Finite Group Databasebeta

← #17040791

Subgroups — #17040791

Order 4352.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762931C211yesmaximal, characteristic, complemented
2C2×#11762926C211yesmaximal, characteristic, complemented
3#14537502C211yesmaximal, characteristic, complemented
4#14537212C211yesmaximal, characteristic, complemented
5#14529704C211yesmaximal, characteristic, complemented
6#14529560C211yesmaximal, characteristic, complemented
7#14529434C211yesmaximal, characteristic, complemented
8#14529434C211yesmaximal, characteristic, complemented
9#14529113C211yesmaximal, characteristic, complemented
10#14529113C211yesmaximal, characteristic, complemented
11#14528804C211yesmaximal, characteristic, complemented
12#14528661C211yesmaximal, characteristic, complemented
13#14528631C211yesmaximal, characteristic, complemented
14#14528624C211yesmaximal, characteristic, complemented
15C17×#3035C211yesmaximal, characteristic
16C2×#10587634C2211yescharacteristic
17C2×#10587634C2211yescharacteristic
18C2×#10587634C2211yescharacteristic
19C2×#10587634C2211yescharacteristic
20#11762931—24no—
21#11762926—24no—
22#11762881—21no—
23#11762881—21no—
24#11762881—21no—
25#11762881—21no—
26C2×#10587490C2211yescharacteristic
27C2×#10587490C2211yescharacteristic
28#11762833C2211yescharacteristic
29C2×#10587508C2211yescharacteristic
30C2×#10587508C2211yescharacteristic
31C2×#10587508C2211yescharacteristic
32C2×#10587508C2211yescharacteristic
33C2×#10587508C2211yescharacteristic
34C2×#10587508C2211yescharacteristic
35#11762776C2211yescharacteristic
36#11762776C2211yescharacteristic
37#11762765—21no—
38#11762765—21no—
39#11762765C2211yescharacteristic
40#11762765C2211yescharacteristic
41C4×#63223—21no—
42C4×#63223C2211yescharacteristic
43C2×#10587474—21no—
44C2×#10587474C2211yescharacteristic
45C2×#10587486C2211yescharacteristic
46C2×C8×Dic17C2211yescharacteristic
47C4×C4⋊Dic17C2211yescharacteristic
48#11762574C2211yescharacteristic
49#11762574C2211yescharacteristic
50#11762568C2211yescharacteristic
51#11762568C2211yescharacteristic
52#11762563C2211yescharacteristic
53#11762563C2211yescharacteristic
54C2×C17×#135C2211yescharacteristic
55C2×C17×#135C2211yescharacteristic
56C17×#532C2211yescharacteristic
57C4×#41×C17C2211yescharacteristic
58C17×#464C411yescharacteristic, complemented
59C17×#464C411yescharacteristic, complemented
60C17×#463C411yescharacteristic, complemented
61C17×#463C411yescharacteristic, complemented
62C17×#462C411yescharacteristic, complemented
63C17×#461C411yescharacteristic, complemented
64C17×#460C411yescharacteristic, complemented
65C17×#459C411yescharacteristic, complemented
66C2×C17×C4⋊C8C2211yescharacteristic
67C17×#416C2211yescharacteristic
68C17×#416C2211yescharacteristic
69C2×#41×C17C2311yescharacteristic
70C2×#41×C17C2311yescharacteristic
71C2×#41×C17C2311yescharacteristic
72C17×#135—22no—
73C17×#135—22no—
74C17×#135—22no—
75C17×#135—22no—
76C2×Q16×C17C2×C411yescharacteristic
77C2×Q16×C17C2×C411yescharacteristic
78C2×SD16×C17C2×C411yescharacteristic
79C2×SD16×C17C2×C411yescharacteristic
80C2×SD16×C17C2×C411yescharacteristic
81C2×SD16×C17C2×C411yescharacteristic
82C2×D8×C17C2×C411yescharacteristic
83C2×D8×C17C2×C411yescharacteristic
84C22×C8×C17C2311yescharacteristic
85C22×C8×C17C2311yescharacteristic
86C17×C4⋊Q8C2×C411yescharacteristic
87C17×#127C2×C411yescharacteristic
88C17×#124C2×C411yescharacteristic
89C17×#124C2×C411yescharacteristic
90C17×#121—21no—
91C17×#121—21no—
92C4×Q8×C17C2×C411yescharacteristic
93C4×Q8×C17C2×C411yescharacteristic
94C4×D4×C17—21no—
95C4×D4×C17—21no—
96C4×D4×C17—21no—
97C4×D4×C17—21no—
98C4×D4×C17C2×C411yescharacteristic
99C4×D4×C17C2×C411yescharacteristic
100C17×#117—21no—
101C17×#117C2311yescharacteristic
102C2×C42×C17—21no—
103C2×C42×C17C2311yescharacteristic
104#10587634—22no—
105#10587634—22no—
106#10587634—22no—
107#10587634—22no—
108#10587634—22no—
109#10587634—22no—
110#10587634—22no—
111#10587634D414yescomplemented
112C2×C4⋊Dic17—21no—
113C2×C4×Dic17C2311yescharacteristic
114C2×C4×Dic17C2311yescharacteristic
115C2×#63223—21no—
116C2×#63223—21no—
117C2×#63223—21no—
118C2×#63223—21no—
119C2×#63223C2311yescharacteristic
120C2×#63223C2311yescharacteristic
121C2×#63223C2311yescharacteristic
122C2×#63223C2311yescharacteristic
123C22×#3622—21no—
124C22×#3622—21no—
125C22×#3622—21no—
126C22×#3622—21no—
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C17×C4⋊C8C2×C411yescharacteristic
130C17×C4⋊C8C2×C411yescharacteristic
131C17×C4⋊C8C2×C411yescharacteristic
132C17×C4⋊C8C2×C411yescharacteristic
133C17×#103C2×C411yescharacteristic
134C17×#103C2×C411yescharacteristic
135C17×#103C2×C411yescharacteristic
136C17×#103C2×C411yescharacteristic
137C17×#102C2×C411yescharacteristic
138C17×#102C2×C411yescharacteristic
139C17×#102C2×C411yescharacteristic
140C17×#102C2×C411yescharacteristic
141#10587508—22no—
142#10587508—22no—
143#10587508—22no—
144#10587508—22no—
145#10587508—22no—
146#10587508—22no—
147#10587502—21no—
148C22⋊#3622—21no—
149C22⋊#3622—21no—
150C22⋊#3622—21no—
151C22⋊#3622—21no—
152#10587490—22no—
153#10587490—22no—
154#10587486—22no—
155C8×Dic17—22no—
156C4⋊#3622—21no—
157C4⋊#3622—21no—
158#10587474—21no—
159#10587474—21no—
160#10587474—21no—
161#10587474D411yescharacteristic
162#10587474D411yescharacteristic
163#10587474D411yescharacteristic
164#10587474D411yescharacteristic
165C4×#3622—21no—
166C4×#3622—21no—
167C4×#3622—21no—
168#41×C17—21no—
169#41×C17—21no—
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×C17C2×D412yes—
179#41×C17#4112yes—
180C2×Q8×C17C22×C411yescharacteristic
181C2×Q8×C17C22×C411yescharacteristic
182C2×Q8×C17C22×C411yescharacteristic
183C2×D4×C17—21no—
184C2×D4×C17—21no—
185C2×D4×C17—21no—
186C2×D4×C17—21no—
187C2×D4×C17—21no—
188C2×D4×C17C22×C411yescharacteristic
189C2×D4×C17C22×C411yescharacteristic
190C2×D4×C17C22×C411yescharacteristic
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
196C22×C4×C17#4111yescharacteristic
197C22×C4×C17#4111yescharacteristic
198C22×C4×C17C2411yescharacteristic
199C22×Dic17—21no—
200C22×Dic17—21no—
201Q16×C17—22no—
202Q16×C17—22no—
203SD16×C17—22no—
204SD16×C17—22no—
205SD16×C17—22no—
206SD16×C17—22no—
207D8×C17—22no—
208D8×C17—22no—
209C2×C8×C17—21no—
210C2×C8×C17—21no—
211C2×C8×C17—21no—
212C2×C8×C17—21no—
213C2×C8×C17C22×C411yescharacteristic
214C2×C8×C17C22×C411yescharacteristic
215C2×C8×C17C22×C411yescharacteristic
216C2×C8×C17C22×C411yescharacteristic
217C4⋊C4×C17—21no—
218C4⋊C4×C17—21no—
219C4⋊C4×C17—21no—
220C4⋊C4×C17—21no—
221C4⋊C4×C17C22×C411yescharacteristic
222C4⋊C4×C17C22×C411yescharacteristic
223C22⋊C4×C17—21no—
224C22⋊C4×C17—21no—
225C22⋊C4×C17—21no—
226C22⋊C4×C17—21no—
227C22⋊C4×C17—21no—
228C22⋊C4×C17—21no—
229C22⋊C4×C17—21no—
230C42×C17—21no—
231C42×C17—21no—
232C42×C17—21no—
233C42×C17C22×C411yescharacteristic
234C42×C17C22×C411yescharacteristic
235C42×C17C2×D411yescharacteristic
236C42×C17C2×D411yescharacteristic
237C4⋊Dic17—42no—
238C4×Dic17—21no—
239C4×Dic17—21no—
240C4×Dic17—21no—
241C4×Dic17—21no—
242#63223—24no—
243#63223—21no—
244#63223—21no—
245#63223—24no—
246#63223—21no—
247#63223—21no—
248#63223—21no—
249#63223—21no—
250#63223—42no—
251#63223—42no—
252#63223C2×D412yes—
253#63223#4112yes—
254C2×#3622—24no—
255C2×#3622—21no—
256C2×#3622—21no—
257C2×#3622—21no—
258C2×#3622—21no—
259C2×#3622—24no—
260C2×#3622—21no—
261C2×#3622—21no—
262C2×#3622—42no—
263C2×#3622—42no—
264C2×#3622C2×D411yescharacteristic
265C2×#3622C2×D411yescharacteristic
266C2×#3622C2×D411yescharacteristic
267C2×#3622C2×D411yescharacteristic
268C2×#3622C2×D412yes—
269C2×#3622#4112yes—
270#21519—171nomaximal, Sylow
271C23×C17—21no—
272C23×C17—21no—
273C23×C17—21no—
274C23×C17C2×#4111yescharacteristic
275Q8×C17—21no—
276Q8×C17—21no—
277Q8×C17—21no—
278Q8×C17—21no—
279Q8×C17—21no—
280Q8×C17C4×D412yes—
281D4×C17—22no—
282D4×C17—22no—
283D4×C17—21no—
284D4×C17—21no—
285D4×C17—21no—
286D4×C17—21no—
287D4×C17—21no—
288D4×C17—41no—
289D4×C17—41no—
290D4×C17—41no—
291D4×C17—41no—
292D4×C17—81no—
293D4×C17—81no—
294D4×C17C4×D412yes—
295C2×C4×C17—21no—
296C2×C4×C17—22no—
297C2×C4×C17—22no—
298C2×C4×C17—21no—
299C2×C4×C17—21no—
300C2×C4×C17—21no—
301C2×C4×C17—21no—
302C2×C4×C17—41no—
303C2×C4×C17—41no—
304C2×C4×C17—41no—
305C2×C4×C17—41no—
306C2×C4×C17—41no—
307C2×C4×C17—41no—
308C2×C4×C17—81no—
309C2×C4×C17—81no—
310C2×C4×C17C4×D411yescharacteristic
311C2×C4×C17C4×D411yescharacteristic
312C2×C4×C17C4×D411yescharacteristic
313C2×C4×C17C4×D411yescharacteristic
314C2×C4×C17C23×C411yescharacteristic
315C2×C4×C17C22×D411yescharacteristic
316C2×C4×C17C22×D411yescharacteristic
317C2×C4×C17C2×#4111yescharacteristic
318C2×C4×C17C2×#4111yescharacteristic
319C2×C4×C17C2×#4111yescharacteristic
320C2×Dic17—22no—
321C2×Dic17—41no—
322C2×Dic17—41no—
323C2×Dic17—41no—
324C2×Dic17—41no—
325C2×Dic17—41no—
326C8×C17—21no—
327C8×C17—21no—
328C8×C17—21no—
329C8×C17—21no—
330#3622—22no—
331#3622—21no—
332#3622—22no—
333#3622—21no—
334#3622—41no—
335#3622—41no—
336#3622#12112yes—
337#3622#12112yes—
338#3035D1711yescharacteristic
339C2×#444—171no—
340C2×#443—171no—
341#2932—171no—
342#2875—171no—
343#1980—171no—
344#1950—171no—
345#1929—171no—
346#1929—171no—
347#1876—171no—
348#1876—171no—
349#1806—171no—
350#1771—171no—
351#1765—171no—
352#1764—171no—
353C22×C17—21no—
354C22×C17—21no—
355C22×C17—22no—
356C22×C17—41no—
357C22×C17—41no—
358C22×C17—41no—
359C22×C17—41no—
360C22×C17—41no—
361C22×C17—41no—
362C22×C17—41no—
363C22×C17—41no—
364C22×C17C2×C4×D411yescharacteristic
365C22×C17#52911yescharacteristic
366C22×C17#53211yescharacteristic
367C4×C17—21no—
368C4×C17—21no—
369C4×C17—21no—
370C4×C17—21no—
371C4×C17—22no—
372C4×C17—41no—
373C4×C17—41no—
374C4×C17—41no—
375C4×C17—41no—
376C4×C17C2×C4×D411yescharacteristic
377C4×C17C4×#4111yescharacteristic
378C4×C17C2×#12111yescharacteristic
379C4×C17#52511yescharacteristic
380Dic17—42no—
381Dic17—81no—
382C2×#135C2×D1711yescharacteristic
383C2×#135C2×D1711yescharacteristic
384C2×#131—171no—
385C2×#131—171no—
386C2×#131—171no—
387C2×#131—171no—
388#532C2×D1711yescharacteristic
389C4×#41C2×D1711yescharacteristic
390#464Dic1711yescharacteristic, complemented
391#464Dic1711yescharacteristic, complemented
392#463Dic1711yescharacteristic, complemented
393#463Dic1711yescharacteristic, complemented
394#462Dic1711yescharacteristic, complemented
395#461Dic1711yescharacteristic, complemented
396#460Dic1711yescharacteristic, complemented
397#459Dic1711yescharacteristic, complemented
398#444—344no—
399#443—344no—
400#435—341no—
401#435—341no—
402#435—341no—
403#435—341no—
404C2×#108—171no—
405C2×#108—171no—
406#423—171no—
407C2×C4⋊C8C2×D1711yescharacteristic
408C2×#104—171no—
409C2×#104—171no—
410C2×#104—171no—
411C2×#104—171no—
412C2×#104—171no—
413C2×#104—171no—
414#416C2×D1711yescharacteristic
415#416C2×D1711yescharacteristic
416#408—171no—
417#408—171no—
418#405—171no—
419#405—171no—
420#405—341no—
421#405—341no—
422C4×M16—171no—
423C4×M16—341no—
424C2×#97—171no—
425C2×#97—171no—
426C2×#97—341no—
427C2×C4×C8—171no—
428C4×C4⋊C4—171no—
429#341—171no—
430#341—171no—
431#339—171no—
432#339—171no—
433#336—171no—
434#336—171no—
435C2×C17—21no—
436C2×C17—21no—
437C2×C17—42no—
438C2×C17—81no—
439C2×C17—81no—
440C2×C17C4×#12111yescharacteristic
441C2×C17#295611yescharacteristic
442C2×C17#295711yescharacteristic
443C2×#41C22×D1711yescharacteristic
444C2×#41C22×D1711yescharacteristic
445C2×#41C22×D1711yescharacteristic
446#135—22no—
447#135—22no—
448#135—22no—
449#135—22no—
450C2×Q16C2×Dic1711yescharacteristic
451C2×Q16C2×Dic1711yescharacteristic
452C2×SD16C2×Dic1711yescharacteristic
453C2×SD16C2×Dic1711yescharacteristic
454C2×SD16C2×Dic1711yescharacteristic
455C2×SD16C2×Dic1711yescharacteristic
456C2×D8C2×Dic1711yescharacteristic
457C2×D8C2×Dic1711yescharacteristic
458#131—174no—
459#131—342no—
460#131—342no—
461#131—342no—
462#131—342no—
463#131—342no—
464#131—342no—
465#131—342no—
466C2×M16—171no—
467C2×M16—171no—
468C2×M16—171no—
469C2×M16—171no—
470C2×M16—341no—
471C2×M16—341no—
472C2×M16—341no—
473C2×M16—341no—
474C22×C8—171no—
475C22×C8—171no—
476C22×C8—341no—
477C22×C8—341no—
478C22×C8—341no—
479C22×C8—341no—
480C22×C8C22×D1711yescharacteristic
481C22×C8C22×D1711yescharacteristic
482C4⋊Q8C2×Dic1711yescharacteristic
483#127C2×Dic1711yescharacteristic
484#124C2×Dic1711yescharacteristic
485#124C2×Dic1711yescharacteristic
486#121—21no—
487#121—21no—
488C4×Q8C2×Dic1711yescharacteristic
489C4×Q8C2×Dic1711yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C2×Dic1711yescharacteristic
495C4×D4C2×Dic1711yescharacteristic
496#117—21no—
497#117C22×D1711yescharacteristic
498C2×C4⋊C4—341no—
499C2×C42—21no—
500C2×C42—171no—
501C2×C42—171no—
502C2×C42C22×D1711yescharacteristic
503#108—342no—
504#108—342no—
505C4⋊C8—341no—
506C4⋊C8—341no—
507C4⋊C8C2×Dic1711yescharacteristic
508C4⋊C8C2×Dic1711yescharacteristic
509C4⋊C8C2×Dic1711yescharacteristic
510C4⋊C8C2×Dic1711yescharacteristic
511#104—342no—
512#104—342no—
513#104—342no—
514#104—342no—
515#104—342no—
516#104—342no—
517#103C2×Dic1711yescharacteristic
518#103C2×Dic1711yescharacteristic
519#103C2×Dic1711yescharacteristic
520#103C2×Dic1711yescharacteristic
521#102C2×Dic1711yescharacteristic
522#102C2×Dic1711yescharacteristic
523#102C2×Dic1711yescharacteristic
524#102C2×Dic1711yescharacteristic
525C22⋊C8—341no—
526C22⋊C8—341no—
527C22⋊C8—341no—
528C22⋊C8—341no—
529#97—171no—
530#97—171no—
531#97—171no—
532#97—171no—
533#97—341no—
534#97—341no—
535#97—342no—
536#97—341no—
537C4×C8—341no—
538C4×C8—341no—
539C4×C8—342no—
540C4×C8—341no—
541#95—341no—
542C17#2151911yescharacteristic, complemented, Sylow
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41D4×D1712yes—
554#41#6325412yes—
555C2×Q8C22×Dic1711yescharacteristic
556C2×Q8C22×Dic1711yescharacteristic
557C2×Q8C22×Dic1711yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×Dic1711yescharacteristic
564C2×D4C22×Dic1711yescharacteristic
565C2×D4C22×Dic1711yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—341no—
572C22×C4—341no—
573C22×C4#6325411yescharacteristic
574C22×C4#6325411yescharacteristic
575C22×C4C23×D1711yescharacteristic
576Q16—22no—
577Q16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582D8—22no—
583D8—22no—
584M16—172no—
585M16—172no—
586M16—344no—
587M16—344no—
588M16—341no—
589M16—341no—
590M16—341no—
591M16—341no—
592M16—341no—
593M16—341no—
594M16—682no—
595M16—682no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—172no—
601C2×C8—171no—
602C2×C8—171no—
603C2×C8—172no—
604C2×C8—171no—
605C2×C8—171no—
606C2×C8—344no—
607C2×C8—344no—
608C2×C8—341no—
609C2×C8—341no—
610C2×C8—341no—
611C2×C8—341no—
612C2×C8—341no—
613C2×C8—341no—
614C2×C8—682no—
615C2×C8—682no—
616C2×C8C22×Dic1711yescharacteristic
617C2×C8C22×Dic1711yescharacteristic
618C2×C8C22×Dic1711yescharacteristic
619C2×C8C22×Dic1711yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—682no—
625C4⋊C4C22×Dic1711yescharacteristic
626C4⋊C4C22×Dic1711yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—341no—
638C42—341no—
639C42—341no—
640C42—341no—
641C42D4×D1711yescharacteristic
642C42D4×D1711yescharacteristic
643C42C22×Dic1711yescharacteristic
644C42C22×Dic1711yescharacteristic
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#6325411yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8D4×Dic1712yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4D4×Dic1712yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—342no—
685C2×C4—681no—
686C2×C4—681no—
687C2×C4—681no—
688C2×C4—681no—
689C2×C4—681no—
690C2×C4D4×Dic1711yescharacteristic
691C2×C4D4×Dic1711yescharacteristic
692C2×C4D4×Dic1711yescharacteristic
693C2×C4D4×Dic1711yescharacteristic
694C2×C4C2×D4×D1711yescharacteristic
695C2×C4C2×D4×D1711yescharacteristic
696C2×C4C2×#6325411yescharacteristic
697C2×C4#41×D1711yescharacteristic
698C2×C4#41×D1711yescharacteristic
699C2×C4C23×Dic1711yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—172no—
705C8—172no—
706C8—342no—
707C8—341no—
708C8—341no—
709C8—342no—
710C8—681no—
711C8—681no—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×D4×Dic1711yescharacteristic
724C22#1176334011yescharacteristic
725C22#1176335411yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—682no—
736C4—1361no—
737C4C2×D4×Dic1711yescharacteristic
738C4#41×Dic1711yescharacteristic
739C4#121×D1711yescharacteristic
740C4#1176331911yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2#121×Dic1711yescharacteristic
747C2#1453769411yescharacteristic
748C2#1453770111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
Fitting, prime radicalC17×#3035C2
socleC22×C17C2×C4×D4
cosocleC22×C4×C17C24
hypercenter#3035D17
hypocenterC17#21519
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#11762931C2semidirect
2. C2×#11762926C2semidirect
3. #14537502C2semidirect
4. #14537212C2semidirect
5. #14529704C2semidirect
6. #14529560C2semidirect
7. #14529434C2semidirect
8. #14529434C2semidirect
9. #14529113C2semidirect
10. #14529113C2semidirect
11. #14528804C2semidirect
12. #14528661C2semidirect
13. #14528631C2semidirect
14. #14528624C2semidirect
58. C17×#464C4semidirect
59. C17×#464C4semidirect
60. C17×#463C4semidirect
61. C17×#463C4semidirect
62. C17×#462C4semidirect
63. C17×#461C4semidirect
64. C17×#460C4semidirect
65. C17×#459C4semidirect
111. #10587634D4semidirect
390. #464Dic17semidirect
391. #464Dic17semidirect
392. #463Dic17semidirect
393. #463Dic17semidirect
394. #462Dic17semidirect
395. #461Dic17semidirect
396. #460Dic17semidirect
397. #459Dic17semidirect
542. C17#21519semidirect

Maximal subgroups

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

subgroupindex
C2×#117629312
C2×#117629262
#145375022
#145372122
#145297042
#145295602
#145294342
#145291132
#145288042
#145286612
#145286312
#145286242
C17×#30352
#2151917