Finite Group Databasebeta

← #17045751

Subgroups — #17045751

Order 4352.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537488C211yesmaximal, characteristic, complemented
2#14537229C211yesmaximal, characteristic, complemented
3#14529678C211yesmaximal, characteristic, complemented
4#14529673C211yesmaximal, characteristic, complemented
5#14529497C211yesmaximal, characteristic, complemented
6#14529490C211yesmaximal, characteristic, complemented
7#14529434C211yesmaximal, characteristic, complemented
8#14529434C211yesmaximal, characteristic, complemented
9#14529113C211yesmaximal, characteristic, complemented
10#14529113C211yesmaximal, characteristic, complemented
11#14529087C211yesmaximal, characteristic, complemented
12#14528991C211yesmaximal, characteristic, complemented
13#14528728C211yesmaximal, characteristic, complemented
14#14528570C211yesmaximal, characteristic, complemented
15C17×#3002C211yesmaximal, characteristic
16C2×#10587634C2211yescharacteristic, complemented
17C22×#63223C2211yescharacteristic
18C22×#63223C2211yescharacteristic
19#11762887—21no—
20#11762887—21no—
21#11762881—21no—
22#11762881—21no—
23C2×#10587490C2211yescharacteristic, complemented
24C2×#10587490C2211yescharacteristic, complemented
25#11762836C2211yescharacteristic, complemented
26C2×#10587508C2211yescharacteristic
27C2×#10587508C2211yescharacteristic
28C2×#10587508C2211yescharacteristic
29C2×#10587508C2211yescharacteristic
30C2×#10587508C2211yescharacteristic, complemented
31C2×#10587508C2211yescharacteristic, complemented
32#11762776—21no—
33#11762776—21no—
34#11762776C2211yescharacteristic
35#11762776C2211yescharacteristic
36#11762776C2211yescharacteristic
37#11762776C2211yescharacteristic
38#11762776C2211yescharacteristic, complemented
39#11762773—21no—
40#11762773—21no—
41#11762773C2211yescharacteristic
42#11762765C2211yescharacteristic, complemented
43C2×#10587486C2211yescharacteristic, complemented
44C2×C8×Dic17C2211yescharacteristic, complemented
45C4×C22⋊Dic17C2211yescharacteristic
46#11762574C2211yescharacteristic, complemented
47#11762574C2211yescharacteristic, complemented
48#11762568C2211yescharacteristic, complemented
49#11762568C2211yescharacteristic, complemented
50#11762563C2211yescharacteristic, complemented
51#11762563C2211yescharacteristic, complemented
52C22×#41×C17C2211yescharacteristic
53C2×C17×#135C2211yescharacteristic
54C2×C17×#135C2211yescharacteristic
55C17×#525C2211yescharacteristic
56C17×#452C411yescharacteristic, complemented
57C17×#452C411yescharacteristic, complemented
58C17×#451C411yescharacteristic, complemented
59C17×#450C411yescharacteristic, complemented
60C17×#449C411yescharacteristic, complemented
61C17×#449C411yescharacteristic, complemented
62C17×#448C411yescharacteristic, complemented
63C17×#447C411yescharacteristic, complemented
64C17×#416C2211yescharacteristic
65C17×#416C2211yescharacteristic
66C2×C17×C22⋊C8C2211yescharacteristic
67C2×#41×C17—21no—
68C2×#41×C17—21no—
69C2×#41×C17—41no—
70C2×#41×C17—41no—
71C2×#41×C17—41no—
72C2×#41×C17—41no—
73C2×#41×C17C2×C411yescharacteristic
74C2×#41×C17C2×C411yescharacteristic
75C2×#41×C17C2311yescharacteristic
76C2×#41×C17C2311yescharacteristic
77C2×#41×C17C2311yescharacteristic
78C22×Q8×C17C2×C411yescharacteristic
79C22×D4×C17—21no—
80C22×D4×C17C2×C411yescharacteristic
81C23×C4×C17—21no—
82C23×C4×C17C2311yescharacteristic
83C17×#135—41no—
84C17×#135—41no—
85C17×#135—41no—
86C17×#135—41no—
87C2×Q16×C17C2×C411yescharacteristic
88C2×Q16×C17C2×C411yescharacteristic
89C2×SD16×C17C2×C411yescharacteristic
90C2×SD16×C17C2×C411yescharacteristic
91C2×SD16×C17C2×C411yescharacteristic
92C2×SD16×C17C2×C411yescharacteristic
93C2×D8×C17C2×C411yescharacteristic
94C2×D8×C17C2×C411yescharacteristic
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C17×#123—21no—
98C17×C22⋊Q8C2×C411yescharacteristic
99C17×C22⋊Q8C2×C411yescharacteristic
100C17×#121C2×C411yescharacteristic
101C17×#121C2×C411yescharacteristic
102C17×#120—21no—
103C4×D4×C17—21no—
104C4×D4×C17—21no—
105C17×#117C2311yescharacteristic
106C2×C22⋊Dic17—21no—
107#10587634—41no—
108#10587634—41no—
109C2×C4×Dic17C2311yescharacteristic
110C2×C4×Dic17C2311yescharacteristic
111C2×#63223—21no—
112C2×#63223—21no—
113C2×#63223—41no—
114C2×#63223—41no—
115C2×#63223—41no—
116C2×#63223—41no—
117C2×#63223D411yescharacteristic
118C2×#63223D411yescharacteristic
119C2×#63223D411yescharacteristic
120C2×#63223D411yescharacteristic
121C2×#63223C2311yescharacteristic
122C2×#63223C2311yescharacteristic
123C2×#63223C2311yescharacteristic
124C2×#63223C2311yescharacteristic
125C22×#3622—21no—
126C22×#3622—21no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C17×#103C2×C411yescharacteristic
130C17×#103C2×C411yescharacteristic
131C17×#103C2×C411yescharacteristic
132C17×#103C2×C411yescharacteristic
133C17×#102C2×C411yescharacteristic
134C17×#102C2×C411yescharacteristic
135C17×#102C2×C411yescharacteristic
136C17×#102C2×C411yescharacteristic
137C17×C22⋊C8C2×C411yescharacteristic
138C17×C22⋊C8C2×C411yescharacteristic
139C17×C22⋊C8C2×C411yescharacteristic
140C17×C22⋊C8C2×C411yescharacteristic
141#10587508—41no—
142#10587508—41no—
143#10587508—41no—
144#10587508—41no—
145#10587508—41no—
146#10587508—41no—
147#10587502—21no—
148C22⋊#3622—21no—
149C22⋊#3622—21no—
150C22⋊#3622—21no—
151C22⋊#3622—21no—
152C22⋊#3622—21no—
153C22⋊#3622—21no—
154C22⋊#3622—21no—
155C22⋊#3622—21no—
156C22⋊#3622—21no—
157C22⋊#3622—21no—
158C22⋊#3622—21no—
159C22⋊#3622—21no—
160#10587490—41no—
161#10587490—41no—
162#10587486—41no—
163C8×Dic17—41no—
164C4⋊#3622—21no—
165C4⋊#3622—21no—
166#10587474—21no—
167C4×#3622—21no—
168C24×C17—21no—
169C24×C17#4111yescharacteristic
170#41×C17—21no—
171#41×C17—21no—
172#41×C17—21no—
173#41×C17—21no—
174#41×C17—21no—
175#41×C17—21no—
176#41×C17—21no—
177#41×C17—21no—
178#41×C17—21no—
179#41×C17—21no—
180#41×C17—21no—
181#41×C17—21no—
182#41×C17—41no—
183#41×C17—41no—
184#41×C17—41no—
185#41×C17—41no—
186#41×C17—42no—
187#41×C17—42no—
188#41×C17—42no—
189#41×C17—42no—
190C2×Q8×C17—21no—
191C2×Q8×C17—41no—
192C2×Q8×C17—41no—
193C2×Q8×C17C22×C411yescharacteristic
194C2×Q8×C17C22×C411yescharacteristic
195C2×Q8×C17C22×C411yescharacteristic
196C2×D4×C17—21no—
197C2×D4×C17—21no—
198C2×D4×C17—21no—
199C2×D4×C17—21no—
200C2×D4×C17—21no—
201C2×D4×C17—21no—
202C2×D4×C17—21no—
203C2×D4×C17—21no—
204C2×D4×C17—41no—
205C2×D4×C17—41no—
206C2×D4×C17—42no—
207C2×D4×C17—42no—
208C2×D4×C17C22×C411yescharacteristic
209C2×D4×C17C22×C411yescharacteristic
210C2×D4×C17C22×C411yescharacteristic
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—42no—
222C22×C4×C17—42no—
223C22×C4×C17C22×C411yescharacteristic
224C22×C4×C17C22×C411yescharacteristic
225C22×C4×C17C2×D411yescharacteristic
226C22×C4×C17C2×D411yescharacteristic
227C22×C4×C17#4111yescharacteristic
228C22×C4×C17C2411yescharacteristic
229C22×Dic17—21no—
230C22×Dic17—21no—
231Q16×C17—41no—
232Q16×C17—41no—
233SD16×C17—41no—
234SD16×C17—41no—
235SD16×C17—41no—
236SD16×C17—41no—
237D8×C17—41no—
238D8×C17—41no—
239C2×C8×C17—21no—
240C2×C8×C17—21no—
241C2×C8×C17—21no—
242C2×C8×C17—21no—
243C2×C8×C17C22×C411yescharacteristic
244C2×C8×C17C22×C411yescharacteristic
245C2×C8×C17C22×C411yescharacteristic
246C2×C8×C17C22×C411yescharacteristic
247C4⋊C4×C17—21no—
248C4⋊C4×C17—21no—
249C4⋊C4×C17C22×C411yescharacteristic
250C4⋊C4×C17C22×C411yescharacteristic
251C22⋊C4×C17—21no—
252C22⋊C4×C17—21no—
253C22⋊C4×C17—21no—
254C22⋊C4×C17—21no—
255C22⋊C4×C17—21no—
256C42×C17—21no—
257C22⋊Dic17—42no—
258C4×Dic17—21no—
259C4×Dic17—21no—
260C4×Dic17—21no—
261C4×Dic17—21no—
262#63223—21no—
263#63223—21no—
264#63223—21no—
265#63223—21no—
266#63223—21no—
267#63223—21no—
268#63223—21no—
269#63223—21no—
270#63223—41no—
271#63223—41no—
272#63223—41no—
273#63223—41no—
274#63223—42no—
275#63223—42no—
276C2×#3622—21no—
277C2×#3622—21no—
278C2×#3622—21no—
279C2×#3622—21no—
280C2×#3622—21no—
281C2×#3622—21no—
282C2×#3622—21no—
283C2×#3622—21no—
284C2×#3622—42no—
285C2×#3622—42no—
286C2×#3622C2×D411yescharacteristic
287C2×#3622C2×D411yescharacteristic
288C2×#3622C2×D411yescharacteristic
289C2×#3622C2×D411yescharacteristic
290#22062—171nomaximal, Sylow
291C23×C17—21no—
292C23×C17—21no—
293C23×C17—21no—
294C23×C17—21no—
295C23×C17—21no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—42no—
299C23×C17—81no—
300C23×C17—81no—
301C23×C17C4×D411yescharacteristic
302C23×C17C4×D411yescharacteristic
303C23×C17C2×#4111yescharacteristic
304Q8×C17—21no—
305Q8×C17—21no—
306Q8×C17—21no—
307Q8×C17—21no—
308Q8×C17—21no—
309Q8×C17—21no—
310Q8×C17—42no—
311D4×C17—21no—
312D4×C17—21no—
313D4×C17—21no—
314D4×C17—21no—
315D4×C17—21no—
316D4×C17—21no—
317D4×C17—42no—
318D4×C17—42no—
319D4×C17—42no—
320D4×C17—41no—
321D4×C17—41no—
322D4×C17—41no—
323D4×C17—41no—
324D4×C17—41no—
325D4×C17—41no—
326D4×C17—81no—
327D4×C17—81no—
328C2×C4×C17—21no—
329C2×C4×C17—21no—
330C2×C4×C17—21no—
331C2×C4×C17—21no—
332C2×C4×C17—21no—
333C2×C4×C17—21no—
334C2×C4×C17—21no—
335C2×C4×C17—21no—
336C2×C4×C17—21no—
337C2×C4×C17—21no—
338C2×C4×C17—21no—
339C2×C4×C17—21no—
340C2×C4×C17—21no—
341C2×C4×C17—21no—
342C2×C4×C17—21no—
343C2×C4×C17—42no—
344C2×C4×C17—42no—
345C2×C4×C17—42no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17C4×D411yescharacteristic
353C2×C4×C17C4×D411yescharacteristic
354C2×C4×C17C23×C411yescharacteristic
355C2×C4×C17C22×D411yescharacteristic
356C2×C4×C17H(5,𝔽2)11yescharacteristic
357C2×C4×C17H(5,𝔽2)11yescharacteristic
358C2×C4×C17H(5,𝔽2)11yescharacteristic
359C2×C4×C17H(5,𝔽2)11yescharacteristic
360C2×Dic17—22no—
361C2×Dic17—41no—
362C2×Dic17—41no—
363C2×Dic17—41no—
364C2×Dic17—41no—
365C2×Dic17—41no—
366C8×C17—21no—
367C8×C17—21no—
368C8×C17—21no—
369C8×C17—21no—
370#3622—21no—
371#3622—21no—
372#3622—21no—
373#3622—21no—
374#3622—41no—
375#3622—41no—
376#3622—41no—
377#3622—41no—
378#3002D1711yescharacteristic
379#2930—171no—
380#2879—171no—
381#1975—171no—
382#1974—171no—
383#1938—171no—
384#1937—171no—
385#1929—171no—
386#1929—171no—
387#1876—171no—
388#1876—171no—
389#1871—171no—
390#1855—171no—
391#1789—171no—
392#1753—171no—
393C22×C17—21no—
394C22×C17—21no—
395C22×C17—21no—
396C22×C17—21no—
397C22×C17—21no—
398C22×C17—21no—
399C22×C17—21no—
400C22×C17—21no—
401C22×C17—41no—
402C22×C17—41no—
403C22×C17—41no—
404C22×C17—41no—
405C22×C17—41no—
406C22×C17—41no—
407C22×C17—41no—
408C22×C17—41no—
409C22×C17—41no—
410C22×C17—81no—
411C22×C17—81no—
412C22×C17—84no—
413C22×C17C2×C4×D411yescharacteristic
414C22×C17#53811yescharacteristic
415C22×C17#53811yescharacteristic
416C4×C17—21no—
417C4×C17—21no—
418C4×C17—41no—
419C4×C17—41no—
420C4×C17—41no—
421C4×C17—41no—
422C4×C17—41no—
423C4×C17#51811yescharacteristic
424C4×C17#51811yescharacteristic
425C4×C17#53411yescharacteristic
426C4×C17#53511yescharacteristic
427Dic17—42no—
428Dic17—81no—
429C22×#41C2×D1711yescharacteristic
430C2×#135C2×D1711yescharacteristic
431C2×#135C2×D1711yescharacteristic
432C2×#131—171no—
433C22×M16—171no—
434C22×M16—171no—
435#525C2×D1711yescharacteristic
436#452Dic1711yescharacteristic, complemented
437#452Dic1711yescharacteristic, complemented
438#451Dic1711yescharacteristic, complemented
439#450Dic1711yescharacteristic, complemented
440#449Dic1711yescharacteristic, complemented
441#449Dic1711yescharacteristic, complemented
442#448Dic1711yescharacteristic, complemented
443#447Dic1711yescharacteristic, complemented
444#436—341no—
445#436—341no—
446#435—341no—
447#435—341no—
448C2×#108—171no—
449C2×#108—171no—
450#424—171no—
451C2×#104—171no—
452C2×#104—171no—
453C2×#104—171no—
454C2×#104—171no—
455C2×#104—171no—
456C2×#104—171no—
457#416C2×D1711yescharacteristic
458#416C2×D1711yescharacteristic
459#408—171no—
460#408—171no—
461#408—171no—
462#408—171no—
463#408—171no—
464#408—341no—
465#408—341no—
466#407—171no—
467#407—341no—
468#407—341no—
469C2×C22⋊C8C2×D1711yescharacteristic
470#405—171no—
471C2×#97—171no—
472C2×C4×C8—171no—
473C4×C22⋊C4—171no—
474#341—171no—
475#341—171no—
476#339—171no—
477#339—171no—
478#336—171no—
479#336—171no—
480C2×C17—21no—
481C2×C17—21no—
482C2×C17—41no—
483C2×C17—41no—
484C2×C17—81no—
485C2×C17—81no—
486C2×C17—81no—
487C2×C17#232111yescharacteristic
488C2×C17#295611yescharacteristic
489C2×C17#295711yescharacteristic
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—41no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×Dic1711yescharacteristic
497C2×#41C2×Dic1711yescharacteristic
498C2×#41C22×D1711yescharacteristic
499C2×#41C22×D1711yescharacteristic
500C2×#41C22×D1711yescharacteristic
501C22×Q8C2×Dic1711yescharacteristic
502C22×D4—21no—
503C22×D4C2×Dic1711yescharacteristic
504C23×C4—21no—
505C23×C4C22×D1711yescharacteristic
506#135—41no—
507#135—41no—
508#135—41no—
509#135—41no—
510C2×Q16C2×Dic1711yescharacteristic
511C2×Q16C2×Dic1711yescharacteristic
512C2×SD16C2×Dic1711yescharacteristic
513C2×SD16C2×Dic1711yescharacteristic
514C2×SD16C2×Dic1711yescharacteristic
515C2×SD16C2×Dic1711yescharacteristic
516C2×D8C2×Dic1711yescharacteristic
517C2×D8C2×Dic1711yescharacteristic
518#131—681no—
519#131—681no—
520C2×M16—171no—
521C2×M16—171no—
522C2×M16—171no—
523C2×M16—171no—
524C2×M16—171no—
525C2×M16—171no—
526C2×M16—171no—
527C2×M16—171no—
528C2×M16—341no—
529C2×M16—341no—
530C2×M16—681no—
531C2×M16—681no—
532C2×M16—681no—
533C2×M16—681no—
534C22×C8—171no—
535C22×C8—171no—
536C22×C8—341no—
537C22×C8—341no—
538C22×C8C22×D1711yescharacteristic
539C22×C8C22×D1711yescharacteristic
540#123—21no—
541C22⋊Q8C2×Dic1711yescharacteristic
542C22⋊Q8C2×Dic1711yescharacteristic
543#121C2×Dic1711yescharacteristic
544#121C2×Dic1711yescharacteristic
545#120—21no—
546C4×D4—21no—
547C4×D4—21no—
548#117C22×D1711yescharacteristic
549C2×C22⋊C4—341no—
550C2×C42—171no—
551C2×C42—171no—
552#108—681no—
553#108—681no—
554C4⋊C8—341no—
555C4⋊C8—341no—
556#104—681no—
557#104—681no—
558#104—681no—
559#104—681no—
560#104—681no—
561#104—681no—
562#103C2×Dic1711yescharacteristic
563#103C2×Dic1711yescharacteristic
564#103C2×Dic1711yescharacteristic
565#103C2×Dic1711yescharacteristic
566#102C2×Dic1711yescharacteristic
567#102C2×Dic1711yescharacteristic
568#102C2×Dic1711yescharacteristic
569#102C2×Dic1711yescharacteristic
570C22⋊C8—341no—
571C22⋊C8—341no—
572C22⋊C8—341no—
573C22⋊C8—341no—
574C22⋊C8—341no—
575C22⋊C8—341no—
576C22⋊C8—341no—
577C22⋊C8—341no—
578C22⋊C8—341no—
579C22⋊C8—341no—
580C22⋊C8—341no—
581C22⋊C8—341no—
582C22⋊C8C2×Dic1711yescharacteristic
583C22⋊C8C2×Dic1711yescharacteristic
584C22⋊C8C2×Dic1711yescharacteristic
585C22⋊C8C2×Dic1711yescharacteristic
586#97—341no—
587#97—681no—
588C4×C8—341no—
589C4×C8—681no—
590#95—341no—
591C17#2206211yescharacteristic, complemented, Sylow
592C24—21no—
593C24#6325411yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×Dic1711yescharacteristic
618C2×Q8C22×Dic1711yescharacteristic
619C2×Q8C22×Dic1711yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×Dic1711yescharacteristic
633C2×D4C22×Dic1711yescharacteristic
634C2×D4C22×Dic1711yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—341no—
648C22×C4—341no—
649C22×C4D4×D1711yescharacteristic
650C22×C4D4×D1711yescharacteristic
651C22×C4#6325411yescharacteristic
652C22×C4C22×Dic1711yescharacteristic
653C22×C4C22×Dic1711yescharacteristic
654C22×C4C23×D1711yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—341no—
664M16—341no—
665M16—341no—
666M16—341no—
667M16—341no—
668M16—341no—
669M16—341no—
670M16—341no—
671M16—681no—
672M16—681no—
673M16—681no—
674M16—681no—
675M16—682no—
676M16—682no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—171no—
682C2×C8—171no—
683C2×C8—171no—
684C2×C8—171no—
685C2×C8—341no—
686C2×C8—341no—
687C2×C8—341no—
688C2×C8—341no—
689C2×C8—341no—
690C2×C8—341no—
691C2×C8—341no—
692C2×C8—341no—
693C2×C8—682no—
694C2×C8—682no—
695C2×C8C22×Dic1711yescharacteristic
696C2×C8C22×Dic1711yescharacteristic
697C2×C8C22×Dic1711yescharacteristic
698C2×C8C22×Dic1711yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×Dic1711yescharacteristic
702C4⋊C4C22×Dic1711yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—682no—
709C42—21no—
710C42—341no—
711C42—341no—
712C42—341no—
713C42—341no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23D4×Dic1711yescharacteristic
725C23D4×Dic1711yescharacteristic
726C23C2×#6325411yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—342no—
776C2×C4—681no—
777C2×C4—681no—
778C2×C4—681no—
779C2×C4—681no—
780C2×C4—681no—
781C2×C4D4×Dic1711yescharacteristic
782C2×C4D4×Dic1711yescharacteristic
783C2×C4C2×D4×D1711yescharacteristic
784C2×C4#1058769111yescharacteristic
785C2×C4#1058769111yescharacteristic
786C2×C4#1058769111yescharacteristic
787C2×C4#1058769111yescharacteristic
788C2×C4C23×Dic1711yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—341no—
794C8—341no—
795C8—341no—
796C8—341no—
797C8—681no—
798C8—681no—
799C8—681no—
800C8—681no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×D4×Dic1711yescharacteristic
822C22#1176339411yescharacteristic
823C22#1176339411yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—682no—
832C4—1361no—
833C4#1176328411yescharacteristic
834C4#1176328411yescharacteristic
835C4#1176336911yescharacteristic
836C4#1176337411yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#1453144511yescharacteristic
845C2#1453769411yescharacteristic
846C2#1453770111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC17×#3002C2
socleC22×C17C2×C4×D4
cosocleC22×C4×C17C24
hypercenter#3002D17
hypocenterC17#22062
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #14537488C2semidirect
2. #14537229C2semidirect
3. #14529678C2semidirect
4. #14529673C2semidirect
5. #14529497C2semidirect
6. #14529490C2semidirect
7. #14529434C2semidirect
8. #14529434C2semidirect
9. #14529113C2semidirect
10. #14529113C2semidirect
11. #14529087C2semidirect
12. #14528991C2semidirect
13. #14528728C2semidirect
14. #14528570C2semidirect
16. C2×#10587634C22semidirect
23. C2×#10587490C22semidirect
24. C2×#10587490C22semidirect
25. #11762836C22semidirect
30. C2×#10587508C22semidirect
31. C2×#10587508C22semidirect
38. #11762776C22semidirect
42. #11762765C22semidirect
43. C2×#10587486C22semidirect
44. C2×C8×Dic17C22semidirect
46. #11762574C22semidirect
47. #11762574C22semidirect
48. #11762568C22semidirect
49. #11762568C22semidirect
50. #11762563C22semidirect
51. #11762563C22semidirect
56. C17×#452C4semidirect
57. C17×#452C4semidirect
58. C17×#451C4semidirect
59. C17×#450C4semidirect
60. C17×#449C4semidirect
61. C17×#449C4semidirect
62. C17×#448C4semidirect
63. C17×#447C4semidirect
436. #452Dic17semidirect
437. #452Dic17semidirect
438. #451Dic17semidirect
439. #450Dic17semidirect
440. #449Dic17semidirect
441. #449Dic17semidirect
442. #448Dic17semidirect
443. #447Dic17semidirect
591. C17#22062semidirect

Maximal subgroups

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

subgroupindex
#145374882
#145372292
#145296782
#145296732
#145294972
#145294902
#145294342
#145291132
#145290872
#145289912
#145287282
#145285702
C17×#30022
#2206217