Finite Group Databasebeta

← #17957165

Subgroups — #17957165

Order 4352.

974 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587544C211yesmaximal, characteristic
2C22×C4×#3624C211yesmaximal, characteristic
3C2×#11763675C211yesmaximal, characteristic
4C2×#11763675C211yesmaximal, characteristic
5C2×#11763675C211yesmaximal, characteristic
6C2×#11763675C211yesmaximal, characteristic
7#95×Dic17C211yesmaximal, characteristic
8C23×#3624C2211yescharacteristic
9C23×#3624C2211yescharacteristic
10C23×#3624C2211yescharacteristic
11C23×#3624C2211yescharacteristic
12C2×#10587544—22no—
13C2×#10587544—22no—
14C2×#10587544C414yescomplemented
15C2×C4×#3624—22no—
16C2×C4×#3624—22no—
17C2×C4×#3624—22no—
18#11763675—22no—
19#11763675—22no—
20#11763675—22no—
21#11763675C414yescomplemented
22C22×C4×Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C2×#10587502C411yescharacteristic
26C2×#10587502C411yescharacteristic
27C2×#10587502C411yescharacteristic
28C2×C17×#95C411yescharacteristic
29C23×C4×C17C2×C411yescharacteristic
30C23×C4×C17C2×C411yescharacteristic
31C23×C4×C17C2×C411yescharacteristic
32C23×Dic17C2×C411yescharacteristic
33C23×Dic17C2×C411yescharacteristic
34C23×Dic17C2×C411yescharacteristic
35C23×Dic17C2311yescharacteristic
36C22×#3624—21no—
37C22×#3624—21no—
38C22×#3624—21no—
39C22×#3624—21no—
40C22×#3624—21no—
41C22×#3624—21no—
42C22×#3624—21no—
43C22×#3624—21no—
44C22×#3624—21no—
45C22×#3624—21no—
46C22×#3624—21no—
47C22×#3624—21no—
48C22×#3624—21no—
49C22×#3624—21no—
50C22×#3624—21no—
51C22×#3624—21no—
52C22×#3624—21no—
53C22×#3624—21no—
54C22×#3624—21no—
55C22×#3624—21no—
56C22×#3624C2×C412yes—
57C22×#3624C2×C412yes—
58C22×#3624C2×C412yes—
59C22×#3624C2×C412yes—
60C22×#3624D412yes—
61C22×#3624D412yes—
62C22×#3624D412yes—
63C22×#3624Q812yes—
64C2×C4×Dic17—21no—
65C2×C4×Dic17—21no—
66C2×C4×Dic17—21no—
67C2×C4×Dic17—21no—
68C2×C4×Dic17—21no—
69C2×C4×Dic17—21no—
70C2×C4×Dic17—21no—
71C2×C4×Dic17—21no—
72C2×C4×Dic17—21no—
73C2×C4×Dic17—21no—
74C2×C4×Dic17—21no—
75C2×C4×Dic17—21no—
76C2×C4×Dic17—21no—
77C2×C4×Dic17—21no—
78C2×C4×Dic17C2×C412yes—
79C2×C4×Dic17C2×C412yes—
80C2×C4×Dic17D412yes—
81C2×C4×Dic17Q812yes—
82#10587544—28no—
83C4×#3624—28no—
84C17×#95—22no—
85#10587502—22no—
86#10587502C814yescomplemented
87#10587502C814yescomplemented
88C24×C17C22×C411yescharacteristic
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—21no—
96C22×C4×C17—21no—
97C22×C4×C17—21no—
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—21no—
102C22×C4×C17—21no—
103C22×C4×C17—21no—
104C22×C4×C17—21no—
105C22×C4×C17C4212yes—
106C22×C4×C17C4⋊C412yes—
107C22×C4×C17C2×C812yes—
108C22×C4×C17C2×C812yes—
109C22×C4×C17M1612yes—
110C22×Dic17—21no—
111C22×Dic17—21no—
112C22×Dic17—21no—
113C22×Dic17—21no—
114C22×Dic17—21no—
115C22×Dic17—21no—
116C22×Dic17—21no—
117C22×Dic17—21no—
118C22×Dic17—21no—
119C22×Dic17—21no—
120C22×Dic17—21no—
121C22×Dic17—21no—
122C22×Dic17—21no—
123C22×Dic17—21no—
124C22×Dic17C4212yes—
125C22×Dic17C4⋊C412yes—
126C22×Dic17C2×C812yes—
127C22×Dic17C2×C812yes—
128C22×Dic17C2×C812yes—
129C22×Dic17C2×C812yes—
130C22×Dic17M1612yes—
131C22×Dic17C22×C411yescharacteristic
132C22×Dic17C22×C411yescharacteristic
133C22×Dic17C2×D411yescharacteristic
134C22×Dic17C2×D411yescharacteristic
135C22×Dic17C2×D411yescharacteristic
136C22×Dic17C2×D411yescharacteristic
137C22×Dic17C2×Q811yescharacteristic
138C22×Dic17C2×Q811yescharacteristic
139C22×Dic17#4111yescharacteristic
140C22×Dic17#4111yescharacteristic
141C22×Dic17#4111yescharacteristic
142C22×Dic17#4111yescharacteristic
143C22×Dic17#4111yescharacteristic
144C22×Dic17#4111yescharacteristic
145C2×#3624—22no—
146C2×#3624—22no—
147C2×#3624—22no—
148C2×#3624—22no—
149C2×#3624—22no—
150C2×#3624—22no—
151C2×#3624—22no—
152C2×#3624—22no—
153C2×#3624—22no—
154C2×#3624—22no—
155C2×#3624—22no—
156C2×#3624—22no—
157C2×#3624—22no—
158C2×#3624—22no—
159C2×#3624—22no—
160C2×#3624—22no—
161C2×#3624—22no—
162C2×#3624—22no—
163C2×#3624—41no—
164C2×#3624—41no—
165C2×#3624—41no—
166C2×#3624—41no—
167C2×#3624—41no—
168C2×#3624—41no—
169C2×#3624—41no—
170C2×#3624—41no—
171C2×#3624C22⋊C414yes—
172C2×#3624C4⋊C414yes—
173C4×Dic17—22no—
174C4×Dic17—22no—
175C4×Dic17—22no—
176C4×Dic17—22no—
177C4×Dic17—22no—
178C4×Dic17—22no—
179C4×Dic17—22no—
180C4×Dic17—22no—
181C4×Dic17—41no—
182C4×Dic17—41no—
183C4×Dic17—41no—
184C4×Dic17—41no—
185#10876—171nomaximal, Sylow
186C23×C17C2×C4211yescharacteristic
187C23×C17C2×C4⋊C411yescharacteristic
188C23×C17#11711yescharacteristic
189C23×C17C4×D411yescharacteristic
190C23×C17C4×D411yescharacteristic
191C23×C17C4×D411yescharacteristic
192C23×C17C4×Q811yescharacteristic
193C23×C17C22×C811yescharacteristic
194C23×C17C22×C811yescharacteristic
195C23×C17C2×M1611yescharacteristic
196C23×C17C2×M1611yescharacteristic
197C23×C17#13111yescharacteristic
198C23×C17#13111yescharacteristic
199C23×C17#13111yescharacteristic
200C23×C17#13111yescharacteristic
201C2×C4×C17—22no—
202C2×C4×C17—22no—
203C2×C4×C17—22no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17—22no—
212C2×C4×C17—22no—
213C2×C4×C17—41no—
214C2×C4×C17—41no—
215C2×C4×C17—41no—
216C2×C4×C17—41no—
217C2×C4×C17—41no—
218C2×C4×C17—41no—
219C2×C4×C17—41no—
220C2×C4×C17—41no—
221C2×C4×C17C4⋊C814yescomplemented
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17—22no—
225C2×Dic17—22no—
226C2×Dic17—22no—
227C2×Dic17—22no—
228C2×Dic17—22no—
229C2×Dic17—22no—
230C2×Dic17—22no—
231C2×Dic17—22no—
232C2×Dic17—22no—
233C2×Dic17—22no—
234C2×Dic17—22no—
235C2×Dic17—22no—
236C2×Dic17—22no—
237C2×Dic17—41no—
238C2×Dic17—41no—
239C2×Dic17—41no—
240C2×Dic17—41no—
241C2×Dic17C4×C814yescomplemented
242C2×Dic17C4⋊C814yescomplemented
243C2×Dic17C2×C22⋊C411yescharacteristic
244C2×Dic17C2×C4⋊C411yescharacteristic
245C2×Dic17#11711yescharacteristic
246C2×Dic17#11711yescharacteristic
247C2×Dic17C4×D411yescharacteristic
248C2×Dic17C4×D411yescharacteristic
249C2×Dic17C4×D411yescharacteristic
250C2×Dic17C4×D411yescharacteristic
251C2×Dic17C4×D411yescharacteristic
252C2×Dic17C4×Q811yescharacteristic
253C2×Dic17C4×Q811yescharacteristic
254C2×Dic17C4×Q811yescharacteristic
255C2×Dic17#12011yescharacteristic
256C2×Dic17#12111yescharacteristic
257C2×Dic17#12111yescharacteristic
258C2×Dic17C22⋊Q811yescharacteristic
259C2×Dic17C22⋊Q811yescharacteristic
260C2×Dic17C22⋊Q811yescharacteristic
261C2×Dic17C22⋊Q811yescharacteristic
262C2×Dic17#12311yescharacteristic
263C2×Dic17#12311yescharacteristic
264C2×Dic17#12311yescharacteristic
265C2×Dic17#12411yescharacteristic
266C2×Dic17#12511yescharacteristic
267C2×Dic17#12511yescharacteristic
268C2×Dic17#12611yescharacteristic
269C2×Dic17#12611yescharacteristic
270C2×Dic17C4⋊Q811yescharacteristic
271#3624—24no—
272#3624—24no—
273#3624—42no—
274#3624—42no—
275C22×C4⋊C8—171no—
276C22×C4×C8—171no—
277C2×#336—171no—
278C2×#336—171no—
279C2×#336—171no—
280C2×#336—171no—
281C4×#95—171no—
282C22×C17C4×C22⋊C411yescharacteristic
283C22×C17C4×C4⋊C411yescharacteristic
284C22×C17C4×C4⋊C411yescharacteristic
285C22×C17#38511yescharacteristic
286C22×C17#38711yescharacteristic
287C22×C17#38811yescharacteristic
288C22×C17#38911yescharacteristic
289C22×C17C2×C4×C811yescharacteristic
290C22×C17C4×M1611yescharacteristic
291C22×C17#40511yescharacteristic
292C22×C17#40511yescharacteristic
293C22×C17C2×C4⋊C811yescharacteristic
294C22×C17C2×C4⋊C811yescharacteristic
295C22×C17#42411yescharacteristic
296C22×C17#42411yescharacteristic
297C22×C17#43111yescharacteristic
298C22×C17#43111yescharacteristic
299C22×C17#43311yescharacteristic
300C22×C17#43311yescharacteristic
301C22×C17C8×D411yescharacteristic
302C22×C17C8×D411yescharacteristic
303C22×C17C8×D411yescharacteristic
304C22×C17C8×D411yescharacteristic
305C22×C17C8×D411yescharacteristic
306C22×C17C8×D411yescharacteristic
307C22×C17#43511yescharacteristic
308C22×C17#43511yescharacteristic
309C22×C17#43511yescharacteristic
310C22×C17#43511yescharacteristic
311C22×C17#43611yescharacteristic
312C22×C17#43611yescharacteristic
313C22×C17C8×Q811yescharacteristic
314C22×C17C8×Q811yescharacteristic
315C22×C17#44611yescharacteristic
316C22×C17#44611yescharacteristic
317C4×C17—24no—
318C4×C17—42no—
319C4×C17—42no—
320Dic17—24no—
321Dic17—24no—
322Dic17—42no—
323Dic17#38511yescharacteristic
324Dic17#38611yescharacteristic
325Dic17#38711yescharacteristic
326Dic17#38711yescharacteristic
327Dic17#38711yescharacteristic
328Dic17#38811yescharacteristic
329Dic17#38911yescharacteristic
330Dic17#39111yescharacteristic
331C23×C8—171no—
332C23×C8—171no—
333C23×C8—171no—
334C23×C8—171no—
335C22×C42—171no—
336C22×C42—171no—
337C22×C42—171no—
338C2×C4⋊C8—174no—
339C2×C4⋊C8—342no—
340C2×C4⋊C8—342no—
341C2×C4×C8—342no—
342C2×C4×C8—342no—
343C2×C4×C8—342no—
344C2×#95—171no—
345C2×#95—171no—
346C2×#95—171no—
347C2×#95#59511yescharacteristic
348#336—174no—
349#336—342no—
350#336—342no—
351#336—342no—
352C2×C17#143611yescharacteristic
353C2×C17C8×C22⋊C411yescharacteristic
354C2×C17#175311yescharacteristic
355C2×C17C4×C4⋊C811yescharacteristic
356C2×C17#176811yescharacteristic
357C2×C17C8×C4⋊C411yescharacteristic
358C2×C17#177111yescharacteristic
359C2×C17#185011yescharacteristic
360C2×C17#185011yescharacteristic
361C2×C17#191611yescharacteristic
362C2×C17#191611yescharacteristic
363C2×C17#192311yescharacteristic
364C2×C17#192311yescharacteristic
365C2×C17#193911yescharacteristic
366C2×C17#193911yescharacteristic
367C23×C4—171no—
368C23×C4—171no—
369C23×C4—171no—
370C23×C4—171no—
371C23×C4C2×#59511yescharacteristic
372C23×C4C2×#59511yescharacteristic
373C23×C4C2×#59511yescharacteristic
374C22×C8—172no—
375C22×C8—172no—
376C22×C8—172no—
377C22×C8—172no—
378C22×C8—172no—
379C22×C8—172no—
380C22×C8—172no—
381C22×C8—172no—
382C22×C8—341no—
383C22×C8—341no—
384C22×C8—341no—
385C22×C8—341no—
386C22×C8—341no—
387C22×C8—341no—
388C22×C8—341no—
389C22×C8—341no—
390C22×C8—341no—
391C22×C8—341no—
392C22×C8—341no—
393C22×C8—341no—
394C22×C8—341no—
395C22×C8—341no—
396C22×C8—341no—
397C22×C8—341no—
398C22×C8—341no—
399C22×C8—341no—
400C22×C8—341no—
401C22×C8—341no—
402C2×C42—172no—
403C2×C42—172no—
404C2×C42—172no—
405C2×C42—172no—
406C2×C42—341no—
407C2×C42—341no—
408C2×C42—341no—
409C2×C42—341no—
410C2×C42—341no—
411C2×C42—341no—
412C2×C42—341no—
413C2×C42—341no—
414C2×C42—341no—
415C2×C42—341no—
416C2×C42—341no—
417C2×C42—341no—
418C2×C42—341no—
419C2×C42—341no—
420C4⋊C8—348no—
421C4×C8—348no—
422#95—22no—
423#95—174no—
424#95—174no—
425#95—342no—
426C17#1087611yescharacteristic, complemented, Sylow
427C24C22×#59511yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—171no—
445C22×C4—171no—
446C22×C4—171no—
447C22×C4—171no—
448C22×C4—171no—
449C22×C4—171no—
450C22×C4—171no—
451C22×C4—171no—
452C22×C4—171no—
453C22×C4—171no—
454C22×C4—171no—
455C22×C4—171no—
456C22×C4—171no—
457C22×C4—171no—
458C22×C4—172no—
459C22×C4—172no—
460C22×C4—172no—
461C22×C4—172no—
462C22×C4—172no—
463C22×C4—172no—
464C22×C4—172no—
465C22×C4—341no—
466C22×C4—341no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—341no—
471C22×C4—341no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—341no—
477C22×C4—341no—
478C22×C4—341no—
479C22×C4#6324212yes—
480C22×C4#6324212yes—
481C22×C4C4×#59512yes—
482C22×C4C4⋊#59512yes—
483C22×C4#6324712yes—
484C2×C8—174no—
485C2×C8—174no—
486C2×C8—342no—
487C2×C8—342no—
488C2×C8—342no—
489C2×C8—342no—
490C2×C8—342no—
491C2×C8—342no—
492C2×C8—342no—
493C2×C8—342no—
494C2×C8—342no—
495C2×C8—342no—
496C2×C8—342no—
497C2×C8—342no—
498C2×C8—342no—
499C2×C8—342no—
500C2×C8—342no—
501C2×C8—342no—
502C2×C8—342no—
503C2×C8—342no—
504C2×C8—681no—
505C2×C8—681no—
506C2×C8—681no—
507C2×C8—681no—
508C2×C8—681no—
509C2×C8—681no—
510C2×C8—681no—
511C2×C8—681no—
512C42—342no—
513C42—342no—
514C42—342no—
515C42—342no—
516C42—342no—
517C42—342no—
518C42—342no—
519C42—342no—
520C42—681no—
521C42—681no—
522C42—681no—
523C42—681no—
524C23C2×#6324211yescharacteristic
525C23C2×#6324211yescharacteristic
526C23D17⋊M1611yescharacteristic
527C23C2×C4×#59511yescharacteristic
528C23C2×C4⋊#59511yescharacteristic
529C23#1058767711yescharacteristic
530C23#1058767811yescharacteristic
531C23#1058767811yescharacteristic
532C23#1058767811yescharacteristic
533C23D4×#59511yescharacteristic
534C23D4×#59511yescharacteristic
535C23D4×#59511yescharacteristic
536C23#1058768011yescharacteristic
537C23Q8×#59511yescharacteristic
538C23C2×#6324711yescharacteristic
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—171no—
560C2×C4—171no—
561C2×C4—171no—
562C2×C4—171no—
563C2×C4—171no—
564C2×C4—171no—
565C2×C4—171no—
566C2×C4—171no—
567C2×C4—171no—
568C2×C4—171no—
569C2×C4—171no—
570C2×C4—171no—
571C2×C4—171no—
572C2×C4—171no—
573C2×C4—171no—
574C2×C4—171no—
575C2×C4—171no—
576C2×C4—171no—
577C2×C4—171no—
578C2×C4—171no—
579C2×C4—171no—
580C2×C4—171no—
581C2×C4—171no—
582C2×C4—171no—
583C2×C4—171no—
584C2×C4—171no—
585C2×C4—171no—
586C2×C4—171no—
587C2×C4—174no—
588C2×C4—174no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—342no—
592C2×C4—342no—
593C2×C4—342no—
594C2×C4—342no—
595C2×C4—342no—
596C2×C4—342no—
597C2×C4—342no—
598C2×C4—342no—
599C2×C4—342no—
600C2×C4—342no—
601C2×C4—342no—
602C2×C4—342no—
603C2×C4—342no—
604C2×C4—681no—
605C2×C4—681no—
606C2×C4—681no—
607C2×C4—681no—
608C2×C4#1058754414yescomplemented
609C8—344no—
610C8—344no—
611C8—682no—
612C8—682no—
613C22C22⋊C4×#59511yescharacteristic
614C22C4×C4⋊#59511yescharacteristic
615C22C4⋊C4×#59511yescharacteristic
616C22#1176375611yescharacteristic
617C22#1176375811yescharacteristic
618C22#1176375911yescharacteristic
619C22#1176376011yescharacteristic
620C22C4×#6324211yescharacteristic
621C22C4×#6324711yescharacteristic
622C22#1176377311yescharacteristic
623C22#1176377411yescharacteristic
624C22#1176381011yescharacteristic
625C22C2×#1058754411yescharacteristic
626C22#1176381511yescharacteristic
627C22#1176381611yescharacteristic
628C22#1176382611yescharacteristic
629C22#1176382711yescharacteristic
630C22#1176383311yescharacteristic
631C22#1176383411yescharacteristic
632C22#1176383611yescharacteristic
633C22#1176383611yescharacteristic
634C22#1176383611yescharacteristic
635C22#1176383611yescharacteristic
636C22#1176383711yescharacteristic
637C22#1176383711yescharacteristic
638C22#1176383911yescharacteristic
639C22#1176384011yescharacteristic
640C22#1176384011yescharacteristic
641C22#1176384111yescharacteristic
642C22#1176384211yescharacteristic
643C22#1176384411yescharacteristic
644C22#1176385811yescharacteristic
645C22#1176385811yescharacteristic
646C22#1176386011yescharacteristic
647C22#1176386111yescharacteristic
648C4—24no—
649C4—42no—
650C4—42no—
651C4—171no—
652C4—171no—
653C4—171no—
654C4—171no—
655C4—171no—
656C4—171no—
657C4—171no—
658C4—171no—
659C4—344no—
660C4—344no—
661C4—682no—
662C2#1454396411yescharacteristic
663C2#1454451811yescharacteristic
664C2#1454452611yescharacteristic
665C2C4×#1058754411yescharacteristic
666C2#1454457211yescharacteristic
667C2#1454457611yescharacteristic
668C2#1454458411yescharacteristic
669C2#1454472811yescharacteristic
670C2#1454472911yescharacteristic
671C2#1454483911yescharacteristic
672C2#1454484011yescharacteristic
673C2#1454485411yescharacteristic
674C2#1454485511yescharacteristic
675C2#1454488211yescharacteristic
676C2#1454488311yescharacteristic
subgroupG/H
center, FrattiniC24C22×#595
commutatorC22×C17C2×C4×C8
FittingC2×C17×#95C4
socle, prime radicalC24×C17C22×C4
cosocleC23×Dic17C23
hypercenterC2×#95#595
hypocenterC17#10876
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
14. C2×#10587544C4semidirect
21. #11763675C4semidirect
86. #10587502C8semidirect
87. #10587502C8semidirect
221. C2×C4×C17C4⋊C8semidirect
241. C2×Dic17C4×C8semidirect
242. C2×Dic17C4⋊C8semidirect
426. C17#10876semidirect
608. C2×C4#10587544semidirect

Maximal subgroups

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

subgroupindex
C22×#105875442
C22×C4×#36242
C2×#117636752
#95×Dic172
#1087617