Finite Group Databasebeta

← #17963001

Subgroups — #17963001

Order 4352.

1522 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763760C211yesmaximal, characteristic
2C2×#11763758C211yesmaximal, characteristic
3C2×C4⋊C4×#595C211yesmaximal, characteristic
4C2×C4×C4⋊#595C211yesmaximal, characteristic
5#14543964C211yesmaximal, characteristic
6#14543964C211yesmaximal, characteristic
7#14543964C211yesmaximal, characteristic
8#14543964C211yesmaximal, characteristic
9#14543964C211yesmaximal, characteristic
10#14543963C211yesmaximal, characteristic
11#14543960C211yesmaximal, characteristic
12#14543959C211yesmaximal, characteristic
13#14543959C211yesmaximal, characteristic
14#95×#595C211yesmaximal, characteristic
15D17×#387C211yesmaximal, characteristic
16C22×C4⋊#595C2211yescharacteristic
17C22×C4⋊#595C2211yescharacteristic
18C22×C4⋊#595C2211yescharacteristic
19C22×C4⋊#595C2211yescharacteristic
20C22×C4×#595C2211yescharacteristic
21C22×C4×#595C2211yescharacteristic
22C22×C4×#595C2211yescharacteristic
23C22×C4×#595C2211yescharacteristic
24C22×C4×#595C2211yescharacteristic
25C22×C4×#595C2211yescharacteristic
26#11763760C418yescomplemented
27#11763758C418yescomplemented
28C4⋊C4×#595—24no—
29C4×C4⋊#595—24no—
30C2×(C2×#595)⋊C4C2211yescharacteristic
31C2×(C2×#595)⋊C4C2211yescharacteristic
32C2×(C2×#595)⋊C4C2211yescharacteristic
33C2×(C2×#595)⋊C4C2211yescharacteristic
34C2×(C2×#595)⋊C4C2211yescharacteristic
35C2×(C2×#595)⋊C4C2211yescharacteristic
36C2×(C2×#595)⋊C4C2211yescharacteristic
37C2×(C2×#595)⋊C4C2211yescharacteristic
38C2×(C2×#595)⋊C4C2211yescharacteristic
39C2×(C2×#595)⋊C4C2211yescharacteristic
40C2×(C2×#595)⋊C4C2211yescharacteristic
41C2×(C2×#595)⋊C4C2211yescharacteristic
42C2×(C2×#595)⋊C4C2211yescharacteristic
43C2×(C2×#595)⋊C4C2211yescharacteristic
44C2×(C2×#595)⋊C4C2211yescharacteristic
45C2×(C2×#595)⋊C4C2211yescharacteristic
46C2×(C2×#595)⋊C4C2211yescharacteristic
47C2×(C2×#595)⋊C4C2211yescharacteristic
48C2×C4⋊C4×D17C2211yescharacteristic
49C2×C4⋊C4×D17C2211yescharacteristic
50C2×C42×D17C2211yescharacteristic
51#11762696C411yescharacteristic, complemented
52#11762695C411yescharacteristic, complemented
53#11762694C411yescharacteristic, complemented
54#11762693C411yescharacteristic, complemented
55#11762692C411yescharacteristic, complemented
56#11762691C411yescharacteristic, complemented
57#11762690C411yescharacteristic, complemented
58#95×D17C2211yescharacteristic
59#95×D17C2211yescharacteristic
60#95×D17C2211yescharacteristic
61#95×D17C2211yescharacteristic
62C17×#387C411yescharacteristic, complemented
63C23×#595C2311yescharacteristic
64C23×#595C2311yescharacteristic
65C23×#595C2311yescharacteristic
66C23×#595C2311yescharacteristic
67C23×#595C2311yescharacteristic
68C23×#595C2311yescharacteristic
69C23×#595C2311yescharacteristic
70C23×#595C2311yescharacteristic
71C22×C4×D17C2311yescharacteristic
72C22×C4×D17C2311yescharacteristic
73C22×C4×D17C2311yescharacteristic
74C22×C4×D17C2311yescharacteristic
75C22×C4×D17C2311yescharacteristic
76C22×C4×D17C2311yescharacteristic
77C22×C4×D17C2311yescharacteristic
78C2×C4⋊#595—22no—
79C2×C4⋊#595—22no—
80C2×C4⋊#595—22no—
81C2×C4⋊#595—22no—
82C2×C4⋊#595—22no—
83C2×C4⋊#595—22no—
84C2×C4⋊#595—41no—
85C2×C4⋊#595—41no—
86C2×C4⋊#595C2×C414yes—
87C2×C4⋊#595C2×C414yes—
88C2×C4⋊#595C2×C414yes—
89C2×C4⋊#595C2×C414yes—
90C2×C4×#595—22no—
91C2×C4×#595—22no—
92C2×C4×#595—22no—
93C2×C4×#595—22no—
94C2×C4×#595—22no—
95C2×C4×#595—41no—
96C2×C4×#595—41no—
97C2×C4×#595—41no—
98C2×C4×#595—41no—
99C2×C4×#595—41no—
100C2×C4×#595—41no—
101C2×C4×#595—41no—
102C2×C4×#595—41no—
103C2×C4×#595—41no—
104C2×C4×#595—41no—
105C2×C4×#595C2×C414yes—
106C2×C4×#595C2×C414yes—
107C2×C4×#595D414yes—
108C2×C4⋊C4×C17C2×C411yescharacteristic
109C2×C4⋊C4×C17C2×C411yescharacteristic
110C2×C42×C17C2×C411yescharacteristic
111C2×C4⋊Dic17C2×C411yescharacteristic
112C2×C4⋊Dic17C2×C411yescharacteristic
113C2×#63225C2×C411yescharacteristic
114C2×#63225C2×C411yescharacteristic
115C2×#63225C2×C411yescharacteristic
116C2×#63225C2×C411yescharacteristic
117C2×C4×Dic17C2×C411yescharacteristic
118C2×C4×Dic17C2×C411yescharacteristic
119C2×C4×Dic17C2×C411yescharacteristic
120C4⋊C4×D17—22no—
121C4⋊C4×D17—22no—
122C4⋊C4×D17C2×C414yes—
123C4⋊C4×D17C2×C414yes—
124C42×D17—22no—
125C42×D17—22no—
126(C2×#595)⋊C4—22no—
127(C2×#595)⋊C4—22no—
128(C2×#595)⋊C4—22no—
129(C2×#595)⋊C4—22no—
130(C2×#595)⋊C4—22no—
131(C2×#595)⋊C4—22no—
132(C2×#595)⋊C4—41no—
133(C2×#595)⋊C4—41no—
134(C2×#595)⋊C4—41no—
135(C2×#595)⋊C4—41no—
136(C2×#595)⋊C4—41no—
137(C2×#595)⋊C4—41no—
138(C2×#595)⋊C4C2×C414yes—
139(C2×#595)⋊C4C2×C414yes—
140(C2×#595)⋊C4C2×C414yes—
141(C2×#595)⋊C4C2×C414yes—
142(C2×#595)⋊C4C2×C414yes—
143(C2×#595)⋊C4C2×C414yes—
144C17×#95C2×C411yescharacteristic
145C17×#95C2×C411yescharacteristic
146C17×#95C2×C411yescharacteristic
147C17×#95C2×C411yescharacteristic
148#10587502C2×C411yescharacteristic
149#10587502C2×C411yescharacteristic
150#10587502C2×C411yescharacteristic
151#10587502C2×C411yescharacteristic
152#10587502C2×C411yescharacteristic
153#10587502C2×C411yescharacteristic
154#10587502C2×C411yescharacteristic
155#10587502C2×C411yescharacteristic
156#10587502C2×C411yescharacteristic
157#10587502C2×C411yescharacteristic
158#10587502C2×C411yescharacteristic
159#10587502C2×C411yescharacteristic
160C23×D17C2411yescharacteristic
161C22×#595—21no—
162C22×#595—21no—
163C22×#595—21no—
164C22×#595—21no—
165C22×#595—21no—
166C22×#595—21no—
167C22×#595—21no—
168C22×#595—21no—
169C22×#595—21no—
170C22×#595—21no—
171C22×#595—21no—
172C22×#595—21no—
173C22×#595—21no—
174C22×#595—21no—
175C22×#595—21no—
176C22×#595—21no—
177C22×#595—21no—
178C22×#595—21no—
179C22×#595—21no—
180C22×#595—21no—
181C22×#595—21no—
182C22×#595—21no—
183C22×#595—21no—
184C22×#595—21no—
185C22×#595—21no—
186C22×#595—21no—
187C22×#595—21no—
188C22×#595—21no—
189C22×#595—21no—
190C22×#595—21no—
191C22×#595—21no—
192C22×#595—21no—
193C22×#595—21no—
194C22×#595—21no—
195C22×#595—21no—
196C22×#595—21no—
197C22×#595—21no—
198C22×#595—21no—
199C22×#595—21no—
200C22×#595—21no—
201C22×#595—21no—
202C22×#595—21no—
203C22×#595—21no—
204C22×#595—21no—
205C22×#595C22×C412yes—
206C22×#595C22×C412yes—
207C22×#595C22×C412yes—
208C22×#595C22×C412yes—
209C22×#595C22×C412yes—
210C22×#595C22×C412yes—
211C22×#595C22×C412yes—
212C22×#595C22×C412yes—
213C22×#595C2×D412yes—
214C22×#595C2×D412yes—
215C22×#595#4112yes—
216C22×#595#4112yes—
217C22×C4×C17C22×C411yescharacteristic
218C22×C4×C17C22×C411yescharacteristic
219C22×C4×C17C22×C411yescharacteristic
220C22×C4×C17C22×C411yescharacteristic
221C22×C4×C17C22×C411yescharacteristic
222C22×C4×C17C22×C411yescharacteristic
223C22×C4×C17C22×C411yescharacteristic
224C22×Dic17C22×C411yescharacteristic
225C22×Dic17C22×C411yescharacteristic
226C22×Dic17C22×C411yescharacteristic
227C22×Dic17C22×C411yescharacteristic
228C22×Dic17C22×C411yescharacteristic
229C22×Dic17C22×C411yescharacteristic
230C22×Dic17C22×C411yescharacteristic
231C2×C4×D17—21no—
232C2×C4×D17—21no—
233C2×C4×D17—21no—
234C2×C4×D17—21no—
235C2×C4×D17—21no—
236C2×C4×D17—21no—
237C2×C4×D17—21no—
238C2×C4×D17—21no—
239C2×C4×D17—21no—
240C2×C4×D17—21no—
241C2×C4×D17—21no—
242C2×C4×D17—21no—
243C2×C4×D17—21no—
244C2×C4×D17—21no—
245C2×C4×D17—21no—
246C2×C4×D17—21no—
247C2×C4×D17—21no—
248C2×C4×D17—21no—
249C2×C4×D17—21no—
250C2×C4×D17—21no—
251C2×C4×D17—21no—
252C2×C4×D17—21no—
253C2×C4×D17—21no—
254C2×C4×D17—21no—
255C2×C4×D17—21no—
256C2×C4×D17—21no—
257C2×C4×D17—21no—
258C2×C4×D17—21no—
259C2×C4×D17—21no—
260C2×C4×D17—21no—
261C2×C4×D17—21no—
262C2×C4×D17—21no—
263C2×C4×D17—21no—
264C2×C4×D17—21no—
265C2×C4×D17C22×C412yes—
266C2×C4×D17C22×C412yes—
267C2×C4×D17C22×C412yes—
268C2×C4×D17C22×C412yes—
269C2×C4×D17C22×C412yes—
270C2×C4×D17C22×C412yes—
271C2×C4×D17C2×D412yes—
272C2×C4×D17#4112yes—
273C4⋊#595—28no—
274C4⋊#595—28no—
275C4⋊#595—28no—
276C4⋊#595—44no—
277C4×#595—28no—
278C4×#595—44no—
279C4×#595—44no—
280C4×#595—44no—
281C4×#595—44no—
282C4×#595—44no—
283C4⋊C4×C17—22no—
284C4⋊C4×C17C4214yescomplemented
285C42×C17—22no—
286C4⋊Dic17—22no—
287C4⋊Dic17C4214yescomplemented
288#63225—22no—
289#63225—22no—
290#63225C4214yescomplemented
291#63225C4214yescomplemented
292C4×Dic17—22no—
293C4×Dic17—22no—
294C4×Dic17—22no—
295#13790—171nomaximal, Sylow
296C23×C17C23×C411yescharacteristic
297C22×D17C23×C411yescharacteristic
298C22×D17C23×C411yescharacteristic
299C22×D17C22×D411yescharacteristic
300C22×D17C2×#4111yescharacteristic
301C22×D17C2×#4111yescharacteristic
302C22×D17C2×#4111yescharacteristic
303C22×D17H(5,𝔽2)11yescharacteristic
304C22×D17H(5,𝔽2)11yescharacteristic
305C22×D17H(5,𝔽2)11yescharacteristic
306C22×D172−1+411yescharacteristic
307C22×D172−1+411yescharacteristic
308C22×D172−1+411yescharacteristic
309C22×D172−1+411yescharacteristic
310C22×D172−1+411yescharacteristic
311C2×#595—22no—
312C2×#595—22no—
313C2×#595—22no—
314C2×#595—22no—
315C2×#595—22no—
316C2×#595—22no—
317C2×#595—22no—
318C2×#595—22no—
319C2×#595—22no—
320C2×#595—22no—
321C2×#595—22no—
322C2×#595—22no—
323C2×#595—22no—
324C2×#595—22no—
325C2×#595—22no—
326C2×#595—22no—
327C2×#595—22no—
328C2×#595—22no—
329C2×#595—22no—
330C2×#595—22no—
331C2×#595—22no—
332C2×#595—22no—
333C2×#595—22no—
334C2×#595—22no—
335C2×#595—22no—
336C2×#595—22no—
337C2×#595—22no—
338C2×#595—22no—
339C2×#595—22no—
340C2×#595—22no—
341C2×#595—41no—
342C2×#595—41no—
343C2×#595—41no—
344C2×#595—41no—
345C2×#595—41no—
346C2×#595—41no—
347C2×#595—41no—
348C2×#595—41no—
349C2×#595—41no—
350C2×#595—41no—
351C2×#595—41no—
352C2×#595—41no—
353C2×#595—41no—
354C2×#595—41no—
355C2×#595—41no—
356C2×#595—41no—
357C2×#595—41no—
358C2×#595—41no—
359C2×#595—41no—
360C2×#595—41no—
361C2×#595—41no—
362C2×#595—41no—
363C2×#595—41no—
364C2×#595—41no—
365C2×#595C4×D414yes—
366C2×#595C4×D414yes—
367C2×C4×C17—21no—
368C2×C4×C17—21no—
369C2×C4×C17—21no—
370C2×C4×C17—21no—
371C2×C4×C17—21no—
372C2×C4×C17—21no—
373C2×C4×C17—21no—
374C2×C4×C17—21no—
375C2×C4×C17—21no—
376C2×C4×C17—21no—
377C2×C4×C17—21no—
378C2×C4×C17—21no—
379C2×C4×C17—21no—
380C2×C4×C17—21no—
381C2×C4×C17—21no—
382C2×C4×C17—21no—
383C2×C4×C17—21no—
384C2×C4×C17C2×C4212yes—
385C2×C4×C17C2×C4212yes—
386C2×C4×C17C2×C4212yes—
387C2×C4×C17C4×D412yes—
388C2×Dic17—21no—
389C2×Dic17—21no—
390C2×Dic17—21no—
391C2×Dic17—21no—
392C2×Dic17—21no—
393C2×Dic17—21no—
394C2×Dic17—21no—
395C2×Dic17—21no—
396C2×Dic17—21no—
397C2×Dic17—21no—
398C2×Dic17—21no—
399C2×Dic17—21no—
400C2×Dic17—21no—
401C2×Dic17—21no—
402C2×Dic17—21no—
403C2×Dic17—21no—
404C2×Dic17—21no—
405C2×Dic17C2×C4212yes—
406C2×Dic17C2×C4212yes—
407C2×Dic17C2×C4212yes—
408C2×Dic17C4×D412yes—
409C4×D17—22no—
410C4×D17—22no—
411C4×D17—22no—
412C4×D17—22no—
413C4×D17—22no—
414C4×D17—22no—
415C4×D17—22no—
416C4×D17—22no—
417C4×D17—22no—
418C4×D17—22no—
419C4×D17—22no—
420C4×D17—22no—
421C4×D17—22no—
422C4×D17—22no—
423C4×D17—22no—
424C4×D17—22no—
425C4×D17—41no—
426C4×D17—41no—
427C4×D17—41no—
428C4×D17—41no—
429C4×D17—41no—
430C4×D17—41no—
431C4×D17—41no—
432C4×D17—41no—
433C4×D17—41no—
434C4×D17—41no—
435C4×D17—41no—
436C4×D17—41no—
437C2×#389—171no—
438C2×#387—171no—
439C2×#387—171no—
440C2×C4×C4⋊C4—171no—
441C2×C4×C4⋊C4—171no—
442#1436—171no—
443#1436—171no—
444#1436—171no—
445#1436—171no—
446#1436—171no—
447#1436—171no—
448#1434—171no—
449#1434—171no—
450#1434—171no—
451C4×#95—171no—
452C22×C17C22×C4211yescharacteristic
453C22×C17C2×C4×D411yescharacteristic
454C22×C17C4×#4111yescharacteristic
455C22×C17#51911yescharacteristic
456C22×C17#52011yescharacteristic
457C22×C17#52011yescharacteristic
458C22×C17#52011yescharacteristic
459C2×D17C2×C4×D411yescharacteristic
460C2×D17C2×C4×D411yescharacteristic
461C2×D17C4×#4111yescharacteristic
462C2×D17C4×#4111yescharacteristic
463C2×D17#51811yescharacteristic
464C2×D17#51911yescharacteristic
465C2×D17#51911yescharacteristic
466C2×D17#51911yescharacteristic
467C2×D17#52011yescharacteristic
468C2×D17#52011yescharacteristic
469C2×D17#52011yescharacteristic
470C2×D17#52011yescharacteristic
471C2×D17#53411yescharacteristic
472C2×D17#53611yescharacteristic
473C2×D17#53611yescharacteristic
474C2×D17#53711yescharacteristic
475C2×D17#53811yescharacteristic
476C2×D17#53911yescharacteristic
477C2×D17#53911yescharacteristic
478C2×D17#53911yescharacteristic
479C2×D17#53911yescharacteristic
480C2×D17#53911yescharacteristic
481C2×D17#54111yescharacteristic
482C2×D17#54111yescharacteristic
483C2×D17#54111yescharacteristic
484C2×D17#54111yescharacteristic
485C2×D17#54211yescharacteristic
486C2×D17#54211yescharacteristic
487#595—24no—
488#595—24no—
489#595—42no—
490#595—42no—
491#595—42no—
492#595—42no—
493#595—42no—
494#595—42no—
495C4×C17—22no—
496C4×C17—22no—
497C4×C17—22no—
498C4×C17—22no—
499C4×C17—41no—
500C4×C17—41no—
501C4×C17—41no—
502Dic17—22no—
503Dic17—22no—
504Dic17—22no—
505Dic17—22no—
506Dic17—41no—
507Dic17—41no—
508Dic17—41no—
509C22×C4⋊C4—171no—
510C22×C4⋊C4—171no—
511C22×C4⋊C4—171no—
512C22×C4⋊C4—171no—
513C22×C4⋊C4—171no—
514C22×C4⋊C4—171no—
515C22×C42—171no—
516C22×C42—171no—
517C22×C42—171no—
518C22×C42—171no—
519C22×C42—171no—
520C22×C42—171no—
521C22×C42—171no—
522#389—178no—
523#387—178no—
524#387—171no—
525#387—171no—
526#387—171no—
527#387—171no—
528#387—171no—
529#387—171no—
530#387—171no—
531#387#59511yescharacteristic, complemented
532C4×C4⋊C4—344no—
533C4×C4⋊C4—344no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—171no—
545C2×#95—171no—
546C2×#95—171no—
547C2×#95—171no—
548C2×#95—171no—
549C2×#95—171no—
550C2×#95—171no—
551C2×#95—171no—
552C2×#95—171no—
553C2×#95—171no—
554C2×#95—171no—
555C2×#95—171no—
556C2×C17C42×D411yescharacteristic
557C2×C17#227411yescharacteristic
558C2×C17#227611yescharacteristic
559C2×C17#232211yescharacteristic
560C2×C17#232311yescharacteristic
561C2×C17#233411yescharacteristic
562C2×C17#233611yescharacteristic
563D17#232211yescharacteristic
564D17#232311yescharacteristic
565D17#232511yescharacteristic
566D17#232711yescharacteristic
567D17#233211yescharacteristic
568D17#233411yescharacteristic
569D17#233611yescharacteristic
570D17#233611yescharacteristic
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—171no—
574C23×C4—171no—
575C23×C4—171no—
576C23×C4—171no—
577C23×C4—171no—
578C23×C4—171no—
579C23×C4—171no—
580C23×C4—171no—
581C23×C4—171no—
582C23×C4—171no—
583C23×C4—171no—
584C23×C4—171no—
585C23×C4—171no—
586C2×C4⋊C4—171no—
587C2×C4⋊C4—171no—
588C2×C4⋊C4—171no—
589C2×C4⋊C4—174no—
590C2×C4⋊C4—174no—
591C2×C4⋊C4—174no—
592C2×C4⋊C4—174no—
593C2×C4⋊C4—174no—
594C2×C4⋊C4—171no—
595C2×C4⋊C4—171no—
596C2×C4⋊C4—171no—
597C2×C4⋊C4—174no—
598C2×C4⋊C4—342no—
599C2×C4⋊C4—342no—
600C2×C4⋊C4—342no—
601C2×C4⋊C4—342no—
602C2×C4⋊C4—342no—
603C2×C4⋊C4—342no—
604C2×C4⋊C4—342no—
605C2×C4⋊C4—342no—
606C2×C4⋊C4—681no—
607C2×C4⋊C4—681no—
608C2×C4⋊C4C2×#59511yescharacteristic
609C2×C4⋊C4C2×#59511yescharacteristic
610C2×C42—174no—
611C2×C42—171no—
612C2×C42—171no—
613C2×C42—171no—
614C2×C42—174no—
615C2×C42—174no—
616C2×C42—342no—
617C2×C42—342no—
618C2×C42—342no—
619C2×C42—342no—
620C2×C42—342no—
621C2×C42—342no—
622C2×C42—342no—
623C2×C42—681no—
624C2×C42—681no—
625C2×C42—681no—
626C2×C42—681no—
627C2×C42—681no—
628C2×C42—681no—
629C2×C42—681no—
630C2×C42—681no—
631C2×C42—681no—
632C2×C42—681no—
633C2×C42C2×#59511yescharacteristic
634#95—174no—
635#95—174no—
636#95—174no—
637#95—174no—
638#95—174no—
639#95—174no—
640#95—171no—
641#95—171no—
642#95—171no—
643#95—171no—
644#95—171no—
645#95—171no—
646#95—171no—
647#95—171no—
648#95—171no—
649#95—171no—
650#95—171no—
651#95—171no—
652#95—342no—
653#95—342no—
654#95—342no—
655#95—342no—
656#95—342no—
657#95—342no—
658#95—681no—
659#95—681no—
660#95—681no—
661#95—681no—
662#95—681no—
663#95—681no—
664#95C2×#59511yescharacteristic
665#95C2×#59511yescharacteristic
666#95C2×#59511yescharacteristic
667#95C2×#59511yescharacteristic
668C17#1379011yescharacteristic, complemented, Sylow
669C24—171no—
670C22×C4—172no—
671C22×C4—172no—
672C22×C4—172no—
673C22×C4—172no—
674C22×C4—172no—
675C22×C4—172no—
676C22×C4—171no—
677C22×C4—171no—
678C22×C4—171no—
679C22×C4—171no—
680C22×C4—172no—
681C22×C4—172no—
682C22×C4—172no—
683C22×C4—172no—
684C22×C4—172no—
685C22×C4—172no—
686C22×C4—172no—
687C22×C4—172no—
688C22×C4—172no—
689C22×C4—172no—
690C22×C4—172no—
691C22×C4—172no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—171no—
695C22×C4—171no—
696C22×C4—171no—
697C22×C4—341no—
698C22×C4—341no—
699C22×C4—341no—
700C22×C4—341no—
701C22×C4—341no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—341no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—341no—
762C22×C4—341no—
763C22×C4—341no—
764C22×C4—341no—
765C22×C4—341no—
766C22×C4—341no—
767C22×C4—341no—
768C22×C4—341no—
769C22×C4—341no—
770C22×C4—341no—
771C22×C4—341no—
772C22×C4—341no—
773C22×C4—341no—
774C22×C4—341no—
775C22×C4C22×#59511yescharacteristic
776C22×C4C22×#59511yescharacteristic
777C22×C4C22×#59511yescharacteristic
778C22×C4C22×#59511yescharacteristic
779C22×C4C22×#59511yescharacteristic
780C22×C4C22×#59511yescharacteristic
781C22×C4C22×#59511yescharacteristic
782C4⋊C4—22no—
783C4⋊C4—174no—
784C4⋊C4—174no—
785C4⋊C4—174no—
786C4⋊C4—342no—
787C4⋊C4—342no—
788C4⋊C4—348no—
789C4⋊C4—348no—
790C4⋊C4—348no—
791C4⋊C4—342no—
792C4⋊C4—684no—
793C4⋊C4C4×#59514yescomplemented
794C42—22no—
795C42—342no—
796C42—342no—
797C42—348no—
798C42—342no—
799C42—684no—
800C42—684no—
801C42—684no—
802C42—684no—
803C42—684no—
804C23—171no—
805C23—171no—
806C23—171no—
807C23—171no—
808C23—171no—
809C23—171no—
810C23—171no—
811C23—171no—
812C23—171no—
813C23—171no—
814C23—171no—
815C23—171no—
816C23—171no—
817C23—171no—
818C23C23×#59511yescharacteristic
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—174no—
837C2×C4—174no—
838C2×C4—172no—
839C2×C4—172no—
840C2×C4—172no—
841C2×C4—172no—
842C2×C4—342no—
843C2×C4—342no—
844C2×C4—342no—
845C2×C4—342no—
846C2×C4—342no—
847C2×C4—342no—
848C2×C4—342no—
849C2×C4—342no—
850C2×C4—342no—
851C2×C4—342no—
852C2×C4—342no—
853C2×C4—342no—
854C2×C4—342no—
855C2×C4—342no—
856C2×C4—342no—
857C2×C4—342no—
858C2×C4—342no—
859C2×C4—342no—
860C2×C4—342no—
861C2×C4—342no—
862C2×C4—342no—
863C2×C4—342no—
864C2×C4—342no—
865C2×C4—342no—
866C2×C4—342no—
867C2×C4—342no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—341no—
871C2×C4—341no—
872C2×C4—341no—
873C2×C4—341no—
874C2×C4—341no—
875C2×C4—341no—
876C2×C4—341no—
877C2×C4—341no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—342no—
895C2×C4—342no—
896C2×C4—341no—
897C2×C4—341no—
898C2×C4—341no—
899C2×C4—341no—
900C2×C4—341no—
901C2×C4—341no—
902C2×C4—341no—
903C2×C4—341no—
904C2×C4—341no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
928C2×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4C2×C4×#59512yes—
942C2×C4C2×C4×#59512yes—
943C2×C4C2×C4×#59512yes—
944C2×C4D4×#59512yes—
945C22—171no—
946C22—171no—
947C22—171no—
948C22—171no—
949C22—171no—
950C22—171no—
951C22—171no—
952C22—171no—
953C22—171no—
954C22—171no—
955C22—171no—
956C22—171no—
957C22—171no—
958C22—171no—
959C22—171no—
960C22—171no—
961C22—171no—
962C22—171no—
963C22—171no—
964C22—171no—
965C22—171no—
966C22—171no—
967C22—171no—
968C22—171no—
969C22—171no—
970C22—171no—
971C22—171no—
972C22—171no—
973C22C22×C4×#59511yescharacteristic
974C22C2×D4×#59511yescharacteristic
975C22#41×#59511yescharacteristic
976C22#1176387711yescharacteristic
977C22#1176387811yescharacteristic
978C22#1176387811yescharacteristic
979C22#1176387811yescharacteristic
980C4—22no—
981C4—22no—
982C4—22no—
983C4—22no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—344no—
988C4—344no—
989C4—342no—
990C4—342no—
991C4—342no—
992C4—342no—
993C4—682no—
994C4—682no—
995C4—682no—
996C4—682no—
997C4—682no—
998C4—682no—
999C4—681no—
1000C4—681no—
1001C4—681no—
1002C2—171no—
1003C2—171no—
1004C2—171no—
1005C2—171no—
1006C2—171no—
1007C2—171no—
1008C2—171no—
1009C2—171no—
1010C2C4×D4×#59511yescharacteristic
1011C2#1454522111yescharacteristic
1012C2#1454522411yescharacteristic
1013C2#1454527011yescharacteristic
1014C2#1454527111yescharacteristic
1015C2#1454528211yescharacteristic
1016C2#1454528411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C22×C42
FittingC17×#387C4
socleC23×C17C23×C4
prime radical, cosocleC23×D17C24
hypercenter#387#595
hypocenterC17#13790
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
26. #11763760C4semidirect
27. #11763758C4semidirect
51. #11762696C4semidirect
52. #11762695C4semidirect
53. #11762694C4semidirect
54. #11762693C4semidirect
55. #11762692C4semidirect
56. #11762691C4semidirect
57. #11762690C4semidirect
62. C17×#387C4semidirect
284. C4⋊C4×C17C42semidirect
287. C4⋊Dic17C42semidirect
290. #63225C42semidirect
291. #63225C42semidirect
531. #387#595semidirect
668. C17#13790semidirect
793. C4⋊C4C4×#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637602
C2×#117637582
C2×C4⋊C4×#5952
C2×C4×C4⋊#5952
#145439642
#145439632
#145439602
#145439592
#95×#5952
D17×#3872
#1379017