Finite Group Databasebeta

← C2×#14543626 #17950615

Subgroups — C2×#14543626 #17950615

Order 4352.

1130 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763777C211yesmaximal, characteristic
2C2×C4×C22⋊#595C211yesmaximal, characteristic
3#14543626C214yesmaximal, direct product factor
4C22×#10587491C211yesmaximal, characteristic
5C22×#63242—21no—
6C22×C22⋊#595C412yes—
7C22×C4×#595—21no—
8C2×#10587543—21no—
9#11763777—21no—
10#11763777—21no—
11#11763777C412yescomplemented
12#11763777C2212yes—
13C2×C22⋊#3624C412yescomplemented
14C4×C22⋊#595—21no—
15C4×C22⋊#595—21no—
16C4×C22⋊#595C412yes—
17C4×C22⋊#595C2212yes—
18C2×(C2×#595)⋊C4—21no—
19C23×C4×D17C2211yescharacteristic
20C23×#3622C411yescharacteristic, complemented
21C2×#10587491—21no—
22C2×#10587491—21no—
23C2×#10587491—21no—
24C2×#10587491—21no—
25C2×#10587491C412yescomplemented
26C2×#10587491C2212yes—
27C23×C8×C17C411yescharacteristic, complemented
28C24×D17C2×C411yescharacteristic
29C23×#595—22no—
30C23×C4×C17C2×C411yescharacteristic
31C23×Dic17C2×C411yescharacteristic
32C22×C4×D17—42no—
33C22×C4×D17—42no—
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17C2×C411yescharacteristic
36C22×C4×D17C2×C411yescharacteristic
37C22×C4×D17D411yescharacteristic
38C22×C4×D17D411yescharacteristic
39C22×C4×D17D411yescharacteristic
40C22×C4×D17D411yescharacteristic
41C22×C4×D17D411yescharacteristic
42C22×C4×D17D411yescharacteristic
43C22×C4×D17Q811yescharacteristic
44C22×C4×D17Q811yescharacteristic
45C22×C4×D17C2311yescharacteristic
46C2×C22⋊#595—22no—
47C2×C22⋊#595—24no—
48C2×C22⋊#595C818yescomplemented
49C2×C22⋊#595C2×C414yes—
50C22×#3624—22no—
51C2×C4×#595—22no—
52C2×C4×#595—22no—
53C2×C4×#595—42no—
54C2×C4×#595—42no—
55C2×#63242—22no—
56C2×#63242—22no—
57C2×#63242—42no—
58C2×#63242—42no—
59C22×C8×C17—21no—
60C22×C8×C17—21no—
61C22×C8×C17—42no—
62C22×C8×C17C2×C412yescomplemented
63C22×#3622—21no—
64C22×#3622—21no—
65C22×#3622—42no—
66C22×#3622C2×C412yescomplemented
67C22⋊#3624—22no—
68C22⋊#3624C2×C414yescomplemented
69(C2×#595)⋊C4—22no—
70(C2×#595)⋊C4—22no—
71#10587543—22no—
72#10587543—22no—
73#10587491—22no—
74#10587491—22no—
75#10587491—22no—
76#10587491—22no—
77C24×C17C4211yescharacteristic
78C23×D17—42no—
79C23×D17—42no—
80C23×D17C4211yescharacteristic
81C23×D17C22⋊C411yescharacteristic
82C23×D17C22⋊C411yescharacteristic
83C23×D17C4⋊C411yescharacteristic
84C23×D17C4⋊C411yescharacteristic
85C23×D17C2×C814yes—
86C23×D17M1614yes—
87C23×D17C22×C411yescharacteristic
88C22×#595—28no—
89C22×#595—24no—
90C22×#595—44no—
91C22×#595—44no—
92C22×C4×C17—22no—
93C22×C4×C17—22no—
94C22×C4×C17C4211yescharacteristic
95C22×C4×C17C22⋊C411yescharacteristic
96C22×C4×C17C22⋊C411yescharacteristic
97C22×C4×C17C4⋊C411yescharacteristic
98C22×C4×C17C4⋊C411yescharacteristic
99C22×C4×C17C22×C411yescharacteristic
100C22×Dic17—42no—
101C22×Dic17C4211yescharacteristic
102C22×Dic17C22⋊C411yescharacteristic
103C22×Dic17C22⋊C411yescharacteristic
104C22×Dic17C4⋊C411yescharacteristic
105C22×Dic17C4⋊C411yescharacteristic
106C22×Dic17C22×C411yescharacteristic
107C2×C4×D17—22no—
108C2×C4×D17—22no—
109C2×C4×D17—22no—
110C2×C4×D17—22no—
111C2×C4×D17—42no—
112C2×C4×D17—42no—
113C2×C4×D17—41no—
114C2×C4×D17—41no—
115C2×C4×D17—42no—
116C2×C4×D17—41no—
117C2×C4×D17—41no—
118C2×C4×D17—41no—
119C2×C4×D17—41no—
120C2×C4×D17—42no—
121C2×C4×D17—41no—
122C2×C4×D17—41no—
123C2×C4×D17—42no—
124C2×C4×D17—42no—
125C2×C4×D17C22⋊C411yescharacteristic
126C2×C4×D17C22⋊C411yescharacteristic
127C2×C4×D17C22⋊C411yescharacteristic
128C2×C4×D17C22⋊C411yescharacteristic
129C2×C4×D17C22⋊C411yescharacteristic
130C2×C4×D17C22⋊C411yescharacteristic
131C2×C4×D17C4⋊C411yescharacteristic
132C2×C4×D17C4⋊C411yescharacteristic
133C2×C4×D17C4⋊C411yescharacteristic
134C2×C4×D17C4⋊C411yescharacteristic
135C2×C4×D17C4⋊C411yescharacteristic
136C2×C4×D17C4⋊C411yescharacteristic
137C2×C4×D17C2×D411yescharacteristic
138C2×C4×D17C2×D411yescharacteristic
139C2×C4×D17C2×D411yescharacteristic
140C2×C4×D17C2×Q811yescharacteristic
141C22⋊#595—28no—
142C22⋊#595—24no—
143C22⋊#595C2×C818yescomplemented
144C2×#3624—24no—
145C2×#3624—44no—
146C4×#595—44no—
147C4×#595—42no—
148C4×#595—42no—
149#63242—44no—
150#63242—42no—
151#63242—42no—
152C2×C8×C17—22no—
153C2×C8×C17—42no—
154C2×C8×C17—42no—
155C2×C8×C17—42no—
156C2×#3622—22no—
157C2×#3622—42no—
158C2×#3622—42no—
159C2×#3622—42no—
160C2×#1282—171nomaximal, Sylow
161C23×C17—22no—
162C23×C17—22no—
163C23×C17#9511yescharacteristic
164C23×C17#9511yescharacteristic
165C23×C17C4×C812yes—
166C23×C17#9712yes—
167C23×C17C2×C4211yescharacteristic
168C22×D17—22no—
169C22×D17—22no—
170C22×D17—22no—
171C22×D17—22no—
172C22×D17—41no—
173C22×D17—41no—
174C22×D17—41no—
175C22×D17—41no—
176C22×D17—41no—
177C22×D17—41no—
178C22×D17—41no—
179C22×D17—48no—
180C22×D17—48no—
181C22×D17—41no—
182C22×D17#9511yescharacteristic
183C22×D17#9511yescharacteristic
184C22×D17C4×C812yes—
185C22×D17#9712yes—
186C22×D17C22⋊C814yes—
187C22×D17C22⋊C814yes—
188C22×D17C4⋊C814yes—
189C22×D17C4⋊C814yes—
190C22×D17C2×C22⋊C411yescharacteristic
191C22×D17C2×C4⋊C411yescharacteristic
192C22×D17C22×C812yes—
193C22×D17C2×M1612yes—
194C2×#595—28no—
195C2×#595—44no—
196C2×#595—416no—
197C2×#595—44no—
198C2×C4×C17—22no—
199C2×C4×C17—22no—
200C2×C4×C17—22no—
201C2×C4×C17—21no—
202C2×C4×C17—21no—
203C2×C4×C17—21no—
204C2×C4×C17—21no—
205C2×C4×C17#9511yescharacteristic
206C2×C4×C17#9511yescharacteristic
207C2×C4×C17#9912yes—
208C2×C4×C17#9912yes—
209C2×C4×C17C2×C22⋊C411yescharacteristic
210C2×C4×C17C2×C4⋊C411yescharacteristic
211C2×Dic17—22no—
212C2×Dic17—22no—
213C2×Dic17—41no—
214C2×Dic17—41no—
215C2×Dic17—41no—
216C2×Dic17—41no—
217C2×Dic17#9511yescharacteristic
218C2×Dic17#9511yescharacteristic
219C2×Dic17C2×C22⋊C411yescharacteristic
220C2×Dic17C2×C4⋊C411yescharacteristic
221C4×D17—22no—
222C4×D17—22no—
223C4×D17—22no—
224C4×D17—22no—
225C4×D17—21no—
226C4×D17—21no—
227C4×D17—21no—
228C4×D17—21no—
229C4×D17—21no—
230C4×D17—21no—
231C4×D17—21no—
232C4×D17—21no—
233C4×D17—41no—
234C4×D17—41no—
235C4×D17—41no—
236C4×D17—41no—
237C4×D17—41no—
238C4×D17—41no—
239C4×D17—41no—
240C4×D17—41no—
241#3624—44no—
242C8×C17—42no—
243#3622—42no—
244C22×C22⋊C8—171no—
245C22×C22⋊C8—171no—
246C2×C4×C22⋊C4—171no—
247#1282—174no—
248C22×C17—24no—
249C22×C17—24no—
250C22×C17—21no—
251C22×C17—21no—
252C22×C17—21no—
253C22×C17—21no—
254C22×C17#33612yes—
255C22×C17#33612yes—
256C22×C17#34212yes—
257C22×C17#34412yes—
258C22×C17C2×#9511yescharacteristic
259C22×C17C2×C4×C811yescharacteristic
260C22×C17C2×#9711yescharacteristic
261C2×D17—28no—
262C2×D17—28no—
263C2×D17—21no—
264C2×D17—21no—
265C2×D17—21no—
266C2×D17—21no—
267C2×D17—21no—
268C2×D17—21no—
269C2×D17—21no—
270C2×D17—21no—
271C2×D17—42no—
272C2×D17—42no—
273C2×D17—44no—
274C2×D17—44no—
275C2×D17—42no—
276C2×D17—42no—
277C2×D17#33612yes—
278C2×D17#33612yes—
279C2×D17C2×C22⋊C812yes—
280C2×D17C2×C4⋊C812yes—
281#595—48no—
282C4×C17—21no—
283C4×C17—21no—
284C4×C17#34212yes—
285C4×C17C2×#9911yescharacteristic
286C4×C17C2×#9911yescharacteristic
287Dic17—21no—
288Dic17—21no—
289Dic17—21no—
290Dic17—21no—
291C24×C4—171no—
292C23×C8—171no—
293C23×C8—341no—
294C23×C8#59511yescharacteristic, complemented
295C22×C22⋊C4—172no—
296C22×C42—341no—
297C2×C22⋊C8—172no—
298C2×C22⋊C8—172no—
299C2×C22⋊C8—172no—
300C2×C22⋊C8—172no—
301C2×C22⋊C8—172no—
302C2×C22⋊C8—341no—
303C2×C22⋊C8—341no—
304C2×C22⋊C8—341no—
305C2×C22⋊C8—341no—
306C2×C22⋊C8—341no—
307C2×C22⋊C8—341no—
308C2×C22⋊C8—341no—
309C4×C22⋊C4—172no—
310C4×C22⋊C4—172no—
311C4×C22⋊C4—341no—
312C4×C22⋊C4—341no—
313C2×#95—341no—
314C2×C17—22no—
315C2×C17—21no—
316C2×C17—21no—
317C2×C17#128214yescomplemented
318C2×C17C2×#33611yescharacteristic
319C2×C17C2×#34211yescharacteristic
320C2×C17C2×#34411yescharacteristic
321D17—22no—
322D17—22no—
323D17—22no—
324D17—22no—
325C25—171no—
326C23×C4—171no—
327C23×C4—171no—
328C23×C4—171no—
329C23×C4—171no—
330C23×C4—171no—
331C23×C4—171no—
332C23×C4—171no—
333C23×C4—171no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—171no—
337C23×C4—171no—
338C23×C4—171no—
339C23×C4—342no—
340C23×C4—682no—
341C23×C4—682no—
342C23×C4C2×#59511yescharacteristic
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—42no—
346C22×C8—172no—
347C22×C8—342no—
348C22×C8—342no—
349C22×C8—342no—
350C22×C8—341no—
351C22×C8—341no—
352C22×C8—682no—
353C22×C8—682no—
354C22×C8—682no—
355C22×C8C2×#59512yescomplemented
356C2×C22⋊C4—178no—
357C2×C22⋊C4—174no—
358C2×C22⋊C4—344no—
359C2×C22⋊C4—342no—
360C2×C42—342no—
361C2×C42—342no—
362C2×C42—682no—
363C2×C42—682no—
364C22⋊C8—174no—
365C22⋊C8—342no—
366C22⋊C8—342no—
367C22⋊C8—342no—
368C22⋊C8—342no—
369C22⋊C8—342no—
370C22⋊C8—342no—
371C22⋊C8—342no—
372#95—342no—
373#95—342no—
374C17C2×#128211yescharacteristic, complemented, Sylow
375C24—171no—
376C24—171no—
377C24—171no—
378C24—171no—
379C24—174no—
380C24—174no—
381C24—171no—
382C24—171no—
383C24—682no—
384C24—682no—
385C24C4×#59511yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—171no—
389C22×C4—171no—
390C22×C4—171no—
391C22×C4—171no—
392C22×C4—171no—
393C22×C4—171no—
394C22×C4—171no—
395C22×C4—171no—
396C22×C4—171no—
397C22×C4—171no—
398C22×C4—171no—
399C22×C4—171no—
400C22×C4—171no—
401C22×C4—171no—
402C22×C4—171no—
403C22×C4—171no—
404C22×C4—171no—
405C22×C4—171no—
406C22×C4—171no—
407C22×C4—171no—
408C22×C4—171no—
409C22×C4—171no—
410C22×C4—342no—
411C22×C4—342no—
412C22×C4—342no—
413C22×C4—342no—
414C22×C4—344no—
415C22×C4—348no—
416C22×C4—681no—
417C22×C4—681no—
418C22×C4—681no—
419C22×C4—681no—
420C22×C4—681no—
421C22×C4—681no—
422C22×C4—681no—
423C22×C4—681no—
424C22×C4—682no—
425C22×C4—682no—
426C22×C4—682no—
427C22×C4—682no—
428C22×C4—682no—
429C22×C4—682no—
430C22×C4—682no—
431C22×C4—684no—
432C22×C4—684no—
433C22×C4C4×#59511yescharacteristic
434C22×C4C4⋊#59511yescharacteristic
435C22×C4C4⋊#59511yescharacteristic
436C22×C4C22⋊#59511yescharacteristic
437C22×C4C22⋊#59511yescharacteristic
438C22×C4C22×#59511yescharacteristic
439C2×C8—22no—
440C2×C8—42no—
441C2×C8—42no—
442C2×C8—42no—
443C2×C8—344no—
444C2×C8—342no—
445C2×C8—682no—
446C2×C8—682no—
447C2×C8—682no—
448C2×C8—684no—
449C2×C8—684no—
450C2×C8—682no—
451C2×C8—682no—
452C22⋊C4—178no—
453C22⋊C4—344no—
454C22⋊C4—348no—
455C42—682no—
456C42—682no—
457C42—684no—
458C23—22no—
459C23—22no—
460C23—171no—
461C23—171no—
462C23—171no—
463C23—171no—
464C23—174no—
465C23—174no—
466C23—172no—
467C23—172no—
468C23—172no—
469C23—172no—
470C23—174no—
471C23—174no—
472C23—342no—
473C23—342no—
474C23—342no—
475C23—342no—
476C23—681no—
477C23—681no—
478C23—681no—
479C23—681no—
480C23—688no—
481C23—688no—
482C23—681no—
483C23—681no—
484C23—681no—
485C23—681no—
486C23C8×#59512yes—
487C23#1058753212yes—
488C23(C2×#595)⋊C411yescharacteristic
489C23(C2×#595)⋊C411yescharacteristic
490C23C2×C4×#59511yescharacteristic
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—171no—
499C2×C4—171no—
500C2×C4—171no—
501C2×C4—171no—
502C2×C4—342no—
503C2×C4—342no—
504C2×C4—341no—
505C2×C4—341no—
506C2×C4—341no—
507C2×C4—341no—
508C2×C4—341no—
509C2×C4—341no—
510C2×C4—341no—
511C2×C4—341no—
512C2×C4—342no—
513C2×C4—342no—
514C2×C4—342no—
515C2×C4—342no—
516C2×C4—348no—
517C2×C4—681no—
518C2×C4—681no—
519C2×C4—681no—
520C2×C4—681no—
521C2×C4—681no—
522C2×C4—681no—
523C2×C4—681no—
524C2×C4—681no—
525C2×C4—681no—
526C2×C4—681no—
527C2×C4—681no—
528C2×C4—681no—
529C2×C4—684no—
530C2×C4—6816no—
531C2×C4—684no—
532C2×C4#1058753912yes—
533C2×C4(C2×#595)⋊C411yescharacteristic
534C2×C4(C2×#595)⋊C411yescharacteristic
535C2×C4#1058755112yes—
536C2×C4C2×C4⋊#59511yescharacteristic
537C2×C4C2×C22⋊#59511yescharacteristic
538C8—42no—
539C8—684no—
540C8—682no—
541C22—24no—
542C22—24no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—172no—
548C22—172no—
549C22—172no—
550C22—172no—
551C22—348no—
552C22—348no—
553C22—341no—
554C22—341no—
555C22—341no—
556C22—341no—
557C22—341no—
558C22—341no—
559C22—341no—
560C22—341no—
561C22—682no—
562C22—682no—
563C22—682no—
564C22—682no—
565C22—684no—
566C22—684no—
567C22#1176367412yes—
568C22#1176367412yes—
569C22#1176368712yes—
570C22#1176369112yes—
571C22C2×(C2×#595)⋊C411yescharacteristic
572C22C2×C8×#59511yescharacteristic
573C22C2×#1058753211yescharacteristic
574C4—21no—
575C4—21no—
576C4—341no—
577C4—341no—
578C4—341no—
579C4—341no—
580C4—688no—
581C4#1176368712yes—
582C4C2×#1058755111yescharacteristic
583C4C2×#1058753911yescharacteristic
584C2—21no—
585C2—21no—
586C2—22no—
587C2—342no—
588C2—342no—
589C2—342no—
590C2—342no—
591C2#1454362614yesdirect product factor
592C2C2×#1176367411yescharacteristic
593C2C2×#1176368711yescharacteristic
594C2C2×#1176369111yescharacteristic
subgroupG/H
centerC22×C4C22⋊#595
commutatorC22×C17C2×C4×C8
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC23×C17#95
prime radicalC24×D17C2×C4
cosocleC22×C4×D17C23
hypercenterC23×C8#595
hypocenterC17C2×#1282
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
3. #14543626C2direct (N × H)
11. #11763777C4semidirect
13. C2×C22⋊#3624C4semidirect
20. C23×#3622C4semidirect
25. C2×#10587491C4semidirect
27. C23×C8×C17C4semidirect
48. C2×C22⋊#595C8semidirect
62. C22×C8×C17C2×C4semidirect
66. C22×#3622C2×C4semidirect
68. C22⋊#3624C2×C4semidirect
143. C22⋊#595C2×C8semidirect
294. C23×C8#595semidirect
317. C2×C17#1282semidirect
355. C22×C8C2×#595semidirect
374. C17C2×#1282semidirect
591. C2#14543626direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637772
C2×C4×C22⋊#5952
#145436262
C22×#105874912
C2×#128217