Finite Group Databasebeta

← #28598330

Subgroups — #28598330

Order 15104.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837463C211yesmaximal, characteristic, complemented
2C2×#16837429C211yesmaximal, characteristic, complemented
3#21425037C211yesmaximal, characteristic, complemented
4#21425033C211yesmaximal, characteristic, complemented
5#21424895C211yesmaximal, characteristic, complemented
6#21424891C211yesmaximal, characteristic, complemented
7#21424394C211yesmaximal, characteristic, complemented
8#21424394C211yesmaximal, characteristic, complemented
9#21424389C211yesmaximal, characteristic, complemented
10#21424389C211yesmaximal, characteristic, complemented
11#21424080C211yesmaximal, characteristic, complemented
12#21424080C211yesmaximal, characteristic, complemented
13#21424076C211yesmaximal, characteristic, complemented
14#21424076C211yesmaximal, characteristic, complemented
15C2×C59×#529C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18#16837463—24no—
19#16837429—24no—
20C2×C4⋊(C59⋊C8)C2211yescharacteristic
21C2×C4⋊(C59⋊C8)C2211yescharacteristic
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23C2×C4⋊(C59⋊C8)C2211yescharacteristic
24C2×C4⋊(C59⋊C8)C2211yescharacteristic
25C2×C4⋊(C59⋊C8)C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×C22⋊(C59⋊C8)C2211yescharacteristic
28C2×C22⋊(C59⋊C8)C2211yescharacteristic
29C2×C22⋊(C59⋊C8)C2211yescharacteristic
30C2×C22⋊(C59⋊C8)C2211yescharacteristic
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×C22⋊(C59⋊C8)C2211yescharacteristic
34C2×C22⋊(C59⋊C8)C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837157C2211yescharacteristic
39#16837157C2211yescharacteristic
40#16837157C2211yescharacteristic
41#16837157C2211yescharacteristic
42#16837157C2211yescharacteristic
43#16837157C2211yescharacteristic
44#16837157C2211yescharacteristic
45#16837157C2211yescharacteristic
46C59×#529—24no—
47C59×#529—24no—
48C2×#126×C59C411yescharacteristic
49C2×#126×C59C411yescharacteristic
50C2×#125×C59C411yescharacteristic
51C2×#124×C59C411yescharacteristic
52C2×#123×C59C411yescharacteristic
53C2×#123×C59C411yescharacteristic
54C2×C22⋊Q8×C59C411yescharacteristic
55C2×#121×C59C411yescharacteristic
56C2×C4×Q8×C59C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C2×C4×D4×C59C2211yescharacteristic
59C2×C4×D4×C59C2211yescharacteristic
60C2×#117×C59C2211yescharacteristic
61C2×#117×C59C2211yescharacteristic
62C22×C42×C59C2211yescharacteristic
63C2×#11745664—22no—
64C2×#11745664—41no—
65C2×#11745664—41no—
66C22×C59⋊C8—22no—
67C22×C59⋊C8—41no—
68C22×C59⋊C8—41no—
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C22×C59⋊C8C2311yescharacteristic
77C4⋊(C59⋊C8)—22no—
78C4⋊(C59⋊C8)—22no—
79C4⋊(C59⋊C8)—22no—
80C4⋊(C59⋊C8)—22no—
81C4⋊(C59⋊C8)—22no—
82C4⋊(C59⋊C8)—22no—
83C22⋊(C59⋊C8)—22no—
84C22⋊(C59⋊C8)—22no—
85C22⋊(C59⋊C8)—41no—
86C22⋊(C59⋊C8)—41no—
87C22⋊(C59⋊C8)—41no—
88C22⋊(C59⋊C8)—41no—
89C22⋊(C59⋊C8)—41no—
90C22⋊(C59⋊C8)—41no—
91C22⋊(C59⋊C8)—41no—
92C22⋊(C59⋊C8)—41no—
93#14273638—22no—
94C4×C59⋊C8—22no—
95C22×Q8×C59C2×C411yescharacteristic
96C22×D4×C59C2×C411yescharacteristic
97C22×D4×C59C2×C411yescharacteristic
98C22×D4×C59C2×C411yescharacteristic
99C23×C4×C59C2×C411yescharacteristic
100C23×C4×C59C2×C411yescharacteristic
101C23×C4×C59C2311yescharacteristic
102C23×C4×C59C2311yescharacteristic
103C23×C4×C59C2311yescharacteristic
104#126×C59—24no—
105#126×C59—24no—
106#125×C59—24no—
107#124×C59—24no—
108#123×C59—24no—
109#123×C59—24no—
110C22⋊Q8×C59—24no—
111#121×C59—24no—
112C4×Q8×C59—22no—
113C4×Q8×C59—22no—
114C4×D4×C59—22no—
115C4×D4×C59—22no—
116C4×D4×C59—22no—
117C4×D4×C59—22no—
118C4×D4×C59—22no—
119C4×D4×C59—22no—
120#117×C59—22no—
121#117×C59—22no—
122#117×C59D414yes—
123#117×C59D414yes—
124C2×C4⋊C4×C59C2×C411yescharacteristic
125C2×C4⋊C4×C59C2×C411yescharacteristic
126C2×C4⋊C4×C59C2×C411yescharacteristic
127C2×C4⋊C4×C59C2×C411yescharacteristic
128C2×C4⋊C4×C59C2×C411yescharacteristic
129C2×C4⋊C4×C59C2×C411yescharacteristic
130C2×C4⋊C4×C59C2×C411yescharacteristic
131C2×C4⋊C4×C59C2×C411yescharacteristic
132C2×C4⋊C4×C59C2×C411yescharacteristic
133C2×C4⋊C4×C59C2×C411yescharacteristic
134C2×C22⋊C4×C59C2×C411yescharacteristic
135C2×C22⋊C4×C59C2×C411yescharacteristic
136C2×C22⋊C4×C59C2×C411yescharacteristic
137C2×C22⋊C4×C59C2×C411yescharacteristic
138C2×C22⋊C4×C59C2×C411yescharacteristic
139C2×C22⋊C4×C59C2×C411yescharacteristic
140C2×C22⋊C4×C59C2×C411yescharacteristic
141C2×C22⋊C4×C59C2×C411yescharacteristic
142C2×C22⋊C4×C59C2×C411yescharacteristic
143C2×C22⋊C4×C59C2×C411yescharacteristic
144C2×C42×C59—22no—
145C2×C42×C59—22no—
146C2×C42×C59C2×C411yescharacteristic
147C2×C42×C59C2×C411yescharacteristic
148C2×C42×C59C2311yescharacteristic
149C2×C42×C59C2311yescharacteristic
150C2×C42×C59C2311yescharacteristic
151C2×C42×C59C2311yescharacteristic
152C24×C59C22×C411yescharacteristic
153C24×C59C22×C411yescharacteristic
154C24×C59C22×C411yescharacteristic
155C2×Q8×C59—22no—
156C2×Q8×C59—22no—
157C2×Q8×C59—41no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—22no—
163C2×D4×C59—22no—
164C2×D4×C59—41no—
165C2×D4×C59—41no—
166C2×D4×C59—41no—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—22no—
172C22×C4×C59—22no—
173C22×C4×C59—22no—
174C22×C4×C59—22no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59—21no—
184C22×C4×C59—21no—
185C22×C4×C59—21no—
186C22×C4×C59—21no—
187C22×C4×C59—41no—
188C22×C4×C59—41no—
189C22×C4×C59C22×C411yescharacteristic
190C22×C4×C59C22×C411yescharacteristic
191C22×C4×C59C22×C411yescharacteristic
192C22×C4×C59C22×C411yescharacteristic
193C22×C4×C59C22×C411yescharacteristic
194C22×C4×C59C22×C411yescharacteristic
195C22×C4×C59C22×C411yescharacteristic
196C22×C4×C59C22×C411yescharacteristic
197C22×C4×C59C22×C411yescharacteristic
198C22×C4×C59C22×C411yescharacteristic
199C22×C4×C59C22×C411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2×D412yes—
202C22×C4×C59C2411yescharacteristic
203C4⋊C4×C59—22no—
204C4⋊C4×C59—22no—
205C4⋊C4×C59—22no—
206C4⋊C4×C59—22no—
207C4⋊C4×C59—22no—
208C4⋊C4×C59—22no—
209C4⋊C4×C59—22no—
210C4⋊C4×C59—22no—
211C4⋊C4×C59C22⋊C414yes—
212C4⋊C4×C59C22⋊C414yes—
213C22⋊C4×C59—22no—
214C22⋊C4×C59—22no—
215C22⋊C4×C59—22no—
216C22⋊C4×C59—22no—
217C22⋊C4×C59—22no—
218C22⋊C4×C59—22no—
219C22⋊C4×C59—22no—
220C22⋊C4×C59—22no—
221C22⋊C4×C59C22⋊C414yes—
222C22⋊C4×C59C22⋊C414yes—
223C42×C59—22no—
224C42×C59—22no—
225C42×C59—21no—
226C42×C59—21no—
227C42×C59—21no—
228C42×C59—21no—
229C42×C59C2×D412yes—
230C42×C59C2×D412yes—
231C42×C59C2×D412yes—
232C42×C59C2×D412yes—
233#11745664—44no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8—21no—
251C2×C59⋊C8—21no—
252C2×C59⋊C8—21no—
253C2×C59⋊C8—21no—
254C2×C59⋊C8—21no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—44no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59—21no—
262C23×C59—21no—
263C23×C59—21no—
264C23×C59—21no—
265C23×C59—21no—
266C23×C59—21no—
267C23×C59—21no—
268C23×C59—21no—
269C23×C59—21no—
270C23×C59—21no—
271C23×C59—21no—
272C23×C59—21no—
273C23×C59—21no—
274C23×C59—21no—
275C23×C59—21no—
276C23×C59—21no—
277C23×C59—21no—
278C23×C59C2×C22⋊C412yes—
279C23×C59#13112yes—
280C23×C59C23×C411yescharacteristic
281Q8×C59—44no—
282D4×C59—44no—
283D4×C59—44no—
284D4×C59—44no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—21no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—21no—
293C2×C4×C59—21no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—22no—
301C2×C4×C59—21no—
302C2×C4×C59—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—21no—
308C2×C4×C59—21no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—21no—
312C2×C4×C59—21no—
313C2×C4×C59—21no—
314C2×C4×C59—21no—
315C2×C4×C59—21no—
316C2×C4×C59—44no—
317C2×C4×C59—44no—
318C2×C4×C59—41no—
319C2×C4×C59—41no—
320C2×C4×C59—41no—
321C2×C4×C59—41no—
322C2×C4×C59—41no—
323C2×C4×C59—41no—
324C2×C4×C59—41no—
325C2×C4×C59—41no—
326C2×C4×C59C2×C22⋊C412yes—
327C2×C4×C59C2×C22⋊C412yes—
328C2×C4×C59C2×C22⋊C412yes—
329C2×C4×C59C2×C22⋊C412yes—
330C2×C4×C59C2×C22⋊C412yes—
331C2×C4×C59#13112yes—
332C2×C4×C59C22×D411yescharacteristic
333C2×C4×C59C22×D411yescharacteristic
334C2×C4×C59H(5,𝔽2)11yescharacteristic
335C2×C4×C59H(5,𝔽2)11yescharacteristic
336C2×C4×C592−1+411yescharacteristic
337C2×C4×C592−1+411yescharacteristic
338C59⋊C8—41no—
339C59⋊C8—41no—
340C59⋊C8—41no—
341C59⋊C8—41no—
342C59⋊C8—41no—
343C59⋊C8—41no—
344C59⋊C8—41no—
345C59⋊C8—41no—
346#21855—591nomaximal, Sylow
347C22×C59—22no—
348C22×C59—22no—
349C22×C59—22no—
350C22×C59—22no—
351C22×C59—22no—
352C22×C59—22no—
353C22×C59—41no—
354C22×C59—41no—
355C22×C59—41no—
356C22×C59—41no—
357C22×C59—41no—
358C22×C59—41no—
359C22×C59—41no—
360C22×C59—41no—
361C22×C59—41no—
362C22×C59—41no—
363C22×C59—41no—
364C22×C59—41no—
365C22×C59—41no—
366C22×C59—41no—
367C22×C59—41no—
368C22×C59C22×C22⋊C411yescharacteristic
369C22×C59#52011yescharacteristic
370C22×C59#52011yescharacteristic
371C22×C59C2×#13111yescharacteristic
372C22×C59C2×#13111yescharacteristic
373C22×C59#56811yescharacteristic
374C22×C59#56811yescharacteristic
375C4×C59—22no—
376C4×C59—22no—
377C4×C59—22no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—22no—
381C4×C59—41no—
382C4×C59—41no—
383C4×C59—41no—
384C4×C59—41no—
385C4×C59—41no—
386C4×C59#53511yescharacteristic
387C4×C59#53611yescharacteristic
388C4×C59#53711yescharacteristic
389C4×C59#53711yescharacteristic
390C2×#529D5911yescharacteristic
391C2×#433—591no—
392C2×#424—591no—
393#1985—591no—
394#1984—591no—
395#1955—591no—
396#1954—591no—
397#1870—591no—
398#1870—591no—
399#1869—591no—
400#1869—591no—
401#1798—591no—
402#1798—591no—
403#1797—591no—
404#1797—591no—
405C2×C59—42no—
406C2×C59—42no—
407C2×C59—81no—
408C2×C59#231111yescharacteristic
409C2×C59#288011yescharacteristic
410C2×C59#288011yescharacteristic
411C2×C59#299211yescharacteristic
412C2×C59#299311yescharacteristic
413C2×C59#299411yescharacteristic
414C2×C59#299511yescharacteristic
415C22×M16—591no—
416C23×C8—591no—
417#529—24no—
418#529—24no—
419C2×#126Dic5911yescharacteristic
420C2×#126Dic5911yescharacteristic
421C2×#125Dic5911yescharacteristic
422C2×#124Dic5911yescharacteristic
423C2×#123Dic5911yescharacteristic
424C2×#123Dic5911yescharacteristic
425C2×C22⋊Q8Dic5911yescharacteristic
426C2×#121Dic5911yescharacteristic
427C2×C4×Q8C2×D5911yescharacteristic
428C2×C4×D4C2×D5911yescharacteristic
429C2×C4×D4C2×D5911yescharacteristic
430C2×C4×D4C2×D5911yescharacteristic
431C2×#117C2×D5911yescharacteristic
432C2×#117C2×D5911yescharacteristic
433C22×C42C2×D5911yescharacteristic
434#433—1184no—
435#424—1184no—
436C2×C4⋊C8—591no—
437C2×C4⋊C8—591no—
438C2×C4⋊C8—591no—
439C2×C4⋊C8—591no—
440C2×C4⋊C8—591no—
441C2×C4⋊C8—591no—
442C2×C22⋊C8—591no—
443C2×C22⋊C8—591no—
444C2×C22⋊C8—591no—
445C2×C22⋊C8—591no—
446C2×C22⋊C8—591no—
447C2×C22⋊C8—591no—
448C2×C22⋊C8—591no—
449C2×C22⋊C8—591no—
450C2×C22⋊C8—591no—
451C2×C22⋊C8—591no—
452C2×#97—591no—
453C2×C4×C8—591no—
454#336—591no—
455#336—591no—
456#336—591no—
457#336—591no—
458#336—591no—
459#336—591no—
460#336—591no—
461#336—591no—
462C59#2185511yescharacteristic, complemented, Sylow
463C22×Q8C2×Dic5911yescharacteristic
464C22×D4C2×Dic5911yescharacteristic
465C22×D4C2×Dic5911yescharacteristic
466C22×D4C2×Dic5911yescharacteristic
467C23×C4C2×Dic5911yescharacteristic
468C23×C4C2×Dic5911yescharacteristic
469C23×C4C22×D5911yescharacteristic
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C2×M16—1182no—
473C2×M16—2361no—
474C2×M16—2361no—
475C22×C8—591no—
476C22×C8—591no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8—591no—
480C22×C8—591no—
481C22×C8—591no—
482C22×C8—591no—
483C22×C8—1182no—
484C22×C8—2361no—
485C22×C8—2361no—
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117C22⋊D5914yes—
505#117C22⋊D5914yes—
506C2×C4⋊C4C2×Dic5911yescharacteristic
507C2×C4⋊C4C2×Dic5911yescharacteristic
508C2×C4⋊C4C2×Dic5911yescharacteristic
509C2×C4⋊C4C2×Dic5911yescharacteristic
510C2×C4⋊C4C2×Dic5911yescharacteristic
511C2×C4⋊C4C2×Dic5911yescharacteristic
512C2×C4⋊C4C2×Dic5911yescharacteristic
513C2×C4⋊C4C2×Dic5911yescharacteristic
514C2×C4⋊C4C2×Dic5911yescharacteristic
515C2×C4⋊C4C2×Dic5911yescharacteristic
516C2×C22⋊C4C2×Dic5911yescharacteristic
517C2×C22⋊C4C2×Dic5911yescharacteristic
518C2×C22⋊C4C2×Dic5911yescharacteristic
519C2×C22⋊C4C2×Dic5911yescharacteristic
520C2×C22⋊C4C2×Dic5911yescharacteristic
521C2×C22⋊C4C2×Dic5911yescharacteristic
522C2×C22⋊C4C2×Dic5911yescharacteristic
523C2×C22⋊C4C2×Dic5911yescharacteristic
524C2×C22⋊C4C2×Dic5911yescharacteristic
525C2×C22⋊C4C2×Dic5911yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×Dic5911yescharacteristic
529C2×C42C2×Dic5911yescharacteristic
530C2×C42C22×D5911yescharacteristic
531C2×C42C22×D5911yescharacteristic
532C2×C42C22×D5911yescharacteristic
533C2×C42C22×D5911yescharacteristic
534C4⋊C8—1182no—
535C4⋊C8—1182no—
536C4⋊C8—1182no—
537C4⋊C8—1182no—
538C4⋊C8—1182no—
539C4⋊C8—1182no—
540C22⋊C8—1182no—
541C22⋊C8—1182no—
542C22⋊C8—2361no—
543C22⋊C8—2361no—
544C22⋊C8—2361no—
545C22⋊C8—2361no—
546C22⋊C8—2361no—
547C22⋊C8—2361no—
548C22⋊C8—2361no—
549C22⋊C8—2361no—
550#97—1182no—
551C4×C8—1182no—
552C24C22×Dic5911yescharacteristic
553C24C22×Dic5911yescharacteristic
554C24C22×Dic5911yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic5911yescharacteristic
590C22×C4C22×Dic5911yescharacteristic
591C22×C4C22×Dic5911yescharacteristic
592C22×C4C22×Dic5911yescharacteristic
593C22×C4C22×Dic5911yescharacteristic
594C22×C4C22×Dic5911yescharacteristic
595C22×C4C22×Dic5911yescharacteristic
596C22×C4C22×Dic5911yescharacteristic
597C22×C4C22×Dic5911yescharacteristic
598C22×C4C22×Dic5911yescharacteristic
599C22×C4C22×Dic5911yescharacteristic
600C22×C4C2×C22⋊D5912yes—
601C22×C4C2×C22⋊D5912yes—
602C22×C4C23×D5911yescharacteristic
603M16—2364no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—1181no—
613C2×C8—1181no—
614C2×C8—1181no—
615C2×C8—1181no—
616C2×C8—1181no—
617C2×C8—1181no—
618C2×C8—1181no—
619C2×C8—1181no—
620C2×C8—1181no—
621C2×C8—1181no—
622C2×C8—1181no—
623C2×C8—1181no—
624C2×C8—1181no—
625C2×C8—1181no—
626C2×C8—1181no—
627C2×C8—1181no—
628C2×C8—2364no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊Dic5914yes—
638C4⋊C4C22⋊Dic5914yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊Dic5914yes—
648C22⋊C4C22⋊Dic5914yes—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42C2×C22⋊D5912yes—
656C42C2×C22⋊D5912yes—
657C42C2×C22⋊D5912yes—
658C42C2×C22⋊D5912yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊Dic5912yes—
679C23#1427373412yes—
680C23C23×Dic5911yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊Dic5912yes—
727C2×C4C2×C22⋊Dic5912yes—
728C2×C4C2×C22⋊Dic5912yes—
729C2×C4C2×C22⋊Dic5912yes—
730C2×C4C2×C22⋊Dic5912yes—
731C2×C4#1427373412yes—
732C2×C4C22×C22⋊D5911yescharacteristic
733C2×C4C22×C22⋊D5911yescharacteristic
734C2×C4#1427377311yescharacteristic
735C2×C4#1427377311yescharacteristic
736C2×C4#1427377411yescharacteristic
737C2×C4#1427377411yescharacteristic
738C8—2361no—
739C8—2361no—
740C8—2361no—
741C8—2361no—
742C8—2361no—
743C8—2361no—
744C8—2361no—
745C8—2361no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊Dic5911yescharacteristic
768C22#1683788511yescharacteristic
769C22#1683788511yescharacteristic
770C22C2×#1427373411yescharacteristic
771C22C2×#1427373411yescharacteristic
772C22#1683816911yescharacteristic
773C22#1683816911yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#1683796611yescharacteristic
786C4#1683797311yescharacteristic
787C4#1683798011yescharacteristic
788C4#1683798011yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2142668811yescharacteristic
793C2#2143254511yescharacteristic
794C2#2143254511yescharacteristic
795C2#2143323511yescharacteristic
796C2#2143324511yescharacteristic
797C2#2143325611yescharacteristic
798C2#2143326611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC2×C59×#529C2
prime radicalC2×#121×C59C4
cosocleC22×C4×C59C24
hypercenterC2×#529D59
hypocenterC59#21855
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16837463C2semidirect
2. C2×#16837429C2semidirect
3. #21425037C2semidirect
4. #21425033C2semidirect
5. #21424895C2semidirect
6. #21424891C2semidirect
7. #21424394C2semidirect
8. #21424394C2semidirect
9. #21424389C2semidirect
10. #21424389C2semidirect
11. #21424080C2semidirect
12. #21424080C2semidirect
13. #21424076C2semidirect
14. #21424076C2semidirect
462. C59#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#168374632
C2×#168374292
#214250372
#214250332
#214248952
#214248912
#214243942
#214243892
#214240802
#214240762
C2×C59×#5292
#2185559