Finite Group Databasebeta

← #16942135

Subgroups — #16942135

Order 4352.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587480C211yesmaximal, characteristic
2C22×#10587480C211yesmaximal, characteristic
3C2×#11762711C211yesmaximal, characteristic
4C2×#11762571C211yesmaximal, characteristic, complemented
5C2×#11762571C211yesmaximal, characteristic, complemented
6C2×#11762564C211yesmaximal, characteristic, complemented
7C17×C4⋊#95C211yesmaximal, characteristic, complemented
8C23×D68C2211yescharacteristic
9C23×#3622C2211yescharacteristic
10C23×#3622C2211yescharacteristic
11C22×C4⋊Dic17C2211yescharacteristic
12C22×#63227—21no—
13C22×#63227—21no—
14C2×#10587480—22no—
15C2×#10587480—22no—
16C2×#10587480—22no—
17C2×#10587480—22no—
18C2×#10587480—22no—
19C2×#10587480C414yescomplemented
20#11762711—22no—
21#11762711—22no—
22#11762571—22no—
23#11762571—22no—
24#11762564—22no—
25C22×C4⋊C4×C17C2211yescharacteristic
26C22×C4⋊C4×C17C2211yescharacteristic
27C22×C42×C17C2211yescharacteristic
28C2×C17×#95—21no—
29C2×C17×#95—21no—
30C24×D17—21no—
31C23×C4×C17—21no—
32C23×C4×C17—21no—
33C23×C4×C17D411yescharacteristic
34C23×C4×C17D411yescharacteristic
35C23×C4×C17C2311yescharacteristic
36C23×Dic17—21no—
37C22×D68—21no—
38C22×D68—21no—
39C22×D68—21no—
40C22×D68—21no—
41C22×D68—21no—
42C22×D68—21no—
43C22×D68—21no—
44C22×D68—21no—
45C22×D68—21no—
46C22×D68—21no—
47C22×D68—21no—
48C22×D68C2×C412yes—
49C22×D68D412yes—
50C22×D68D412yes—
51C2×C4⋊C4×C17—21no—
52C2×C4⋊C4×C17—21no—
53C2×C4⋊C4×C17—21no—
54C2×C4⋊C4×C17—21no—
55C2×C4⋊C4×C17—21no—
56C2×C4⋊C4×C17—21no—
57C2×C4⋊C4×C17—21no—
58C2×C4⋊C4×C17—21no—
59C2×C4⋊C4×C17—21no—
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17C2×C412yes—
62C2×C4⋊C4×C17D412yes—
63C2×C42×C17—21no—
64C2×C42×C17—21no—
65C2×C42×C17—21no—
66C2×C42×C17—21no—
67C2×C42×C17—21no—
68C2×C42×C17—21no—
69C2×#63227—24no—
70C2×#63227—24no—
71C2×#63227—42no—
72C2×#63227—42no—
73C2×#63227—42no—
74C2×#63227—42no—
75C2×C4⋊Dic17—21no—
76C2×C4⋊Dic17—21no—
77C2×C4⋊Dic17—21no—
78C2×C4⋊Dic17—21no—
79C2×C4⋊Dic17—21no—
80C2×C4⋊Dic17D412yes—
81C22×#3622—21no—
82C22×#3622—21no—
83C22×#3622—21no—
84C22×#3622—21no—
85C22×#3622—21no—
86C22×#3622—21no—
87C22×#3622—21no—
88C22×#3622—21no—
89C22×#3622—21no—
90C22×#3622—21no—
91C22×#3622—21no—
92C22×#3622—21no—
93C22×#3622C2×C412yes—
94C22×#3622D412yes—
95C17×#95—42no—
96C17×#95—42no—
97#10587480—28no—
98#10587480—28no—
99C24×C17C2×D411yescharacteristic
100C23×D17—22no—
101C23×D17—22no—
102C23×D17—22no—
103C23×D17—41no—
104C23×D17—41no—
105C23×D17—41no—
106C23×D17—41no—
107C23×D17—41no—
108C23×D17—41no—
109C23×D17—41no—
110C23×D17—41no—
111C23×D17—41no—
112C23×D17—41no—
113C23×D17—41no—
114C23×D17—41no—
115C22×C4×C17—21no—
116C22×C4×C17—21no—
117C22×C4×C17—21no—
118C22×C4×C17—21no—
119C22×C4×C17—21no—
120C22×C4×C17—21no—
121C22×C4×C17—21no—
122C22×C4×C17—21no—
123C22×C4×C17—21no—
124C22×C4×C17—21no—
125C22×C4×C17—21no—
126C22×C4×C17—21no—
127C22×C4×C17—22no—
128C22×C4×C17—22no—
129C22×C4×C17—41no—
130C22×C4×C17—41no—
131C22×C4×C17—41no—
132C22×C4×C17—41no—
133C22×C4×C17—41no—
134C22×C4×C17—41no—
135C22×C4×C17—41no—
136C22×C4×C17—41no—
137C22×C4×C17—41no—
138C22×C4×C17—41no—
139C22×C4×C17—41no—
140C22×C4×C17—41no—
141C22×C4×C17D812yes—
142C22×C4×C17SD1612yes—
143C22×C4×C17C22×C411yescharacteristic
144C22×C4×C17C2×D411yescharacteristic
145C22×C4×C17C2×D411yescharacteristic
146C22×C4×C17C2×D411yescharacteristic
147C22×C4×C17C2×D411yescharacteristic
148C22×C4×C17C2×D411yescharacteristic
149C22×C4×C17#4111yescharacteristic
150C22×C4×C17#4111yescharacteristic
151C22×C4×C17#4111yescharacteristic
152C22×C4×C17#4111yescharacteristic
153C22×C4×C17#4111yescharacteristic
154C22×C4×C17#4111yescharacteristic
155C22×C4×C17#4111yescharacteristic
156C22×C4×C17#4111yescharacteristic
157C22×Dic17—22no—
158C22×Dic17—41no—
159C22×Dic17—41no—
160C22×Dic17—41no—
161C22×Dic17—41no—
162C22×Dic17—41no—
163C22×Dic17—41no—
164C2×D68—22no—
165C2×D68—22no—
166C2×D68—22no—
167C2×D68—22no—
168C2×D68—22no—
169C2×D68—22no—
170C2×D68—22no—
171C2×D68—22no—
172C2×D68—22no—
173C2×D68—22no—
174C2×D68—22no—
175C2×D68—22no—
176C2×D68—22no—
177C2×D68—22no—
178C2×D68—22no—
179C2×D68—41no—
180C2×D68—41no—
181C2×D68—41no—
182C2×D68—41no—
183C2×D68—41no—
184C2×D68—41no—
185C2×D68—41no—
186C2×D68—41no—
187C2×D68—41no—
188C2×D68—41no—
189C2×D68—41no—
190C2×D68—41no—
191C2×D68C22⋊C414yes—
192C4⋊C4×C17—22no—
193C4⋊C4×C17—22no—
194C4⋊C4×C17—22no—
195C4⋊C4×C17—22no—
196C4⋊C4×C17—41no—
197C4⋊C4×C17—41no—
198C4⋊C4×C17—41no—
199C4⋊C4×C17—41no—
200C42×C17—41no—
201C42×C17—41no—
202C42×C17—41no—
203C42×C17—41no—
204#63227—48no—
205#63227—48no—
206C4⋊Dic17—22no—
207C4⋊Dic17—22no—
208C4⋊Dic17—41no—
209C4⋊Dic17—41no—
210C2×#3622—22no—
211C2×#3622—22no—
212C2×#3622—22no—
213C2×#3622—22no—
214C2×#3622—22no—
215C2×#3622—22no—
216C2×#3622—41no—
217C2×#3622—41no—
218C2×#3622—41no—
219C2×#3622—41no—
220C2×#3622—41no—
221C2×#3622—41no—
222C2×#3622—41no—
223C2×#3622—41no—
224#11189—171nomaximal, Sylow
225C23×C17C4×D411yescharacteristic
226C23×C17#12011yescharacteristic
227C23×C17#12111yescharacteristic
228C23×C17#12111yescharacteristic
229C23×C17#12111yescharacteristic
230C23×C17#12311yescharacteristic
231C23×C17#12411yescharacteristic
232C23×C17C2×D811yescharacteristic
233C23×C17C2×SD1611yescharacteristic
234C23×C17#13511yescharacteristic
235C23×C17#13511yescharacteristic
236C23×C17AGL(1,ℤ/8)11yescharacteristic
237C23×C17AGL(1,ℤ/8)11yescharacteristic
238C23×C17AGL(1,ℤ/8)11yescharacteristic
239C23×C17#13711yescharacteristic
240C22×D17—24no—
241C22×D17—42no—
242C22×D17—42no—
243C22×D17—42no—
244C22×D17—42no—
245C22×D17—42no—
246C22×D17—42no—
247C22×D17—42no—
248C22×D17—42no—
249C22×D17—42no—
250C22×D17—42no—
251C22×D17—42no—
252C22×D17—42no—
253C22×D17—42no—
254C22×D17—42no—
255C22×D17—42no—
256C22×D17—42no—
257C22×D17—42no—
258C22×D17—42no—
259C22×D17—81no—
260C22×D17—81no—
261C22×D17—81no—
262C22×D17—81no—
263C22×D17—81no—
264C22×D17—81no—
265C22×D17—81no—
266C22×D17—81no—
267C22×D17—81no—
268C22×D17—81no—
269C22×D17—81no—
270C22×D17—81no—
271C22×D17—81no—
272C22×D17—81no—
273C22×D17—81no—
274C22×D17—81no—
275C2×C4×C17—22no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—42no—
290C2×C4×C17—42no—
291C2×C4×C17—42no—
292C2×C4×C17—42no—
293C2×C4×C17—42no—
294C2×C4×C17—42no—
295C2×C4×C17—81no—
296C2×C4×C17—81no—
297C2×C4×C17—81no—
298C2×C4×C17—81no—
299C2×C4×C17—81no—
300C2×C4×C17—81no—
301C2×C4×C17—81no—
302C2×C4×C17—81no—
303C2×C4×C17C2×C22⋊C411yescharacteristic
304C2×C4×C17#11711yescharacteristic
305C2×C4×C17#11711yescharacteristic
306C2×C4×C17C4×D411yescharacteristic
307C2×C4×C17C4×D411yescharacteristic
308C2×C4×C17C4×D411yescharacteristic
309C2×C4×C17#12011yescharacteristic
310C2×C4×C17#12111yescharacteristic
311C2×C4×C17#12111yescharacteristic
312C2×C4×C17#12111yescharacteristic
313C2×C4×C17#12111yescharacteristic
314C2×C4×C17#12111yescharacteristic
315C2×C4×C17#12311yescharacteristic
316C2×C4×C17#12311yescharacteristic
317C2×C4×C17#12311yescharacteristic
318C2×C4×C17#12311yescharacteristic
319C2×C4×C17#12311yescharacteristic
320C2×C4×C17#12311yescharacteristic
321C2×C4×C17#12311yescharacteristic
322C2×C4×C17#12311yescharacteristic
323C2×C4×C17#12311yescharacteristic
324C2×C4×C17#12411yescharacteristic
325C2×C4×C17#12411yescharacteristic
326C2×C4×C17#12411yescharacteristic
327C2×C4×C17#12611yescharacteristic
328C2×C4×C17#12611yescharacteristic
329C2×C4×C17#12611yescharacteristic
330C2×C4×C17#12611yescharacteristic
331C2×Dic17—42no—
332C2×Dic17—42no—
333C2×Dic17—42no—
334C2×Dic17—81no—
335C2×Dic17—81no—
336C2×Dic17—81no—
337C2×Dic17—81no—
338D68—24no—
339D68—24no—
340D68—42no—
341D68—42no—
342D68—42no—
343D68—42no—
344D68—42no—
345D68—42no—
346#3622—42no—
347#3622—42no—
348C22×#102—171no—
349C22×#102—171no—
350C2×#390—171no—
351C2×#340—171no—
352C2×#340—171no—
353C2×#336—171no—
354C4⋊#95D1711yescharacteristic, complemented
355C22×C17#38611yescharacteristic
356C22×C17#38811yescharacteristic
357C22×C17#38811yescharacteristic
358C22×C17#39411yescharacteristic
359C22×C17#39411yescharacteristic
360C22×C17#39411yescharacteristic
361C22×C17#39711yescharacteristic
362C22×C17C4×D811yescharacteristic
363C22×C17C4×SD1611yescharacteristic
364C22×C17#44011yescharacteristic
365C22×C17#44211yescharacteristic
366C22×C17#44711yescharacteristic
367C22×C17#44911yescharacteristic
368C22×C17#45011yescharacteristic
369C22×C17#45211yescharacteristic
370C22×C17#45911yescharacteristic
371C22×C17#45911yescharacteristic
372C22×C17#46011yescharacteristic
373C22×C17#46111yescharacteristic
374C22×C17#46311yescharacteristic
375C22×C17#46311yescharacteristic
376C22×C17#46311yescharacteristic
377C22×C17#46411yescharacteristic
378C22×C17#46511yescharacteristic
379C22×C17#46611yescharacteristic
380C22×C17#46811yescharacteristic
381C22×C17#46911yescharacteristic
382C22×C17#48011yescharacteristic
383C22×C17#48111yescharacteristic
384C22×C17#48211yescharacteristic
385C22×C17#48211yescharacteristic
386C22×C17#48611yescharacteristic
387C22×C17#48811yescharacteristic
388C22×C17#48911yescharacteristic
389C22×C17#49011yescharacteristic
390C2×D17—44no—
391C2×D17—44no—
392C2×D17—44no—
393C2×D17—82no—
394C2×D17—82no—
395C2×D17—82no—
396C2×D17—82no—
397C2×D17—82no—
398C2×D17—82no—
399C2×D17—82no—
400C2×D17—82no—
401C2×D17—82no—
402C2×D17—82no—
403C2×D17—82no—
404C2×D17—82no—
405C4×C17—42no—
406C4×C17—42no—
407C4×C17—82no—
408C4×C17—82no—
409C4×C17#38111yescharacteristic
410C4×C17#38611yescharacteristic
411C4×C17#38811yescharacteristic
412C4×C17#38811yescharacteristic
413C4×C17#39411yescharacteristic
414C4×C17#39711yescharacteristic
415C4×C17#39711yescharacteristic
416C4×C17#39711yescharacteristic
417Dic17—82no—
418C23×D4—171no—
419C23×C8—171no—
420C23×C8—171no—
421C22×C4⋊C4—171no—
422C22×C4⋊C4C2×D1711yescharacteristic
423C22×C4⋊C4C2×D1711yescharacteristic
424C22×C22⋊C4—341no—
425C22×C22⋊C4—341no—
426C22×C42C2×D1711yescharacteristic
427C2×#102—174no—
428C2×#102—342no—
429C2×#102—342no—
430C2×#102—342no—
431C2×#102—342no—
432C2×#102—342no—
433#390—342no—
434#390—342no—
435C2×#95—21no—
436C2×#95—21no—
437#340—342no—
438#340—342no—
439#336—342no—
440C2×C17#144011yescharacteristic
441C2×C17#187711yescharacteristic
442C2×C17#187911yescharacteristic
443C2×C17#192511yescharacteristic
444C2×C17#192611yescharacteristic
445C2×C17#193411yescharacteristic
446C2×C17#193611yescharacteristic
447C2×C17#203311yescharacteristic
448C2×C17#203411yescharacteristic
449C2×C17#204111yescharacteristic
450C2×C17#204211yescharacteristic
451C2×C17#205411yescharacteristic
452C2×C17#205511yescharacteristic
453C2×C17#207111yescharacteristic
454C2×C17#207311yescharacteristic
455D17—84no—
456C25—341no—
457C22×D4—172no—
458C22×D4—172no—
459C22×D4—172no—
460C22×D4—341no—
461C22×D4—341no—
462C22×D4—341no—
463C22×D4—341no—
464C22×D4—341no—
465C22×D4—341no—
466C22×D4—341no—
467C22×D4—341no—
468C22×D4—341no—
469C22×D4—341no—
470C22×D4—341no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—341no—
474C23×C4C22⋊D1711yescharacteristic
475C23×C4C22⋊D1711yescharacteristic
476C23×C4C22×D1711yescharacteristic
477C22×C8—172no—
478C22×C8—172no—
479C22×C8—341no—
480C22×C8—341no—
481C22×C8—341no—
482C22×C8—341no—
483C22×C8—341no—
484C22×C8—341no—
485C22×C8—341no—
486C22×C8—341no—
487C22×C8—341no—
488C22×C8—341no—
489C22×C8—341no—
490C22×C8—341no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—172no—
502C2×C4⋊C4—341no—
503C2×C4⋊C4—341no—
504C2×C4⋊C4—341no—
505C2×C4⋊C4—341no—
506C2×C4⋊C4—341no—
507C2×C4⋊C4C4×D1712yes—
508C2×C4⋊C4D6812yes—
509C2×C22⋊C4—344no—
510C2×C22⋊C4—344no—
511C2×C22⋊C4—682no—
512C2×C22⋊C4—682no—
513C2×C22⋊C4—682no—
514C2×C22⋊C4—682no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521#102—348no—
522#102—348no—
523#95—42no—
524#95—42no—
525C17#1118911yescharacteristic, complemented, Sylow
526C24—342no—
527C24—342no—
528C24—342no—
529C24—681no—
530C24—681no—
531C24—681no—
532C24—681no—
533C24—681no—
534C24—681no—
535C24—681no—
536C24—681no—
537C24—681no—
538C24—681no—
539C24—681no—
540C24—681no—
541C24C2×C22⋊D1711yescharacteristic
542C2×D4—174no—
543C2×D4—342no—
544C2×D4—342no—
545C2×D4—342no—
546C2×D4—342no—
547C2×D4—342no—
548C2×D4—342no—
549C2×D4—342no—
550C2×D4—342no—
551C2×D4—342no—
552C2×D4—342no—
553C2×D4—342no—
554C2×D4—342no—
555C2×D4—342no—
556C2×D4—342no—
557C2×D4—342no—
558C2×D4—681no—
559C2×D4—681no—
560C2×D4—681no—
561C2×D4—681no—
562C2×D4—681no—
563C2×D4—681no—
564C2×D4—681no—
565C2×D4—681no—
566C2×D4—681no—
567C2×D4—681no—
568C2×D4—681no—
569C2×D4—681no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—342no—
597C22×C4—681no—
598C22×C4—681no—
599C22×C4—681no—
600C22×C4—681no—
601C22×C4—681no—
602C22×C4—681no—
603C22×C4#6322812yes—
604C22×C4#6323012yes—
605C22×C4C2×C4×D1711yescharacteristic
606C22×C4C2×D6811yescharacteristic
607C22×C4#6325211yescharacteristic
608C22×C4#6325211yescharacteristic
609C22×C4#6325211yescharacteristic
610C22×C4#6325211yescharacteristic
611C22×C4D4×D1711yescharacteristic
612C22×C4D4×D1711yescharacteristic
613C22×C4D4×D1711yescharacteristic
614C22×C4D4×D1711yescharacteristic
615C22×C4#6325411yescharacteristic
616C22×C4#6325411yescharacteristic
617C22×C4#6325611yescharacteristic
618C22×C4#6325611yescharacteristic
619C2×C8—342no—
620C2×C8—342no—
621C2×C8—342no—
622C2×C8—342no—
623C2×C8—342no—
624C2×C8—342no—
625C2×C8—681no—
626C2×C8—681no—
627C2×C8—681no—
628C2×C8—681no—
629C2×C8—681no—
630C2×C8—681no—
631C2×C8—681no—
632C2×C8—681no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—342no—
642C4⋊C4—342no—
643C4⋊C4—681no—
644C4⋊C4—681no—
645C22⋊C4—688no—
646C22⋊C4—688no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C23—344no—
652C23—682no—
653C23—682no—
654C23—682no—
655C23—682no—
656C23—682no—
657C23—682no—
658C23—682no—
659C23—682no—
660C23—682no—
661C23—682no—
662C23—682no—
663C23—682no—
664C23—682no—
665C23—682no—
666C23—682no—
667C23—682no—
668C23—682no—
669C23—682no—
670C23—1361no—
671C23—1361no—
672C23—1361no—
673C23—1361no—
674C23—1361no—
675C23—1361no—
676C23—1361no—
677C23—1361no—
678C23—1361no—
679C23—1361no—
680C23—1361no—
681C23—1361no—
682C23—1361no—
683C23—1361no—
684C23—1361no—
685C23—1361no—
686C23C4×C22⋊D1711yescharacteristic
687C23#1058761511yescharacteristic
688C23#1058761611yescharacteristic
689C23C2×#6322811yescharacteristic
690C23#1058761811yescharacteristic
691C23#1058762311yescharacteristic
692C23#1058762411yescharacteristic
693C23#1058762511yescharacteristic
694C23C2×#6323011yescharacteristic
695C23#1058762811yescharacteristic
696C23#1058763311yescharacteristic
697C23#1058763511yescharacteristic
698C23#1058763511yescharacteristic
699C23#1058763611yescharacteristic
700C23#1058763611yescharacteristic
701D4—344no—
702D4—344no—
703D4—682no—
704D4—682no—
705D4—682no—
706D4—682no—
707D4—682no—
708D4—682no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—682no—
738C2×C4—682no—
739C2×C4—682no—
740C2×C4—1361no—
741C2×C4—1361no—
742C2×C4—1361no—
743C2×C4—1361no—
744C2×C4#1058755811yescharacteristic
745C2×C4C4×D6811yescharacteristic
746C2×C4#1058756111yescharacteristic
747C2×C4#1058756211yescharacteristic
748C2×C4C22⋊C4×D1711yescharacteristic
749C2×C4#1058756711yescharacteristic
750C2×C4#1058756811yescharacteristic
751C2×C4#1058756911yescharacteristic
752C2×C4#1058756911yescharacteristic
753C2×C4#1058756911yescharacteristic
754C2×C4#1058757011yescharacteristic
755C2×C4#1058757011yescharacteristic
756C2×C4#1058757011yescharacteristic
757C2×C4#1058757111yescharacteristic
758C2×C4#1058757111yescharacteristic
759C2×C4#1058757211yescharacteristic
760C2×C4#1058757811yescharacteristic
761C2×C4#1058757911yescharacteristic
762C2×C4#1058758011yescharacteristic
763C2×C4#1058758011yescharacteristic
764C2×C4#1058758011yescharacteristic
765C2×C4#1058758011yescharacteristic
766C2×C4#1058758011yescharacteristic
767C2×C4#1058758111yescharacteristic
768C2×C4#1058758111yescharacteristic
769C2×C4#1058758411yescharacteristic
770C2×C4#1058758411yescharacteristic
771C2×C4#1058758411yescharacteristic
772C8—682no—
773C8—682no—
774C22—684no—
775C22—684no—
776C22—684no—
777C22—1362no—
778C22—1362no—
779C22—1362no—
780C22—1362no—
781C22—1362no—
782C22—1362no—
783C22—1362no—
784C22—1362no—
785C22—1362no—
786C22—1362no—
787C22—1362no—
788C22—1362no—
789C22#1176268511yescharacteristic
790C22#1176269911yescharacteristic
791C22#1176270011yescharacteristic
792C22#1176272411yescharacteristic
793C22#1176272511yescharacteristic
794C22#1176272611yescharacteristic
795C22#1176273511yescharacteristic
796C22C4×#6322811yescharacteristic
797C22C4×#6323011yescharacteristic
798C22#1176290711yescharacteristic
799C22#1176291911yescharacteristic
800C22#1176294211yescharacteristic
801C22#1176295211yescharacteristic
802C22#1176295911yescharacteristic
803C22#1176296911yescharacteristic
804C22#1176300111yescharacteristic
805C22#1176300411yescharacteristic
806C22#1176300911yescharacteristic
807C22#1176301111yescharacteristic
808C22#1176302111yescharacteristic
809C22#1176302111yescharacteristic
810C22#1176302411yescharacteristic
811C22#1176303111yescharacteristic
812C22#1176304011yescharacteristic
813C22#1176304311yescharacteristic
814C22#1176305711yescharacteristic
815C22#1176306011yescharacteristic
816C22#1176312211yescharacteristic
817C22#1176312711yescharacteristic
818C22#1176313311yescharacteristic
819C22#1176313311yescharacteristic
820C22#1176315711yescharacteristic
821C22#1176316611yescharacteristic
822C22#1176317111yescharacteristic
823C22#1176317511yescharacteristic
824C4—42no—
825C4—42no—
826C4—82no—
827C4—82no—
828C4—1362no—
829C4#1176267111yescharacteristic
830C4#1176268711yescharacteristic
831C4#1176269811yescharacteristic
832C4#1176270111yescharacteristic
833C4#1176272711yescharacteristic
834C4#1176273611yescharacteristic
835C4#1176273811yescharacteristic
836C4#1176273811yescharacteristic
837C2—1364no—
838C2#1452703211yescharacteristic
839C2#1452912111yescharacteristic
840C2#1452913511yescharacteristic
841C2#1452940411yescharacteristic
842C2#1452941111yescharacteristic
843C2#1452946611yescharacteristic
844C2#1452948011yescharacteristic
845C2#1452996611yescharacteristic
846C2#1452997311yescharacteristic
847C2#1453001811yescharacteristic
848C2#1453002511yescharacteristic
849C2#1453009411yescharacteristic
850C2#1453009911yescharacteristic
851C2#1453018811yescharacteristic
852C2#1453019811yescharacteristic
subgroupG/H
centerC24C2×C22⋊D17
commutatorC22×C4×C17C22×C4
FrattiniC23×C4C22×D17
FittingC17×C4⋊#95C2
socleC24×C17C2×D4
prime radicalC23×D68C22
cosocleC23×C4×C17C23
hypercenterC4⋊#95D17
hypocenterC17#11189
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11762571C2semidirect
5. C2×#11762571C2semidirect
6. C2×#11762564C2semidirect
7. C17×C4⋊#95C2semidirect
19. C2×#10587480C4semidirect
354. C4⋊#95D17semidirect
525. C17#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#105874802
C2×#117627112
C2×#117625712
C2×#117625642
C17×C4⋊#952
#1118917