Finite Group Databasebeta

← #17979177

Subgroups — #17979177

Order 4352.

3764 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763876C212yesmaximal, complemented
2#14545314C211yesmaximal, characteristic, complemented
3#14545311C212yesmaximal, complemented
4#14545309C212yesmaximal, complemented
5#14545306C214yesmaximal, complemented
6#14545302C211yesmaximal, characteristic, complemented
7D4×C4⋊#595C211yesmaximal, characteristic, complemented
8D4×C22⋊#595C212yesmaximal, complemented
9D4×C22⋊#595C212yesmaximal, complemented
10#14545272C212yesmaximal, complemented
11#14545269C214yesmaximal, complemented
12#127×#595C211yesmaximal, characteristic, complemented
13#121×#595C212yesmaximal, complemented
14#14545241C211yesmaximal, characteristic, complemented
15C2×#11763761C212yesmaximal, complemented
16C4×D4×#595C211yesmaximal, characteristic, complemented
17D42×D17C211yesmaximal, characteristic
18#11763876—216no—
19C2×D4×#595C2211yescharacteristic
20C2×D4×#595C2212yes—
21C2×D4×#595C2211yescharacteristic
22C2×D4×#595C2214yescomplemented
23C2×D4×#595C2212yescomplemented
24C2×D4×#595C2214yescomplemented
25C2×D4×#595C2212yescomplemented
26C2×D4×#595C2212yescomplemented
27C2×D4×#595C2212yescomplemented
28C2×D4×#595C2212yescomplemented
29C2×#10587677C2212yescomplemented
30C2×#10587677C2212yescomplemented
31C22×C4⋊#595C2212yescomplemented
32C22×C22⋊#595C2214yescomplemented
33C22×C22⋊#595C2214yescomplemented
34C22×C22⋊#595C2214yescomplemented
35C22×C4×#595C2212yescomplemented
36#11763761C2211yescharacteristic
37#11763761C2212yes—
38#11763761C2211yescharacteristic
39#11763761C2212yescomplemented
40#11763761C2214yescomplemented
41#11763761C2214yescomplemented
42#11763761C2212yescomplemented
43#11763761C2212yescomplemented
44#11763761C2212yescomplemented
45#11763761C2212yescomplemented
46#11763760C2211yescharacteristic, complemented
47#11763760C2211yescharacteristic, complemented
48#11763760C2212yescomplemented
49#11763759C2212yescomplemented
50#11763759C2212yescomplemented
51#11763759C2214yescomplemented
52#11763759C2214yescomplemented
53#11763759C2214yescomplemented
54#11763757C2214yescomplemented
55#11763757C2214yescomplemented
56#11763757C2214yescomplemented
57#11763757C2214yescomplemented
58#11763757C2214yescomplemented
59#11763756C2214yescomplemented
60#11763756C2214yescomplemented
61#11763755C2211yescharacteristic, complemented
62#11763751C2212yescomplemented
63#11763751C2212yescomplemented
64#11763750C2214yescomplemented
65C4⋊C4×#595C2211yescharacteristic, complemented
66C4⋊C4×#595C2211yescharacteristic, complemented
67C4⋊C4×#595C2212yescomplemented
68C4×C4⋊#595C2211yescharacteristic, complemented
69C4×C4⋊#595C2211yescharacteristic, complemented
70C22⋊C4×#595C2212yescomplemented
71C22⋊C4×#595C2212yescomplemented
72C22⋊C4×#595C2214yescomplemented
73C4×C22⋊#595C2212yescomplemented
74C4×C22⋊#595C2212yescomplemented
75C42×#595C2211yescharacteristic, complemented
76C22×D4×D17C2212yes—
77C22×D4×D17C2212yes—
78D4×D68C411yescharacteristic, complemented
79D4×D68C411yescharacteristic, complemented
80#11763444C411yescharacteristic, complemented
81#11763443C412yescomplemented
82#11763443C412yescomplemented
83D4×C22⋊D17C412yescomplemented
84D4×C22⋊D17C412yescomplemented
85#11763441C414yescomplemented
86#127×D17C2211yescharacteristic
87#121×D17C2212yes—
88#121×D17C2212yes—
89#120×D17C2214yes—
90C4×D4×D17C2211yescharacteristic
91C4×D4×D17C2211yescharacteristic
92D42×C17C411yescharacteristic, complemented
93C24×D17C2314yes—
94C23×#595C2312yes—
95C23×#595C2314yes—
96C23×#595C2314yes—
97C23×#595C2314yes—
98C23×#595C2312yes—
99C22×D4×C17C2×C412yescomplemented
100C22×D4×C17C2×C412yescomplemented
101C22×C22⋊D17C2×C414yescomplemented
102C22×C22⋊D17C2×C414yescomplemented
103C2×D4×D17—28no—
104C2×D4×D17—28no—
105C2×D4×D17—44no—
106C2×D4×D17—44no—
107C2×D4×D17C2×C414yescomplemented
108C2×D4×D17C2×C412yescomplemented
109C2×D4×D17C2×C412yescomplemented
110C2×D4×D17C2×C414yescomplemented
111C2×D4×D17C2×C412yescomplemented
112C2×D4×D17C2×C412yescomplemented
113C2×D4×D17C2314yes—
114C2×D4×D17C2311yescharacteristic
115C2×D4×D17C2312yes—
116C2×D4×D17C2312yes—
117C2×D4×D17C2314yes—
118C2×D4×D17C2312yes—
119C2×D4×D17C2311yescharacteristic
120C22×D68C2×C412yescomplemented
121C22×D68C2×C412yescomplemented
122C22×C4×D17C2312yes—
123C22×C4×D17C2312yes—
124C2×C22⋊#595—216no—
125C2×C22⋊#595—216no—
126C2×C22⋊#595—48no—
127C2×C22⋊#595C2312yes—
128C2×C22⋊#595C2312yes—
129C2×C22⋊#595C2314yes—
130C2×C22⋊#595C2314yes—
131C2×C22⋊#595C2312yes—
132C2×C22⋊#595C2314yes—
133C2×C22⋊#595C2314yes—
134C2×C22⋊#595C2312yes—
135C2×C22⋊#595C2314yes—
136C2×C22⋊#595C2312yes—
137C2×C22⋊#595C2314yes—
138C2×C22⋊#595C2314yes—
139C2×C22⋊#595C2314yes—
140C2×C22⋊#595C2314yes—
141C2×C22⋊#595C2312yes—
142D4×#595—216no—
143D4×#595—28no—
144D4×#595—24no—
145D4×#595—216no—
146D4×#595—28no—
147D4×#595—28no—
148D4×#595—44no—
149D4×#595—44no—
150D4×#595—44no—
151D4×#595D418yescomplemented
152#10587677—28no—
153#10587677—28no—
154C2×C4⋊#595—44no—
155C2×C4⋊#595C2311yescharacteristic
156C2×C4⋊#595C2311yescharacteristic
157C2×C4⋊#595C2311yescharacteristic
158C2×C4⋊#595C2312yes—
159C2×C4⋊#595C2312yes—
160C2×C4⋊#595C2312yes—
161C2×C4⋊#595C2312yes—
162C2×C4⋊#595C2312yes—
163C2×C4⋊#595C2314yes—
164C2×C4⋊#595C2311yescharacteristic
165C2×C4×#595—44no—
166C2×C4×#595C2311yescharacteristic
167C2×C4×#595C2311yescharacteristic
168C2×C4×#595C2311yescharacteristic
169C2×C4×#595C2311yescharacteristic
170C2×C4×#595C2312yes—
171C2×C4×#595C2312yes—
172C2×C4×#595C2314yes—
173C2×C4×#595C2311yescharacteristic
174C2×C4×#595C2312yes—
175C2×C4×#595C2312yes—
176C2×C4×#595C2311yescharacteristic
177C17×#127C2×C411yescharacteristic, complemented
178C17×#121C2×C412yescomplemented
179C17×#121C2×C412yescomplemented
180C17×#120C2×C414yescomplemented
181C4×D4×C17C2×C411yescharacteristic, complemented
182C4×D4×C17C2×C411yescharacteristic, complemented
183#10587639C2×C414yescomplemented
184#10587626C2×C412yescomplemented
185#10587626C2×C412yescomplemented
186#10587626C2×C412yescomplemented
187#10587625C2×C414yescomplemented
188#10587625C2×C414yescomplemented
189#10587624C2×C412yescomplemented
190#10587624C2×C412yescomplemented
191#10587623C2×C414yescomplemented
192#10587623C2×C414yescomplemented
193#10587623C2×C414yescomplemented
194D4×Dic17C2×C411yescharacteristic, complemented
195D4×Dic17C2×C411yescharacteristic, complemented
196#10587616C2×C412yescomplemented
197#10587616C2×C412yescomplemented
198C4×C22⋊D17C2×C412yescomplemented
199C4×C22⋊D17C2×C412yescomplemented
200#10587581C2×C412yescomplemented
201#10587581C2×C412yescomplemented
202#10587579C2×C411yescharacteristic, complemented
203#10587579C2×C411yescharacteristic, complemented
204C4⋊C4×D17C2311yescharacteristic
205C4⋊C4×D17C2311yescharacteristic
206#10587570C2×C414yescomplemented
207#10587570C2×C414yescomplemented
208#10587568C2×C414yescomplemented
209#10587568C2×C414yescomplemented
210#10587568C2×C414yescomplemented
211#10587567C2×C412yescomplemented
212#10587567C2×C412yescomplemented
213C22⋊C4×D17C2312yes—
214C22⋊C4×D17C2314yes—
215C22⋊C4×D17C2312yes—
216#10587560C2×C411yescharacteristic, complemented
217C4×D68C2×C411yescharacteristic, complemented
218C4×D68C2×C411yescharacteristic, complemented
219C42×D17C2311yescharacteristic
220(C2×#595)⋊C4C2312yes—
221(C2×#595)⋊C4C2312yes—
222(C2×#595)⋊C4C2312yes—
223(C2×#595)⋊C4C2312yes—
224(C2×#595)⋊C4C2312yes—
225(C2×#595)⋊C4C2314yes—
226(C2×#595)⋊C4C2312yes—
227(C2×#595)⋊C4C2314yes—
228C24×C17C22×C414yes—
229C23×D17—28no—
230C23×D17—28no—
231C23×D17—44no—
232C23×D17—44no—
233C23×D17—44no—
234C23×D17—44no—
235C23×D17C22×C414yes—
236C23×D17C22×C414yes—
237C23×D17C22×C414yes—
238C23×D17C2412yes—
239C23×D17C2414yes—
240C23×D17C2412yes—
241C22×#595—24no—
242C22×#595—28no—
243C22×#595—24no—
244C22×#595—28no—
245C22×#595—28no—
246C22×#595—42no—
247C22×#595—42no—
248C22×#595—42no—
249C22×#595—44no—
250C22×#595—44no—
251C22×#595—44no—
252C22×#595—44no—
253C22×#595—44no—
254C22×#595—44no—
255C22×#595C2×D418yescomplemented
256C22×#595C2411yescharacteristic
257C22×#595C2412yes—
258C22×#595C2412yes—
259C22×#595C2414yes—
260C22×#595C2412yes—
261C22×#595C2411yescharacteristic
262C22×#595C2412yes—
263C22×#595C2411yescharacteristic
264C22×#595C2411yescharacteristic
265C2×D4×C17—28no—
266C2×D4×C17—44no—
267C2×D4×C17C22×C412yes—
268C2×D4×C17C22×C412yes—
269C2×D4×C17C22×C411yescharacteristic
270C2×D4×C17C22×C414yes—
271C2×D4×C17C22×C412yes—
272C2×D4×C17C22×C414yes—
273C2×D4×C17C22×C411yescharacteristic
274C22×C4×C17C22×C412yes—
275C22×C4×C17C22×C412yes—
276C2×C22⋊D17—216no—
277C2×C22⋊D17—48no—
278C2×C22⋊D17C22×C412yes—
279C2×C22⋊D17C22×C414yes—
280C2×C22⋊D17C22×C414yes—
281C2×C22⋊D17C22×C414yes—
282C2×C22⋊D17C22×C414yes—
283C2×C22⋊D17C22×C414yes—
284C2×C22⋊D17C22×C414yes—
285C2×C22⋊D17C22×C414yes—
286C2×C22⋊D17C22×C412yes—
287C22×Dic17C22×C412yes—
288C22×Dic17C22×C412yes—
289D4×D17—28no—
290D4×D17—28no—
291D4×D17—28no—
292D4×D17—216no—
293D4×D17—28no—
294D4×D17—24no—
295D4×D17—24no—
296D4×D17—24no—
297D4×D17—24no—
298D4×D17—22no—
299D4×D17—22no—
300D4×D17—44no—
301D4×D17—44no—
302D4×D17—48no—
303D4×D17—42no—
304D4×D17—44no—
305D4×D17—44no—
306D4×D17—42no—
307D4×D17C2×D414yes—
308D4×D17#4114yes—
309C2×D68—28no—
310C2×D68—44no—
311C2×D68C22×C411yescharacteristic
312C2×D68C22×C412yes—
313C2×D68C22×C412yes—
314C2×D68C22×C414yes—
315C2×D68C22×C414yes—
316C2×D68C22×C412yes—
317C2×D68C22×C411yescharacteristic
318C2×C4×D17—24no—
319C2×C4×D17—24no—
320C2×C4×D17—24no—
321C2×C4×D17—24no—
322C2×C4×D17C22×C412yes—
323C2×C4×D17C22×C412yes—
324C2×C4×D17C22×C412yes—
325C2×C4×D17C22×C412yes—
326C2×C4×D17C2412yes—
327C2×C4×D17C2412yes—
328C2×C4×D17C2411yescharacteristic
329C2×C4×D17C2411yescharacteristic
330C2×C4×D17C2411yescharacteristic
331C22⋊#595—28no—
332C22⋊#595—24no—
333C22⋊#595—28no—
334C22⋊#595—24no—
335C22⋊#595—24no—
336C22⋊#595—28no—
337C22⋊#595—28no—
338C22⋊#595—28no—
339C22⋊#595—24no—
340C22⋊#595—44no—
341C22⋊#595—44no—
342C22⋊#595—44no—
343C22⋊#595—44no—
344C22⋊#595—42no—
345C22⋊#595C2×D418yescomplemented
346C4⋊#595—24no—
347C4⋊#595—24no—
348C4⋊#595—24no—
349C4⋊#595—22no—
350C4⋊#595—22no—
351C4⋊#595—24no—
352C4⋊#595—22no—
353C4⋊#595—44no—
354C4⋊#595—42no—
355C4⋊#595C2×D414yescomplemented
356C4×#595—28no—
357C4×#595—22no—
358C4×#595—24no—
359C4×#595—22no—
360C4×#595—22no—
361C4×#595—24no—
362C4×#595—22no—
363C4×#595—42no—
364C4×#595—42no—
365C4×#595—41no—
366C4×#595C2×D414yescomplemented
367C4⋊C4×C17C22×C411yescharacteristic
368C4⋊C4×C17C22×C411yescharacteristic
369C22⋊C4×C17C22×C412yes—
370C22⋊C4×C17C22×C412yes—
371C22⋊C4×C17C22×C414yes—
372C42×C17C22×C411yescharacteristic
373C22⋊Dic17C22×C412yes—
374C22⋊Dic17C22×C412yes—
375C22⋊Dic17C22×C414yes—
376#63227C22×C412yes—
377#63227C22×C412yes—
378#63227C22×C412yes—
379#63227C22×C412yes—
380#63227C22×C414yes—
381#63227C22×C414yes—
382C4⋊Dic17C22×C411yescharacteristic
383C4⋊Dic17C22×C411yescharacteristic
384#63225C22×C412yes—
385#63225C22×C412yes—
386C4×Dic17C22×C411yescharacteristic
387C4×Dic17C22×C411yescharacteristic
388C4×Dic17C22×C411yescharacteristic
389#34310—171nomaximal, Sylow
390C23×C17—28no—
391C23×C17—44no—
392C23×C17—44no—
393C23×C17C23×C412yes—
394C23×C17C23×C414yes—
395C23×C17C23×C412yes—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17—28no—
401C22×D17—22no—
402C22×D17—24no—
403C22×D17—22no—
404C22×D17—24no—
405C22×D17—22no—
406C22×D17—24no—
407C22×D17—24no—
408C22×D17—24no—
409C22×D17—22no—
410C22×D17—22no—
411C22×D17—22no—
412C22×D17—24no—
413C22×D17—28no—
414C22×D17—28no—
415C22×D17—44no—
416C22×D17—44no—
417C22×D17—44no—
418C22×D17—44no—
419C22×D17—44no—
420C22×D17—44no—
421C22×D17—88no—
422C22×D17—88no—
423C22×D17—88no—
424C22×D17—88no—
425C22×D17C23×C412yes—
426C22×D17C23×C414yes—
427C22×D17C23×C412yes—
428C22×D17C22×D414yes—
429C22×D17C2×#4114yes—
430C22×D17C2511yescharacteristic
431C2×#595—21no—
432C2×#595—21no—
433C2×#595—21no—
434C2×#595—22no—
435C2×#595—21no—
436C2×#595—21no—
437C2×#595—21no—
438C2×#595—22no—
439C2×#595—22no—
440C2×#595—24no—
441C2×#595—22no—
442C2×#595—21no—
443C2×#595—22no—
444C2×#595—22no—
445C2×#595—21no—
446C2×#595—22no—
447C2×#595—24no—
448C2×#595—22no—
449C2×#595—24no—
450C2×#595—22no—
451C2×#595—22no—
452C2×#595—21no—
453C2×#595—22no—
454C2×#595—48no—
455C2×#595—48no—
456C2×#595—88no—
457C2×#595—88no—
458C2×#595—88no—
459C2×#595C22×D414yes—
460C2×#595C22×D412yes—
461C2×#595C22×D412yes—
462C2×#595H(5,𝔽2)12yes—
463D4×C17—28no—
464D4×C17—24no—
465D4×C17—22no—
466D4×C17—24no—
467D4×C17—44no—
468D4×C17—42no—
469D4×C17C4×D414yescomplemented
470C2×C4×C17—24no—
471C2×C4×C17—24no—
472C2×C4×C17C23×C411yescharacteristic
473C2×C4×C17C23×C412yes—
474C2×C4×C17C23×C412yes—
475C2×C4×C17C23×C411yescharacteristic
476C2×C4×C17C23×C411yescharacteristic
477C22⋊D17—28no—
478C22⋊D17—28no—
479C22⋊D17—28no—
480C22⋊D17—24no—
481C22⋊D17—28no—
482C22⋊D17—44no—
483C22⋊D17—44no—
484C22⋊D17—44no—
485C22⋊D17C4×D418yescomplemented
486C2×Dic17—24no—
487C2×Dic17—24no—
488C2×Dic17C23×C411yescharacteristic
489C2×Dic17C23×C412yes—
490C2×Dic17C23×C412yes—
491C2×Dic17C23×C411yescharacteristic
492C2×Dic17C23×C411yescharacteristic
493D68—28no—
494D68—24no—
495D68—22no—
496D68—24no—
497D68—44no—
498D68—42no—
499D68C4×D414yescomplemented
500C4×D17—22no—
501C4×D17—22no—
502C4×D17—21no—
503C4×D17—22no—
504C4×D17—22no—
505C4×D17—21no—
506C4×D17—24no—
507C4×D17—24no—
508C4×D17—24no—
509C4×D17—24no—
510C4×D17C22×D412yes—
511C4×D17C2×#4112yes—
512C4×D17H(5,𝔽2)12yes—
513C4×D17H(5,𝔽2)12yes—
514C2×D42—171no—
515C2×#518—172no—
516#2366—171no—
517#2363—172no—
518#2361—172no—
519#2358—174no—
520#2354—171no—
521D4×C4⋊C4—171no—
522D4×C22⋊C4—172no—
523D4×C22⋊C4—172no—
524#2324—172no—
525#2321—174no—
526C4×#127—171no—
527C4×#121—172no—
528#2293—171no—
529C2×#390—172no—
530C42×D4—171no—
531C22×C17—22no—
532C22×C17—22no—
533C22×C17—22no—
534C22×C17—24no—
535C22×C17—22no—
536C22×C17—24no—
537C22×C17—24no—
538C22×C17—22no—
539C22×C17—88no—
540C22×C17C2×C4×D414yes—
541C22×C17C24×C411yescharacteristic
542C2×D17—22no—
543C2×D17—22no—
544C2×D17—24no—
545C2×D17—24no—
546C2×D17—24no—
547C2×D17—24no—
548C2×D17—22no—
549C2×D17—24no—
550C2×D17—22no—
551C2×D17—24no—
552C2×D17—24no—
553C2×D17—22no—
554C2×D17—44no—
555C2×D17—42no—
556C2×D17—44no—
557C2×D17—42no—
558C2×D17—44no—
559C2×D17—42no—
560C2×D17—44no—
561C2×D17—42no—
562C2×D17—88no—
563C2×D17—88no—
564C2×D17—88no—
565C2×D17C2×C4×D414yes—
566C2×D17C23×D411yescharacteristic
567C2×D17C22×#4111yescharacteristic
568C2×D17C2×H(5,𝔽2)11yescharacteristic
569C2×D17C2×H(5,𝔽2)11yescharacteristic
570C2×D17C2×H(5,𝔽2)11yescharacteristic
571C2×D17#58511yescharacteristic
572#595—22no—
573#595—24no—
574#595—22no—
575#595—22no—
576#595—42no—
577#595—42no—
578#595—44no—
579#595—41no—
580#595—42no—
581C4×C17—22no—
582C4×C17—22no—
583C4×C17—21no—
584C4×C17C2×C4×D412yes—
585C4×C17#51812yescomplemented
586Dic17—22no—
587Dic17—22no—
588Dic17—21no—
589Dic17C2×C4×D412yes—
590Dic17#51812yescomplemented
591C23×D4—172no—
592C23×D4—172no—
593D42—172no—
594D42—172no—
595D42—171no—
596D42—172no—
597D42—172no—
598D42—174no—
599D42—171no—
600D42—171no—
601D42#59511yescharacteristic, complemented
602C2×#127—171no—
603C2×#121—172no—
604C2×#121—172no—
605C2×#120—174no—
606#518—3416no—
607C2×C4×D4—171no—
608C2×C4×D4—171no—
609C2×C4×D4—171no—
610C2×C4×D4—172no—
611C2×C4×D4—174no—
612C2×C4×D4—171no—
613C2×C4×D4—172no—
614C2×C4×D4—174no—
615C2×C4×D4—172no—
616C2×C4×D4—172no—
617C2×C4×D4—172no—
618C2×C4×D4—172no—
619C2×#117—172no—
620C2×#117—172no—
621C22×C4⋊C4—172no—
622C22×C22⋊C4—174no—
623C22×C22⋊C4—174no—
624C22×C22⋊C4—174no—
625C22×C42—172no—
626#390—172no—
627#390—172no—
628#390—172no—
629#390—174no—
630#390—172no—
631#390—171no—
632#390—172no—
633#390—171no—
634#390—174no—
635#390—172no—
636#389—172no—
637#389—171no—
638#389—171no—
639#388—172no—
640#388—174no—
641#388—174no—
642#388—174no—
643#388—172no—
644#386—174no—
645#386—174no—
646#386—174no—
647#386—174no—
648#386—174no—
649#385—174no—
650#385—174no—
651#384—171no—
652#380—172no—
653#380—172no—
654#379—174no—
655C4×C4⋊C4—171no—
656C4×C4⋊C4—171no—
657C4×C4⋊C4—171no—
658C4×C4⋊C4—172no—
659C4×C4⋊C4—171no—
660C4×C22⋊C4—172no—
661C4×C22⋊C4—172no—
662C4×C22⋊C4—172no—
663C4×C22⋊C4—172no—
664C4×C22⋊C4—174no—
665C43—171no—
666C2×C17—24no—
667C2×C17—42no—
668C2×C17—44no—
669C2×C17C22×C4×D411yescharacteristic
670C2×C17C2×#51811yescharacteristic
671C2×C17C4×H(5,𝔽2)11yescharacteristic
672D17—24no—
673D17—44no—
674D17—42no—
675D17#349611yescharacteristic
676D17#349811yescharacteristic
677D17#351411yescharacteristic
678D17#351911yescharacteristic
679C25—174no—
680C22×D4—171no—
681C22×D4—174no—
682C22×D4—174no—
683C22×D4—174no—
684C22×D4—172no—
685C22×D4—172no—
686C22×D4—171no—
687C22×D4—174no—
688C22×D4—172no—
689C22×D4—172no—
690C22×D4—172no—
691C22×D4—174no—
692C22×D4—174no—
693C22×D4—172no—
694C22×D4—172no—
695C22×D4—172no—
696C22×D4—172no—
697C22×D4—348no—
698C22×D4—348no—
699C22×D4—684no—
700C22×D4—684no—
701C22×D4C2×#59512yescomplemented
702C22×D4C2×#59512yescomplemented
703C23×C4—172no—
704C23×C4—172no—
705C23×C4—172no—
706C23×C4—172no—
707C23×C4—174no—
708C23×C4—174no—
709C23×C4—174no—
710#127—172no—
711#127—172no—
712#127—172no—
713#127—171no—
714#127C2×#59511yescharacteristic, complemented
715#121—172no—
716#121—172no—
717#121—174no—
718#121—174no—
719#121—172no—
720#121—172no—
721#121—172no—
722#121—172no—
723#121—174no—
724#121—174no—
725#121C2×#59512yescomplemented
726#121C2×#59512yescomplemented
727#120—174no—
728#120—174no—
729#120—174no—
730#120—174no—
731#120—174no—
732#120—174no—
733#120—174no—
734#120C2×#59514yescomplemented
735C4×D4—178no—
736C4×D4—171no—
737C4×D4—171no—
738C4×D4—172no—
739C4×D4—172no—
740C4×D4—171no—
741C4×D4—171no—
742C4×D4—172no—
743C4×D4—172no—
744C4×D4—171no—
745C4×D4—171no—
746C4×D4—348no—
747C4×D4—3416no—
748C4×D4—348no—
749C4×D4—3416no—
750C4×D4—348no—
751C4×D4—344no—
752C4×D4—684no—
753C4×D4—684no—
754C4×D4—684no—
755C4×D4C2×#59511yescharacteristic, complemented
756C4×D4C2×#59511yescharacteristic, complemented
757#117—348no—
758#117—348no—
759C2×C4⋊C4—171no—
760C2×C4⋊C4—171no—
761C2×C4⋊C4—171no—
762C2×C4⋊C4—171no—
763C2×C4⋊C4—172no—
764C2×C4⋊C4—172no—
765C2×C4⋊C4—172no—
766C2×C4⋊C4—172no—
767C2×C4⋊C4—171no—
768C2×C4⋊C4—171no—
769C2×C4⋊C4—174no—
770C2×C4⋊C4—172no—
771C2×C4⋊C4—684no—
772C2×C22⋊C4—172no—
773C2×C22⋊C4—172no—
774C2×C22⋊C4—172no—
775C2×C22⋊C4—174no—
776C2×C22⋊C4—172no—
777C2×C22⋊C4—174no—
778C2×C22⋊C4—172no—
779C2×C22⋊C4—172no—
780C2×C22⋊C4—174no—
781C2×C22⋊C4—174no—
782C2×C22⋊C4—174no—
783C2×C22⋊C4—174no—
784C2×C22⋊C4—172no—
785C2×C22⋊C4—174no—
786C2×C22⋊C4—174no—
787C2×C22⋊C4—174no—
788C2×C22⋊C4—174no—
789C2×C22⋊C4—172no—
790C2×C22⋊C4—3416no—
791C2×C22⋊C4—3416no—
792C2×C22⋊C4—688no—
793C2×C42—171no—
794C2×C42—171no—
795C2×C42—174no—
796C2×C42—172no—
797C2×C42—171no—
798C2×C42—171no—
799C2×C42—171no—
800C2×C42—172no—
801C2×C42—171no—
802C2×C42—171no—
803C2×C42—172no—
804C2×C42—172no—
805C2×C42—684no—
806#95—172no—
807#95—172no—
808#95—172no—
809#95—172no—
810#95—174no—
811#95—172no—
812#95—174no—
813#95—172no—
814C17#3431011yescharacteristic, complemented, Sylow
815C24—172no—
816C24—172no—
817C24—174no—
818C24—174no—
819C24—174no—
820C24—174no—
821C24—348no—
822C24—348no—
823C24—684no—
824C24—684no—
825C24—684no—
826C24—684no—
827C24C22×#59514yes—
828C2×D4—28no—
829C2×D4—44no—
830C2×D4—172no—
831C2×D4—174no—
832C2×D4—174no—
833C2×D4—172no—
834C2×D4—174no—
835C2×D4—174no—
836C2×D4—174no—
837C2×D4—174no—
838C2×D4—174no—
839C2×D4—174no—
840C2×D4—174no—
841C2×D4—171no—
842C2×D4—171no—
843C2×D4—174no—
844C2×D4—172no—
845C2×D4—172no—
846C2×D4—172no—
847C2×D4—174no—
848C2×D4—348no—
849C2×D4—344no—
850C2×D4—344no—
851C2×D4—344no—
852C2×D4—344no—
853C2×D4—342no—
854C2×D4—342no—
855C2×D4—3416no—
856C2×D4—348no—
857C2×D4—348no—
858C2×D4—348no—
859C2×D4—3416no—
860C2×D4—348no—
861C2×D4—684no—
862C2×D4—684no—
863C2×D4—684no—
864C2×D4—688no—
865C2×D4—682no—
866C2×D4—682no—
867C2×D4—684no—
868C2×D4—684no—
869C2×D4—688no—
870C2×D4C22×#59511yescharacteristic
871C2×D4C22×#59514yes—
872C2×D4C22×#59512yes—
873C2×D4C22×#59512yes—
874C2×D4C22×#59512yes—
875C2×D4C22×#59514yes—
876C2×D4C22×#59511yescharacteristic
877C22×C4—171no—
878C22×C4—171no—
879C22×C4—171no—
880C22×C4—172no—
881C22×C4—171no—
882C22×C4—171no—
883C22×C4—172no—
884C22×C4—172no—
885C22×C4—178no—
886C22×C4—172no—
887C22×C4—172no—
888C22×C4—172no—
889C22×C4—172no—
890C22×C4—171no—
891C22×C4—172no—
892C22×C4—172no—
893C22×C4—171no—
894C22×C4—172no—
895C22×C4—172no—
896C22×C4—172no—
897C22×C4—174no—
898C22×C4—344no—
899C22×C4—344no—
900C22×C4—344no—
901C22×C4—344no—
902C22×C4—344no—
903C22×C4—348no—
904C22×C4—348no—
905C22×C4—344no—
906C22×C4—348no—
907C22×C4—682no—
908C22×C4—682no—
909C22×C4—682no—
910C22×C4—684no—
911C22×C4—684no—
912C22×C4—684no—
913C22×C4—684no—
914C22×C4—684no—
915C22×C4—684no—
916C22×C4C22×#59512yes—
917C22×C4C22×#59512yes—
918C4⋊C4—174no—
919C4⋊C4—172no—
920C4⋊C4—172no—
921C4⋊C4—171no—
922C4⋊C4—171no—
923C4⋊C4—342no—
924C4⋊C4—344no—
925C4⋊C4—344no—
926C4⋊C4—344no—
927C4⋊C4—344no—
928C4⋊C4—342no—
929C4⋊C4—342no—
930C4⋊C4—684no—
931C4⋊C4—682no—
932C4⋊C4C22×#59511yescharacteristic
933C4⋊C4C22×#59511yescharacteristic
934C22⋊C4—178no—
935C22⋊C4—172no—
936C22⋊C4—172no—
937C22⋊C4—174no—
938C22⋊C4—172no—
939C22⋊C4—172no—
940C22⋊C4—172no—
941C22⋊C4—172no—
942C22⋊C4—174no—
943C22⋊C4—174no—
944C22⋊C4—344no—
945C22⋊C4—344no—
946C22⋊C4—348no—
947C22⋊C4—348no—
948C22⋊C4—348no—
949C22⋊C4—344no—
950C22⋊C4—348no—
951C22⋊C4—348no—
952C22⋊C4—344no—
953C22⋊C4—682no—
954C22⋊C4—684no—
955C22⋊C4—684no—
956C22⋊C4—684no—
957C22⋊C4—684no—
958C22⋊C4C22×#59512yes—
959C22⋊C4C22×#59512yes—
960C22⋊C4C22×#59514yes—
961C42—174no—
962C42—171no—
963C42—171no—
964C42—171no—
965C42—342no—
966C42—344no—
967C42—344no—
968C42—348no—
969C42—342no—
970C42—342no—
971C42—342no—
972C42—681no—
973C42—682no—
974C42—682no—
975C42C22×#59511yescharacteristic
976C23—28no—
977C23—44no—
978C23—44no—
979C23—171no—
980C23—174no—
981C23—174no—
982C23—172no—
983C23—172no—
984C23—174no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23—342no—
989C23—342no—
990C23—344no—
991C23—342no—
992C23—344no—
993C23—344no—
994C23—344no—
995C23—342no—
996C23—342no—
997C23—344no—
998C23—344no—
999C23—342no—
1000C23—342no—
1001C23—348no—
1002C23—348no—
1003C23—348no—
1004C23—684no—
1005C23—684no—
1006C23—684no—
1007C23—684no—
1008C23—684no—
1009C23—684no—
1010C23—1368no—
1011C23—1368no—
1012C23—1368no—
1013C23—1368no—
1014C23C23×#59512yes—
1015C23C23×#59514yes—
1016C23C23×#59512yes—
1017D4—28no—
1018D4—24no—
1019D4—22no—
1020D4—24no—
1021D4—44no—
1022D4—42no—
1023D4—178no—
1024D4—174no—
1025D4—348no—
1026D4—348no—
1027D4—344no—
1028D4—348no—
1029D4—348no—
1030D4—348no—
1031D4—344no—
1032D4—342no—
1033D4—344no—
1034D4—684no—
1035D4—682no—
1036D4—684no—
1037D4—684no—
1038D4—684no—
1039D4D4×#59514yescomplemented
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—171no—
1043C2×C4—171no—
1044C2×C4—172no—
1045C2×C4—172no—
1046C2×C4—172no—
1047C2×C4—172no—
1048C2×C4—172no—
1049C2×C4—172no—
1050C2×C4—174no—
1051C2×C4—172no—
1052C2×C4—171no—
1053C2×C4—172no—
1054C2×C4—172no—
1055C2×C4—344no—
1056C2×C4—344no—
1057C2×C4—342no—
1058C2×C4—341no—
1059C2×C4—342no—
1060C2×C4—341no—
1061C2×C4—342no—
1062C2×C4—342no—
1063C2×C4—344no—
1064C2×C4—344no—
1065C2×C4—341no—
1066C2×C4—341no—
1067C2×C4—342no—
1068C2×C4—341no—
1069C2×C4—341no—
1070C2×C4—341no—
1071C2×C4—341no—
1072C2×C4—342no—
1073C2×C4—344no—
1074C2×C4—344no—
1075C2×C4—342no—
1076C2×C4—342no—
1077C2×C4—344no—
1078C2×C4—342no—
1079C2×C4—341no—
1080C2×C4—341no—
1081C2×C4—341no—
1082C2×C4—342no—
1083C2×C4—344no—
1084C2×C4—342no—
1085C2×C4—342no—
1086C2×C4—342no—
1087C2×C4—344no—
1088C2×C4—342no—
1089C2×C4—342no—
1090C2×C4—688no—
1091C2×C4—688no—
1092C2×C4—1368no—
1093C2×C4—1368no—
1094C2×C4—1368no—
1095C2×C4C23×#59511yescharacteristic
1096C2×C4C23×#59512yes—
1097C2×C4C23×#59512yes—
1098C2×C4C23×#59511yescharacteristic
1099C2×C4C23×#59511yescharacteristic
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—24no—
1104C22—22no—
1105C22—24no—
1106C22—24no—
1107C22—22no—
1108C22—88no—
1109C22—171no—
1110C22—171no—
1111C22—171no—
1112C22—171no—
1113C22—171no—
1114C22—171no—
1115C22—174no—
1116C22—344no—
1117C22—344no—
1118C22—344no—
1119C22—344no—
1120C22—342no—
1121C22—342no—
1122C22—342no—
1123C22—344no—
1124C22—342no—
1125C22—344no—
1126C22—344no—
1127C22—342no—
1128C22—684no—
1129C22—684no—
1130C22—682no—
1131C22—682no—
1132C22—682no—
1133C22—682no—
1134C22—684no—
1135C22—684no—
1136C22—1368no—
1137C22—1368no—
1138C22—1368no—
1139C22C2×D4×#59514yes—
1140C22C24×#59511yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—21no—
1144C4—172no—
1145C4—172no—
1146C4—342no—
1147C4—342no—
1148C4—344no—
1149C4—342no—
1150C4—342no—
1151C4—342no—
1152C4—341no—
1153C4—682no—
1154C4—682no—
1155C4—682no—
1156C4—684no—
1157C4—681no—
1158C4C2×D4×#59512yes—
1159C4#1176387612yescomplemented
1160C2—24no—
1161C2—42no—
1162C2—44no—
1163C2—171no—
1164C2—171no—
1165C2—171no—
1166C2—171no—
1167C2—344no—
1168C2—682no—
1169C2—684no—
1170C2C22×D4×#59511yescharacteristic
1171C2C2×#1176387611yescharacteristic
1172C2H(5,𝔽2)×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingD42×C17C4
prime radicalD42×D17C2
cosocleC22×D17C25
hypercenterD42#595
hypocenterC17#34310
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#11763876C2semidirect
2. #14545314C2semidirect
3. #14545311C2semidirect
4. #14545309C2semidirect
5. #14545306C2semidirect
6. #14545302C2semidirect
7. D4×C4⋊#595C2semidirect
8. D4×C22⋊#595C2semidirect
9. D4×C22⋊#595C2semidirect
10. #14545272C2semidirect
11. #14545269C2semidirect
12. #127×#595C2semidirect
13. #121×#595C2semidirect
14. #14545241C2semidirect
15. C2×#11763761C2semidirect
16. C4×D4×#595C2semidirect
22. C2×D4×#595C22semidirect
23. C2×D4×#595C22semidirect
24. C2×D4×#595C22semidirect
25. C2×D4×#595C22semidirect
26. C2×D4×#595C22semidirect
27. C2×D4×#595C22semidirect
28. C2×D4×#595C22semidirect
29. C2×#10587677C22semidirect
30. C2×#10587677C22semidirect
31. C22×C4⋊#595C22semidirect
32. C22×C22⋊#595C22semidirect
33. C22×C22⋊#595C22semidirect
34. C22×C22⋊#595C22semidirect
35. C22×C4×#595C22semidirect
39. #11763761C22semidirect
40. #11763761C22semidirect
41. #11763761C22semidirect
42. #11763761C22semidirect
43. #11763761C22semidirect
44. #11763761C22semidirect
45. #11763761C22semidirect
46. #11763760C22semidirect
47. #11763760C22semidirect
48. #11763760C22semidirect
49. #11763759C22semidirect
50. #11763759C22semidirect
51. #11763759C22semidirect
52. #11763759C22semidirect
53. #11763759C22semidirect
54. #11763757C22semidirect
55. #11763757C22semidirect
56. #11763757C22semidirect
57. #11763757C22semidirect
58. #11763757C22semidirect
59. #11763756C22semidirect
60. #11763756C22semidirect
61. #11763755C22semidirect
62. #11763751C22semidirect
63. #11763751C22semidirect
64. #11763750C22semidirect
65. C4⋊C4×#595C22semidirect
66. C4⋊C4×#595C22semidirect
67. C4⋊C4×#595C22semidirect
68. C4×C4⋊#595C22semidirect
69. C4×C4⋊#595C22semidirect
70. C22⋊C4×#595C22semidirect
71. C22⋊C4×#595C22semidirect
72. C22⋊C4×#595C22semidirect
73. C4×C22⋊#595C22semidirect
74. C4×C22⋊#595C22semidirect
75. C42×#595C22semidirect
78. D4×D68C4semidirect
79. D4×D68C4semidirect
80. #11763444C4semidirect
81. #11763443C4semidirect
82. #11763443C4semidirect
83. D4×C22⋊D17C4semidirect
84. D4×C22⋊D17C4semidirect
85. #11763441C4semidirect
92. D42×C17C4semidirect
99. C22×D4×C17C2×C4semidirect
100. C22×D4×C17C2×C4semidirect
101. C22×C22⋊D17C2×C4semidirect
102. C22×C22⋊D17C2×C4semidirect
107. C2×D4×D17C2×C4semidirect
108. C2×D4×D17C2×C4semidirect
109. C2×D4×D17C2×C4semidirect
110. C2×D4×D17C2×C4semidirect
111. C2×D4×D17C2×C4semidirect
112. C2×D4×D17C2×C4semidirect
120. C22×D68C2×C4semidirect
121. C22×D68C2×C4semidirect
151. D4×#595D4semidirect
177. C17×#127C2×C4semidirect
178. C17×#121C2×C4semidirect
179. C17×#121C2×C4semidirect
180. C17×#120C2×C4semidirect
181. C4×D4×C17C2×C4semidirect
182. C4×D4×C17C2×C4semidirect
183. #10587639C2×C4semidirect
184. #10587626C2×C4semidirect
185. #10587626C2×C4semidirect
186. #10587626C2×C4semidirect
187. #10587625C2×C4semidirect
188. #10587625C2×C4semidirect
189. #10587624C2×C4semidirect
190. #10587624C2×C4semidirect
191. #10587623C2×C4semidirect
192. #10587623C2×C4semidirect
193. #10587623C2×C4semidirect
194. D4×Dic17C2×C4semidirect
195. D4×Dic17C2×C4semidirect
196. #10587616C2×C4semidirect
197. #10587616C2×C4semidirect
198. C4×C22⋊D17C2×C4semidirect
199. C4×C22⋊D17C2×C4semidirect
200. #10587581C2×C4semidirect
201. #10587581C2×C4semidirect
202. #10587579C2×C4semidirect
203. #10587579C2×C4semidirect
206. #10587570C2×C4semidirect
207. #10587570C2×C4semidirect
208. #10587568C2×C4semidirect
209. #10587568C2×C4semidirect
210. #10587568C2×C4semidirect
211. #10587567C2×C4semidirect
212. #10587567C2×C4semidirect
216. #10587560C2×C4semidirect
217. C4×D68C2×C4semidirect
218. C4×D68C2×C4semidirect
255. C22×#595C2×D4semidirect
345. C22⋊#595C2×D4semidirect
355. C4⋊#595C2×D4semidirect
366. C4×#595C2×D4semidirect
469. D4×C17C4×D4semidirect
485. C22⋊D17C4×D4semidirect
499. D68C4×D4semidirect
585. C4×C17#518semidirect
590. Dic17#518semidirect
601. D42#595semidirect
701. C22×D4C2×#595semidirect
702. C22×D4C2×#595semidirect
714. #127C2×#595semidirect
725. #121C2×#595semidirect
726. #121C2×#595semidirect
734. #120C2×#595semidirect
755. C4×D4C2×#595semidirect
756. C4×D4C2×#595semidirect
814. C17#34310semidirect
1039. D4D4×#595semidirect
1159. C4#11763876semidirect

Maximal subgroups

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

subgroupindex
C2×#117638762
#145453142
#145453112
#145453092
#145453062
#145453022
D4×C4⋊#5952
D4×C22⋊#5952
#145452722
#145452692
#127×#5952
#121×#5952
#145452412
C2×#117637612
C4×D4×#5952
D42×D172
#3431017