Finite Group Databasebeta

← #46839949

Subgroups — #46839949

Order 34688.

832 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576156C211yesmaximal, characteristic, complemented
2C2×#22576133C211yesmaximal, characteristic, complemented
3C2×#22576132C211yesmaximal, characteristic, complemented
4C2×#22576132C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D271C211yesmaximal, characteristic, complemented
6#31773814C211yesmaximal, characteristic, complemented
7#31773811C211yesmaximal, characteristic, complemented
8#31773805C211yesmaximal, characteristic, complemented
9#31773805C211yesmaximal, characteristic, complemented
10#31773797C211yesmaximal, characteristic, complemented
11#31773792C211yesmaximal, characteristic, complemented
12#31773776C211yesmaximal, characteristic, complemented
13#31773773C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic271C211yesmaximal, characteristic, complemented
15C2×#121×C271C211yesmaximal, characteristic, complemented
16C22×D1084C2211yescharacteristic
17C22×C22⋊D271C2211yescharacteristic
18C22×C22⋊D271C2211yescharacteristic
19C22×C22⋊D271C2211yescharacteristic
20C22×C22⋊D271C2211yescharacteristic
21C22×C22⋊D271C2211yescharacteristic
22C22×C22⋊D271C2211yescharacteristic
23C23×Dic271C2211yescharacteristic
24C22×C4×D271C2211yescharacteristic
25#22576156—24no—
26#22576133—24no—
27#22576132—24no—
28#22576132—24no—
29C4×C22⋊D271—24no—
30C2×Dic271⋊C4C2211yescharacteristic
31C2×Dic271⋊C4C2211yescharacteristic
32C2×Dic271⋊C4C2211yescharacteristic
33C2×C22⋊Dic271C2211yescharacteristic
34C2×C22⋊Dic271C2211yescharacteristic
35C2×C22⋊Dic271C2211yescharacteristic
36C2×C22⋊Dic271C2211yescharacteristic
37C2×C22⋊Dic271C2211yescharacteristic
38C2×(C2×D271)⋊C4C2211yescharacteristic
39C2×(C2×D271)⋊C4C2211yescharacteristic
40C2×(C2×D271)⋊C4C2211yescharacteristic
41C2×(C2×D271)⋊C4C2211yescharacteristic
42C2×(C2×D271)⋊C4C2211yescharacteristic
43C2×C4×Dic271C2211yescharacteristic
44C2×C4×Dic271C2211yescharacteristic
45C271⋊#95C2211yescharacteristic
46C271⋊#95C2211yescharacteristic
47C271⋊#95C2211yescharacteristic
48C271⋊#95C2211yescharacteristic
49C22×D4×C271C2211yescharacteristic
50C22×D4×C271C2211yescharacteristic
51C22×D4×C271C2211yescharacteristic
52C23×C4×C271C2211yescharacteristic
53#121×C271—24no—
54C2×C4⋊C4×C271C2211yescharacteristic
55C2×C22⋊C4×C271C2211yescharacteristic
56C2×C22⋊C4×C271C2211yescharacteristic
57C23×D271C2311yescharacteristic
58C23×D271C2311yescharacteristic
59C2×D1084—22no—
60C2×D1084—22no—
61C2×D1084—41no—
62C2×C22⋊D271—22no—
63C2×C22⋊D271—22no—
64C2×C22⋊D271—22no—
65C2×C22⋊D271—22no—
66C2×C22⋊D271—22no—
67C2×C22⋊D271—22no—
68C2×C22⋊D271—22no—
69C2×C22⋊D271—22no—
70C2×C22⋊D271—22no—
71C2×C22⋊D271—22no—
72C2×C22⋊D271—22no—
73C2×C22⋊D271—22no—
74C2×C22⋊D271—22no—
75C2×C22⋊D271—41no—
76C2×C22⋊D271—41no—
77C2×C22⋊D271—41no—
78C2×C22⋊D271—41no—
79C2×C22⋊D271D414yescomplemented
80C22×Dic271—22no—
81C22×Dic271—22no—
82C22×Dic271—22no—
83C22×Dic271C2311yescharacteristic
84C22×Dic271C2311yescharacteristic
85C22×Dic271C2311yescharacteristic
86C22×Dic271C2311yescharacteristic
87C22×Dic271C2311yescharacteristic
88C22×Dic271C2311yescharacteristic
89C2×C4×D271—22no—
90C2×C4×D271—22no—
91C2×C4×D271—41no—
92Dic271⋊C4—22no—
93Dic271⋊C4—22no—
94Dic271⋊C4D414yescomplemented
95C22⋊Dic271—22no—
96C22⋊Dic271—22no—
97C22⋊Dic271—22no—
98C22⋊Dic271—22no—
99C22⋊Dic271—41no—
100(C2×D271)⋊C4—22no—
101(C2×D271)⋊C4—22no—
102(C2×D271)⋊C4—22no—
103(C2×D271)⋊C4—22no—
104(C2×D271)⋊C4—41no—
105C4×Dic271—22no—
106C4×Dic271—22no—
107C24×C271C2311yescharacteristic
108C24×C271C2311yescharacteristic
109C24×C271C2311yescharacteristic
110C2×D4×C271—22no—
111C2×D4×C271—22no—
112C2×D4×C271—22no—
113C2×D4×C271—22no—
114C2×D4×C271—22no—
115C2×D4×C271—22no—
116C2×D4×C271—41no—
117C2×D4×C271—41no—
118C2×D4×C271—41no—
119C22×C4×C271—22no—
120C22×C4×C271—22no—
121C22×C4×C271—41no—
122C22×C4×C271C2311yescharacteristic
123C22×C4×C271C2311yescharacteristic
124C22×C4×C271C2311yescharacteristic
125C22×C4×C271C2311yescharacteristic
126C4⋊C4×C271—22no—
127C22⋊C4×C271—22no—
128C22⋊C4×C271D414yescomplemented
129C22×D271—21no—
130C22×D271—21no—
131C22×D271—21no—
132C22×D271—21no—
133C22×D271—21no—
134C22×D271—21no—
135C22×D271—21no—
136C22×D271—21no—
137C22×D271—21no—
138C22×D271—21no—
139C22×D271—21no—
140C22×D271—21no—
141C22×D271—21no—
142C22×D271C2×D412yes—
143D1084—44no—
144C22⋊D271—28no—
145C22⋊D271—44no—
146C22⋊D271—44no—
147C22⋊D271—44no—
148C22⋊D271—44no—
149C22⋊D271—44no—
150C2×Dic271—21no—
151C2×Dic271—21no—
152C2×Dic271—21no—
153C2×Dic271—21no—
154C2×Dic271—21no—
155C2×Dic271—21no—
156C2×Dic271—21no—
157C2×Dic271—21no—
158C2×Dic271—21no—
159C2×Dic271—21no—
160C2×Dic271—21no—
161C2×Dic271—21no—
162C2×Dic271—21no—
163C2×Dic271—44no—
164C2×Dic271C2×D412yes—
165C2×Dic271C2×D412yes—
166C2×Dic271C2×D412yes—
167C2×Dic271#4112yes—
168C2×Dic271#4112yes—
169C4×D271—44no—
170C23×C271—21no—
171C23×C271—21no—
172C23×C271—21no—
173C23×C271—21no—
174C23×C271—21no—
175C23×C271—21no—
176C23×C271—21no—
177C23×C271—21no—
178C23×C271—21no—
179C23×C271—21no—
180C23×C271—21no—
181C23×C271—21no—
182C23×C271—21no—
183C23×C271—21no—
184C23×C271—21no—
185C23×C271—21no—
186C23×C271—21no—
187C23×C271—21no—
188C23×C271—21no—
189C23×C271C2×D412yes—
190C23×C271C2×D412yes—
191C23×C271C2411yescharacteristic
192D4×C271—44no—
193D4×C271—44no—
194D4×C271—44no—
195C2×C4×C271—21no—
196C2×C4×C271—21no—
197C2×C4×C271—21no—
198C2×C4×C271—21no—
199C2×C4×C271—21no—
200C2×C4×C271—21no—
201C2×C4×C271—21no—
202C2×C4×C271—21no—
203C2×C4×C271—21no—
204C2×C4×C271—44no—
205C2×C4×C271C2×D412yes—
206C2×C4×C271C2×D412yes—
207C2×C4×C271C2×D412yes—
208C22×C271—22no—
209C22×C271—22no—
210C22×C271—22no—
211C22×C271—22no—
212C22×C271—22no—
213C22×C271—22no—
214C22×C271—41no—
215C22×C271—41no—
216C22×C271—41no—
217C22×C271—41no—
218C22×C271—41no—
219C22×C271—41no—
220C22×C271—41no—
221C22×C271—41no—
222C22×C271—41no—
223C22×C271—41no—
224C22×C271—41no—
225C22×C271—41no—
226C22×C271—41no—
227C22×C271—41no—
228C22×C271—41no—
229C22×C271C22×D411yescharacteristic
230C22×C271C22×D411yescharacteristic
231C22×C271C22×D411yescharacteristic
232C22×C271C2×#4111yescharacteristic
233C22×C271C2×#4111yescharacteristic
234C22×C271H(5,𝔽2)11yescharacteristic
235C22×C271H(5,𝔽2)11yescharacteristic
236C2×D271—22no—
237C2×D271—22no—
238C2×D271—22no—
239C2×D271—41no—
240C2×D271—41no—
241C2×D271—41no—
242C2×D271—41no—
243C2×D271—41no—
244C2×D271—41no—
245C2×D271—41no—
246C2×D271—41no—
247C2×D271—41no—
248C2×D271—41no—
249C2×D271—41no—
250C4×C271—22no—
251C4×C271—22no—
252C4×C271—22no—
253C4×C271—41no—
254Dic271—22no—
255Dic271—22no—
256Dic271—41no—
257Dic271—41no—
258Dic271—41no—
259Dic271#12114yescomplemented
260C2×C271—42no—
261C2×C271—42no—
262C2×C271—81no—
263C2×C271C2×#12111yescharacteristic
264C2×C271#53211yescharacteristic
265C2×C271#54011yescharacteristic
266C2×C271D4211yescharacteristic
267C2×C271D4211yescharacteristic
268C2×C271#54611yescharacteristic
269C2×C271#55011yescharacteristic
270D271—42no—
271D271—81no—
272C271#242811yescharacteristic, complemented, Sylow
273#2428—2711nomaximal, Sylow
274C2×#127—2711no—
275C2×#121—2711no—
276C2×#121—2711no—
277C2×#121—2711no—
278C2×#121D27111yescharacteristic, complemented
279C2×C4×D4—2711no—
280#394—2711no—
281#394—2711no—
282#392—2711no—
283#392—2711no—
284#390—2711no—
285#389—2711no—
286#386—2711no—
287#386—2711no—
288C4×C22⋊C4—2711no—
289C22×D4—2711no—
290C22×D4—2711no—
291C22×D4—2711no—
292C22×D4—2711no—
293C22×D4—2711no—
294C22×D4—2711no—
295C22×D4—2711no—
296C22×D4C2×D27111yescharacteristic
297C22×D4C2×D27111yescharacteristic
298C22×D4C2×D27111yescharacteristic
299C23×C4—2711no—
300C23×C4—2711no—
301C23×C4C2×D27111yescharacteristic
302#127—5424no—
303#121—24no—
304#121—5424no—
305#121—5424no—
306#121—5424no—
307C4×D4—5424no—
308C2×C4⋊C4—2711no—
309C2×C4⋊C4—2711no—
310C2×C4⋊C4—2711no—
311C2×C4⋊C4C2×D27111yescharacteristic
312C2×C22⋊C4—2711no—
313C2×C22⋊C4—2711no—
314C2×C22⋊C4—2711no—
315C2×C22⋊C4—2711no—
316C2×C22⋊C4—2711no—
317C2×C22⋊C4—2711no—
318C2×C22⋊C4—2711no—
319C2×C22⋊C4—2711no—
320C2×C22⋊C4—2711no—
321C2×C22⋊C4—2711no—
322C2×C22⋊C4C2×D27111yescharacteristic
323C2×C22⋊C4C2×D27111yescharacteristic
324C2×C42—2711no—
325C2×C42—2711no—
326#95—2711no—
327#95—2711no—
328#95—2711no—
329#95—2711no—
330C24—2711no—
331C24—2711no—
332C24C22×D27111yescharacteristic
333C24C22×D27111yescharacteristic
334C24C22×D27111yescharacteristic
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—2714no—
345C2×D4—5422no—
346C2×D4—5422no—
347C2×D4—5422no—
348C2×D4—5422no—
349C2×D4—5422no—
350C2×D4—5422no—
351C2×D4—5422no—
352C2×D4—5422no—
353C2×D4—5422no—
354C2×D4—5422no—
355C2×D4—5422no—
356C2×D4—5422no—
357C2×D4—5422no—
358C2×D4—5422no—
359C2×D4—5422no—
360C2×D4—10841no—
361C2×D4—10841no—
362C2×D4—10841no—
363C2×D4—10841no—
364C2×D4—10841no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4—2711no—
369C22×C4—2711no—
370C22×C4—2711no—
371C22×C4—2711no—
372C22×C4—2711no—
373C22×C4—2711no—
374C22×C4—5422no—
375C22×C4—5422no—
376C22×C4—5422no—
377C22×C4—5422no—
378C22×C4—5422no—
379C22×C4—10841no—
380C22×C4C22×D27111yescharacteristic
381C22×C4C22×D27111yescharacteristic
382C22×C4C22×D27111yescharacteristic
383C22×C4C22×D27111yescharacteristic
384C4⋊C4—22no—
385C4⋊C4—2714no—
386C4⋊C4—5422no—
387C4⋊C4—5422no—
388C22⋊C4—22no—
389C22⋊C4—5422no—
390C22⋊C4—5422no—
391C22⋊C4—5422no—
392C22⋊C4—5422no—
393C22⋊C4—5422no—
394C22⋊C4—5422no—
395C22⋊C4—5422no—
396C22⋊C4—5422no—
397C22⋊C4—10841no—
398C22⋊C4—10841no—
399C22⋊C4C22⋊D27114yescomplemented
400C42—5422no—
401C42—5422no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—2712no—
422C23—5421no—
423C23—5421no—
424C23—5421no—
425C23—5421no—
426C23—5421no—
427C23—5421no—
428C23—5421no—
429C23—5421no—
430C23—5421no—
431C23—5421no—
432C23—5421no—
433C23—5421no—
434C23—5421no—
435C23D4×D27112yes—
436C23C2×C22⋊D27112yes—
437C23C23×D27111yescharacteristic
438D4—44no—
439D4—44no—
440D4—44no—
441D4—5428no—
442D4—10844no—
443D4—10844no—
444D4—10844no—
445D4—10844no—
446D4—10844no—
447D4—10844no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—44no—
458C2×C4—2712no—
459C2×C4—2712no—
460C2×C4—2712no—
461C2×C4—2712no—
462C2×C4—2712no—
463C2×C4—5421no—
464C2×C4—5421no—
465C2×C4—5421no—
466C2×C4—5421no—
467C2×C4—5421no—
468C2×C4—5421no—
469C2×C4—5421no—
470C2×C4—5421no—
471C2×C4—5421no—
472C2×C4—5421no—
473C2×C4—5421no—
474C2×C4—5421no—
475C2×C4—5421no—
476C2×C4—10844no—
477C2×C4—10844no—
478C2×C4D4×D27112yes—
479C2×C4C2×C22⋊D27112yes—
480C2×C4C2×C22⋊D27112yes—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—5422no—
503C22—5422no—
504C22—5422no—
505C22—10841no—
506C22—10841no—
507C22—10841no—
508C22—10841no—
509C22—10841no—
510C22—10841no—
511C22—10841no—
512C22—10841no—
513C22—10841no—
514C22—10841no—
515C22—10841no—
516C22C2×D4×D27111yescharacteristic
517C22C2×D4×D27111yescharacteristic
518C22C22×C22⋊D27111yescharacteristic
519C22#41×D27111yescharacteristic
520C22#41×D27111yescharacteristic
521C22#2257620511yescharacteristic
522C22#2257620511yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—41no—
527C4—2714no—
528C4—5422no—
529C4—5422no—
530C4—10841no—
531C4—10841no—
532C4—10841no—
533C2—42no—
534C2—42no—
535C2—81no—
536C2—10842no—
537C2—21681no—
538C2#121×D27111yescharacteristic
539C2#3177444311yescharacteristic
540C2#3177449711yescharacteristic
541C2D4×C22⋊D27111yescharacteristic
542C2D4×C22⋊D27111yescharacteristic
543C2#3177453611yescharacteristic
544C2#3177456511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, cosocleC23×C271C24
FittingC2×#121×C271C2
hypercenterC2×#121D271
hypocenterC271#2428
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#22576156C2semidirect
2. C2×#22576133C2semidirect
3. C2×#22576132C2semidirect
4. C2×#22576132C2semidirect
5. C2×C4×C22⋊D271C2semidirect
6. #31773814C2semidirect
7. #31773811C2semidirect
8. #31773805C2semidirect
9. #31773805C2semidirect
10. #31773797C2semidirect
11. #31773792C2semidirect
12. #31773776C2semidirect
13. #31773773C2semidirect
14. C22⋊C4×Dic271C2semidirect
15. C2×#121×C271C2semidirect
79. C2×C22⋊D271D4semidirect
94. Dic271⋊C4D4semidirect
128. C22⋊C4×C271D4semidirect
259. Dic271#121semidirect
272. C271#2428semidirect
278. C2×#121D271semidirect
399. C22⋊C4C22⋊D271semidirect

Maximal subgroups

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

subgroupindex
C2×#225761562
C2×#225761332
C2×#225761322
C2×C4×C22⋊D2712
#317738142
#317738112
#317738052
#317737972
#317737922
#317737762
#317737732
C22⋊C4×Dic2712
C2×#121×C2712
#2428271