Finite Group Databasebeta

← C2×#21436657 #29467368

Subgroups — C2×#21436657 #29467368

Order 15104.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838100C211yesmaximal, characteristic
2C2×#16838091C211yesmaximal, characteristic, complemented
3#21436657C2116yesmaximal, direct product factor
4C2×#16837803C211yesmaximal, characteristic, complemented
5C2×#16837722C211yesmaximal, characteristic, complemented
6C2×#16837745C211yesmaximal, characteristic, complemented
7C2×#16837726C211yesmaximal, characteristic, complemented
8C2×#16837732C211yesmaximal, characteristic, complemented
9C2×#16837712C211yesmaximal, characteristic, complemented
10C2×#16837705C211yesmaximal, characteristic, complemented
11C2×#16837649C211yesmaximal, characteristic, complemented
12C2×#16837648C211yesmaximal, characteristic, complemented
13C2×#16837489C211yesmaximal, characteristic, complemented
14C2×#16837478C211yesmaximal, characteristic, complemented
15C2×#16837441C211yesmaximal, characteristic, complemented
16C2×C59×#428C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×#11745659C2211yescharacteristic
19#16838100—24no—
20#16838100C2218yes—
21#16838091—24no—
22#16838091C2218yescomplemented
23C2×#14273722—21no—
24C2×#14273720—21no—
25C2×#14273719—21no—
26C2×#14273718C2211yescharacteristic
27C2×#14273718C2211yescharacteristic
28C2×#14273712—21no—
29C2×#14273709—21no—
30C2×#14273707C2211yescharacteristic
31C2×#14273706C2211yescharacteristic
32C2×#14273702C2211yescharacteristic
33C2×#14273701—21no—
34C2×#14273701C2211yescharacteristic
35C2×#14273692C2211yescharacteristic
36C2×#14273689C2211yescharacteristic
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39C2×#14273685C2211yescharacteristic
40C2×#14273684—21no—
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837803C2218yescomplemented
43#16837745C2218yescomplemented
44#16837732C2218yescomplemented
45#16837726C2218yescomplemented
46#16837722C2218yescomplemented
47#16837712C2218yescomplemented
48#16837705C2218yescomplemented
49#16837649C2218yescomplemented
50#16837648C2218yescomplemented
51#16837489C2218yescomplemented
52#16837478C2218yescomplemented
53#16837441C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C22×C4⋊C4×C59C2211yescharacteristic
72C59×#428C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#107×C59C2211yescharacteristic
75C2×#106×C59C2211yescharacteristic
76C2×#106×C59C2211yescharacteristic
77C22×Dic118C2311yescharacteristic
78C22×D236—21no—
79C22×D236C2311yescharacteristic
80C22×C22⋊D59—21no—
81C22×C22⋊D59D411yescharacteristic
82C22×C4×D59—21no—
83C22×C4×D59—21no—
84C22×C4×D59C2311yescharacteristic
85C2×#11745660—24no—
86C2×#11745660C2314yes—
87C2×#11745659—24no—
88C2×#11745659C2314yes—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91#14273722—28no—
92#14273720—28no—
93#14273719—28no—
94#14273718—22no—
95#14273718—22no—
96#14273718C2314yes—
97#14273718C2314yes—
98#14273712—28no—
99#14273709—28no—
100#14273707—22no—
101#14273707C2314yes—
102#14273706—22no—
103#14273706C2314yes—
104#14273702—22no—
105#14273702C2314yes—
106#14273701—22no—
107#14273701—28no—
108#14273701C2314yes—
109#14273692—22no—
110#14273692C2314yes—
111#14273689—22no—
112#14273689C2314yes—
113C4×C22⋊D59—28no—
114C4×C22⋊D59D414yes—
115C4×C22⋊D59C2314yes—
116#14273685—22no—
117#14273685C2314yes—
118#14273684—28no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59—21no—
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×Dic59⋊C4—21no—
125C2×Dic59⋊C4—21no—
126C2×Dic59⋊C4—21no—
127C2×Dic59⋊C4—21no—
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4D411yescharacteristic
130C4⋊C4×D59—22no—
131C4⋊C4×D59C2314yes—
132C2×C22⋊Dic59—21no—
133C2×C22⋊Dic59D411yescharacteristic
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4D411yescharacteristic
140C2×C4×Dic59—21no—
141C2×C4×Dic59—21no—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273660C2314yes—
145#14273658C2314yes—
146#14273658C2314yes—
147#14273658C2314yes—
148Dic59⋊C8C2314yes—
149#14273652C2314yes—
150#14273650C2314yes—
151#14273650C2314yes—
152#14273649C2314yes—
153#14273647C2314yes—
154#14273647C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156(C2×D59)⋊C8C2314yes—
157C8×Dic59C2314yes—
158C23×C4×C59—21no—
159C23×C4×C59C2311yescharacteristic
160C2×M16×C59—24no—
161C2×M16×C59C2314yes—
162C22×C8×C59C2311yescharacteristic
163C22×C8×C59C2311yescharacteristic
164#117×C59—22no—
165#117×C59C2314yes—
166C2×C4⋊C4×C59—21no—
167C2×C4⋊C4×C59—22no—
168C2×C4⋊C4×C59C2311yescharacteristic
169C2×C4⋊C4×C59C2311yescharacteristic
170C2×C4⋊C4×C59C2311yescharacteristic
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2314yes—
173C2×C22⋊C4×C59—21no—
174C2×C42×C59—21no—
175#107×C59C2314yes—
176#107×C59C2314yes—
177#106×C59C2314yes—
178#106×C59C2314yes—
179C24×C59C2×D411yescharacteristic
180C23×D59—21no—
181C23×D59C2×D411yescharacteristic
182C22×C4×C59—22no—
183C22×C4×C59—22no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—21no—
188C22×C4×C59—24no—
189C22×C4×C59—82no—
190C22×C4×C59C2×D411yescharacteristic
191C22×C4×C59C2×D412yes—
192C22×C4×C59C2412yes—
193C22×C4×C59C2411yescharacteristic
194C2×C22⋊D59—24no—
195C2×C22⋊D59—42no—
196C2×C22⋊D59—44no—
197C2×C22⋊D59C2×D414yes—
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59C2×D411yescharacteristic
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C2×D236—22no—
205C2×D236—22no—
206C2×D236—21no—
207C2×D236—24no—
208C2×D236—82no—
209C2×D236C2412yes—
210C2×C4×D59—22no—
211C2×C4×D59—22no—
212C2×C4×D59—24no—
213C2×C4×D59—24no—
214C2×C4×D59—44no—
215C2×C4×D59—82no—
216C2×C4×D59C2×D412yes—
217C2×C4×D59C2412yes—
218C2×Dic118—22no—
219C2×Dic118—22no—
220C2×Dic118—21no—
221C2×Dic118C2412yes—
222M16×C59—28no—
223C2×C8×C59—22no—
224C2×C8×C59#4114yes—
225C2×C8×C59C2412yes—
226C2×C8×C59C2412yes—
227C4⋊C4×C59—21no—
228C4⋊C4×C59—21no—
229C4⋊C4×C59—24no—
230C4⋊C4×C59—21no—
231C4⋊C4×C59—21no—
232C4⋊C4×C59C2412yes—
233C4⋊C4×C59C2412yes—
234C4⋊C4×C59C2412yes—
235C4⋊C4×C59C2412yes—
236C22⋊C4×C59—24no—
237C42×C59—24no—
238C22⋊Dic59—24no—
239C22⋊Dic59C2×D414yes—
240(C2×D59)⋊C4—24no—
241(C2×D59)⋊C4—24no—
242(C2×D59)⋊C4—24no—
243(C2×D59)⋊C4—24no—
244(C2×D59)⋊C4—24no—
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⋊C4C2×D414yes—
259C4×Dic59—24no—
260C4×Dic59—24no—
261C4×Dic59C2×D412yes—
262C4×Dic59C2412yes—
263C2×C59⋊C8—22no—
264C2×C59⋊C8—22no—
265C2×C59⋊C8C2412yes—
266C2×C59⋊C8C2412yes—
267#11745660—28no—
268#11745659—28no—
269C23×C59—22no—
270C23×C59—22no—
271C23×C59—22no—
272C23×C59C22×D412yes—
273C23×C59C22×D411yescharacteristic
274C22×D59—22no—
275C22×D59—22no—
276C22×D59—22no—
277C22×D59—22no—
278C22×D59—42no—
279C22×D59—42no—
280C22×D59—42no—
281C22×D59C22×D412yes—
282C2×C4×C59—22no—
283C2×C4×C59—24no—
284C2×C4×C59—22no—
285C2×C4×C59—22no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—42no—
291C2×C4×C59—42no—
292C2×C4×C59—42no—
293C2×C4×C59—42no—
294C2×C4×C59—84no—
295C2×C4×C59C22×D412yes—
296C2×C4×C59C22×D411yescharacteristic
297C2×C4×C59C2×#4112yes—
298C2×C4×C592−1+412yes—
299C2×C4×C59C2511yescharacteristic
300C22⋊D59—44no—
301C22⋊D59—48no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—22no—
305C2×Dic59—22no—
306C2×Dic59—22no—
307C2×Dic59—22no—
308C2×Dic59—42no—
309C2×Dic59—42no—
310C2×Dic59—42no—
311C2×Dic59C22×D412yes—
312C2×Dic59C22×D412yes—
313C2×Dic59C22×D412yes—
314D236—22no—
315D236—22no—
316D236—42no—
317D236—84no—
318C4×D59—24no—
319C4×D59—22no—
320C4×D59—22no—
321C4×D59—48no—
322C4×D59—84no—
323Dic118—22no—
324Dic118—22no—
325Dic118—42no—
326C8×C59—22no—
327C8×C59C2×#4114yes—
328C59⋊C8—22no—
329C59⋊C8—22no—
330C2×#3351—591nomaximal, Sylow
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—44no—
335C22×C59#54712yes—
336C22×C59#57512yes—
337C22×C59#57712yes—
338C22×C59C23×D411yescharacteristic
339C2×D59—22no—
340C2×D59—22no—
341C2×D59—22no—
342C2×D59—44no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—84no—
347C4×C59—22no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—42no—
351C4×C59—42no—
352C4×C59#54712yes—
353C4×C59C22×#4111yescharacteristic
354C4×C59C2×2−1+411yescharacteristic
355Dic59—22no—
356Dic59—22no—
357Dic59—22no—
358Dic59—42no—
359Dic59—42no—
360Dic59—42no—
361C2×#553—591no—
362C2×#552—591no—
363#3351—5916no—
364C2×#499—591no—
365C2×#481—591no—
366C2×#485—591no—
367C2×#482—591no—
368C2×#483—591no—
369C2×#479—591no—
370C2×#478—591no—
371C2×#468—591no—
372C2×#468—591no—
373C2×C4×SD16—591no—
374C2×#436—591no—
375C2×#428—591no—
376C2×#428D5911yescharacteristic, complemented
377C2×C59—42no—
378C2×C59#335114yescomplemented
379C2×C59C2×#54711yescharacteristic
380C2×C59C2×#57511yescharacteristic
381C2×C59C2×#57711yescharacteristic
382D59—42no—
383D59—82no—
384C22×SD16—591no—
385C22×M16—591no—
386C22×M16C2×D5911yescharacteristic
387#553—598no—
388#553—1184no—
389#552—598no—
390#552—1184no—
391C2×#126—1181no—
392C2×#126—1181no—
393C2×#125—591no—
394C2×#125—591no—
395C2×#125—1181no—
396C2×#123—1181no—
397C2×#123—1181no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8—591no—
400C2×#121—591no—
401C2×#121—591no—
402C2×#121—1181no—
403C2×C4×Q8—591no—
404C2×C4×D4—591no—
405C2×C4×D4—591no—
406C2×C4×D4—1181no—
407C2×#117—591no—
408C2×#117—1181no—
409C2×#117C2×D5911yescharacteristic
410C22×C4⋊C4—591no—
411C22×C4⋊C4C2×D5911yescharacteristic
412#499—598no—
413#485—598no—
414#483—598no—
415#482—598no—
416#481—598no—
417#479—598no—
418#478—598no—
419#468—598no—
420#468—598no—
421C4×SD16—598no—
422#436—598no—
423#428—598no—
424#428C2×D5918yescomplemented
425C2×#107—591no—
426C2×#107—591no—
427C2×#107C2×D5911yescharacteristic
428C2×#107C2×D5911yescharacteristic
429C2×#106—591no—
430C2×#106—591no—
431C2×#106—591no—
432C2×#106C2×D5911yescharacteristic
433C2×#106C2×D5911yescharacteristic
434C2×C4⋊C8—591no—
435C2×#103—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#102—591no—
439C2×#102—591no—
440C2×#102—591no—
441C2×C22⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×C4×C8—591no—
444C59C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8—591no—
446C22×D4—591no—
447C22×D4—591no—
448C22×D4—1181no—
449C22×D4—1181no—
450C23×C4—21no—
451C23×C4—591no—
452C23×C4—1181no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C2×SD16—594no—
456C2×SD16—1184no—
457C2×M16—24no—
458C2×M16—594no—
459C2×M16—1184no—
460C2×M16C22×D5914yes—
461C22×C8—591no—
462C22×C8—591no—
463C22×C8C22×D5911yescharacteristic
464C22×C8C22×D5911yescharacteristic
465#126—1188no—
466#126—1188no—
467#125—594no—
468#125—594no—
469#125—1188no—
470#125—1182no—
471#125—1182no—
472#123—1188no—
473#123—1188no—
474C22⋊Q8—594no—
475C22⋊Q8—594no—
476C22⋊Q8—1182no—
477C22⋊Q8—1182no—
478#121—594no—
479#121—594no—
480#121—1182no—
481#121—1188no—
482#121—1182no—
483C4×Q8—594no—
484C4×Q8—1182no—
485C4×D4—594no—
486C4×D4—594no—
487C4×D4—594no—
488C4×D4—1182no—
489C4×D4—1188no—
490#117—22no—
491#117—594no—
492#117—1188no—
493#117—1182no—
494#117C22×D5914yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4—591no—
500C2×C4⋊C4—594no—
501C2×C4⋊C4—1182no—
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⋊C4—1181no—
509C2×C4⋊C4—1181no—
510C2×C4⋊C4C22×D5911yescharacteristic
511C2×C4⋊C4C22×D5911yescharacteristic
512C2×C4⋊C4C22×D5911yescharacteristic
513C2×C4⋊C4C22×D5914yes—
514C2×C4⋊C4C22×D5911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—591no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—1181no—
519C2×C22⋊C4—1181no—
520C2×C22⋊C4—1181no—
521C2×C22⋊C4—1181no—
522C2×C22⋊C4—1181no—
523C2×C22⋊C4—1181no—
524C2×C42—21no—
525C2×C42—591no—
526C2×C42—1181no—
527C2×C42—1181no—
528#107—594no—
529#107—594no—
530#107C22×D5914yes—
531#107C22×D5914yes—
532#106—594no—
533#106—594no—
534#106—594no—
535#106C22×D5914yes—
536#106C22×D5914yes—
537C4⋊C8—594no—
538#103—594no—
539#103—594no—
540#103—594no—
541#102—594no—
542#102—594no—
543#102—594no—
544C22⋊C8—594no—
545C22⋊C8—594no—
546C4×C8—594no—
547C24—591no—
548C24—1181no—
549C24D4×D5911yescharacteristic
550C2×Q8—592no—
551C2×Q8—1181no—
552C2×Q8—1182no—
553C2×Q8—1182no—
554C2×D4—594no—
555C2×D4—592no—
556C2×D4—1184no—
557C2×D4—1184no—
558C2×D4—1181no—
559C2×D4—1182no—
560C2×D4—1182no—
561C2×D4—4722no—
562C2×D4—2362no—
563C2×D4—2364no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—591no—
573C22×C4—591no—
574C22×C4—591no—
575C22×C4—592no—
576C22×C4—592no—
577C22×C4—1184no—
578C22×C4—1184no—
579C22×C4—1182no—
580C22×C4—1182no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—4722no—
585C22×C4—2364no—
586C22×C4D4×D5912yes—
587C22×C4D4×D5911yescharacteristic
588C22×C4C23×D5912yes—
589C22×C4C23×D5911yescharacteristic
590SD16—1188no—
591M16—28no—
592M16—1188no—
593C2×C8—22no—
594C2×C8—592no—
595C2×C8—592no—
596C2×C8—1182no—
597C2×C8—1182no—
598C2×C8#1174568514yes—
599C2×C8C23×D5912yes—
600C2×C8C23×D5912yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—594no—
607C4⋊C4—592no—
608C4⋊C4—592no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1184no—
613C4⋊C4—1184no—
614C4⋊C4—1184no—
615C4⋊C4—1184no—
616C4⋊C4—1181no—
617C4⋊C4—1181no—
618C4⋊C4—1184no—
619C4⋊C4C23×D5912yes—
620C4⋊C4C23×D5912yes—
621C4⋊C4C23×D5912yes—
622C4⋊C4C23×D5912yes—
623C22⋊C4—24no—
624C22⋊C4—594no—
625C22⋊C4—594no—
626C22⋊C4—1184no—
627C22⋊C4—1184no—
628C22⋊C4—1184no—
629C22⋊C4—1184no—
630C22⋊C4—1184no—
631C22⋊C4—1184no—
632C42—24no—
633C42—592no—
634C42—592no—
635C42—1184no—
636C42—1184no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—592no—
641C23—1182no—
642C23—1182no—
643C23—1182no—
644C23—1182no—
645C23—2362no—
646C23—2362no—
647C23—2362no—
648C23C2×D4×D5912yes—
649C23C2×D4×D5911yescharacteristic
650Q8—1182no—
651Q8—1182no—
652Q8—2362no—
653D4—1182no—
654D4—1182no—
655D4—4724no—
656D4—2364no—
657D4—2368no—
658D4—2362no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—84no—
672C2×C4—592no—
673C2×C4—592no—
674C2×C4—592no—
675C2×C4—1182no—
676C2×C4—1182no—
677C2×C4—1182no—
678C2×C4—1182no—
679C2×C4—1182no—
680C2×C4—1184no—
681C2×C4—1182no—
682C2×C4—1182no—
683C2×C4—1182no—
684C2×C4—4724no—
685C2×C4—2368no—
686C2×C4—2362no—
687C2×C4—2362no—
688C2×C4—2362no—
689C2×C4C2×D4×D5912yes—
690C2×C4C2×D4×D5911yescharacteristic
691C2×C4C2×#1174568512yes—
692C2×C4#1427377512yes—
693C2×C4C24×D5911yescharacteristic
694C8—22no—
695C8—1182no—
696C8—1182no—
697C8C2×#1174568514yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—1182no—
703C22—1182no—
704C22—1182no—
705C22—4724no—
706C22—2362no—
707C22—2362no—
708C22—2362no—
709C22—2364no—
710C22#1683805312yes—
711C22#1683820112yes—
712C22#1683821212yes—
713C22C22×D4×D5911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—1182no—
720C4—1182no—
721C4—1182no—
722C4—2362no—
723C4—2362no—
724C4—2362no—
725C4#1683805312yes—
726C4C22×#1174568511yescharacteristic
727C4C2×#1427377511yescharacteristic
728C2—42no—
729C2—4722no—
730C2—2362no—
731C2#2143665714yesdirect product factor
732C2C2×#1683805311yescharacteristic
733C2C2×#1683820111yescharacteristic
734C2C2×#1683821211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#428C2
socleC23×C59C22×D4
prime radicalC2×#16838100C2
hypercenterC2×#428D59
hypocenterC59C2×#3351
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#16838091C2semidirect
3. #21436657C2direct (N × H)
4. C2×#16837803C2semidirect
5. C2×#16837722C2semidirect
6. C2×#16837745C2semidirect
7. C2×#16837726C2semidirect
8. C2×#16837732C2semidirect
9. C2×#16837712C2semidirect
10. C2×#16837705C2semidirect
11. C2×#16837649C2semidirect
12. C2×#16837648C2semidirect
13. C2×#16837489C2semidirect
14. C2×#16837478C2semidirect
15. C2×#16837441C2semidirect
16. C2×C59×#428C2semidirect
22. #16838091C22semidirect
42. #16837803C22semidirect
43. #16837745C22semidirect
44. #16837732C22semidirect
45. #16837726C22semidirect
46. #16837722C22semidirect
47. #16837712C22semidirect
48. #16837705C22semidirect
49. #16837649C22semidirect
50. #16837648C22semidirect
51. #16837489C22semidirect
52. #16837478C22semidirect
53. #16837441C22semidirect
72. C59×#428C22semidirect
376. C2×#428D59semidirect
378. C2×C59#3351semidirect
424. #428C2×D59semidirect
444. C59C2×#3351semidirect
731. C2#21436657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381002
C2×#168380912
#214366572
C2×#168378032
C2×#168377222
C2×#168377452
C2×#168377262
C2×#168377322
C2×#168377122
C2×#168377052
C2×#168376492
C2×#168376482
C2×#168374892
C2×#168374782
C2×#168374412
C2×C59×#4282
C2×#335159