Finite Group Databasebeta

← #17964700

Subgroups — #17964700

Order 4352.

1282 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545448C211yesmaximal, characteristic
2#14545448C211yesmaximal, characteristic
3#14544088C212yesmaximal, complemented
4#14544087C214yesmaximal, complemented
5#14544086C212yesmaximal, complemented
6#14544073C214yesmaximal, complemented
7C2×C4×Q8×D17C211yesmaximal, characteristic
8#11763828—21no—
9#11763828C2212yes—
10#11763827—21no—
11#11763827C2212yes—
12#11763826—21no—
13#11763826—21no—
14#11763825C2212yes—
15#11763825C2212yes—
16#11763810—21no—
17#11763810C2212yes—
18#11763777—21no—
19#11763777—21no—
20C4×#63242—21no—
21C4×#63242C2212yes—
22#11763659C2218yescomplemented
23Q8⋊#3624C2218yescomplemented
24C22×Q8×D17C411yescharacteristic
25C2×Q8×Dic17C2211yescharacteristic
26C2×C4×Dic34—21no—
27C2×C4×Dic34C411yescharacteristic
28C2×#10587573—21no—
29C2×#10587573C2211yescharacteristic
30C4×Q8×D17—21no—
31C4×Q8×D17—21no—
32C4×Q8×D17—21no—
33C4×Q8×D17—21no—
34C4×Q8×D17C412yes—
35C4×Q8×D17C412yes—
36C4×Q8×D17C2212yes—
37C4×Q8×D17C2212yes—
38C2×C4⋊C4×D17—21no—
39C2×C4⋊C4×D17C411yescharacteristic
40C2×C42×D17—21no—
41C2×C42×D17C2211yescharacteristic
42C2×C4×Q8×C17C411yescharacteristic
43C22×Q8×C17C2×C411yescharacteristic
44C2×Q8×D17—21no—
45C2×Q8×D17—21no—
46C2×Q8×D17—24no—
47C2×Q8×D17C818yescomplemented
48C2×Q8×D17C2×C412yes—
49C2×Q8×D17C2×C412yes—
50C22×C4×D17—21no—
51C22×C4×D17—21no—
52C22×C4×D17C2×C411yescharacteristic
53C22×C4×D17D411yescharacteristic
54C22×C4×D17D411yescharacteristic
55C22×Dic34—21no—
56C22×Dic34C2×C411yescharacteristic
57C2×#63242—22no—
58C2×#63242—22no—
59C4×Q8×C17—21no—
60C4×Q8×C17—21no—
61C4×Q8×C17C2×C412yes—
62C4×Q8×C17C2×C412yes—
63C2×C4⋊C4×C17—21no—
64C2×C4⋊C4×C17C2×C411yescharacteristic
65C2×C42×C17—21no—
66C2×C42×C17C2×C411yescharacteristic
67Q8×Dic17—21no—
68Q8×Dic17—21no—
69Q8×Dic17C2×C412yes—
70Q8×Dic17C2312yes—
71C2×C4⋊Dic17—21no—
72C2×C4⋊Dic17C2×C411yescharacteristic
73C2×#63225—21no—
74C2×#63225—21no—
75C2×#63225—21no—
76C2×C4×Dic17—21no—
77C2×C4×Dic17—21no—
78C2×C4×Dic17—21no—
79C2×C4×Dic17D411yescharacteristic
80C2×C4×Dic17D411yescharacteristic
81C2×C4×Dic17C2311yescharacteristic
82C4⋊C4×D17—22no—
83C4⋊C4×D17—22no—
84C4⋊C4×D17—21no—
85C4⋊C4×D17—21no—
86C4⋊C4×D17—22no—
87C4⋊C4×D17—22no—
88C4⋊C4×D17C2×C412yes—
89C4⋊C4×D17C2×C412yes—
90#10587573—22no—
91#10587573—22no—
92#10587573—21no—
93#10587573—21no—
94#10587573—22no—
95#10587573—22no—
96#10587573C2×C412yes—
97#10587573C2312yes—
98C42×D17—22no—
99C42×D17—22no—
100C42×D17—22no—
101C42×D17—22no—
102C42×D17C2×C411yescharacteristic
103C42×D17C2×C411yescharacteristic
104C42×D17D411yescharacteristic
105C42×D17D411yescharacteristic
106C42×D17D411yescharacteristic
107C42×D17D411yescharacteristic
108C42×D17C2311yescharacteristic
109C42×D17C2311yescharacteristic
110C4×Dic34—22no—
111C4×Dic34—22no—
112C4×Dic34—22no—
113C4×Dic34—22no—
114C4×Dic34—21no—
115C4×Dic34—21no—
116C4×Dic34C2×C412yes—
117C4×Dic34C2×C412yes—
118C22⋊#3624—22no—
119C22⋊#3624—22no—
120#10587544—22no—
121#10587544—22no—
122#10587543—22no—
123#10587543—22no—
124C4⋊#3624—22no—
125C4⋊#3624C2314yes—
126C4×#3624—22no—
127C4×#3624—22no—
128C4×#3624—22no—
129C4×#3624C2314yes—
130C23×D17C22⋊C411yescharacteristic
131C2×Q8×C17—21no—
132C2×Q8×C17—22no—
133C2×Q8×C17C2×C814yescomplemented
134C2×Q8×C17C22×C412yes—
135C22×C4×C17—21no—
136C22×C4×C17—21no—
137C22×C4×C17C22⋊C411yescharacteristic
138C22×C4×C17C22⋊C411yescharacteristic
139C22×C4×C17C22×C411yescharacteristic
140C22×Dic17—21no—
141C22×Dic17—21no—
142C22×Dic17C22⋊C411yescharacteristic
143C22×Dic17C2×D411yescharacteristic
144C22×Dic17C2×D411yescharacteristic
145Q8×D17—28no—
146Q8×D17—28no—
147Q8×D17—24no—
148Q8×D17—24no—
149Q8×D17C2×C818yes—
150Q8×D17C2×C818yescomplemented
151C2×C4×D17—28no—
152C2×C4×D17—22no—
153C2×C4×D17—22no—
154C2×C4×D17—24no—
155C2×C4×D17—22no—
156C2×C4×D17—22no—
157C2×C4×D17—42no—
158C2×C4×D17—44no—
159C2×C4×D17C22⋊C411yescharacteristic
160C2×C4×D17C22⋊C411yescharacteristic
161C2×C4×D17C22⋊C411yescharacteristic
162C2×C4×D17C22⋊C411yescharacteristic
163C2×C4×D17C22⋊C411yescharacteristic
164C2×C4×D17C22⋊C411yescharacteristic
165C2×C4×D17C2×C814yes—
166C2×C4×D17M1614yes—
167C2×C4×D17C22×C411yescharacteristic
168C2×C4×D17C22×C411yescharacteristic
169C2×C4×D17C2×D411yescharacteristic
170C2×C4×D17C2×D411yescharacteristic
171C2×C4×D17C2×D411yescharacteristic
172C2×C4×D17C2×D411yescharacteristic
173C2×Dic34—21no—
174C2×Dic34—22no—
175C2×Dic34—28no—
176C2×Dic34—22no—
177C2×Dic34—22no—
178C2×Dic34C2×C814yescomplemented
179C2×Dic34C22×C412yes—
180C2×#3624—24no—
181C2×#3624—24no—
182#63242—44no—
183#63242—44no—
184C4⋊C4×C17—22no—
185C4⋊C4×C17—22no—
186C4⋊C4×C17—21no—
187C4⋊C4×C17C22×C412yes—
188C42×C17—22no—
189C42×C17—22no—
190C42×C17C22⋊C411yescharacteristic
191C42×C17C22⋊C411yescharacteristic
192C42×C17C22×C411yescharacteristic
193C42×C17C22×C411yescharacteristic
194C4⋊Dic17—21no—
195C4⋊Dic17—22no—
196C4⋊Dic17—22no—
197C4⋊Dic17C22×C412yes—
198#63225—22no—
199#63225—22no—
200#63225—22no—
201#63225—22no—
202#63225—22no—
203#63225—22no—
204C4×Dic17—22no—
205C4×Dic17—22no—
206C4×Dic17—22no—
207C4×Dic17—22no—
208C4×Dic17—22no—
209C4×Dic17—22no—
210C4×Dic17C22⋊C411yescharacteristic
211C4×Dic17C22⋊C411yescharacteristic
212C4×Dic17C22⋊C411yescharacteristic
213C4×Dic17C22⋊C411yescharacteristic
214C4×Dic17C22×C411yescharacteristic
215C4×Dic17C2×D411yescharacteristic
216C4×Dic17C2×D411yescharacteristic
217C4×Dic17C2×D411yescharacteristic
218C4×Dic17C2×D411yescharacteristic
219C4×Dic17C2×D411yescharacteristic
220C4×Dic17C2×D411yescharacteristic
221C4×Dic17C2411yescharacteristic
222C2×#1479—171nomaximal, Sylow
223C23×C17C2×C22⋊C411yescharacteristic
224C22×D17—22no—
225C22×D17—22no—
226C22×D17C22⋊C814yes—
227C22×D17C2×C22⋊C411yescharacteristic
228C22×D17C2×C22⋊C411yescharacteristic
229Q8×C17—22no—
230Q8×C17—24no—
231Q8×C17C22×C814yes—
232C2×C4×C17—22no—
233C2×C4×C17—24no—
234C2×C4×C17—22no—
235C2×C4×C17—22no—
236C2×C4×C17—41no—
237C2×C4×C17—42no—
238C2×C4×C17C2×C22⋊C411yescharacteristic
239C2×C4×C17C2×C22⋊C411yescharacteristic
240C2×C4×C17C2×C22⋊C411yescharacteristic
241C2×C4×C17C2×C22⋊C411yescharacteristic
242C2×C4×C17C2×C22⋊C411yescharacteristic
243C2×C4×C17C22×C812yes—
244C2×C4×C17C2×M1612yes—
245C2×C4×C17C23×C411yescharacteristic
246C2×Dic17—22no—
247C2×Dic17—24no—
248C2×Dic17—22no—
249C2×Dic17—22no—
250C2×Dic17—41no—
251C2×Dic17—42no—
252C2×Dic17C22⋊C814yes—
253C2×Dic17C2×C22⋊C411yescharacteristic
254C2×Dic17C2×C22⋊C411yescharacteristic
255C2×Dic17C2×C22⋊C411yescharacteristic
256C2×Dic17C2×C22⋊C411yescharacteristic
257C2×Dic17C22×D411yescharacteristic
258C2×Dic17C22×D411yescharacteristic
259C4×D17—28no—
260C4×D17—28no—
261C4×D17—22no—
262C4×D17—22no—
263C4×D17—22no—
264C4×D17—22no—
265C4×D17—22no—
266C4×D17—41no—
267C4×D17—41no—
268C4×D17—44no—
269C4×D17—44no—
270C4×D17C22⋊C814yes—
271C4×D17C22⋊C814yes—
272C4×D17C22×C812yes—
273C4×D17C22×C812yes—
274C4×D17C2×M1612yes—
275C4×D17C2×M1612yes—
276C4×D17#13714yes—
277Dic34—22no—
278Dic34—24no—
279Dic34—28no—
280Dic34—28no—
281Dic34C22×C814yes—
282#3624—44no—
283#3624—44no—
284C22×C4×Q8—171no—
285C2×#431—171no—
286C2×#431—171no—
287#1479—172no—
288#1479—174no—
289#1479—172no—
290C2×Q8⋊C8—174no—
291C22×C17—21no—
292C22×C17—21no—
293C22×C17C2×C22⋊C812yes—
294C22×C17C22×C22⋊C411yescharacteristic
295C2×D17—21no—
296C2×D17—21no—
297C2×D17—28no—
298C2×D17C2×C22⋊C812yes—
299C2×D17C2×C22⋊C812yes—
300C2×D17#41912yes—
301C2×D17#42112yes—
302C4×C17—24no—
303C4×C17—21no—
304C4×C17—21no—
305C4×C17—21no—
306C4×C17—42no—
307C4×C17C2×C22⋊C812yes—
308C4×C17#41912yes—
309C4×C17C23×C811yescharacteristic
310C4×C17C22×M1611yescharacteristic
311Dic17—24no—
312Dic17—21no—
313Dic17—21no—
314Dic17—21no—
315Dic17—42no—
316Dic17C2×C22⋊C812yes—
317Dic17C2×C22⋊C812yes—
318Dic17C2×#13712yes—
319C23×Q8—171no—
320C2×C4×Q8—171no—
321C2×C4×Q8—172no—
322C2×C4×Q8—172no—
323C2×C4×Q8—172no—
324C2×C4×Q8—172no—
325C2×C4×Q8—171no—
326C2×C4×Q8—171no—
327C2×C4×Q8—341no—
328C2×C4×Q8—341no—
329C2×C4×Q8—341no—
330C2×C4×Q8—341no—
331C2×C4×Q8—341no—
332C2×C4×Q8—341no—
333C2×C4×Q8#59511yescharacteristic
334C22×C4⋊C4—171no—
335C22×C4⋊C4—341no—
336C22×C42—171no—
337C22×C42—341no—
338#431—172no—
339#431—172no—
340#431—172no—
341#431—172no—
342#431—341no—
343#431—341no—
344#431—341no—
345#431—341no—
346C2×C4⋊C8—172no—
347C2×C4⋊C8—341no—
348C2×C22⋊C8—341no—
349C2×C22⋊C8—341no—
350C2×C4×C8—172no—
351C2×C4×C8—341no—
352Q8⋊C8—178no—
353Q8⋊C8—178no—
354C2×C17—22no—
355C2×C17C22×C22⋊C811yescharacteristic
356C2×C17C2×#41911yescharacteristic
357C2×C17C2×#42111yescharacteristic
358D17—22no—
359D17#147914yescomplemented
360C22×Q8—178no—
361C22×Q8—172no—
362C22×Q8—172no—
363C22×Q8—171no—
364C22×Q8—341no—
365C22×Q8—341no—
366C22×Q8—341no—
367C22×Q8—344no—
368C22×Q8C2×#59511yescharacteristic
369C23×C4—171no—
370C23×C4—171no—
371C23×C4—171no—
372C23×C4—341no—
373C23×C4—341no—
374C22×C8—342no—
375C22×C8—342no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—172no—
379C4×Q8—172no—
380C4×Q8—172no—
381C4×Q8—172no—
382C4×Q8—172no—
383C4×Q8—172no—
384C4×Q8—342no—
385C4×Q8—342no—
386C4×Q8—342no—
387C4×Q8—342no—
388C4×Q8—342no—
389C4×Q8—341no—
390C4×Q8—342no—
391C4×Q8—341no—
392C4×Q8—342no—
393C4×Q8—342no—
394C4×Q8—341no—
395C4×Q8—341no—
396C4×Q8—341no—
397C4×Q8—341no—
398C4×Q8C2×#59512yes—
399C4×Q8C2×#59512yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4—172no—
403C2×C4⋊C4—172no—
404C2×C4⋊C4—341no—
405C2×C4⋊C4—341no—
406C2×C4⋊C4—342no—
407C2×C4⋊C4—342no—
408C2×C4⋊C4—342no—
409C2×C4⋊C4—342no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—341no—
414C2×C4⋊C4C2×#59511yescharacteristic
415C2×C42—21no—
416C2×C42—171no—
417C2×C42—171no—
418C2×C42—171no—
419C2×C42—171no—
420C2×C42—171no—
421C2×C42—171no—
422C2×C42—171no—
423C2×C42—171no—
424C2×C42—171no—
425C2×C42—171no—
426C2×C42—171no—
427C2×C42—342no—
428C2×C42—342no—
429C2×C42—342no—
430C2×C42—342no—
431C2×C42—341no—
432C2×C42—341no—
433C2×C42—341no—
434C2×C42C2×#59511yescharacteristic
435C4⋊C8—174no—
436C4⋊C8—342no—
437C4⋊C8—342no—
438C4⋊C8—342no—
439C22⋊C8—342no—
440C22⋊C8—342no—
441C22⋊C8—342no—
442C22⋊C8—342no—
443C4×C8—174no—
444C4×C8—342no—
445C4×C8—342no—
446C4×C8—342no—
447C17C2×#147911yescharacteristic, complemented, Sylow
448C24—171no—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—178no—
452C2×Q8—178no—
453C2×Q8—174no—
454C2×Q8—172no—
455C2×Q8—342no—
456C2×Q8—342no—
457C2×Q8—348no—
458C2×Q8—348no—
459C2×Q8—348no—
460C2×Q8—344no—
461C2×Q8—344no—
462C2×Q8—342no—
463C2×Q8—341no—
464C2×Q8#6324214yescomplemented
465C2×Q8C22×#59512yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—171no—
469C22×C4—174no—
470C22×C4—174no—
471C22×C4—171no—
472C22×C4—171no—
473C22×C4—171no—
474C22×C4—171no—
475C22×C4—171no—
476C22×C4—171no—
477C22×C4—171no—
478C22×C4—171no—
479C22×C4—171no—
480C22×C4—171no—
481C22×C4—171no—
482C22×C4—171no—
483C22×C4—171no—
484C22×C4—171no—
485C22×C4—344no—
486C22×C4—342no—
487C22×C4—342no—
488C22×C4—348no—
489C22×C4—342no—
490C22×C4—342no—
491C22×C4—341no—
492C22×C4—341no—
493C22×C4—682no—
494C22×C4—684no—
495C22×C4C22⋊#59511yescharacteristic
496C22×C4C22⋊#59511yescharacteristic
497C22×C4C22×#59511yescharacteristic
498C2×C8—344no—
499C2×C8—344no—
500C2×C8—684no—
501C2×C8—684no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—172no—
506C4⋊C4—342no—
507C4⋊C4—342no—
508C4⋊C4—342no—
509C4⋊C4—342no—
510C4⋊C4—342no—
511C4⋊C4—342no—
512C4⋊C4—341no—
513C4⋊C4—342no—
514C4⋊C4—342no—
515C4⋊C4C22×#59512yes—
516C42—22no—
517C42—22no—
518C42—171no—
519C42—171no—
520C42—171no—
521C42—171no—
522C42—171no—
523C42—171no—
524C42—171no—
525C42—171no—
526C42—171no—
527C42—171no—
528C42—171no—
529C42—171no—
530C42—342no—
531C42—342no—
532C42—342no—
533C42—342no—
534C42—342no—
535C42—342no—
536C42C22⋊#59511yescharacteristic
537C42C22⋊#59511yescharacteristic
538C42C22×#59511yescharacteristic
539C42C22×#59511yescharacteristic
540C23—171no—
541C23—174no—
542C23—171no—
543C23—342no—
544C23—342no—
545C23C2×C22⋊#59511yescharacteristic
546Q8—24no—
547Q8—22no—
548Q8—174no—
549Q8—348no—
550Q8—348no—
551Q8—344no—
552Q8—342no—
553Q8C2×#6324214yes—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—174no—
561C2×C4—171no—
562C2×C4—171no—
563C2×C4—171no—
564C2×C4—174no—
565C2×C4—174no—
566C2×C4—174no—
567C2×C4—172no—
568C2×C4—172no—
569C2×C4—172no—
570C2×C4—172no—
571C2×C4—171no—
572C2×C4—171no—
573C2×C4—171no—
574C2×C4—342no—
575C2×C4—342no—
576C2×C4—342no—
577C2×C4—342no—
578C2×C4—348no—
579C2×C4—348no—
580C2×C4—342no—
581C2×C4—344no—
582C2×C4—342no—
583C2×C4—342no—
584C2×C4—342no—
585C2×C4—681no—
586C2×C4—681no—
587C2×C4—684no—
588C2×C4—684no—
589C2×C4—681no—
590C2×C4—682no—
591C2×C4C2×#6324212yes—
592C2×C4D17⋊M1612yes—
593C2×C4C2×C22⋊#59511yescharacteristic
594C2×C4C2×C22⋊#59511yescharacteristic
595C2×C4C2×C22⋊#59511yescharacteristic
596C2×C4C2×C22⋊#59511yescharacteristic
597C2×C4C2×C22⋊#59511yescharacteristic
598C2×C4C23×#59511yescharacteristic
599C8—684no—
600C8—684no—
601C22—21no—
602C22—21no—
603C22—172no—
604C22—172no—
605C22—172no—
606C22—172no—
607C22—348no—
608C22—341no—
609C22—341no—
610C22#1176377712yes—
611C22C22×C22⋊#59511yescharacteristic
612C4—21no—
613C4—21no—
614C4—24no—
615C4—21no—
616C4—42no—
617C4—172no—
618C4—172no—
619C4—172no—
620C4—341no—
621C4—341no—
622C4—344no—
623C4—341no—
624C4—682no—
625C4#1176377712yes—
626C4#1176380212yes—
627C4C22×#6324211yescharacteristic
628C4C2×D17⋊M1611yescharacteristic
629C2—22no—
630C2—174no—
631C2—342no—
632C2C2×#1176377711yescharacteristic
633C2C2×#1176380211yescharacteristic
634C2D17⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C4×Q8×C17C4
socleC22×C17C22×C22⋊C4
prime radicalC23×D17C22⋊C4
cosocleC4×Dic17C24
hypercenterC2×C4×Q8#595
hypocenterC17C2×#1479
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #14544088C2semidirect
4. #14544087C2semidirect
5. #14544086C2semidirect
6. #14544073C2semidirect
22. #11763659C22semidirect
23. Q8⋊#3624C22semidirect
47. C2×Q8×D17C8semidirect
133. C2×Q8×C17C2×C8semidirect
150. Q8×D17C2×C8semidirect
178. C2×Dic34C2×C8semidirect
359. D17#1479semidirect
447. C17C2×#1479semidirect
464. C2×Q8#63242semidirect

Maximal subgroups

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

subgroupindex
#145454482
#145440882
#145440872
#145440862
#145440732
C2×C4×Q8×D172
C2×#147917