Finite Group Databasebeta

← #16956730

Subgroups — #16956730

Order 4352.

1710 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic34C211yesmaximal, characteristic
2C2×#11762674C211yesmaximal, characteristic
3C2×C4⋊C4×Dic17C211yesmaximal, characteristic
4#14527054C212yesmaximal
5#14527050C212yesmaximal
6#14527018C212yesmaximal
7#14527015C212yesmaximal
8#14527014C211yesmaximal, characteristic
9#14527013C211yesmaximal, characteristic
10#14527013C211yesmaximal, characteristic
11C17×C4⋊#95C211yesmaximal, characteristic
12C23×Dic34C2211yescharacteristic
13C2×C4×Dic34—24no—
14C2×C4×Dic34—24no—
15C2×C4×Dic34C418yescomplemented
16C22×C4⋊Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×C4×Dic17C2211yescharacteristic
22C22×C4×Dic17C2212yes—
23C22×C4×Dic17C2211yescharacteristic
24#11762674—24no—
25C4⋊C4×Dic17—24no—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2212yes—
29C2×#10587502C2212yes—
30C2×#10587502C2212yes—
31C2×#10587502C2212yes—
32C2×#10587502C2212yes—
33C2×#10587502C2212yes—
34C2×#10587502C2212yes—
35C22×C4⋊C4×C17C2211yescharacteristic
36C22×C4⋊C4×C17C2211yescharacteristic
37C22×C42×C17C2211yescharacteristic
38C2×C17×#95C2212yes—
39C2×C17×#95C2212yes—
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2312yes—
43C23×C4×C17C2311yescharacteristic
44C23×C4×C17C2311yescharacteristic
45C23×Dic17C2312yes—
46C23×Dic17C2311yescharacteristic
47C23×Dic17C2312yes—
48C23×Dic17C2311yescharacteristic
49C23×Dic17C2311yescharacteristic
50C23×Dic17C2311yescharacteristic
51C22×Dic34—22no—
52C22×Dic34—22no—
53C22×Dic34—22no—
54C22×Dic34—22no—
55C22×Dic34—22no—
56C22×Dic34—22no—
57C22×Dic34C2×C414yes—
58C2×C4⋊C4×C17—22no—
59C2×C4⋊C4×C17—22no—
60C2×C4⋊C4×C17—22no—
61C2×C4⋊C4×C17—22no—
62C2×C4⋊C4×C17—22no—
63C2×C4⋊C4×C17Q814yescomplemented
64C2×C42×C17—22no—
65C2×C42×C17—22no—
66C2×C42×C17C2×C414yes—
67C2×C4⋊Dic17—22no—
68C2×C4⋊Dic17—22no—
69C2×C4⋊Dic17—22no—
70C2×C4⋊Dic17—22no—
71C2×C4⋊Dic17—22no—
72C2×C4⋊Dic17—22no—
73C2×C4⋊Dic17—22no—
74C2×C4⋊Dic17C2×C414yes—
75C2×C4⋊Dic17Q814yescomplemented
76C2×#63225—22no—
77C2×#63225—22no—
78C2×#63225—22no—
79C2×#63225—22no—
80C2×#63225C2×C414yes—
81C2×#63225C2×C414yes—
82C2×C4×Dic17—22no—
83C2×C4×Dic17—22no—
84C2×C4×Dic17—24no—
85C2×C4×Dic17—42no—
86C2×C4×Dic17—42no—
87C2×C4×Dic17C2×C414yes—
88C2×C4×Dic17C2×C414yes—
89C2×C4×Dic17D414yes—
90C2×C4×Dic17D414yes—
91C4×Dic34—232no—
92C17×#95—24no—
93C17×#95—42no—
94#10587502—24no—
95#10587502—24no—
96#10587502—24no—
97#10587502—24no—
98#10587502—24no—
99#10587502—24no—
100#10587502—42no—
101#10587502—42no—
102#10587502—42no—
103C24×C17C2411yescharacteristic
104C22×C4×C17—21no—
105C22×C4×C17—21no—
106C22×C4×C17—21no—
107C22×C4×C17—21no—
108C22×C4×C17—22no—
109C22×C4×C17—21no—
110C22×C4×C17—21no—
111C22×C4×C17—22no—
112C22×C4×C17—22no—
113C22×C4×C17—22no—
114C22×C4×C17—21no—
115C22×C4×C17—22no—
116C22×C4×C17—21no—
117C22×C4×C17—22no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—22no—
121C22×C4×C17—22no—
122C22×C4×C17—22no—
123C22×C4×C17—22no—
124C22×C4×C17—22no—
125C22×C4×C17—22no—
126C22×C4×C17—22no—
127C22×C4×C17C22×C412yes—
128C22×C4×C17C22×C412yes—
129C22×C4×C17C22×C412yes—
130C22×C4×C17C2×D412yes—
131C22×C4×C17C2×D412yes—
132C22×C4×C17C2×Q814yes—
133C22×C4×C17C2×Q812yes—
134C22×C4×C17C2×Q812yes—
135C22×C4×C17#4112yes—
136C22×C4×C17#4112yes—
137C22×C4×C17#4112yes—
138C22×C4×C17#4112yes—
139C22×Dic17—21no—
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17—21no—
143C22×Dic17—21no—
144C22×Dic17—21no—
145C22×Dic17—21no—
146C22×Dic17—21no—
147C22×Dic17—21no—
148C22×Dic17—21no—
149C22×Dic17—21no—
150C22×Dic17—21no—
151C22×Dic17—22no—
152C22×Dic17—21no—
153C22×Dic17—21no—
154C22×Dic17—22no—
155C22×Dic17—22no—
156C22×Dic17—22no—
157C22×Dic17—21no—
158C22×Dic17—21no—
159C22×Dic17—22no—
160C22×Dic17—22no—
161C22×Dic17—21no—
162C22×Dic17—21no—
163C22×Dic17—22no—
164C22×Dic17—22no—
165C22×Dic17—22no—
166C22×Dic17—22no—
167C22×Dic17—22no—
168C22×Dic17—22no—
169C22×Dic17—22no—
170C22×Dic17C22×C412yes—
171C22×Dic17C22×C412yes—
172C22×Dic17C22×C412yes—
173C22×Dic17C22×C412yes—
174C22×Dic17C2×D412yes—
175C22×Dic17C2×D412yes—
176C22×Dic17C2×D412yes—
177C22×Dic17C2×D412yes—
178C22×Dic17C2×Q814yes—
179C22×Dic17#4112yes—
180C22×Dic17#4112yes—
181C2×Dic34—28no—
182C2×Dic34—28no—
183C2×Dic34—28no—
184C2×Dic34—28no—
185C2×Dic34—28no—
186C2×Dic34—28no—
187C2×Dic34—28no—
188C4⋊C4×C17—28no—
189C4⋊C4×C17—44no—
190C42×C17—28no—
191C4⋊Dic17—28no—
192C4⋊Dic17—28no—
193C4⋊Dic17—44no—
194#63225—28no—
195#63225—28no—
196C4×Dic17—28no—
197C4×Dic17—48no—
198C4×Dic17C22⋊C4116yes—
199#13925—171nomaximal, Sylow
200C23×C17C23×C411yescharacteristic
201C23×C17C22×D411yescharacteristic
202C23×C17C22×D411yescharacteristic
203C23×C17C22×Q811yescharacteristic
204C23×C17C22×Q811yescharacteristic
205C23×C17C2×#4111yescharacteristic
206C23×C17C2×#4111yescharacteristic
207C23×C17C2×#4111yescharacteristic
208C23×C17C2×#4111yescharacteristic
209C23×C17C2×#4111yescharacteristic
210C23×C17C2×#4111yescharacteristic
211C23×C17H(5,𝔽2)11yescharacteristic
212C23×C17H(5,𝔽2)11yescharacteristic
213C23×C172−1+411yescharacteristic
214C23×C172−1+411yescharacteristic
215C2×C4×C17—22no—
216C2×C4×C17—22no—
217C2×C4×C17—22no—
218C2×C4×C17—22no—
219C2×C4×C17—22no—
220C2×C4×C17—22no—
221C2×C4×C17—22no—
222C2×C4×C17—22no—
223C2×C4×C17—22no—
224C2×C4×C17—24no—
225C2×C4×C17—24no—
226C2×C4×C17—24no—
227C2×C4×C17—42no—
228C2×C4×C17—41no—
229C2×C4×C17—42no—
230C2×C4×C17—41no—
231C2×C4×C17—41no—
232C2×C4×C17—41no—
233C2×C4×C17—42no—
234C2×C4×C17—42no—
235C2×C4×C17—42no—
236C2×C4×C17—42no—
237C2×C4×C17—42no—
238C2×C4×C17—42no—
239C2×C4×C17—42no—
240C2×C4×C17—42no—
241C2×C4×C17—42no—
242C2×C4×C17C2×C22⋊C414yes—
243C2×C4×C17#11714yes—
244C2×C4×C17C4×Q814yes—
245C2×C4×C17C4×Q814yes—
246C2×C4×C17C22⋊Q814yes—
247C2×C4×C17C22⋊Q814yes—
248C2×C4×C17#12414yes—
249C2×C4×C17C4⋊Q814yes—
250C2×Dic17—22no—
251C2×Dic17—22no—
252C2×Dic17—22no—
253C2×Dic17—22no—
254C2×Dic17—22no—
255C2×Dic17—22no—
256C2×Dic17—22no—
257C2×Dic17—22no—
258C2×Dic17—22no—
259C2×Dic17—22no—
260C2×Dic17—22no—
261C2×Dic17—22no—
262C2×Dic17—22no—
263C2×Dic17—22no—
264C2×Dic17—22no—
265C2×Dic17—22no—
266C2×Dic17—22no—
267C2×Dic17—22no—
268C2×Dic17—22no—
269C2×Dic17—22no—
270C2×Dic17—22no—
271C2×Dic17—24no—
272C2×Dic17—24no—
273C2×Dic17—24no—
274C2×Dic17—42no—
275C2×Dic17—41no—
276C2×Dic17—42no—
277C2×Dic17—41no—
278C2×Dic17—41no—
279C2×Dic17—41no—
280C2×Dic17—42no—
281C2×Dic17—42no—
282C2×Dic17—42no—
283C2×Dic17—42no—
284C2×Dic17—42no—
285C2×Dic17—42no—
286C2×Dic17—42no—
287C2×Dic17—42no—
288C2×Dic17—42no—
289C2×Dic17C2×C22⋊C414yes—
290C2×Dic17C2×C22⋊C414yes—
291C2×Dic17#11714yes—
292Dic34—232no—
293C22×C4×Q8—171no—
294C2×#382—171no—
295C2×C4×C4⋊C4—171no—
296#1446—172no—
297#1445—172no—
298#1436—172no—
299#1436—172no—
300C4⋊#95—171no—
301C4⋊#95—171no—
302C4⋊#95—171no—
303C4⋊#95D1711yescharacteristic
304C22×C17C22×C22⋊C411yescharacteristic
305C22×C17C2×#11711yescharacteristic
306C22×C17C2×#11711yescharacteristic
307C22×C17C2×C4×Q811yescharacteristic
308C22×C17C2×C4×Q811yescharacteristic
309C22×C17#52011yescharacteristic
310C22×C17#52011yescharacteristic
311C22×C17C2×C22⋊Q811yescharacteristic
312C22×C17C2×C22⋊Q811yescharacteristic
313C22×C17#52511yescharacteristic
314C22×C17#52511yescharacteristic
315C22×C17#52511yescharacteristic
316C22×C17#52511yescharacteristic
317C22×C17C2×#12411yescharacteristic
318C22×C17C2×C4⋊Q811yescharacteristic
319C22×C17#53511yescharacteristic
320C22×C17#53611yescharacteristic
321C22×C17#53711yescharacteristic
322C22×C17#53711yescharacteristic
323C22×C17#55411yescharacteristic
324C22×C17#55411yescharacteristic
325C22×C17#55411yescharacteristic
326C22×C17#55411yescharacteristic
327C22×C17#55611yescharacteristic
328C22×C17#55611yescharacteristic
329C22×C17#55611yescharacteristic
330C22×C17#55611yescharacteristic
331C22×C17#55711yescharacteristic
332C22×C17#55711yescharacteristic
333C22×C17#55711yescharacteristic
334C22×C17#55711yescharacteristic
335C22×C17#55911yescharacteristic
336C22×C17#55911yescharacteristic
337C22×C17#55911yescharacteristic
338C22×C17#55911yescharacteristic
339C4×C17—24no—
340C4×C17—42no—
341C4×C17—44no—
342C4×C17—82no—
343C4×C17#39118yes—
344Dic17—24no—
345Dic17—24no—
346Dic17—24no—
347Dic17—42no—
348Dic17—44no—
349Dic17—82no—
350C23×Q8—171no—
351C2×C4×Q8—178no—
352C2×C4×Q8—344no—
353C2×C4×Q8—344no—
354C22×C4⋊C4—171no—
355C22×C4⋊C4—171no—
356C22×C4⋊C4—171no—
357C22×C4⋊C4—171no—
358C22×C4⋊C4—171no—
359C22×C4⋊C4C2×D1711yescharacteristic
360C22×C4⋊C4C2×D1711yescharacteristic
361C22×C42—171no—
362C22×C42—171no—
363C22×C42—172no—
364C22×C42C2×D1711yescharacteristic
365#382—344no—
366C4×C4⋊C4—344no—
367C2×#95—172no—
368C2×#95—172no—
369C2×#95—172no—
370C2×#95—172no—
371C2×#95—172no—
372C2×#95—172no—
373C2×#95—172no—
374C2×#95—172no—
375C2×#95—172no—
376C2×#95C2×D1712yes—
377C2×#95C2×D1712yes—
378C2×C17#228011yescharacteristic
379C2×C17C2×#39111yescharacteristic
380C2×C17#231111yescharacteristic
381C2×C17#235511yescharacteristic
382C2×C17#235511yescharacteristic
383C2×C17#235511yescharacteristic
384C2×C17#235511yescharacteristic
385C2×C17#258011yescharacteristic
386C2×C17#258011yescharacteristic
387C2×C17#258111yescharacteristic
388C2×C17#258111yescharacteristic
389C2×C17#258411yescharacteristic
390C2×C17#258411yescharacteristic
391C2×C17#259211yescharacteristic
392C2×C17#259211yescharacteristic
393C22×Q8—174no—
394C22×Q8—342no—
395C22×Q8—342no—
396C22×Q8—342no—
397C22×Q8—342no—
398C22×Q8—342no—
399C22×Q8—342no—
400C23×C4—171no—
401C23×C4—171no—
402C23×C4—171no—
403C23×C4—171no—
404C23×C4—172no—
405C23×C4—172no—
406C23×C4C22×D1712yes—
407C23×C4C22×D1712yes—
408C23×C4C22×D1711yescharacteristic
409C23×C4C22×D1711yescharacteristic
410C23×C4C22×D1711yescharacteristic
411C4×Q8—3432no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—174no—
418C2×C4⋊C4—174no—
419C2×C4⋊C4—174no—
420C2×C4⋊C4—174no—
421C2×C4⋊C4—342no—
422C2×C4⋊C4—342no—
423C2×C4⋊C4—342no—
424C2×C4⋊C4—342no—
425C2×C4⋊C4—342no—
426C2×C4⋊C4—342no—
427C2×C4⋊C4—342no—
428C2×C4⋊C4—342no—
429C2×C4⋊C4—342no—
430C2×C4⋊C4—342no—
431C2×C4⋊C4—342no—
432C2×C4⋊C4Dic3414yescomplemented
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—174no—
436C2×C42—174no—
437C2×C42—174no—
438C2×C42—174no—
439C2×C42—342no—
440C2×C42—342no—
441C2×C42—344no—
442C2×C42—682no—
443C2×C42—682no—
444C2×C42C4×D1714yes—
445#95—24no—
446#95—42no—
447#95—344no—
448#95—344no—
449#95—344no—
450#95—344no—
451#95—344no—
452#95—344no—
453#95—682no—
454#95—682no—
455#95—682no—
456C17#1392511yescharacteristic, complemented, Sylow
457C24C23×D1711yescharacteristic
458C2×Q8—348no—
459C2×Q8—348no—
460C2×Q8—348no—
461C2×Q8—348no—
462C2×Q8—348no—
463C2×Q8—348no—
464C2×Q8—348no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—172no—
489C22×C4—172no—
490C22×C4—172no—
491C22×C4—172no—
492C22×C4—172no—
493C22×C4—172no—
494C22×C4—172no—
495C22×C4—172no—
496C22×C4—172no—
497C22×C4—172no—
498C22×C4—174no—
499C22×C4—341no—
500C22×C4—341no—
501C22×C4—341no—
502C22×C4—341no—
503C22×C4—341no—
504C22×C4—341no—
505C22×C4—341no—
506C22×C4—341no—
507C22×C4—341no—
508C22×C4—341no—
509C22×C4—341no—
510C22×C4—341no—
511C22×C4—342no—
512C22×C4—342no—
513C22×C4—341no—
514C22×C4—341no—
515C22×C4—341no—
516C22×C4—342no—
517C22×C4—342no—
518C22×C4—341no—
519C22×C4—342no—
520C22×C4—341no—
521C22×C4—342no—
522C22×C4—341no—
523C22×C4—342no—
524C22×C4—342no—
525C22×C4—342no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4C2×Dic3414yes—
531C22×C4C2×Dic3412yes—
532C22×C4C2×C4×D1712yes—
533C22×C4C2×C4×D1712yes—
534C22×C4C2×C4×D1712yes—
535C22×C4#6325212yes—
536C22×C4D4×D1712yes—
537C22×C4D4×D1712yes—
538C22×C4#6325412yes—
539C22×C4#6325412yes—
540C22×C4Q8×D1712yes—
541C22×C4#6325612yes—
542C4⋊C4—28no—
543C4⋊C4—44no—
544C4⋊C4—348no—
545C4⋊C4—348no—
546C4⋊C4—348no—
547C4⋊C4—348no—
548C4⋊C4—684no—
549C42—28no—
550C42—1716no—
551C42—348no—
552C42—688no—
553C23C22×Dic3411yescharacteristic
554C23C22×C4×D1711yescharacteristic
555C23C2×#6325211yescharacteristic
556C23C2×D4×D1711yescharacteristic
557C23C2×D4×D1711yescharacteristic
558C23C2×#6325411yescharacteristic
559C23C2×#6325411yescharacteristic
560C23#1058769111yescharacteristic
561C23C2×Q8×D1711yescharacteristic
562C23C2×#6325611yescharacteristic
563C23#1058769411yescharacteristic
564C23#41×D1711yescharacteristic
565C23#41×D1711yescharacteristic
566C23#1058769611yescharacteristic
567C23#1058769711yescharacteristic
568Q8—3432no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—174no—
597C2×C4—174no—
598C2×C4—174no—
599C2×C4—342no—
600C2×C4—342no—
601C2×C4—342no—
602C2×C4—342no—
603C2×C4—342no—
604C2×C4—342no—
605C2×C4—342no—
606C2×C4—342no—
607C2×C4—342no—
608C2×C4—342no—
609C2×C4—342no—
610C2×C4—342no—
611C2×C4—342no—
612C2×C4—342no—
613C2×C4—342no—
614C2×C4—342no—
615C2×C4—342no—
616C2×C4—342no—
617C2×C4—342no—
618C2×C4—344no—
619C2×C4—344no—
620C2×C4—342no—
621C2×C4—342no—
622C2×C4—344no—
623C2×C4—682no—
624C2×C4—682no—
625C2×C4—682no—
626C2×C4—682no—
627C2×C4—681no—
628C2×C4—681no—
629C2×C4—681no—
630C2×C4—681no—
631C2×C4—682no—
632C2×C4—682no—
633C2×C4—682no—
634C2×C4—682no—
635C2×C4—682no—
636C2×C4—682no—
637C2×C4—682no—
638C2×C4C4×Dic3414yes—
639C2×C4#1058756414yes—
640C2×C4C22⋊C4×D1714yes—
641C2×C4#1058757114yes—
642C2×C4#1058757314yes—
643C2×C4#1058757414yes—
644C2×C4#1058757814yes—
645C2×C4#1058758214yes—
646C22C2×C22⋊C4×D1711yescharacteristic
647C22#117×D1711yescharacteristic
648C22C2×#1058757811yescharacteristic
649C22C2×#1058757311yescharacteristic
650C22C2×C4×Dic3411yescharacteristic
651C22#1176328911yescharacteristic
652C22#1176329011yescharacteristic
653C22C2×#1058756411yescharacteristic
654C22C2×#1058758211yescharacteristic
655C22#1176331911yescharacteristic
656C22#1176331911yescharacteristic
657C22#1176332211yescharacteristic
658C22#1176332211yescharacteristic
659C22C2×#1058757111yescharacteristic
660C22C2×#1058757411yescharacteristic
661C22#1176337511yescharacteristic
662C22#1176338211yescharacteristic
663C22#1176338811yescharacteristic
664C22#1176338911yescharacteristic
665C22#1176351511yescharacteristic
666C22#1176351611yescharacteristic
667C22#1176351811yescharacteristic
668C22#1176352011yescharacteristic
669C22#1176352811yescharacteristic
670C22#1176352911yescharacteristic
671C22#1176353111yescharacteristic
672C22#1176353311yescharacteristic
673C22#1176353411yescharacteristic
674C22#1176353511yescharacteristic
675C22#1176353611yescharacteristic
676C22#1176353811yescharacteristic
677C22#1176354111yescharacteristic
678C22#1176354211yescharacteristic
679C22#1176354411yescharacteristic
680C22#1176354511yescharacteristic
681C4—24no—
682C4—42no—
683C4—44no—
684C4—82no—
685C4—344no—
686C4—344no—
687C4—344no—
688C4—684no—
689C4—682no—
690C4—1362no—
691C4#1176271318yes—
692C2#1453116611yescharacteristic
693C2C2×#1176271311yescharacteristic
694C2#1453137311yescharacteristic
695C2#1453173611yescharacteristic
696C2#1453173911yescharacteristic
697C2#1453174211yescharacteristic
698C2#1453174311yescharacteristic
699C2#1453414011yescharacteristic
700C2#1453414411yescharacteristic
701C2#1453414811yescharacteristic
702C2#1453415211yescharacteristic
703C2#1453416911yescharacteristic
704C2#1453417111yescharacteristic
705C2#1453426911yescharacteristic
706C2#1453427111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×C4⋊#95C2
socle, prime radical, cosocleC24×C17C24
hypercenterC4⋊#95D17
hypocenterC17#13925
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic34C4semidirect
63. C2×C4⋊C4×C17Q8semidirect
75. C2×C4⋊Dic17Q8semidirect
432. C2×C4⋊C4Dic34semidirect
456. C17#13925semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic342
C2×#117626742
C2×C4⋊C4×Dic172
#145270542
#145270502
#145270182
#145270152
#145270142
#145270132
C17×C4⋊#952
#1392517