Finite Group Databasebeta

← #16941116

Subgroups — #16941116

Order 4352.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762810C211yesmaximal, characteristic
2C22×#10587506C211yesmaximal, characteristic, complemented
3C22×#10587507C211yesmaximal, characteristic, complemented
4C2×#11762776C211yesmaximal, characteristic
5C2×#11762577C211yesmaximal, characteristic, complemented
6C2×#11762573C211yesmaximal, characteristic, complemented
7C22×C17×#137C211yesmaximal, characteristic
8C22×#63223C2211yescharacteristic
9C22×#63223C2211yescharacteristic
10C23×#3622C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12#11762810—22no—
13#11762810—22no—
14C2×#10587506—22no—
15C2×#10587506—22no—
16C2×#10587506—22no—
17C2×#10587506—21no—
18C2×#10587503—21no—
19C2×#10587507—22no—
20C2×#10587507—22no—
21C2×#10587507—22no—
22#11762776—22no—
23#11762776—22no—
24C2×C22⋊#3622—22no—
25#11762577—22no—
26#11762573—22no—
27C22×#41×C17C2211yescharacteristic
28C23×Q8×C17C2211yescharacteristic
29C2×C17×#137—22no—
30C2×C17×#137—22no—
31C2×C17×#137—22no—
32C2×C17×#137—22no—
33C2×C17×#137—22no—
34C2×C17×#137C414yescomplemented
35C22×Q16×C17—21no—
36C22×SD16×C17—21no—
37C22×M16×C17C2211yescharacteristic
38C2×#41×C17—21no—
39C2×#41×C17—21no—
40C2×#41×C17—21no—
41C2×#41×C17—21no—
42C2×#41×C17—21no—
43C2×#41×C17—21no—
44C2×#41×C17—21no—
45C2×#41×C17—21no—
46C2×#41×C17—21no—
47C2×#41×C17—21no—
48C2×#41×C17C2×C412yes—
49C2×#41×C17D412yes—
50C22×Q8×C17—21no—
51C22×Q8×C17—21no—
52C22×Q8×C17—21no—
53C22×Q8×C17—21no—
54C22×Q8×C17—21no—
55C22×Q8×C17—21no—
56C22×Q8×C17—21no—
57C22×Q8×C17—21no—
58C22×Q8×C17—21no—
59C22×Q8×C17—21no—
60C22×Q8×C17—21no—
61C22×Q8×C17C2×C412yes—
62C22×Q8×C17D411yescharacteristic
63C22×Q8×C17D412yes—
64C22×Q8×C17D412yes—
65C22×D4×C17—21no—
66C22×D4×C17D411yescharacteristic
67C23×C4×C17—21no—
68C23×C4×C17—21no—
69C23×C4×C17C2311yescharacteristic
70C23×Dic17—21no—
71C17×#137—28no—
72C17×#137—28no—
73C17×#137—28no—
74C17×#137—28no—
75C2×Q16×C17—24no—
76C2×Q16×C17—24no—
77C2×Q16×C17—24no—
78C2×SD16×C17—24no—
79C2×SD16×C17—24no—
80C2×SD16×C17—24no—
81C2×M16×C17—21no—
82C2×M16×C17—21no—
83C2×M16×C17—21no—
84C2×M16×C17C2×C412yes—
85C2×M16×C17D412yes—
86C2×M16×C17D412yes—
87C22×C8×C17—21no—
88C2×C4⋊Dic17—21no—
89C2×C4⋊Dic17—21no—
90C2×C4⋊Dic17—21no—
91C2×C4⋊Dic17—21no—
92C2×C4⋊Dic17—21no—
93C2×C4⋊Dic17D412yes—
94C2×#63223—21no—
95C2×#63223—21no—
96C2×#63223—21no—
97C2×#63223—21no—
98C2×#63223—21no—
99C2×#63223—21no—
100C2×#63223—21no—
101C2×#63223—21no—
102C2×#63223—21no—
103C2×#63223—21no—
104C2×#63223D412yes—
105C2×#63223D412yes—
106C22×#3622—21no—
107C22×#3622—21no—
108C22×#3622—21no—
109C22×#3622—21no—
110C22×#3622—21no—
111C22×#3622—21no—
112C22×#3622—21no—
113C22×#3622—21no—
114C22×#3622D412yes—
115#10587507—28no—
116#10587506—28no—
117#10587506—24no—
118#10587503—24no—
119C22⋊#3622—28no—
120C24×C17—21no—
121C24×C17#4111yescharacteristic
122#41×C17—22no—
123#41×C17—22no—
124#41×C17—22no—
125#41×C17—22no—
126#41×C17—22no—
127#41×C17—22no—
128#41×C17—22no—
129#41×C17—22no—
130#41×C17—41no—
131#41×C17—41no—
132#41×C17—41no—
133#41×C17—41no—
134#41×C17—41no—
135#41×C17—41no—
136#41×C17—41no—
137#41×C17—41no—
138C2×Q8×C17—22no—
139C2×Q8×C17—22no—
140C2×Q8×C17—22no—
141C2×Q8×C17—21no—
142C2×Q8×C17—22no—
143C2×Q8×C17—22no—
144C2×Q8×C17—22no—
145C2×Q8×C17—22no—
146C2×Q8×C17—22no—
147C2×Q8×C17—22no—
148C2×Q8×C17—21no—
149C2×Q8×C17—21no—
150C2×Q8×C17—22no—
151C2×Q8×C17—22no—
152C2×Q8×C17—22no—
153C2×Q8×C17—21no—
154C2×Q8×C17—22no—
155C2×Q8×C17—22no—
156C2×Q8×C17—22no—
157C2×Q8×C17—21no—
158C2×Q8×C17—41no—
159C2×Q8×C17—41no—
160C2×Q8×C17—41no—
161C2×Q8×C17—41no—
162C2×Q8×C17—41no—
163C2×Q8×C17—41no—
164C2×Q8×C17—41no—
165C2×Q8×C17—41no—
166C2×Q8×C17—41no—
167C2×Q8×C17—41no—
168C2×Q8×C17—41no—
169C2×Q8×C17—41no—
170C2×Q8×C17C22⋊C412yes—
171C2×Q8×C17C22⋊C414yes—
172C2×D4×C17—22no—
173C2×D4×C17—22no—
174C2×D4×C17—21no—
175C2×D4×C17—21no—
176C2×D4×C17—21no—
177C2×D4×C17—21no—
178C2×D4×C17—21no—
179C2×D4×C17—41no—
180C2×D4×C17—41no—
181C2×D4×C17—41no—
182C2×D4×C17—41no—
183C2×D4×C17C22⋊C412yes—
184C22×C4×C17—22no—
185C22×C4×C17—21no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17—22no—
189C22×C4×C17—22no—
190C22×C4×C17—41no—
191C22×C4×C17—41no—
192C22×C4×C17—41no—
193C22×C4×C17—41no—
194C22×C4×C17—41no—
195C22×C4×C17—41no—
196C22×C4×C17—41no—
197C22×C4×C17—41no—
198C22×C4×C17C22×C411yescharacteristic
199C22×C4×C17C2×D411yescharacteristic
200C22×C4×C17C2×D411yescharacteristic
201C22×C4×C17C2×D411yescharacteristic
202C22×C4×C17C2×D411yescharacteristic
203C22×C4×C17C2×D411yescharacteristic
204C22×C4×C17C2×D411yescharacteristic
205C22×C4×C17C2×D411yescharacteristic
206C22×C4×C17C2×D411yescharacteristic
207C22×C4×C17C2×D411yescharacteristic
208C22×C4×C17C2×D411yescharacteristic
209C22×C4×C17#4111yescharacteristic
210C22×C4×C17#4111yescharacteristic
211C22×C4×C17#4111yescharacteristic
212C22×Dic17—22no—
213C22×Dic17—41no—
214C22×Dic17—41no—
215C22×Dic17—82no—
216Q16×C17—216no—
217SD16×C17—216no—
218M16×C17—22no—
219M16×C17—22no—
220M16×C17—22no—
221M16×C17C22⋊C414yes—
222C2×C8×C17—22no—
223C2×C8×C17—22no—
224C2×C8×C17—22no—
225C4⋊Dic17—22no—
226C4⋊Dic17—22no—
227C4⋊Dic17—41no—
228C4⋊Dic17—41no—
229#63223—22no—
230#63223—22no—
231#63223—22no—
232#63223—22no—
233#63223—41no—
234#63223—41no—
235#63223—41no—
236#63223—41no—
237C2×#3622—22no—
238C2×#3622—22no—
239C2×#3622—22no—
240C2×#3622—22no—
241C2×#3622—22no—
242C2×#3622—41no—
243C2×#3622—41no—
244C2×#3622—41no—
245C2×#3622—41no—
246C2×#3622—41no—
247C2×#3622—41no—
248C2×#3622—41no—
249C2×#3622—41no—
250#11021—171nomaximal, Sylow
251C23×C17—22no—
252C23×C17—22no—
253C23×C17—22no—
254C23×C17—41no—
255C23×C17—41no—
256C23×C17—42no—
257C23×C17—42no—
258C23×C17C4×D411yescharacteristic
259C23×C17#12111yescharacteristic
260C23×C17#12111yescharacteristic
261C23×C17#12111yescharacteristic
262C23×C17#12311yescharacteristic
263C23×C17#12311yescharacteristic
264C23×C17#12411yescharacteristic
265Q8×C17—24no—
266Q8×C17—22no—
267Q8×C17—24no—
268Q8×C17—22no—
269Q8×C17—42no—
270Q8×C17—42no—
271Q8×C17—42no—
272Q8×C17—42no—
273Q8×C17—42no—
274Q8×C17—41no—
275Q8×C17—42no—
276Q8×C17—41no—
277D4×C17—22no—
278D4×C17—22no—
279D4×C17—42no—
280D4×C17—42no—
281D4×C17—42no—
282D4×C17—42no—
283D4×C17—41no—
284D4×C17—41no—
285C2×C4×C17—22no—
286C2×C4×C17—24no—
287C2×C4×C17—42no—
288C2×C4×C17—42no—
289C2×C4×C17—41no—
290C2×C4×C17—42no—
291C2×C4×C17—41no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—42no—
296C2×C4×C17—42no—
297C2×C4×C17—42no—
298C2×C4×C17—42no—
299C2×C4×C17C2×C22⋊C411yescharacteristic
300C2×C4×C17C2×C22⋊C411yescharacteristic
301C2×C4×C17C2×C22⋊C411yescharacteristic
302C2×C4×C17C4×D411yescharacteristic
303C2×C4×C17C4×D411yescharacteristic
304C2×C4×C17C4×D411yescharacteristic
305C2×C4×C17#12011yescharacteristic
306C2×C4×C17#12011yescharacteristic
307C2×C4×C17#12011yescharacteristic
308C2×C4×C17#12011yescharacteristic
309C2×C4×C17#12011yescharacteristic
310C2×C4×C17#12011yescharacteristic
311C2×C4×C17#12011yescharacteristic
312C2×C4×C17#12011yescharacteristic
313C2×C4×C17#12111yescharacteristic
314C2×C4×C17#12111yescharacteristic
315C2×C4×C17#12111yescharacteristic
316C2×C4×C17#12111yescharacteristic
317C2×C4×C17#12111yescharacteristic
318C2×C4×C17#12111yescharacteristic
319C2×C4×C17#12111yescharacteristic
320C2×C4×C17#12111yescharacteristic
321C2×C4×C17#12111yescharacteristic
322C2×C4×C17#12311yescharacteristic
323C2×C4×C17#12311yescharacteristic
324C2×C4×C17#12411yescharacteristic
325C2×C4×C17#12711yescharacteristic
326C2×C4×C17#12711yescharacteristic
327C2×Dic17—42no—
328C2×Dic17—82no—
329C2×Dic17—82no—
330C2×Dic17—82no—
331C8×C17—24no—
332#3622—42no—
333#3622—42no—
334#3622—42no—
335C22×#137D1711yescharacteristic
336C2×#417—171no—
337C22×#103—171no—
338C22×#101—171no—
339C2×#408—171no—
340C2×#343—171no—
341C2×#341—171no—
342C22×C17—22no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—22no—
346C22×C17—21no—
347C22×C17—21no—
348C22×C17—21no—
349C22×C17—21no—
350C22×C17—44no—
351C22×C17—42no—
352C22×C17—82no—
353C22×C17—81no—
354C22×C17—81no—
355C22×C17#38611yescharacteristic
356C22×C17#38611yescharacteristic
357C22×C17#39011yescharacteristic
358C22×C17#39211yescharacteristic
359C22×C17#39411yescharacteristic
360C22×C17#39411yescharacteristic
361C22×C17#39411yescharacteristic
362C22×C17#47112yes—
363C22×C17#47312yes—
364C4×C17—42no—
365C4×C17—44no—
366C4×C17#37911yescharacteristic
367C4×C17#38611yescharacteristic
368C4×C17#38611yescharacteristic
369C4×C17#39011yescharacteristic
370C4×C17#39211yescharacteristic
371C4×C17#39211yescharacteristic
372C4×C17#39211yescharacteristic
373C4×C17#39411yescharacteristic
374Dic17—82no—
375C22×#41C2×D1711yescharacteristic
376C23×Q8C2×D1711yescharacteristic
377C2×#137—22no—
378C2×#137—22no—
379C2×#137—22no—
380C2×#137—22no—
381C2×#137—22no—
382C2×#137Dic1714yescomplemented
383C22×Q16—21no—
384C22×SD16—21no—
385C22×M16—171no—
386C22×M16—171no—
387C22×M16C2×D1711yescharacteristic
388C23×C8—171no—
389C22×C4⋊C4—171no—
390#417—342no—
391#417—342no—
392C2×#103—342no—
393C2×#103—342no—
394C2×#103—342no—
395C2×#103—341no—
396C2×#102—341no—
397C2×#101—342no—
398C2×#101—342no—
399C2×#101—342no—
400#408—342no—
401#408—342no—
402C2×C22⋊C8—342no—
403#343—342no—
404#341—342no—
405C2×C17—21no—
406C2×C17—21no—
407C2×C17—21no—
408C2×C17—21no—
409C2×C17—82no—
410C2×C17#143811yescharacteristic
411C2×C17#190812yes—
412C2×C17#201911yescharacteristic
413C2×C17#202011yescharacteristic
414C2×C17#205212yes—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41C2×Dic1712yes—
426C2×#41C22⋊D1712yes—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8C2×Dic1712yes—
439C22×Q8C22⋊D1711yescharacteristic
440C22×Q8C22⋊D1712yes—
441C22×Q8C22⋊D1712yes—
442C22×D4—21no—
443C22×D4C22⋊D1711yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—341no—
447C23×C4C22×D1711yescharacteristic
448#137—28no—
449#137—28no—
450#137—28no—
451#137—28no—
452C2×Q16—24no—
453C2×Q16—24no—
454C2×Q16—24no—
455C2×SD16—24no—
456C2×SD16—24no—
457C2×SD16—24no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—172no—
462C2×M16—172no—
463C2×M16—341no—
464C2×M16—341no—
465C2×M16—341no—
466C2×M16—341no—
467C2×M16—341no—
468C2×M16—341no—
469C2×M16—341no—
470C2×M16—341no—
471C2×M16—341no—
472C2×M16—341no—
473C2×M16C2×Dic1712yes—
474C2×M16C22⋊D1712yes—
475C2×M16C22⋊D1712yes—
476C22×C8—21no—
477C22×C8—172no—
478C22×C8—341no—
479C22×C8—341no—
480C22×C8—341no—
481C22×C8—341no—
482C22×C8—341no—
483C22×C8—341no—
484C22×C8—341no—
485C22×C8—341no—
486C2×C4⋊C4—172no—
487C2×C4⋊C4—341no—
488C2×C4⋊C4—341no—
489C2×C4⋊C4—341no—
490C2×C4⋊C4—341no—
491C2×C4⋊C4—341no—
492#103—348no—
493#103—344no—
494#102—344no—
495#101—348no—
496C22⋊C8—348no—
497C17#1102111yescharacteristic, complemented, Sylow
498C24—21no—
499C24#6325411yescharacteristic
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—22no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—21no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C22⋊Dic1712yes—
549C2×Q8C22⋊Dic1714yes—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4C22⋊Dic1712yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—342no—
577C22×C4—681no—
578C22×C4—681no—
579C22×C4—1362no—
580C22×C4D4×D1711yescharacteristic
581C22×C4D4×D1711yescharacteristic
582C22×C4D4×D1711yescharacteristic
583C22×C4D4×D1711yescharacteristic
584C22×C4#6325411yescharacteristic
585C22×C4#6325411yescharacteristic
586C22×C4#6325411yescharacteristic
587C22×C4C22×Dic1711yescharacteristic
588C22×C4C2×C22⋊D1711yescharacteristic
589C22×C4C2×C22⋊D1711yescharacteristic
590C22×C4C2×C22⋊D1711yescharacteristic
591C22×C4C2×C22⋊D1711yescharacteristic
592C22×C4C2×C22⋊D1711yescharacteristic
593C22×C4C2×C22⋊D1711yescharacteristic
594Q16—216no—
595SD16—216no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—342no—
600M16—342no—
601M16—342no—
602M16—342no—
603M16—681no—
604M16—681no—
605M16—681no—
606M16—681no—
607M16C22⋊Dic1714yes—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—342no—
612C2×C8—342no—
613C2×C8—342no—
614C2×C8—342no—
615C2×C8—342no—
616C2×C8—681no—
617C2×C8—681no—
618C2×C8—681no—
619C2×C8—681no—
620C2×C8—681no—
621C2×C8—681no—
622C2×C8—681no—
623C2×C8—681no—
624C4⋊C4—342no—
625C4⋊C4—342no—
626C4⋊C4—681no—
627C4⋊C4—681no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23D4×Dic1711yescharacteristic
636C23#1058762111yescharacteristic
637C23#1058762111yescharacteristic
638C23#1058762211yescharacteristic
639C23#1058762411yescharacteristic
640C23#1058762511yescharacteristic
641C23#1058762511yescharacteristic
642Q8—24no—
643Q8—22no—
644Q8—24no—
645Q8—22no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—42no—
651Q8—41no—
652Q8—42no—
653Q8—41no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—41no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—682no—
677C2×C4—1362no—
678C2×C4—1362no—
679C2×C4—1362no—
680C2×C4D4×Dic1711yescharacteristic
681C2×C4D4×Dic1711yescharacteristic
682C2×C4D4×Dic1711yescharacteristic
683C2×C4#1058762111yescharacteristic
684C2×C4#1058762111yescharacteristic
685C2×C4#1058762211yescharacteristic
686C2×C4#1058762311yescharacteristic
687C2×C4#1058762311yescharacteristic
688C2×C4#1058762311yescharacteristic
689C2×C4#1058762311yescharacteristic
690C2×C4#1058762411yescharacteristic
691C2×C4#1058762411yescharacteristic
692C2×C4#1058762411yescharacteristic
693C2×C4#1058762511yescharacteristic
694C2×C4#1058762511yescharacteristic
695C2×C4#1058762511yescharacteristic
696C2×C4#1058762511yescharacteristic
697C2×C4#1058762511yescharacteristic
698C2×C4#1058762511yescharacteristic
699C2×C4#1058762611yescharacteristic
700C2×C4#1058762611yescharacteristic
701C2×C4C2×C22⋊Dic1711yescharacteristic
702C2×C4C2×C22⋊Dic1711yescharacteristic
703C2×C4C2×C22⋊Dic1711yescharacteristic
704C2×C4#1058763911yescharacteristic
705C2×C4#1058763911yescharacteristic
706C2×C4#1058763911yescharacteristic
707C2×C4#1058763911yescharacteristic
708C8—24no—
709C8—682no—
710C8—682no—
711C8—682no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—44no—
721C22—42no—
722C22—82no—
723C22—81no—
724C22—81no—
725C22#1176268911yescharacteristic
726C22#1176268911yescharacteristic
727C22#1176271211yescharacteristic
728C22#1176271711yescharacteristic
729C22#1176272311yescharacteristic
730C22#1176272311yescharacteristic
731C22#1176272311yescharacteristic
732C22#1176307412yes—
733C22#1176308212yes—
734C4—42no—
735C4—44no—
736C4—1362no—
737C4#1176266511yescharacteristic
738C4#1176268911yescharacteristic
739C4#1176268911yescharacteristic
740C4#1176271211yescharacteristic
741C4#1176271711yescharacteristic
742C4#1176271711yescharacteristic
743C4#1176271711yescharacteristic
744C4#1176272311yescharacteristic
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—82no—
750C2#1452702511yescharacteristic
751C2#1452930112yes—
752C2#1452989511yescharacteristic
753C2#1452990211yescharacteristic
754C2#1453008012yes—
subgroupG/H
centerC23#10587625
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC22×C17×#137C2
socleC23×C17#121
prime radicalC22×#41×C17C22
cosocleC23×C4×C17C23
hypercenterC22×#137D17
hypocenterC17#11021
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C22×#10587506C2semidirect
3. C22×#10587507C2semidirect
5. C2×#11762577C2semidirect
6. C2×#11762573C2semidirect
34. C2×C17×#137C4semidirect
382. C2×#137Dic17semidirect
497. C17#11021semidirect

Maximal subgroups

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

subgroupindex
C2×#117628102
C22×#105875062
C22×#105875072
C2×#117627762
C2×#117625772
C2×#117625732
C22×C17×#1372
#1102117