Finite Group Databasebeta

← #389×#595 #17962952

Subgroups — #389×#595 #17962952

Order 4352.

1918 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763760C211yesmaximal, characteristic
2C2×C4⋊C4×#595C212yesmaximal
3C2×C4⋊C4×#595C211yesmaximal, characteristic
4C2×C4⋊C4×#595C211yesmaximal, characteristic
5C2×C42×#595C211yesmaximal, characteristic
6#14543964C212yesmaximal
7#14543963C212yesmaximal
8#14543962C211yesmaximal, characteristic
9#14543961C211yesmaximal, characteristic
10#95×#595C212yesmaximal
11D17×#389C211yesmaximal, characteristic
12C22×C4⋊#595C2211yescharacteristic
13C22×C4⋊#595C2212yes—
14C22×C4⋊#595C2211yescharacteristic
15C22×C4×#595C2211yescharacteristic
16C22×C4×#595C2211yescharacteristic
17C22×C4×#595C2212yes—
18C22×C4×#595C2211yescharacteristic
19C22×C4×#595C2212yes—
20C22×C4×#595C2211yescharacteristic
21C22×C4×#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23#11763760C418yescomplemented
24C4⋊C4×#595—28no—
25C4⋊C4×#595—24no—
26C4⋊C4×#595C418yescomplemented
27C2×(C2×#595)⋊C4C2212yes—
28C2×(C2×#595)⋊C4C2212yes—
29C2×(C2×#595)⋊C4C2212yes—
30C2×(C2×#595)⋊C4C2212yes—
31C2×(C2×#595)⋊C4C2212yes—
32C2×(C2×#595)⋊C4C2212yes—
33C2×(C2×#595)⋊C4C2212yes—
34C42×#595—24no—
35C2×C4⋊C4×D17C2211yescharacteristic
36C2×C4⋊C4×D17C2212yes—
37C2×C4⋊C4×D17C2211yescharacteristic
38C2×C42×D17C2211yescharacteristic
39#11762708C411yescharacteristic, complemented
40#11762707C411yescharacteristic, complemented
41#11762706C412yescomplemented
42#11762705C411yescharacteristic, complemented
43#11762704C412yescomplemented
44#95×D17C2212yes—
45C17×#389C411yescharacteristic, complemented
46C23×#595C2312yes—
47C23×#595C2312yes—
48C23×#595C2311yescharacteristic
49C23×#595C2311yescharacteristic
50C23×#595C2311yescharacteristic
51C23×#595C2311yescharacteristic
52C22×C4×D17C2312yes—
53C22×C4×D17C2312yes—
54C22×C4×D17C2311yescharacteristic
55C22×C4×D17C2311yescharacteristic
56C22×C4×D17C2311yescharacteristic
57C2×C4⋊#595—24no—
58C2×C4⋊#595—24no—
59C2×C4⋊#595—22no—
60C2×C4⋊#595—22no—
61C2×C4⋊#595—22no—
62C2×C4⋊#595—22no—
63C2×C4⋊#595C2×C414yes—
64C2×C4⋊#595C2×C418yes—
65C2×C4⋊#595C2×C414yes—
66C2×C4×#595—22no—
67C2×C4×#595—22no—
68C2×C4×#595—22no—
69C2×C4×#595—22no—
70C2×C4×#595—24no—
71C2×C4×#595—22no—
72C2×C4×#595—22no—
73C2×C4×#595—24no—
74C2×C4×#595—22no—
75C2×C4×#595—22no—
76C2×C4×#595—22no—
77C2×C4×#595—22no—
78C2×C4×#595—22no—
79C2×C4×#595—22no—
80C2×C4×#595—24no—
81C2×C4×#595—24no—
82C2×C4×#595—24no—
83C2×C4×#595C2×C418yes—
84C2×C4×#595C2×C414yes—
85C2×C4×#595C2×C414yes—
86C2×C4×#595D414yes—
87C2×C4×#595D414yes—
88C2×C4×#595Q814yes—
89C2×C4×#595Q814yes—
90C2×C4⋊C4×C17C2×C412yes—
91C2×C4⋊C4×C17C2×C411yescharacteristic
92C2×C4⋊C4×C17C2×C411yescharacteristic
93C2×C42×C17C2×C411yescharacteristic
94C2×C4⋊Dic17C2×C412yes—
95C2×C4⋊Dic17C2×C411yescharacteristic
96C2×C4⋊Dic17C2×C411yescharacteristic
97C2×#63225C2×C412yes—
98C2×#63225C2×C412yes—
99C2×#63225C2×C412yes—
100C2×#63225C2×C412yes—
101C2×C4×Dic17C2×C411yescharacteristic
102C2×C4×Dic17C2×C411yescharacteristic
103C2×C4×Dic17C2×C411yescharacteristic
104C4⋊C4×D17—24no—
105C4⋊C4×D17—22no—
106C4⋊C4×D17—24no—
107C4⋊C4×D17—22no—
108C4⋊C4×D17C2×C414yes—
109C4⋊C4×D17C2×C414yes—
110C42×D17—22no—
111C42×D17—22no—
112(C2×#595)⋊C4—24no—
113(C2×#595)⋊C4—24no—
114(C2×#595)⋊C4—24no—
115(C2×#595)⋊C4—24no—
116(C2×#595)⋊C4—24no—
117(C2×#595)⋊C4C2×C418yes—
118(C2×#595)⋊C4C2×C418yes—
119C17×#95C2×C412yes—
120#10587502C2×C412yes—
121#10587502C2×C412yes—
122#10587502C2×C412yes—
123C23×D17C2411yescharacteristic
124C22×#595—21no—
125C22×#595—21no—
126C22×#595—21no—
127C22×#595—21no—
128C22×#595—21no—
129C22×#595—21no—
130C22×#595—21no—
131C22×#595—21no—
132C22×#595—21no—
133C22×#595—21no—
134C22×#595—21no—
135C22×#595—21no—
136C22×#595—22no—
137C22×#595—22no—
138C22×#595—22no—
139C22×#595—22no—
140C22×#595—22no—
141C22×#595—22no—
142C22×#595—22no—
143C22×#595—22no—
144C22×#595—22no—
145C22×#595—22no—
146C22×#595—22no—
147C22×#595—22no—
148C22×#595C22×C414yes—
149C22×#595C22×C414yes—
150C22×#595C22×C412yes—
151C22×#595C22×C412yes—
152C22×#595C22×C412yes—
153C22×#595C22×C412yes—
154C22×#595C2×D412yes—
155C22×#595C2×D412yes—
156C22×#595C2×D412yes—
157C22×#595C2×D412yes—
158C22×#595C2×Q812yes—
159C22×#595C2×Q812yes—
160C22×#595C2×Q812yes—
161C22×#595C2×Q812yes—
162C22×#595#4112yes—
163C22×#595#4112yes—
164C22×#595#4112yes—
165C22×#595#4112yes—
166C22×C4×C17C22×C412yes—
167C22×C4×C17C22×C412yes—
168C22×C4×C17C22×C411yescharacteristic
169C22×C4×C17C22×C411yescharacteristic
170C22×C4×C17C22×C411yescharacteristic
171C22×Dic17C22×C412yes—
172C22×Dic17C22×C412yes—
173C22×Dic17C22×C411yescharacteristic
174C22×Dic17C22×C411yescharacteristic
175C22×Dic17C22×C411yescharacteristic
176C2×C4×D17—21no—
177C2×C4×D17—21no—
178C2×C4×D17—22no—
179C2×C4×D17—22no—
180C2×C4×D17—21no—
181C2×C4×D17—21no—
182C2×C4×D17—21no—
183C2×C4×D17—21no—
184C2×C4×D17—22no—
185C2×C4×D17—21no—
186C2×C4×D17—21no—
187C2×C4×D17—22no—
188C2×C4×D17—22no—
189C2×C4×D17—22no—
190C2×C4×D17—22no—
191C2×C4×D17—22no—
192C2×C4×D17—22no—
193C2×C4×D17—22no—
194C2×C4×D17C22×C414yes—
195C2×C4×D17C22×C414yes—
196C2×C4×D17C22×C412yes—
197C2×C4×D17C22×C412yes—
198C2×C4×D17C2×D412yes—
199C2×C4×D17C2×D412yes—
200C2×C4×D17C2×Q812yes—
201C2×C4×D17C2×Q812yes—
202C2×C4×D17#4112yes—
203C2×C4×D17#4112yes—
204C2×C4×D17#4112yes—
205C2×C4×D17#4112yes—
206C4⋊#595—216no—
207C4⋊#595—28no—
208C4⋊#595—28no—
209C4×#595—28no—
210C4×#595—28no—
211C4×#595—216no—
212C4×#595—28no—
213C4×#595—28no—
214C4×#595—28no—
215C4×#595—48no—
216C4×#595C4⋊C4116yescomplemented
217C4⋊C4×C17—24no—
218C4⋊C4×C17—22no—
219C4⋊C4×C17C4214yescomplemented
220C42×C17—22no—
221C4⋊Dic17—22no—
222C4⋊Dic17—24no—
223C4⋊Dic17C4214yescomplemented
224#63225—24no—
225#63225—24no—
226#63225—24no—
227#63225C4218yescomplemented
228C4×Dic17—22no—
229C4×Dic17—22no—
230C4×Dic17—22no—
231C4×#389—171nomaximal, Sylow
232C23×C17C23×C411yescharacteristic
233C22×D17C23×C411yescharacteristic
234C22×D17C23×C411yescharacteristic
235C22×D17C22×D411yescharacteristic
236C22×D17C22×D411yescharacteristic
237C22×D17C22×Q811yescharacteristic
238C22×D17C22×Q811yescharacteristic
239C22×D17C2×#4111yescharacteristic
240C22×D17C2×#4111yescharacteristic
241C22×D17C2×#4111yescharacteristic
242C22×D17C2×#4111yescharacteristic
243C22×D17C2×#4111yescharacteristic
244C22×D17C2×#4111yescharacteristic
245C22×D17C2×#4111yescharacteristic
246C22×D17C2×#4111yescharacteristic
247C2×#595—22no—
248C2×#595—22no—
249C2×#595—22no—
250C2×#595—22no—
251C2×#595—22no—
252C2×#595—22no—
253C2×#595—22no—
254C2×#595—22no—
255C2×#595—22no—
256C2×#595—22no—
257C2×#595—22no—
258C2×#595—22no—
259C2×#595—22no—
260C2×#595—22no—
261C2×#595—22no—
262C2×#595—22no—
263C2×#595—22no—
264C2×#595—22no—
265C2×#595—24no—
266C2×#595—24no—
267C2×#595—24no—
268C2×#595—24no—
269C2×#595—24no—
270C2×#595—24no—
271C2×#595—42no—
272C2×#595—42no—
273C2×#595—42no—
274C2×#595—42no—
275C2×#595—42no—
276C2×#595—42no—
277C2×#595—42no—
278C2×#595—42no—
279C2×#595C2×C4⋊C414yes—
280C2×#595C2×C4⋊C414yes—
281C2×#595C4×D414yes—
282C2×#595C4×D414yes—
283C2×#595C4×Q814yes—
284C2×#595C4×Q814yes—
285C2×#595#12114yes—
286C2×#595C22⋊Q814yes—
287C2×#595#12514yes—
288C2×#595C4⋊Q814yes—
289C2×C4×C17—21no—
290C2×C4×C17—21no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—21no—
294C2×C4×C17—21no—
295C2×C4×C17—22no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17C2×C4214yes—
299C2×C4×C17C2×C4212yes—
300C2×C4×C17C4×D412yes—
301C2×C4×C17C4×D412yes—
302C2×C4×C17C4×Q812yes—
303C2×C4×C17C4×Q812yes—
304C2×Dic17—21no—
305C2×Dic17—21no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—21no—
309C2×Dic17—21no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17C2×C4214yes—
314C2×Dic17C2×C4212yes—
315C2×Dic17C4×D412yes—
316C2×Dic17C4×D412yes—
317C2×Dic17C4×Q812yes—
318C2×Dic17C4×Q812yes—
319C4×D17—24no—
320C4×D17—24no—
321C4×D17—24no—
322C4×D17—24no—
323C4×D17—22no—
324C4×D17—22no—
325C4×D17—22no—
326C4×D17—22no—
327C4×D17—22no—
328C4×D17—22no—
329C4×D17—22no—
330C4×D17—22no—
331C4×D17—42no—
332C4×D17—42no—
333C4×D17—42no—
334C4×D17—42no—
335C4×D17C2×C4⋊C414yes—
336C4×D17#11714yes—
337C4×D17C4×D414yes—
338C4×D17C4×Q814yes—
339C2×#389—171no—
340C2×#389—171no—
341C2×C4×C4⋊C4—171no—
342C2×C4×C4⋊C4—171no—
343C2×C4×C4⋊C4—172no—
344C2×C43—171no—
345#1436—172no—
346#1436—172no—
347C4⋊#95—171no—
348C4⋊#95—171no—
349C4×#95—172no—
350C22×C17C22×C4211yescharacteristic
351C22×C17C2×C4×D411yescharacteristic
352C22×C17C2×C4×D411yescharacteristic
353C22×C17C2×C4×Q811yescharacteristic
354C22×C17C2×C4×Q811yescharacteristic
355C22×C17C4×#4111yescharacteristic
356C22×C17C4×#4111yescharacteristic
357C2×D17C22×C4⋊C411yescharacteristic
358C2×D17C2×#11711yescharacteristic
359C2×D17C2×C4×D411yescharacteristic
360C2×D17C2×C4×D411yescharacteristic
361C2×D17C2×C4×D411yescharacteristic
362C2×D17C2×C4×Q811yescharacteristic
363C2×D17C2×C4×Q811yescharacteristic
364C2×D17C2×C4×Q811yescharacteristic
365C2×D17C4×#4111yescharacteristic
366C2×D17C4×#4111yescharacteristic
367C2×D17C4×#4111yescharacteristic
368C2×D17C4×#4111yescharacteristic
369C2×D17C2×#12111yescharacteristic
370C2×D17C2×C22⋊Q811yescharacteristic
371C2×D17#52511yescharacteristic
372C2×D17#52511yescharacteristic
373C2×D17C2×#12511yescharacteristic
374C2×D17#52911yescharacteristic
375C2×D17#52911yescharacteristic
376C2×D17#52911yescharacteristic
377C2×D17#52911yescharacteristic
378C2×D17C2×C4⋊Q811yescharacteristic
379C2×D17#53211yescharacteristic
380C2×D17#53211yescharacteristic
381C2×D17#53311yescharacteristic
382C2×D17#53311yescharacteristic
383C2×D17#53311yescharacteristic
384C2×D17#53311yescharacteristic
385#595—24no—
386#595—24no—
387#595—24no—
388#595—44no—
389#595—44no—
390#595#38918yesdirect product factor
391C4×C17—24no—
392C4×C17—22no—
393C4×C17—22no—
394C4×C17—42no—
395C4×C17C4×C4⋊C414yescomplemented
396Dic17—24no—
397Dic17—22no—
398Dic17—22no—
399Dic17—42no—
400Dic17C4×C4⋊C414yescomplemented
401C22×C4⋊C4—171no—
402C22×C4⋊C4—171no—
403C22×C4⋊C4—171no—
404C22×C4⋊C4—172no—
405C22×C4⋊C4—171no—
406C22×C4⋊C4—172no—
407C22×C42—171no—
408C22×C42—171no—
409C22×C42—172no—
410C22×C42—171no—
411C22×C42—171no—
412C22×C42—171no—
413C22×C42—172no—
414C22×C42—171no—
415C22×C42—171no—
416#389—178no—
417#389—172no—
418#389—171no—
419#389—171no—
420#389—171no—
421#389—172no—
422#389#59511yescharacteristic, direct product factor
423C4×C4⋊C4—178no—
424C4×C4⋊C4—344no—
425C4×C4⋊C4—348no—
426C2×#95—172no—
427C2×#95—172no—
428C2×#95—172no—
429C2×#95—172no—
430C2×#95—172no—
431C2×#95—172no—
432C2×#95—172no—
433C2×#95—172no—
434C43—344no—
435C2×C17C2×C4×C4⋊C411yescharacteristic
436C2×C17C42×D411yescharacteristic
437C2×C17C42×Q811yescharacteristic
438C2×C17C4×#12111yescharacteristic
439C2×C17C4×C22⋊Q811yescharacteristic
440C2×C17C4×#12511yescharacteristic
441C2×C17C4×C4⋊Q811yescharacteristic
442D17C2×#38911yescharacteristic
443D17#229311yescharacteristic
444D17#229511yescharacteristic
445D17#229611yescharacteristic
446D17C4×#12111yescharacteristic
447D17C4×C22⋊Q811yescharacteristic
448D17C4×#12511yescharacteristic
449D17C4×C4⋊Q811yescharacteristic
450C23×C4—171no—
451C23×C4—171no—
452C23×C4—171no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—172no—
456C23×C4—171no—
457C23×C4—171no—
458C23×C4—172no—
459C23×C4—172no—
460C23×C4—172no—
461C2×C4⋊C4—172no—
462C2×C4⋊C4—171no—
463C2×C4⋊C4—174no—
464C2×C4⋊C4—174no—
465C2×C4⋊C4—174no—
466C2×C4⋊C4—174no—
467C2×C4⋊C4—178no—
468C2×C4⋊C4—172no—
469C2×C4⋊C4—172no—
470C2×C4⋊C4—172no—
471C2×C4⋊C4—172no—
472C2×C4⋊C4—171no—
473C2×C4⋊C4—342no—
474C2×C4⋊C4—344no—
475C2×C4⋊C4—342no—
476C2×C4⋊C4—344no—
477C2×C4⋊C4—342no—
478C2×C4⋊C4—342no—
479C2×C4⋊C4—342no—
480C2×C4⋊C4—344no—
481C2×C4⋊C4—342no—
482C2×C4⋊C4—344no—
483C2×C4⋊C4C2×#59511yescharacteristic
484C2×C4⋊C4C2×#59512yes—
485C2×C4⋊C4C2×#59511yescharacteristic
486C2×C42—174no—
487C2×C42—174no—
488C2×C42—174no—
489C2×C42—178no—
490C2×C42—174no—
491C2×C42—174no—
492C2×C42—174no—
493C2×C42—171no—
494C2×C42—171no—
495C2×C42—171no—
496C2×C42—342no—
497C2×C42—342no—
498C2×C42—342no—
499C2×C42—342no—
500C2×C42—342no—
501C2×C42—342no—
502C2×C42—342no—
503C2×C42—344no—
504C2×C42—342no—
505C2×C42—342no—
506C2×C42—344no—
507C2×C42—342no—
508C2×C42—342no—
509C2×C42—342no—
510C2×C42—342no—
511C2×C42—342no—
512C2×C42—344no—
513C2×C42—344no—
514C2×C42—344no—
515C2×C42C2×#59511yescharacteristic
516#95—178no—
517#95—178no—
518#95—172no—
519#95—172no—
520#95—172no—
521#95—344no—
522#95—344no—
523#95—344no—
524#95—344no—
525#95—344no—
526#95C2×#59512yes—
527C17C4×#38911yescharacteristic, complemented, Sylow
528C24—171no—
529C22×C4—172no—
530C22×C4—172no—
531C22×C4—172no—
532C22×C4—172no—
533C22×C4—172no—
534C22×C4—172no—
535C22×C4—172no—
536C22×C4—171no—
537C22×C4—172no—
538C22×C4—172no—
539C22×C4—172no—
540C22×C4—172no—
541C22×C4—172no—
542C22×C4—172no—
543C22×C4—172no—
544C22×C4—172no—
545C22×C4—172no—
546C22×C4—172no—
547C22×C4—172no—
548C22×C4—172no—
549C22×C4—172no—
550C22×C4—172no—
551C22×C4—172no—
552C22×C4—171no—
553C22×C4—172no—
554C22×C4—171no—
555C22×C4—174no—
556C22×C4—174no—
557C22×C4—172no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—172no—
561C22×C4—174no—
562C22×C4—174no—
563C22×C4—172no—
564C22×C4—341no—
565C22×C4—341no—
566C22×C4—342no—
567C22×C4—341no—
568C22×C4—341no—
569C22×C4—342no—
570C22×C4—341no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4—341no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—341no—
583C22×C4—341no—
584C22×C4—341no—
585C22×C4—341no—
586C22×C4—341no—
587C22×C4—341no—
588C22×C4—341no—
589C22×C4—341no—
590C22×C4—341no—
591C22×C4—341no—
592C22×C4—341no—
593C22×C4—341no—
594C22×C4—342no—
595C22×C4—342no—
596C22×C4—342no—
597C22×C4—342no—
598C22×C4—342no—
599C22×C4—342no—
600C22×C4—342no—
601C22×C4—342no—
602C22×C4—342no—
603C22×C4—342no—
604C22×C4—342no—
605C22×C4—342no—
606C22×C4C22×#59512yes—
607C22×C4C22×#59512yes—
608C22×C4C22×#59511yescharacteristic
609C22×C4C22×#59511yescharacteristic
610C22×C4C22×#59511yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—178no—
614C4⋊C4—174no—
615C4⋊C4—344no—
616C4⋊C4—344no—
617C4⋊C4—344no—
618C4⋊C4—348no—
619C4⋊C4—348no—
620C4⋊C4—3416no—
621C4⋊C4—344no—
622C4⋊C4—342no—
623C4⋊C4C4×#59514yescomplemented
624C42—22no—
625C42—1716no—
626C42—342no—
627C42—342no—
628C42—3416no—
629C42—348no—
630C42—348no—
631C42—348no—
632C42—348no—
633C42—348no—
634C42—342no—
635C42—688no—
636C23—171no—
637C23—171no—
638C23—171no—
639C23—171no—
640C23—171no—
641C23—171no—
642C23—171no—
643C23—171no—
644C23—171no—
645C23—171no—
646C23—171no—
647C23—171no—
648C23—171no—
649C23—171no—
650C23C23×#59511yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—174no—
661C2×C4—174no—
662C2×C4—174no—
663C2×C4—174no—
664C2×C4—174no—
665C2×C4—174no—
666C2×C4—174no—
667C2×C4—172no—
668C2×C4—172no—
669C2×C4—172no—
670C2×C4—174no—
671C2×C4—174no—
672C2×C4—174no—
673C2×C4—174no—
674C2×C4—174no—
675C2×C4—174no—
676C2×C4—174no—
677C2×C4—174no—
678C2×C4—172no—
679C2×C4—172no—
680C2×C4—344no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—344no—
686C2×C4—344no—
687C2×C4—344no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—342no—
696C2×C4—342no—
697C2×C4—342no—
698C2×C4—342no—
699C2×C4—342no—
700C2×C4—342no—
701C2×C4—342no—
702C2×C4—342no—
703C2×C4—342no—
704C2×C4—342no—
705C2×C4—342no—
706C2×C4—342no—
707C2×C4—342no—
708C2×C4—342no—
709C2×C4—342no—
710C2×C4—341no—
711C2×C4—341no—
712C2×C4—342no—
713C2×C4—342no—
714C2×C4—341no—
715C2×C4—341no—
716C2×C4—344no—
717C2×C4—344no—
718C2×C4—344no—
719C2×C4—344no—
720C2×C4—344no—
721C2×C4—344no—
722C2×C4—342no—
723C2×C4—342no—
724C2×C4—342no—
725C2×C4—682no—
726C2×C4—682no—
727C2×C4—682no—
728C2×C4—682no—
729C2×C4—682no—
730C2×C4—682no—
731C2×C4—682no—
732C2×C4—682no—
733C2×C4—682no—
734C2×C4—682no—
735C2×C4—682no—
736C2×C4—682no—
737C2×C4C2×C4×#59514yes—
738C2×C4C2×C4×#59512yes—
739C2×C4D4×#59512yes—
740C2×C4D4×#59512yes—
741C2×C4Q8×#59512yes—
742C2×C4Q8×#59512yes—
743C22—171no—
744C22—171no—
745C22—171no—
746C22—171no—
747C22—171no—
748C22—171no—
749C22—171no—
750C22—171no—
751C22—171no—
752C22—171no—
753C22—171no—
754C22—171no—
755C22—171no—
756C22—171no—
757C22—171no—
758C22—171no—
759C22—171no—
760C22—171no—
761C22—171no—
762C22—171no—
763C22—171no—
764C22—171no—
765C22—171no—
766C22—171no—
767C22—171no—
768C22—171no—
769C22—171no—
770C22—171no—
771C22C22×C4×#59511yescharacteristic
772C22C2×D4×#59511yescharacteristic
773C22C2×D4×#59511yescharacteristic
774C22C2×Q8×#59511yescharacteristic
775C22C2×Q8×#59511yescharacteristic
776C22#41×#59511yescharacteristic
777C22#41×#59511yescharacteristic
778C4—24no—
779C4—22no—
780C4—22no—
781C4—42no—
782C4—178no—
783C4—174no—
784C4—344no—
785C4—344no—
786C4—344no—
787C4—344no—
788C4—342no—
789C4—342no—
790C4—684no—
791C4—684no—
792C4—682no—
793C4C4⋊C4×#59514yescomplemented
794C2—171no—
795C2—171no—
796C2—171no—
797C2—171no—
798C2—171no—
799C2—171no—
800C2—171no—
801C2—171no—
802C2C2×C4⋊C4×#59511yescharacteristic
803C2C4×D4×#59511yescharacteristic
804C2C4×Q8×#59511yescharacteristic
805C2#121×#59511yescharacteristic
806C2C22⋊Q8×#59511yescharacteristic
807C2#125×#59511yescharacteristic
808C2C4⋊Q8×#59511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#389C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#389#595
hypocenterC17C4×#389
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
23. #11763760C4semidirect
26. C4⋊C4×#595C4semidirect
39. #11762708C4semidirect
40. #11762707C4semidirect
41. #11762706C4semidirect
42. #11762705C4semidirect
43. #11762704C4semidirect
45. C17×#389C4semidirect
216. C4×#595C4⋊C4semidirect
219. C4⋊C4×C17C42semidirect
223. C4⋊Dic17C42semidirect
227. #63225C42semidirect
390. #595#389direct (N × H)
395. C4×C17C4×C4⋊C4semidirect
400. Dic17C4×C4⋊C4semidirect
422. #389#595direct (N × H)
527. C17C4×#389semidirect
623. C4⋊C4C4×#595semidirect
793. C4C4⋊C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637602
C2×C4⋊C4×#5952
C2×C42×#5952
#145439642
#145439632
#145439622
#145439612
#95×#5952
D17×#3892
C4×#38917