristic
24C2×#14273722—21no—
25C2×#14273721—21no—
26C2×#14273719—21no—
27C2×#14273718C2211yescharacteristic
28C2×#14273717—21no—
29C2×#14273707C2211yescharacteristic
30C2×#14273703C2211yescharacteristic
31#16837878—24no—
32#16837878C2218yes—
33C2×Q8×Dic59C2211yescharacteristic
34C2×C4×Dic118—21no—
35C2×C4×Dic118C2211yescharacteristic
36C2×C4×Dic118C2211yescharacteristic
37C2×#14273692—21no—
38C2×#14273692C2211yescharacteristic
39C2×#14273685—21no—
40C2×#14273685C2211yescharacteristic
41C2×#14273684—21no—
42C2×#14273684C2211yescharacteristic
43#16837745C2218yes—
44#16837742C2218yes—
45#16837711C2218yescomplemented
46#16837708C2218yescomplemented
47#16837611C2218yescomplemented
48#16837610C2218yescomplemented
49#16837559C2218yes—
50#16837556C2218yes—
51#16837507C2218yescomplemented
52#16837507C2218yescomplemented
53C4×Dic236C2218yescomplemented
54#16837461C2218yes—
55C2×#14273661C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273638C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C4×Q16×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×Dic118C2311yescharacteristic
80C2×Q8×D59—24no—
81C2×Q8×D59—22no—
82C2×Q8×D59—24no—
83C2×Q8×D59C2314yes—
84C22×C4×D59—21no—
85C22×C4×D59C2311yescharacteristic
86C2×Dic236—24no—
87C2×Dic236C2314yes—
88C2×#11745672—24no—
89C2×#11745672—24no—
90C2×#11745672C2314yes—
91C2×#11745672C2314yes—
92C22×C59⋊C8C2311yescharacteristic
93C22×C59⋊C8C2311yescharacteristic
94#14273725—22no—
95#14273725C2314yes—
96#14273722—28no—
97#14273721—28no—
98#14273719—28no—
99#14273718—22no—
100#14273718C2314yes—
101#14273717—28no—
102#14273707—22no—
103#14273707C2314yes—
104#14273703—22no—
105#14273703C2314yes—
106Q8×Dic59—22no—
107Q8×Dic59C2314yes—
108C4×Dic118—22no—
109C4×Dic118—22no—
110C4×Dic118—28no—
111C4×Dic118C2314yes—
112C4×Dic118C2314yes—
113#14273692—28no—
114#14273692—22no—
115#14273692C2314yes—
116#14273685—22no—
117#14273685—28no—
118#14273685C2314yes—
119#14273684—28no—
120#14273684D414yes—
121#14273684C2314yes—
122C2×C4⋊Dic59—21no—
123C2×C4⋊Dic59—21no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4D411yescharacteristic
135C2×Dic59⋊C4D411yescharacteristic
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×C4×Dic59—21no—
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273658C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152#14273652C2314yes—
153#14273652C2314yes—
154#14273651C2314yes—
155#14273651C2314yes—
156#14273650C2314yes—
157#14273650C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160#14273638C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×Q8×C59C2311yescharacteristic
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4×Q8×C59—22no—
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×Q8×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C42×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#107×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C4×C8×C59C2314yes—
182C23×D59C2×D411yescharacteristic
183C2×Q8×C59—21no—
184C2×Q8×C59—21no—
185C2×Q8×C59—22no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59#4114yes—
189C2×Q8×C59C2412yes—
190C2×Q8×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205Q8×D59—216no—
206Q8×D59—28no—
207Q8×D59—28no—
208C2×C4×D59—28no—
209C2×C4×D59—24no—
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59C2×D412yes—
213C2×C4×D59C2412yes—
214C2×Dic118—28no—
215C2×Dic118—21no—
216C2×Dic118—22no—
217C2×Dic118—24no—
218C2×Dic118—22no—
219C2×Dic118—22no—
220C2×Dic118—21no—
221C2×Dic118#4114yes—
222C2×Dic118C2412yes—
223C2×Dic118C2412yes—
224Q16×C59—28no—
225C2×C8×C59—22no—
226C2×C8×C59—22no—
227C2×C8×C59C2412yes—
228C2×C8×C59C2412yes—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—24no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59—21no—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C42×C59—24no—
236C42×C59—24no—
237C42×C59C2×D412yes—
238C42×C59C2412yes—
239#11745672—28no—
240#11745672—28no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4C2×D414yes—
245(C2×D59)⋊C4C2×D414yes—
246C4⋊Dic59—21no—
247C4⋊Dic59—21no—
248C4⋊Dic59—24no—
249C4⋊Dic59—24no—
250C4⋊Dic59—24no—
251C4⋊Dic59C2412yes—
252C4⋊Dic59C2412yes—
253Dic59⋊C4—24no—
254Dic59⋊C4—24no—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4C2×D414yes—
261Dic59⋊C4C2×D414yes—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59C2×D412yes—
268C4×Dic59C2412yes—
269C2×C59⋊C8—22no—
270C2×C59⋊C8—22no—
271C2×C59⋊C8C2412yes—
272C2×C59⋊C8C2412yes—
273Dic236—28no—
274C23×C59C22×D411yescharacteristic
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59C22×D412yes—
279Q8×C59—24no—
280Q8×C59—22no—
281Q8×C59—22no—
282Q8×C59—22no—
283Q8×C59—42no—
284Q8×C59C2×#4114yes—
285C2×C4×C59—24no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—42no—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D412yes—
297C2×C4×C59C22×D411yescharacteristic
298C2×C4×C59C2×#4112yes—
299C2×C4×C59C2×#4112yes—
300C2×C4×C59C2511yescharacteristic
301C2×Dic59—22no—
302C2×Dic59—24no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—22no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59—42no—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314C2×Dic59C22×D412yes—
315C4×D59—216no—
316C4×D59—24no—
317C4×D59—22no—
318C4×D59—22no—
319Dic118—216no—
320Dic118—24no—
321Dic118—22no—
322Dic118—22no—
323Dic118—22no—
324Dic118—42no—
325Dic118C2×#4114yes—
326C8×C59—22no—
327C8×C59—22no—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C2×#3127—591nomaximal, Sylow
331C22×C59#52512yes—
332C22×C59#57812yes—
333C22×C59#57812yes—
334C22×C59C23×D411yescharacteristic
335C2×D59—22no—
336C2×D59—22no—
337C2×D59—22no—
338C2×D59—44no—
339C4×C59—24no—
340C4×C59—22no—
341C4×C59—22no—
342C4×C59—42no—
343C4×C59—42no—
344C4×C59—42no—
345C4×C59#52512yes—
346C4×C59C22×#4111yescharacteristic
347C4×C59C22×#4111yescharacteristic
348Dic59—22no—
349Dic59—24no—
350Dic59—22no—
351Dic59—22no—
352Dic59—42no—
353Dic59—42no—
354Dic59—42no—
355C2×#541—591no—
356C2×#519—591no—
357#3127—5916no—
358C2×#485—591no—
359C2×#485—591no—
360C2×#479—591no—
361C2×#479—591no—
362C2×#462—591no—
363C2×#462—591no—
364C2×#451—591no—
365C2×#451—591no—
366C2×#441—591no—
367C2×#441—591no—
368C2×C4×Q16—591no—
369C2×C4×Q16D5911yescharacteristic, complemented
370C2×#433—591no—
371C2×C59#312714yescomplemented
372C2×C59C2×#52511yescharacteristic
373C2×C59C2×#57811yescharacteristic
374C2×C59C2×#57811yescharacteristic
375D59—42no—
376C23×Q8—591no—
377C22×Q16—591no—
378C22×Q16—591no—
379C22×Q16—591no—
380C22×Q16C2×D5911yescharacteristic
381#541—598no—
382#541—1184no—
383C2×C4⋊Q8—591no—
384C2×#126—1181no—
385C2×#126—1181no—
386C2×#125—591no—
387C2×#125—1181no—
388C2×#125—1181no—
389C2×C22⋊Q8—591no—
390C2×C22⋊Q8—591no—
391#519—598no—
392#519—1184no—
393C2×C4×Q8—591no—
394C2×C4×Q8—591no—
395C2×C4×Q8—591no—
396C2×C4×Q8—591no—
397C2×C4×Q8—1181no—
398C2×C4×Q8—1181no—
399C2×C4×Q8C2×D5911yescharacteristic
400C2×C4×Q8C2×D5911yescharacteristic
401C2×#117—591no—
402C2×#117—591no—
403C2×#117—1181no—
404C2×#117—1181no—
405#485—598no—
406#485—598no—
407#479—598no—
408#479—598no—
409#462—598no—
410#462—598no—
411#451—598no—
412#451—598no—
413#441—598no—
414#441—598no—
415C4×Q16—598no—
416C4×Q16C2×D5918yescomplemented
417#433—598no—
418C2×#107—591no—
419C2×#107C2×D5911yescharacteristic
420C2×#106—591no—
421C2×#106—591no—
422C2×C4⋊C8—591no—
423C2×C4⋊C8—591no—
424C2×#103—591no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#103—591no—
428C2×#103—591no—
429C2×#103—591no—
430C2×#103C2×D5911yescharacteristic
431C2×#103C2×D5911yescharacteristic
432C2×C22⋊C8—591no—
433C2×C22⋊C8—591no—
434C2×#97—591no—
435C2×C4×C8C2×D5911yescharacteristic
436C59C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—594no—
438C22×Q8—591no—
439C22×Q8—591no—
440C22×Q8—1181no—
441C22×Q8—1182no—
442C22×Q8—1184no—
443C22×Q8—1184no—
444C22×Q8C22×D5911yescharacteristic
445C22×Q8C22×D5911yescharacteristic
446C23×C4—591no—
447C23×C4—1181no—
448C2×Q16—24no—
449C2×Q16—594no—
450C2×Q16—594no—
451C2×Q16—594no—
452C2×Q16—1184no—
453C2×Q16—1184no—
454C2×Q16—1184no—
455C2×Q16C22×D5914yes—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8C22×D5911yescharacteristic
459C22×C8C22×D5911yescharacteristic
460C4⋊Q8—594no—
461C4⋊Q8—1182no—
462#126—1188no—
463#126—1188no—
464#125—594no—
465#125—1188no—
466#125—1182no—
467#125—1188no—
468C22⋊Q8—594no—
469C22⋊Q8—594no—
470C22⋊Q8—1182no—
471C22⋊Q8—1182no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—594no—
475C4×Q8—594no—
476C4×Q8—594no—
477C4×Q8—594no—
478C4×Q8—1188no—
479C4×Q8—1182no—
480C4×Q8—1182no—
481C4×Q8—1188no—
482C4×Q8—1182no—
483C4×Q8—1182no—
484C4×Q8C22×D5914yes—
485C4×Q8C22×D5914yes—
486#117—594no—
487#117—594no—
488#117—594no—
489#117—1188no—
490#117—1188no—
491#117—1182no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—1181no—
500C2×C4⋊C4—1181no—
501C2×C4⋊C4—1181no—
502C2×C4⋊C4—1181no—
503C2×C4⋊C4—1181no—
504C2×C4⋊C4—1181no—
505C2×C4⋊C4—1181no—
506C2×C4⋊C4—1181no—
507C2×C4⋊C4—1181no—
508C2×C4⋊C4C22×D5911yescharacteristic
509C2×C4⋊C4C22×D5911yescharacteristic
510C2×C22⋊C4—591no—
511C2×C22⋊C4—591no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—591no—
518C2×C42—1181no—
519C2×C42—1181no—
520C2×C42—1181no—
521C2×C42—1181no—
522C2×C42—1181no—
523C2×C42C22×D5911yescharacteristic
524#107—594no—
525#107C22×D5914yes—
526#106—594no—
527#106—594no—
528C4⋊C8—594no—
529C4⋊C8—594no—
530#103—594no—
531#103—594no—
532#103—594no—
533#103—594no—
534#103—594no—
535#103—594no—
536#103C22×D5914yes—
537#103C22×D5914yes—
538C22⋊C8—594no—
539C22⋊C8—594no—
540#97—594no—
541C4×C8C22×D5914yes—
542C24—591no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—594no—
549C2×Q8—592no—
550C2×Q8—592no—
551C2×Q8—1184no—
552C2×Q8—1188no—
553C2×Q8—1188no—
554C2×Q8—11816no—
555C2×Q8—1188no—
556C2×Q8—1181no—
557C2×Q8—1181no—
558C2×Q8—1182no—
559C2×Q8—1182no—
560C2×Q8—1182no—
561C2×Q8#1174568514yes—
562C2×Q8C23×D5912yes—
563C2×Q8C23×D5912yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—591no—
569C22×C4—591no—
570C22×C4—591no—
571C22×C4—592no—
572C22×C4—592no—
573C22×C4—1184no—
574C22×C4—1188no—
575C22×C4—1181no—
576C22×C4—1182no—
577C22×C4—1182no—
578C22×C4—1181no—
579C22×C4—1181no—
580C22×C4—1181no—
581C22×C4D4×D5911yescharacteristic
582C22×C4D4×D5911yescharacteristic
583C22×C4C23×D5911yescharacteristic
584Q16—28no—
585Q16—1188no—
586Q16—1188no—
587Q16—1188no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—592no—
591C2×C8—592no—
592C2×C8—1182no—
593C2×C8—1182no—
594C2×C8C23×D5912yes—
595C2×C8C23×D5912yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—594no—
601C4⋊C4—594no—
602C4⋊C4—592no—
603C4⋊C4—592no—
604C4⋊C4—1184no—
605C4⋊C4—1184no—
606C4⋊C4—1184no—
607C4⋊C4—1184no—
608C4⋊C4—1184no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1181no—
613C4⋊C4—1181no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4C23×D5912yes—
617C4⋊C4C23×D5912yes—
618C22⋊C4—594no—
619C22⋊C4—594no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—24no—
624C42—24no—
625C42—592no—
626C42—592no—
627C42—1184no—
628C42—1184no—
629C42—1184no—
630C42—1184no—
631C42—1184no—
632C42D4×D5912yes—
633C42C23×D5912yes—
634C23—592no—
635C23—1182no—
636C23—1182no—
637C23—1182no—
638C23C2×D4×D5911yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—42no—
644Q8—594no—
645Q8—11816no—
646Q8—1184no—
647Q8—1182no—
648Q8—1182no—
649Q8—1182no—
650Q8—2362no—
651Q8C2×#1174568514yes—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—592no—
663C2×C4—592no—
664C2×C4—592no—
665C2×C4—11816no—
666C2×C4—1182no—
667C2×C4—1184no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1184no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—2362no—
678C2×C4—2362no—
679C2×C4—2362no—
680C2×C4C2×D4×D5912yes—
681C2×C4C2×D4×D5912yes—
682C2×C4C2×D4×D5911yescharacteristic
683C2×C4#41×D5912yes—
684C2×C4C2×#1174568512yes—
685C2×C4C24×D5911yescharacteristic
686C8—22no—
687C8—22no—
688C8—1182no—
689C8—1182no—
690C22—1182no—
691C22—1182no—
692C22—1182no—
693C22—2364no—
694C22#1683791112yes—
695C22#1683821512yes—
696C22#1683821612yes—
697C22C22×D4×D5911yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—1182no—
705C4—1182no—
706C4—1182no—
707C4—1184no—
708C4—2362no—
709C4—2362no—
710C4—2362no—
711C4#1683791112yes—
712C4C2×#41×D5911yescharacteristic
713C4C22×#1174568511yescharacteristic
714C2—2362no—
715C2#2143439314yesdirect product factor
716C2C2×#1683791111yescharacteristic
717C2C2×#1683821511yescharacteristic
718C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×Q16×C59C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
hypercenterC2×C4×Q16D59
hypocenterC59C2×#3127
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #21434393C2direct (N × H)
6. C2×#16837711C2semidirect
7. C2×#16837708C2semidirect
8. C2×#16837611C2semidirect
9. C2×#16837610C2semidirect
12. C2×#16837507C2semidirect
13. C2×#16837507C2semidirect
14. C2×C4×Dic236C2semidirect
16. C2×C4×Q16×C59C2semidirect
45. #16837711C22semidirect
46. #16837708C22semidirect
47. #16837611C22semidirect
48. #16837610C22semidirect
51. #16837507C22semidirect
52. #16837507C22semidirect
53. C4×Dic236C22semidirect
72. C4×Q16×C59C22semidirect
369. C2×C4×Q16D59semidirect
371. C2×C59#3127semidirect
416. C4×Q16C2×D59semidirect
436. C59C2×#3127semidirect
715. C2#21434393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380102
C2×#168378782
#214343932
C2×#168377452
C2×#168377422
C2×#168377112
C2×#168377082
C2×#168376112
C2×#168376102
C2×#168375592
C2×#168375562
C2×#168375072
C2×C4×Dic2362
C2×#168374612
C2×C4×Q16×C592
C2×#312759