Finite Group Databasebeta

← #46839781

Subgroups — #46839781

Order 34688.

704 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576133C211yesmaximal, characteristic, complemented
2C2×#22576133C211yesmaximal, characteristic, complemented
3C2×#22576122C211yesmaximal, characteristic, complemented
4C2×#22576117C211yesmaximal, characteristic, complemented
5#31773815C211yesmaximal, characteristic, complemented
6#31773813C211yesmaximal, characteristic, complemented
7#31773807C211yesmaximal, characteristic, complemented
8#31773806C211yesmaximal, characteristic, complemented
9#31773799C211yesmaximal, characteristic, complemented
10#31773797C211yesmaximal, characteristic, complemented
11#31773797C211yesmaximal, characteristic, complemented
12#31773794C211yesmaximal, characteristic, complemented
13#31773787C211yesmaximal, characteristic, complemented
14#31773756C211yesmaximal, characteristic, complemented
15#388×C271C211yesmaximal, characteristic, complemented
16C22×D1084C2211yescharacteristic
17C22×D1084C2211yescharacteristic
18C22×D1084C2211yescharacteristic
19C22×C22⋊D271C2211yescharacteristic
20C22×C22⋊D271C2211yescharacteristic
21C22×C22⋊D271C2211yescharacteristic
22C22×C4×D271C2211yescharacteristic
23C22×C4×D271C2211yescharacteristic
24#22576133—24no—
25#22576133—24no—
26#22576122—24no—
27#22576117—24no—
28C2×C4⋊Dic271C2211yescharacteristic
29C2×Dic271⋊C4C2211yescharacteristic
30C2×Dic271⋊C4C2211yescharacteristic
31C2×Dic271⋊C4C2211yescharacteristic
32C2×Dic271⋊C4C2211yescharacteristic
33C2×C22⋊Dic271C2211yescharacteristic
34C2×(C2×D271)⋊C4C2211yescharacteristic
35C2×(C2×D271)⋊C4C2211yescharacteristic
36C2×(C2×D271)⋊C4C2211yescharacteristic
37C2×(C2×D271)⋊C4C2211yescharacteristic
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×C4×Dic271C2211yescharacteristic
45C2×C4×Dic271C2211yescharacteristic
46C271⋊#95C2211yescharacteristic
47C271⋊#95C2211yescharacteristic
48C2×C4⋊C4×C271C2211yescharacteristic
49C2×C22⋊C4×C271C2211yescharacteristic
50C2×C22⋊C4×C271C2211yescharacteristic
51C2×C22⋊C4×C271C2211yescharacteristic
52C2×C42×C271C2211yescharacteristic
53#95×C271C2211yescharacteristic
54#95×C271C2211yescharacteristic
55C23×D271C2311yescharacteristic
56C23×D271C2311yescharacteristic
57C23×D271C2311yescharacteristic
58C2×D1084—22no—
59C2×D1084—22no—
60C2×D1084—22no—
61C2×D1084—22no—
62C2×D1084—22no—
63C2×D1084—22no—
64C2×D1084—41no—
65C2×D1084—41no—
66C2×D1084—41no—
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—41no—
74C2×C22⋊D271—41no—
75C2×C22⋊D271—41no—
76C22×Dic271C2311yescharacteristic
77C22×Dic271C2311yescharacteristic
78C22×Dic271C2311yescharacteristic
79C22×Dic271C2311yescharacteristic
80C22×Dic271C2311yescharacteristic
81C2×C4×D271—22no—
82C2×C4×D271—22no—
83C2×C4×D271—22no—
84C2×C4×D271—22no—
85C2×C4×D271—22no—
86C2×C4×D271D414yescomplemented
87C4⋊Dic271—41no—
88Dic271⋊C4—22no—
89Dic271⋊C4—22no—
90Dic271⋊C4—41no—
91Dic271⋊C4D414yescomplemented
92C22⋊Dic271—41no—
93(C2×D271)⋊C4—22no—
94(C2×D271)⋊C4—22no—
95(C2×D271)⋊C4—22no—
96(C2×D271)⋊C4—22no—
97(C2×D271)⋊C4—22no—
98(C2×D271)⋊C4—22no—
99(C2×D271)⋊C4—22no—
100(C2×D271)⋊C4—41no—
101(C2×D271)⋊C4—41no—
102(C2×D271)⋊C4—41no—
103C4×Dic271—22no—
104C4×Dic271—22no—
105C24×C271C2311yescharacteristic
106C22×C4×C271C2311yescharacteristic
107C22×C4×C271C2311yescharacteristic
108C22×C4×C271C2311yescharacteristic
109C22×C4×C271C2311yescharacteristic
110C22×C4×C271C2311yescharacteristic
111C22×C4×C271C2311yescharacteristic
112C4⋊C4×C271—22no—
113C22⋊C4×C271—22no—
114C22⋊C4×C271—22no—
115C22⋊C4×C271—22no—
116C42×C271—22no—
117C22×D271—21no—
118C22×D271—21no—
119C22×D271—21no—
120C22×D271—21no—
121C22×D271—21no—
122C22×D271—21no—
123C22×D271—21no—
124C22×D271—21no—
125C22×D271—21no—
126C22×D271—21no—
127C22×D271—21no—
128C22×D271—21no—
129C22×D271—21no—
130C22×D271—21no—
131C22×D271—21no—
132C22×D271—21no—
133C22×D271—21no—
134C22×D271—21no—
135C22×D271—21no—
136C22×D271C2×D412yes—
137C22×D271#4112yes—
138D1084—28no—
139D1084—44no—
140D1084—44no—
141C22⋊D271—44no—
142C22⋊D271—44no—
143C22⋊D271—44no—
144C2×Dic271—21no—
145C2×Dic271—21no—
146C2×Dic271—21no—
147C2×Dic271—21no—
148C2×Dic271—21no—
149C2×Dic271—21no—
150C2×Dic271—21no—
151C2×Dic271—21no—
152C2×Dic271—21no—
153C2×Dic271—21no—
154C2×Dic271—21no—
155C2×Dic271C2×D412yes—
156C2×Dic271C2×D412yes—
157C2×Dic271C2×D412yes—
158C2×Dic271#4112yes—
159C4×D271—28no—
160C4×D271—44no—
161C23×C271—21no—
162C23×C271—21no—
163C23×C271—21no—
164C23×C271—21no—
165C23×C271—21no—
166C23×C271—21no—
167C23×C271—21no—
168C23×C271C2411yescharacteristic
169C2×C4×C271—21no—
170C2×C4×C271—21no—
171C2×C4×C271—21no—
172C2×C4×C271—21no—
173C2×C4×C271—21no—
174C2×C4×C271—21no—
175C2×C4×C271—21no—
176C2×C4×C271—21no—
177C2×C4×C271—21no—
178C2×C4×C271—21no—
179C2×C4×C271—21no—
180C2×C4×C271—21no—
181C2×C4×C271—21no—
182C2×C4×C271—21no—
183C2×C4×C271—21no—
184C2×C4×C271C2×D412yes—
185C2×C4×C271C2×D412yes—
186C2×C4×C271#4112yes—
187C22×C271—41no—
188C22×C271—41no—
189C22×C271—41no—
190C22×C271—41no—
191C22×C271—41no—
192C22×C271—41no—
193C22×C271—41no—
194C22×C271C22×D411yescharacteristic
195C22×C271C22×D411yescharacteristic
196C22×C271C2×#4111yescharacteristic
197C22×C271C2×#4111yescharacteristic
198C22×C271C2×#4111yescharacteristic
199C22×C271H(5,𝔽2)11yescharacteristic
200C22×C271H(5,𝔽2)11yescharacteristic
201C2×D271—22no—
202C2×D271—22no—
203C2×D271—22no—
204C2×D271—22no—
205C2×D271—22no—
206C2×D271—22no—
207C2×D271—41no—
208C2×D271—41no—
209C2×D271—41no—
210C2×D271—41no—
211C2×D271—41no—
212C2×D271—41no—
213C2×D271—41no—
214C2×D271—41no—
215C2×D271—41no—
216C2×D271—41no—
217C2×D271—41no—
218C2×D271—41no—
219C2×D271—41no—
220C2×D271—41no—
221C2×D271—41no—
222C4×C271—22no—
223C4×C271—22no—
224C4×C271—22no—
225C4×C271—41no—
226C4×C271—41no—
227C4×C271—41no—
228Dic271—22no—
229Dic271—41no—
230Dic271—41no—
231Dic271—41no—
232Dic271#12114yes—
233C2×C271—81no—
234C2×C271C2×#12111yescharacteristic
235C2×C271#52511yescharacteristic
236C2×C271#53511yescharacteristic
237C2×C271#54611yescharacteristic
238C2×C271#55011yescharacteristic
239C2×C271#55311yescharacteristic
240C2×C271#55511yescharacteristic
241D271—42no—
242D271—42no—
243D271—81no—
244C271#241411yescharacteristic, complemented, Sylow
245#2414—2711nomaximal, Sylow
246C2×#121—2711no—
247C2×#121—2711no—
248C2×C4×D4—2711no—
249C2×#117—2711no—
250#394—2711no—
251#394—2711no—
252#392—2711no—
253#392—2711no—
254#390—2711no—
255#390—2711no—
256#390—2711no—
257#389—2711no—
258#388—2711no—
259#388D27111yescharacteristic, complemented
260#380—2711no—
261C22×D4—2711no—
262C22×D4—2711no—
263C22×D4—2711no—
264C22×D4—2711no—
265C22×D4—2711no—
266C22×D4—2711no—
267C23×C4—2711no—
268C23×C4—2711no—
269#121—5424no—
270#121—5424no—
271C4×D4—5424no—
272#117—5424no—
273C2×C4⋊C4—2711no—
274C2×C4⋊C4—2711no—
275C2×C4⋊C4—2711no—
276C2×C4⋊C4—2711no—
277C2×C4⋊C4—2711no—
278C2×C4⋊C4C2×D27111yescharacteristic
279C2×C22⋊C4—2711no—
280C2×C22⋊C4—2711no—
281C2×C22⋊C4—2711no—
282C2×C22⋊C4—2711no—
283C2×C22⋊C4—2711no—
284C2×C22⋊C4—2711no—
285C2×C22⋊C4—2711no—
286C2×C22⋊C4—2711no—
287C2×C22⋊C4—2711no—
288C2×C22⋊C4—2711no—
289C2×C22⋊C4—2711no—
290C2×C22⋊C4C2×D27111yescharacteristic
291C2×C22⋊C4C2×D27111yescharacteristic
292C2×C22⋊C4C2×D27111yescharacteristic
293C2×C42—2711no—
294C2×C42—2711no—
295C2×C42C2×D27111yescharacteristic
296#95—2711no—
297#95—2711no—
298#95C2×D27111yescharacteristic
299#95C2×D27111yescharacteristic
300C24—2711no—
301C24—2711no—
302C24—2711no—
303C24C22×D27111yescharacteristic
304C2×D4—5422no—
305C2×D4—5422no—
306C2×D4—5422no—
307C2×D4—5422no—
308C2×D4—5422no—
309C2×D4—5422no—
310C2×D4—5422no—
311C2×D4—5422no—
312C2×D4—5422no—
313C2×D4—5422no—
314C2×D4—5422no—
315C2×D4—5422no—
316C2×D4—10841no—
317C2×D4—10841no—
318C2×D4—10841no—
319C2×D4—10841no—
320C2×D4—10841no—
321C2×D4—10841no—
322C22×C4—2711no—
323C22×C4—2711no—
324C22×C4—2714no—
325C22×C4—2711no—
326C22×C4—2711no—
327C22×C4—2711no—
328C22×C4—5422no—
329C22×C4—5422no—
330C22×C4—5422no—
331C22×C4—5422no—
332C22×C4—5422no—
333C22×C4C22×D27111yescharacteristic
334C22×C4C22×D27111yescharacteristic
335C22×C4C22×D27111yescharacteristic
336C22×C4C22×D27111yescharacteristic
337C22×C4C22×D27111yescharacteristic
338C22×C4C22×D27111yescharacteristic
339C4⋊C4—22no—
340C4⋊C4—2714no—
341C4⋊C4—5422no—
342C4⋊C4—5422no—
343C4⋊C4—10841no—
344C4⋊C4—10841no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—5422no—
349C22⋊C4—5422no—
350C22⋊C4—5422no—
351C22⋊C4—5422no—
352C22⋊C4—5422no—
353C22⋊C4—5422no—
354C22⋊C4—5422no—
355C22⋊C4—10841no—
356C22⋊C4—10841no—
357C22⋊C4—10841no—
358C22⋊C4—10841no—
359C42—22no—
360C42—5422no—
361C42—5422no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—2712no—
370C23—2712no—
371C23—5421no—
372C23—5421no—
373C23—5421no—
374C23—5421no—
375C23—5421no—
376C23—5421no—
377C23—5421no—
378C23—5421no—
379C23—5421no—
380C23—5421no—
381C23—5421no—
382C23—5421no—
383C23—5421no—
384C23—5421no—
385C23—5421no—
386C23—5421no—
387C23—5421no—
388C23—5421no—
389C23—5421no—
390C23C23×D27111yescharacteristic
391D4—5428no—
392D4—10844no—
393D4—10844no—
394D4—10844no—
395D4—10844no—
396D4—10844no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—2712no—
413C2×C4—2712no—
414C2×C4—2712no—
415C2×C4—2712no—
416C2×C4—5428no—
417C2×C4—5421no—
418C2×C4—5421no—
419C2×C4—5421no—
420C2×C4—5421no—
421C2×C4—5421no—
422C2×C4—5421no—
423C2×C4—5421no—
424C2×C4—5421no—
425C2×C4—5421no—
426C2×C4—5421no—
427C2×C4—5421no—
428C2×C4—10844no—
429C2×C4D4×D27112yes—
430C2×C4D4×D27112yes—
431C2×C4#1686465412yes—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—5422no—
440C22—5422no—
441C22—5422no—
442C22—5422no—
443C22—5422no—
444C22—5422no—
445C22—10841no—
446C22—10841no—
447C22—10841no—
448C22—10841no—
449C22—10841no—
450C22—10841no—
451C22—10841no—
452C22—10841no—
453C22—10841no—
454C22—10841no—
455C22—10841no—
456C22—10841no—
457C22—10841no—
458C22—10841no—
459C22—10841no—
460C22C2×D4×D27111yescharacteristic
461C22C2×D4×D27111yescharacteristic
462C22#41×D27111yescharacteristic
463C22#41×D27111yescharacteristic
464C22C2×#1686465411yescharacteristic
465C22#2257620611yescharacteristic
466C22#2257620611yescharacteristic
467C4—22no—
468C4—22no—
469C4—22no—
470C4—41no—
471C4—41no—
472C4—41no—
473C4—2714no—
474C4—5422no—
475C4—10841no—
476C4—10841no—
477C4—10841no—
478C2—81no—
479C2—10842no—
480C2—10842no—
481C2—21681no—
482C2#121×D27111yescharacteristic
483C2#3177440611yescharacteristic
484C2#3177446511yescharacteristic
485C2#3177453911yescharacteristic
486C2#3177456811yescharacteristic
487C2#3177459811yescharacteristic
488C2#3177461011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D271
commutator, socle, cosocleC23×C271C24
Fitting#388×C271C2
hypercenter#388D271
hypocenterC271#2414
LCSG ▷ C23×C271 ▷ C271
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#22576133C2semidirect
2. C2×#22576133C2semidirect
3. C2×#22576122C2semidirect
4. C2×#22576117C2semidirect
5. #31773815C2semidirect
6. #31773813C2semidirect
7. #31773807C2semidirect
8. #31773806C2semidirect
9. #31773799C2semidirect
10. #31773797C2semidirect
11. #31773797C2semidirect
12. #31773794C2semidirect
13. #31773787C2semidirect
14. #31773756C2semidirect
15. #388×C271C2semidirect
86. C2×C4×D271D4semidirect
91. Dic271⋊C4D4semidirect
244. C271#2414semidirect
259. #388D271semidirect

Maximal subgroups

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

subgroupindex
C2×#225761332
C2×#225761222
C2×#225761172
#317738152
#317738132
#317738072
#317738062
#317737992
#317737972
#317737942
#317737872
#317737562
#388×C2712
#2414271