Finite Group Databasebeta

← #17956952

Subgroups — #17956952

Order 4352.

914 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×#595C211yesmaximal, characteristic
2C2×#11763683C211yesmaximal, characteristic
3C2×#11763682C211yesmaximal, characteristic
4C2×#11763682C211yesmaximal, characteristic
5C2×#11763674C211yesmaximal, characteristic
6#14543961C211yesmaximal, characteristic
7D17×#340C211yesmaximal, characteristic
8C22×#63242C2211yescharacteristic
9C22×C4⋊#595C2211yescharacteristic
10C22×C4⋊#595C2211yescharacteristic
11C22×C4×#595—21no—
12C22×C4×#595C2211yescharacteristic
13C4⋊C4×#595—22no—
14C4⋊C4×#595C414yescomplemented
15C2×(C2×#595)⋊C4—21no—
16C2×(C2×#595)⋊C4—21no—
17C2×(C2×#595)⋊C4—21no—
18#11763683—22no—
19#11763682—22no—
20#11763682C414yescomplemented
21#11763674—22no—
22C22×C8×D17C2211yescharacteristic
23C2×C4⋊C4×D17C2211yescharacteristic
24C2×C4⋊C4×D17C2211yescharacteristic
25#11762572C411yescharacteristic, complemented
26#11762571C411yescharacteristic, complemented
27#11762571C411yescharacteristic, complemented
28C17×#340C411yescharacteristic, complemented
29C23×#595—21no—
30C23×#595—21no—
31C23×#595D411yescharacteristic
32C23×#595D411yescharacteristic
33C22×C4×D17—21no—
34C22×C4×D17—21no—
35C22×C4×D17C2311yescharacteristic
36C22×#3624—21no—
37C2×C4⋊#595—21no—
38C2×C4⋊#595—21no—
39C2×C4⋊#595—21no—
40C2×C4⋊#595—21no—
41C2×C4⋊#595—21no—
42C2×C4⋊#595—21no—
43C2×C4⋊#595—21no—
44C2×C4⋊#595—21no—
45C2×C4⋊#595C2×C412yes—
46C2×C4⋊#595C2×C412yes—
47C2×C4⋊#595D412yes—
48C2×C4⋊#595Q812yes—
49C2×C4×#595—21no—
50C2×C4×#595—21no—
51C2×C4×#595—21no—
52C2×C4×#595—21no—
53C2×C4×#595—24no—
54C2×C4×#595—42no—
55C2×C4×#595—42no—
56C2×C4×#595C2×C412yes—
57C2×C4×#595D412yes—
58C2×#63242—21no—
59C2×#63242—21no—
60C2×#63242—21no—
61C2×#63242—21no—
62C2×#63242—21no—
63C2×#63242C2×C412yes—
64C22×C8×C17C2×C411yescharacteristic
65C2×C4⋊C4×C17C2×C411yescharacteristic
66C2×C4⋊C4×C17C2×C411yescharacteristic
67C2×C4⋊Dic17C2×C411yescharacteristic
68C2×C4⋊Dic17C2×C411yescharacteristic
69C2×#63225—21no—
70C2×#63225—21no—
71C22×#3622C2×C411yescharacteristic
72C2×C8×D17—21no—
73C2×C8×D17—21no—
74C2×C8×D17—21no—
75C2×C8×D17—21no—
76C2×C8×D17—21no—
77C2×C8×D17—21no—
78C4⋊C4×D17—21no—
79C4⋊C4×D17—21no—
80C4⋊C4×D17—21no—
81C4⋊C4×D17—21no—
82C4⋊C4×D17—21no—
83C4⋊C4×D17—21no—
84C4⋊C4×D17C2×C412yes—
85C4⋊C4×D17C2×C412yes—
86(C2×#595)⋊C4—24no—
87(C2×#595)⋊C4—42no—
88(C2×#595)⋊C4—42no—
89C23×D17C2×D411yescharacteristic
90C22×#595—21no—
91C22×#595—21no—
92C22×#595—21no—
93C22×#595—21no—
94C22×#595—22no—
95C22×#595—22no—
96C22×#595—22no—
97C22×#595—21no—
98C22×#595—21no—
99C22×#595—21no—
100C22×#595—21no—
101C22×#595—21no—
102C22×#595—21no—
103C22×#595—22no—
104C22×#595—41no—
105C22×#595—41no—
106C22×#595—41no—
107C22×#595—41no—
108C22×#595—41no—
109C22×#595—41no—
110C22×#595—41no—
111C22×#595—41no—
112C22×#595—41no—
113C22×#595—41no—
114C22×#595C22⋊C412yes—
115C22×#595C22⋊C412yes—
116C22×#595D812yes—
117C22×#595SD1612yes—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17C22×C411yescharacteristic
121C22×Dic17—21no—
122C22×Dic17—21no—
123C22×Dic17#4111yescharacteristic
124C2×C4×D17—22no—
125C2×C4×D17—22no—
126C2×C4×D17—41no—
127C2×C4×D17—41no—
128C2×C4×D17—41no—
129C2×C4×D17—41no—
130C2×C4×D17—41no—
131C2×C4×D17—41no—
132C2×C4×D17—41no—
133C2×C4×D17—41no—
134C2×C4×D17—41no—
135C2×C4×D17—41no—
136C2×C4×D17C22×C411yescharacteristic
137C2×C4×D17C22×C411yescharacteristic
138C2×C4×D17C2×D411yescharacteristic
139C2×C4×D17C2×D411yescharacteristic
140C2×C4×D17C2×Q811yescharacteristic
141C2×C4×D17#4111yescharacteristic
142C2×C4×D17#4111yescharacteristic
143C2×C4×D17#4111yescharacteristic
144C2×C4×D17#4111yescharacteristic
145C2×C4×D17#4111yescharacteristic
146C2×C4×D17#4111yescharacteristic
147C2×C4×D17#4111yescharacteristic
148C2×#3624—22no—
149C2×#3624—41no—
150C2×#3624—41no—
151C4⋊#595—22no—
152C4⋊#595—22no—
153C4⋊#595—22no—
154C4⋊#595—22no—
155C4⋊#595—22no—
156C4⋊#595—41no—
157C4⋊#595—41no—
158C4⋊#595C4⋊C414yes—
159C4×#595—22no—
160C4×#595—22no—
161C4×#595—22no—
162C4×#595—22no—
163C4×#595—48no—
164#63242—22no—
165#63242—22no—
166#63242—41no—
167#63242—41no—
168C2×C8×C17—21no—
169C2×C8×C17—21no—
170C2×C8×C17—21no—
171C4⋊C4×C17—21no—
172C4⋊C4×C17—21no—
173C4⋊C4×C17—21no—
174C4⋊C4×C17C4212yes—
175C4⋊Dic17—21no—
176C4⋊Dic17—21no—
177C4⋊Dic17—21no—
178C4⋊Dic17C4212yes—
179#63225—22no—
180#63225—22no—
181#63225—41no—
182#63225—41no—
183C2×#3622—21no—
184C2×#3622—21no—
185C2×#3622—21no—
186C8×D17—41no—
187C8×D17—41no—
188C8×D17—41no—
189C8×D17—41no—
190#10806—171nomaximal, Sylow
191C23×C17C4×D411yescharacteristic
192C22×D17C2×C22⋊C411yescharacteristic
193C22×D17C4×D411yescharacteristic
194C22×D17#12111yescharacteristic
195C22×D17C22⋊Q811yescharacteristic
196C22×D17#12311yescharacteristic
197C22×D17#12311yescharacteristic
198C22×D17C2×D811yescharacteristic
199C22×D17C2×SD1611yescharacteristic
200C22×D17#13511yescharacteristic
201C22×D17#13511yescharacteristic
202C22×D17AGL(1,ℤ/8)11yescharacteristic
203C22×D17#13711yescharacteristic
204C22×D17#13711yescharacteristic
205C22×D17#13711yescharacteristic
206C2×#595—22no—
207C2×#595—22no—
208C2×#595—22no—
209C2×#595—22no—
210C2×#595—22no—
211C2×#595—22no—
212C2×#595—24no—
213C2×#595—22no—
214C2×#595—22no—
215C2×#595—22no—
216C2×#595—42no—
217C2×#595—42no—
218C2×#595—42no—
219C2×#595—42no—
220C2×#595—42no—
221C2×#595—42no—
222C2×#595—41no—
223C2×#595—41no—
224C2×#595—41no—
225C2×#595—41no—
226C2×#595—42no—
227C2×#595—42no—
228C2×#595—42no—
229C2×#595—81no—
230C2×#595—81no—
231C2×#595—81no—
232C2×#595—81no—
233C2×#595#10214yes—
234C2×C4×C17—22no—
235C2×C4×C17—41no—
236C2×C4×C17—41no—
237C2×C4×C17—41no—
238C2×C4×C17—41no—
239C2×C4×C17—41no—
240C2×C4×C17C2×C4211yescharacteristic
241C2×C4×C17#11711yescharacteristic
242C2×C4×C17#11711yescharacteristic
243C2×C4×C17C4×D411yescharacteristic
244C2×C4×C17C4×D411yescharacteristic
245C2×C4×C17C4×Q811yescharacteristic
246C2×Dic17—22no—
247C2×Dic17—41no—
248C2×Dic17—41no—
249C2×Dic17—41no—
250C2×Dic17—41no—
251C2×Dic17—41no—
252C2×Dic17#11711yescharacteristic
253C2×Dic17C4×D411yescharacteristic
254C2×Dic17#12411yescharacteristic
255C2×Dic17#12511yescharacteristic
256C2×Dic17#12611yescharacteristic
257C2×Dic17#12611yescharacteristic
258C4×D17—42no—
259C4×D17—42no—
260C4×D17—42no—
261C4×D17—42no—
262C4×D17—81no—
263C4×D17—81no—
264C4×D17—81no—
265C4×D17—81no—
266C4×D17C2×C4⋊C411yescharacteristic
267C4×D17#11711yescharacteristic
268C4×D17#11711yescharacteristic
269C4×D17#11711yescharacteristic
270C4×D17#11711yescharacteristic
271C4×D17#11711yescharacteristic
272C4×D17C4×D411yescharacteristic
273C4×D17C4×Q811yescharacteristic
274C4×D17#12111yescharacteristic
275C4×D17C22⋊Q811yescharacteristic
276C4×D17#12311yescharacteristic
277C4×D17#12311yescharacteristic
278C4×D17#12411yescharacteristic
279C4×D17#12511yescharacteristic
280C4×D17#12611yescharacteristic
281C4×D17#12611yescharacteristic
282#3624—42no—
283C8×C17—41no—
284#3622—41no—
285C2×C4×C4⋊C4—171no—
286C2×#340—171no—
287C2×#340—171no—
288C2×#340—171no—
289C2×#340—171no—
290C2×#336—171no—
291C4⋊#95—171no—
292C22×C17C4×C22⋊C411yescharacteristic
293C22×C17#38711yescharacteristic
294C22×C17#38811yescharacteristic
295C22×C17C4×D811yescharacteristic
296C22×C17C4×SD1611yescharacteristic
297C22×C17#44011yescharacteristic
298C22×C17#44111yescharacteristic
299C2×D17#38011yescharacteristic
300C2×D17#38111yescharacteristic
301C2×D17#38711yescharacteristic
302C2×D17#38811yescharacteristic
303C2×D17C2×#10211yescharacteristic
304C2×D17#41611yescharacteristic
305C2×D17#41711yescharacteristic
306C2×D17#41911yescharacteristic
307C2×D17C4×D811yescharacteristic
308C2×D17C4×SD1611yescharacteristic
309C2×D17#44011yescharacteristic
310C2×D17#44111yescharacteristic
311C2×D17#45911yescharacteristic
312C2×D17#46111yescharacteristic
313C2×D17#46411yescharacteristic
314C2×D17#46411yescharacteristic
315C2×D17#47411yescharacteristic
316C2×D17#47611yescharacteristic
317C2×D17#47911yescharacteristic
318C2×D17#47911yescharacteristic
319C2×D17#48011yescharacteristic
320C2×D17#48011yescharacteristic
321C2×D17#48211yescharacteristic
322C2×D17#48211yescharacteristic
323C2×D17#48311yescharacteristic
324C2×D17#48311yescharacteristic
325C2×D17#48511yescharacteristic
326C2×D17#48511yescharacteristic
327#595—24no—
328#595—44no—
329#595—42no—
330#595—82no—
331C4×C17—42no—
332C4×C17—81no—
333C4×C17#37611yescharacteristic
334C4×C17C4×C4⋊C411yescharacteristic
335C4×C17#38711yescharacteristic
336C4×C17#38811yescharacteristic
337Dic17—42no—
338Dic17—81no—
339Dic17#38211yescharacteristic
340Dic17#38311yescharacteristic
341Dic17#38711yescharacteristic
342Dic17#38811yescharacteristic
343C23×C8—171no—
344C23×C8—171no—
345C22×C4⋊C4—171no—
346C22×C4⋊C4—171no—
347C22×C4⋊C4—171no—
348C22×C4⋊C4—171no—
349C22×C42—171no—
350C22×C42—341no—
351C4×C4⋊C4—174no—
352C4×C4⋊C4—342no—
353C2×#95—341no—
354C2×#95—341no—
355C2×#95—341no—
356#340—174no—
357#340—171no—
358#340—171no—
359#340—171no—
360#340—342no—
361#340—342no—
362#340#59511yescharacteristic, complemented
363#336—342no—
364C2×C17#143411yescharacteristic
365C2×C17C4×#10211yescharacteristic
366C2×C17#176311yescharacteristic
367C2×C17#191811yescharacteristic
368C2×C17#192011yescharacteristic
369C2×C17#192511yescharacteristic
370C2×C17#192711yescharacteristic
371D17#180211yescharacteristic
372D17#180511yescharacteristic
373D17#182311yescharacteristic
374D17#182511yescharacteristic
375D17#191811yescharacteristic
376D17#192011yescharacteristic
377D17#192511yescharacteristic
378D17#192711yescharacteristic
379C23×C4—171no—
380C23×C4—171no—
381C23×C4—171no—
382C23×C4—341no—
383C23×C4—341no—
384C23×C4—341no—
385C23×C4—341no—
386C22×C8—172no—
387C22×C8—171no—
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×C8C2×#59511yescharacteristic
401C2×C4⋊C4—172no—
402C2×C4⋊C4—172no—
403C2×C4⋊C4—172no—
404C2×C4⋊C4—171no—
405C2×C4⋊C4—172no—
406C2×C4⋊C4—172no—
407C2×C4⋊C4—172no—
408C2×C4⋊C4—171no—
409C2×C4⋊C4—341no—
410C2×C4⋊C4—341no—
411C2×C4⋊C4—341no—
412C2×C4⋊C4—341no—
413C2×C4⋊C4—341no—
414C2×C4⋊C4—341no—
415C2×C4⋊C4—341no—
416C2×C4⋊C4—341no—
417C2×C4⋊C4—341no—
418C2×C4⋊C4—341no—
419C2×C4⋊C4—341no—
420C2×C4⋊C4—341no—
421C2×C4⋊C4—341no—
422C2×C4⋊C4—341no—
423C2×C4⋊C4—341no—
424C2×C4⋊C4—341no—
425C2×C4⋊C4C2×#59511yescharacteristic
426C2×C4⋊C4C2×#59511yescharacteristic
427C2×C42—172no—
428C2×C42—172no—
429C2×C42—341no—
430C2×C42—341no—
431C2×C42—341no—
432C2×C42—341no—
433C2×C42—344no—
434C2×C42—682no—
435C2×C42—682no—
436#95—344no—
437#95—682no—
438#95—682no—
439C17#1080611yescharacteristic, complemented, Sylow
440C24—171no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—171no—
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—172no—
457C22×C4—172no—
458C22×C4—172no—
459C22×C4—172no—
460C22×C4—342no—
461C22×C4—342no—
462C22×C4—341no—
463C22×C4—341no—
464C22×C4—341no—
465C22×C4—341no—
466C22×C4—342no—
467C22×C4—341no—
468C22×C4—341no—
469C22×C4—341no—
470C22×C4—342no—
471C22×C4—342no—
472C22×C4—341no—
473C22×C4—341no—
474C22×C4—341no—
475C22×C4—341no—
476C22×C4—342no—
477C22×C4—341no—
478C22×C4—681no—
479C22×C4—681no—
480C22×C4—681no—
481C22×C4—681no—
482C22×C4—681no—
483C22×C4—681no—
484C22×C4—681no—
485C22×C4—681no—
486C22×C4—681no—
487C22×C4—681no—
488C22×C4—681no—
489C22×C4—681no—
490C22×C4—681no—
491C22×C4—681no—
492C22×C4—681no—
493C22×C4—681no—
494C22×C4—681no—
495C22×C4—681no—
496C22×C4—681no—
497C22×C4—681no—
498C22×C4C22×#59511yescharacteristic
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—342no—
503C2×C8—342no—
504C2×C8—342no—
505C2×C8—341no—
506C2×C8—341no—
507C2×C8—341no—
508C2×C8—681no—
509C2×C8—681no—
510C2×C8—681no—
511C2×C8—681no—
512C2×C8—681no—
513C2×C8—681no—
514C2×C8—681no—
515C2×C8—681no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—174no—
520C4⋊C4—172no—
521C4⋊C4—342no—
522C4⋊C4—342no—
523C4⋊C4—342no—
524C4⋊C4—342no—
525C4⋊C4—342no—
526C4⋊C4—342no—
527C4⋊C4—342no—
528C4⋊C4—341no—
529C4⋊C4—341no—
530C4⋊C4—341no—
531C4⋊C4—681no—
532C4⋊C4—681no—
533C4⋊C4—681no—
534C4⋊C4—681no—
535C4⋊C4C4×#59512yes—
536C42—342no—
537C42—342no—
538C42—342no—
539C42—342no—
540C42—688no—
541C23—171no—
542C23—171no—
543C23—171no—
544C23—171no—
545C23—171no—
546C23—171no—
547C23—171no—
548C23—171no—
549C23—171no—
550C23—171no—
551C23—171no—
552C23—171no—
553C23—171no—
554C23—171no—
555C23D4×#59511yescharacteristic
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
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—174no—
585C2×C4—342no—
586C2×C4—342no—
587C2×C4—342no—
588C2×C4—342no—
589C2×C4—342no—
590C2×C4—342no—
591C2×C4—342no—
592C2×C4—344no—
593C2×C4—342no—
594C2×C4—342no—
595C2×C4—342no—
596C2×C4—682no—
597C2×C4—682no—
598C2×C4—682no—
599C2×C4—682no—
600C2×C4—682no—
601C2×C4—681no—
602C2×C4—681no—
603C2×C4—681no—
604C2×C4—681no—
605C2×C4—682no—
606C2×C4—682no—
607C2×C4—682no—
608C2×C4—682no—
609C2×C4—682no—
610C2×C4—681no—
611C2×C4—681no—
612C2×C4—682no—
613C2×C4—682no—
614C2×C4—682no—
615C2×C4—681no—
616C2×C4—681no—
617C2×C4—681no—
618C2×C4—1361no—
619C2×C4—1361no—
620C2×C4—1361no—
621C2×C4—1361no—
622C2×C4—1361no—
623C2×C4—1361no—
624C2×C4—1361no—
625C2×C4—1361no—
626C2×C4C2×C4×#59511yescharacteristic
627C2×C4#1058767711yescharacteristic
628C2×C4#1058767711yescharacteristic
629C2×C4D4×#59511yescharacteristic
630C2×C4D4×#59511yescharacteristic
631C2×C4Q8×#59511yescharacteristic
632C8—41no—
633C8—682no—
634C8—681no—
635C22—171no—
636C22—171no—
637C22—171no—
638C22—171no—
639C22—171no—
640C22—171no—
641C22—171no—
642C22—171no—
643C22—171no—
644C22—171no—
645C22—171no—
646C22—171no—
647C22—171no—
648C22—171no—
649C22—171no—
650C22—171no—
651C22—171no—
652C22—171no—
653C22—171no—
654C22—171no—
655C22—171no—
656C22—171no—
657C22—171no—
658C22—171no—
659C22—171no—
660C22—171no—
661C22—171no—
662C22—171no—
663C22C22⋊C4×#59511yescharacteristic
664C22#1176375811yescharacteristic
665C22#1176375911yescharacteristic
666C22D8×#59511yescharacteristic
667C22SD16×#59511yescharacteristic
668C22#1176384811yescharacteristic
669C22#1176384911yescharacteristic
670C4—42no—
671C4—81no—
672C4—171no—
673C4—171no—
674C4—171no—
675C4—171no—
676C4—344no—
677C4—682no—
678C4—684no—
679C4—682no—
680C4—1362no—
681C4—1361no—
682C4#1176374511yescharacteristic
683C4C4⋊C4×#59511yescharacteristic
684C4#1176375811yescharacteristic
685C4#1176375911yescharacteristic
686C2—171no—
687C2—171no—
688C2—171no—
689C2—171no—
690C2—171no—
691C2—171no—
692C2—171no—
693C2—171no—
694C2#1454395911yescharacteristic
695C2#102×#59511yescharacteristic
696C2#1454455711yescharacteristic
697C2#1454484511yescharacteristic
698C2#1454484711yescharacteristic
699C2#1454486111yescharacteristic
700C2#1454486311yescharacteristic
subgroupG/H
centerC23D4×#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC17×#340C4
socleC23×C17C4×D4
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenter#340#595
hypocenterC17#10806
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
14. C4⋊C4×#595C4semidirect
20. #11763682C4semidirect
25. #11762572C4semidirect
26. #11762571C4semidirect
27. #11762571C4semidirect
28. C17×#340C4semidirect
362. #340#595semidirect
439. C17#10806semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×#5952
C2×#117636832
C2×#117636822
C2×#117636742
#145439612
D17×#3402
#1080617