Finite Group Databasebeta

← #46839947

Subgroups — #46839947

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×#22576135C211yesmaximal, characteristic, complemented
3C2×#22576133C211yesmaximal, characteristic, complemented
4C2×#22576133C211yesmaximal, characteristic, complemented
5C2×#22576132C211yesmaximal, characteristic, complemented
6C2×(C22⋊D271)⋊C4C211yesmaximal, characteristic, complemented
7#31773815C211yesmaximal, characteristic, complemented
8#31773806C211yesmaximal, characteristic, complemented
9#31773806C211yesmaximal, characteristic, complemented
10#31773797C211yesmaximal, characteristic, complemented
11#31773792C211yesmaximal, characteristic, complemented
12#31773774C211yesmaximal, characteristic, complemented
13#31773773C211yesmaximal, characteristic, complemented
14#31773744C211yesmaximal, characteristic, complemented
15#394×C271C211yesmaximal, characteristic, complemented
16C22×D1084C2211yescharacteristic
17C22×D1084C2211yescharacteristic
18C22×D1084C2211yescharacteristic
19C22×C22⋊D271C2211yescharacteristic
20C22×C22⋊D271C2211yescharacteristic
21C22×C22⋊D271C2211yescharacteristic
22C22×C22⋊D271C2211yescharacteristic
23C22×C22⋊D271C2211yescharacteristic
24C22×C22⋊D271C2211yescharacteristic
25C23×Dic271C2211yescharacteristic
26C22×C4×D271C2211yescharacteristic
27C22×C4×D271C2211yescharacteristic
28#22576156—24no—
29#22576135—24no—
30#22576133—24no—
31#22576133—24no—
32#22576132—24no—
33(C22⋊D271)⋊C4—24no—
34C2×Dic271⋊C4C2211yescharacteristic
35C2×Dic271⋊C4C2211yescharacteristic
36C2×Dic271⋊C4C2211yescharacteristic
37C2×C22⋊Dic271C2211yescharacteristic
38C2×(C2×D271)⋊C4C2211yescharacteristic
39C2×(C2×D271)⋊C4C2211yescharacteristic
40C2×(C2×D271)⋊C4C2211yescharacteristic
41C2×(C2×D271)⋊C4C2211yescharacteristic
42C2×(C2×D271)⋊C4C2211yescharacteristic
43C2×(C2×D271)⋊C4C2211yescharacteristic
44C2×(C2×D271)⋊C4C2211yescharacteristic
45C2×C4×Dic271C2211yescharacteristic
46C2×C4×Dic271C2211yescharacteristic
47C271⋊#95C2211yescharacteristic
48C271⋊#95C2211yescharacteristic
49C271⋊#95C2211yescharacteristic
50C22×D4×C271C2211yescharacteristic
51C2×C4⋊C4×C271C2211yescharacteristic
52C2×C22⋊C4×C271C2211yescharacteristic
53C2×C22⋊C4×C271C2211yescharacteristic
54C2×C22⋊C4×C271C2211yescharacteristic
55C2×C22⋊C4×C271C2211yescharacteristic
56#95×C271C2211yescharacteristic
57C23×D271C2311yescharacteristic
58C23×D271C2311yescharacteristic
59C23×D271C2311yescharacteristic
60C2×D1084—22no—
61C2×D1084—22no—
62C2×D1084—22no—
63C2×D1084—22no—
64C2×D1084—22no—
65C2×D1084—22no—
66C2×D1084—41no—
67C2×D1084—41no—
68C2×D1084—41no—
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—22no—
76C2×C22⋊D271—22no—
77C2×C22⋊D271—22no—
78C2×C22⋊D271—22no—
79C2×C22⋊D271—22no—
80C2×C22⋊D271—22no—
81C2×C22⋊D271—22no—
82C2×C22⋊D271—41no—
83C2×C22⋊D271—41no—
84C2×C22⋊D271—41no—
85C2×C22⋊D271—41no—
86C2×C22⋊D271D414yescomplemented
87C22×Dic271—22no—
88C22×Dic271—22no—
89C22×Dic271—41no—
90C22×Dic271C2311yescharacteristic
91C22×Dic271C2311yescharacteristic
92C22×Dic271C2311yescharacteristic
93C22×Dic271C2311yescharacteristic
94C22×Dic271C2311yescharacteristic
95C2×C4×D271—22no—
96C2×C4×D271—22no—
97C2×C4×D271—22no—
98C2×C4×D271—22no—
99C2×C4×D271—22no—
100C2×C4×D271—41no—
101Dic271⋊C4—22no—
102Dic271⋊C4—22no—
103Dic271⋊C4D414yescomplemented
104C22⋊Dic271—22no—
105(C2×D271)⋊C4—22no—
106(C2×D271)⋊C4—22no—
107(C2×D271)⋊C4—22no—
108(C2×D271)⋊C4—22no—
109(C2×D271)⋊C4—22no—
110(C2×D271)⋊C4—41no—
111(C2×D271)⋊C4D414yescomplemented
112C4×Dic271—22no—
113C4×Dic271—22no—
114C24×C271C2311yescharacteristic
115C24×C271C2311yescharacteristic
116C2×D4×C271—22no—
117C2×D4×C271—22no—
118C2×D4×C271—41no—
119C22×C4×C271C2311yescharacteristic
120C22×C4×C271C2311yescharacteristic
121C22×C4×C271C2311yescharacteristic
122C22×C4×C271C2311yescharacteristic
123C22×C4×C271C2311yescharacteristic
124C4⋊C4×C271—22no—
125C22⋊C4×C271—22no—
126C22⋊C4×C271—22no—
127C22⋊C4×C271—22no—
128C22⋊C4×C271—41no—
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×D271—21no—
143C22×D271—21no—
144C22×D271—21no—
145C22×D271—21no—
146C22×D271—21no—
147C22×D271—21no—
148C22×D271C2×D412yes—
149C22×D271C2×D412yes—
150D1084—44no—
151D1084—44no—
152D1084—44no—
153C22⋊D271—28no—
154C22⋊D271—44no—
155C22⋊D271—44no—
156C22⋊D271—44no—
157C22⋊D271—44no—
158C22⋊D271—44no—
159C2×Dic271—21no—
160C2×Dic271—21no—
161C2×Dic271—21no—
162C2×Dic271—21no—
163C2×Dic271—21no—
164C2×Dic271—21no—
165C2×Dic271—21no—
166C2×Dic271—21no—
167C2×Dic271—21no—
168C2×Dic271—44no—
169C2×Dic271C2×D412yes—
170C2×Dic271C2×D412yes—
171C2×Dic271C2×D412yes—
172C2×Dic271C2×D412yes—
173C2×Dic271#4112yes—
174C2×Dic271#4112yes—
175C4×D271—44no—
176C4×D271—44no—
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×C271—21no—
190C23×C271C2×D412yes—
191C23×C271C2411yescharacteristic
192D4×C271—44no—
193C2×C4×C271—21no—
194C2×C4×C271—21no—
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—21no—
205C2×C4×C271—21no—
206C2×C4×C271C2×D412yes—
207C2×C4×C271C2×D412yes—
208C22×C271—22no—
209C22×C271—22no—
210C22×C271—22no—
211C22×C271—41no—
212C22×C271—41no—
213C22×C271—41no—
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×C271C22×D411yescharacteristic
223C22×C271C22×D411yescharacteristic
224C22×C271C22×D411yescharacteristic
225C22×C271C2×#4111yescharacteristic
226C22×C271C2×#4111yescharacteristic
227C22×C271H(5,𝔽2)11yescharacteristic
228C22×C271H(5,𝔽2)11yescharacteristic
229C2×D271—22no—
230C2×D271—22no—
231C2×D271—22no—
232C2×D271—22no—
233C2×D271—22no—
234C2×D271—22no—
235C2×D271—41no—
236C2×D271—41no—
237C2×D271—41no—
238C2×D271—41no—
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—41no—
253C4×C271—41no—
254C4×C271—41no—
255Dic271—22no—
256Dic271—22no—
257Dic271—22no—
258Dic271—41no—
259Dic271#12114yescomplemented
260C2×C271—42no—
261C2×C271—81no—
262C2×C271C2×#12111yescharacteristic
263C2×C271#53211yescharacteristic
264C2×C271#54011yescharacteristic
265C2×C271D4211yescharacteristic
266C2×C271D4211yescharacteristic
267C2×C271#54611yescharacteristic
268C2×C271#55011yescharacteristic
269D271—42no—
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×#121—2711no—
279C2×C4×D4—2711no—
280#394—2711no—
281#394D27111yescharacteristic, complemented
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×D4—2711no—
297C22×D4—2711no—
298C22×D4C2×D27111yescharacteristic
299C23×C4—2711no—
300C23×C4—2711no—
301C23×C4—2711no—
302#127—5424no—
303#121—5424no—
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⋊C4C2×D27111yescharacteristic
321C2×C22⋊C4C2×D27111yescharacteristic
322C2×C22⋊C4C2×D27111yescharacteristic
323C2×C22⋊C4C2×D27111yescharacteristic
324C2×C42—2711no—
325C2×C42—2711no—
326#95—2711no—
327#95—2711no—
328#95—2711no—
329#95C2×D27111yescharacteristic
330C24—2711no—
331C24—2711no—
332C24—2711no—
333C24C22×D27111yescharacteristic
334C24C22×D27111yescharacteristic
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—41no—
338C2×D4—2714no—
339C2×D4—5422no—
340C2×D4—5422no—
341C2×D4—5422no—
342C2×D4—5422no—
343C2×D4—5422no—
344C2×D4—5422no—
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—10841no—
359C2×D4—10841no—
360C2×D4—10841no—
361C2×D4—10841no—
362C2×D4—10841no—
363C2×D4—10841no—
364C2×D4—10841no—
365C22×C4—2711no—
366C22×C4—2711no—
367C22×C4—2711no—
368C22×C4—2711no—
369C22×C4—2711no—
370C22×C4—5422no—
371C22×C4—5422no—
372C22×C4—5422no—
373C22×C4—5422no—
374C22×C4—5422no—
375C22×C4—5422no—
376C22×C4—5422no—
377C22×C4—10841no—
378C22×C4—10841no—
379C22×C4C22×D27111yescharacteristic
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—22no—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—2714no—
393C22⋊C4—5422no—
394C22⋊C4—5422no—
395C22⋊C4—5422no—
396C22⋊C4—5422no—
397C22⋊C4—5422no—
398C22⋊C4—5422no—
399C22⋊C4—10841no—
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—2712no—
416C23—2712no—
417C23—5421no—
418C23—5421no—
419C23—5421no—
420C23—5421no—
421C23—5421no—
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—
435C23—5421no—
436C23D4×D27112yes—
437C23C23×D27111yescharacteristic
438D4—44no—
439D4—5428no—
440D4—10844no—
441D4—10844no—
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—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—2712no—
462C2×C4—2712no—
463C2×C4—2712no—
464C2×C4—2712no—
465C2×C4—2712no—
466C2×C4—2712no—
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×C4—10844no—
479C2×C4D4×D27112yes—
480C2×C4D4×D27112yes—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—5422no—
496C22—5422no—
497C22—5422no—
498C22—5422no—
499C22—5422no—
500C22—5422no—
501C22—10841no—
502C22—10841no—
503C22—10841no—
504C22—10841no—
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
518C22C2×D4×D27111yescharacteristic
519C22#41×D27111yescharacteristic
520C22#41×D27111yescharacteristic
521C22#2257620511yescharacteristic
522C22#2257620611yescharacteristic
523C4—22no—
524C4—22no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—2714no—
529C4—5422no—
530C4—5422no—
531C4—5422no—
532C4—10841no—
533C2—42no—
534C2—81no—
535C2—10842no—
536C2—10842no—
537C2—21681no—
538C2#121×D27111yescharacteristic
539C2#3177444611yescharacteristic
540C2#3177449911yescharacteristic
541C2#3177452911yescharacteristic
542C2#3177453111yescharacteristic
543C2#3177453911yescharacteristic
544C2#3177456511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, cosocleC23×C271C24
Fitting#394×C271C2
hypercenter#394D271
hypocenterC271#2428
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#22576156C2semidirect
2. C2×#22576135C2semidirect
3. C2×#22576133C2semidirect
4. C2×#22576133C2semidirect
5. C2×#22576132C2semidirect
6. C2×(C22⋊D271)⋊C4C2semidirect
7. #31773815C2semidirect
8. #31773806C2semidirect
9. #31773806C2semidirect
10. #31773797C2semidirect
11. #31773792C2semidirect
12. #31773774C2semidirect
13. #31773773C2semidirect
14. #31773744C2semidirect
15. #394×C271C2semidirect
86. C2×C22⋊D271D4semidirect
103. Dic271⋊C4D4semidirect
111. (C2×D271)⋊C4D4semidirect
259. Dic271#121semidirect
272. C271#2428semidirect
281. #394D271semidirect

Maximal subgroups

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

subgroupindex
C2×#225761562
C2×#225761352
C2×#225761332
C2×#225761322
C2×(C22⋊D271)⋊C42
#317738152
#317738062
#317737972
#317737922
#317737742
#317737732
#317737442
#394×C2712
#2428271