Finite Group Databasebeta

← #34033352

Subgroups — #34033352

Order 18688.

500 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989700C211yesmaximal, characteristic
2#22627071C211yesmaximal, characteristic
3C2×#17989677C211yesmaximal, characteristic, complemented
4C2×#17989676C211yesmaximal, characteristic, complemented
5#22626937C211yesmaximal, characteristic, complemented
6#22626937C211yesmaximal, characteristic, complemented
7C22⋊C8×#64408C211yesmaximal, characteristic
8#17989700—22no—
9#17989700—22no—
10C2×C4⋊#10596842C2211yescharacteristic
11C2×C4⋊#10596842C2211yescharacteristic
12C2×C4⋊#10596842C2211yescharacteristic
13C2×C4⋊#10596842C2211yescharacteristic
14C2×C22⋊#10596842—21no—
15C2×C22⋊#10596842—21no—
16C2×C4×#10596842—21no—
17(C2×#10596842)⋊C4—21no—
18#17989677—22no—
19#17989676—22no—
20C22×C4×#64408C2211yescharacteristic
21#17989555C411yescharacteristic
22C2×C8×#64408C2211yescharacteristic
23C2×C8×#64408C2211yescharacteristic
24#17989452C411yescharacteristic
25#17989452C411yescharacteristic
26C22⋊C8×D73C411yescharacteristic
27C22×#10596842—21no—
28C22×#10596842—21no—
29C22×#10596842—21no—
30C22×#10596842—21no—
31C4⋊#10596842—21no—
32C4⋊#10596842—21no—
33C4⋊#10596842—21no—
34C4⋊#10596842—21no—
35C4⋊#10596842—21no—
36C4⋊#10596842—21no—
37C4⋊#10596842D412yes—
38C4⋊#10596842D412yes—
39C22⋊#10596842—24no—
40C22⋊#10596842—42no—
41C4×#10596842—24no—
42C23×#64408D411yescharacteristic
43C23×#64408Q811yescharacteristic
44C2×#11924036C2×C411yescharacteristic
45C2×#11924036C2×C411yescharacteristic
46C2×C4×#64408—21no—
47C2×C4×#64408—21no—
48C2×C4×#64408—21no—
49C2×C4×#64408—21no—
50C2×C4×#64408C2×C411yescharacteristic
51C2×C4×#64408D411yescharacteristic
52C2×C4×#64408Q811yescharacteristic
53C2×C4×#64408C2311yescharacteristic
54#14556648—21no—
55C22⋊#10596833—21no—
56C8×#64408—21no—
57C8×#64408—21no—
58C8×#64408—21no—
59C8×#64408—21no—
60C22×C4×D73C2×C411yescharacteristic
61C2×C8×D73C2×C411yescharacteristic
62C2×C8×D73C2×C411yescharacteristic
63C22⋊#10596831C811yescharacteristic, complemented
64#14556503C811yescharacteristic, complemented
65#14556503C811yescharacteristic, complemented
66C22⋊C8×C73C811yescharacteristic, complemented
67C2×#10596842—22no—
68C2×#10596842—22no—
69C2×#10596842—41no—
70C2×#10596842—41no—
71C2×#10596842—41no—
72C2×#10596842—41no—
73C2×#10596842—41no—
74C2×#10596842—41no—
75C2×#10596842—41no—
76C2×#10596842—41no—
77C2×#10596842—41no—
78C2×#10596842—41no—
79C22×#64408—22no—
80C22×#64408—21no—
81C22×#64408—21no—
82C22×#64408—21no—
83C22×#64408—21no—
84C22×#64408—21no—
85C22×#64408—21no—
86C22×#64408—21no—
87C22×#64408—21no—
88C22×#64408—41no—
89C22×#64408C4⋊C411yescharacteristic
90C22×#64408C4⋊C411yescharacteristic
91C22×#64408C2×D411yescharacteristic
92C22×#64408C2×Q811yescharacteristic
93#11924036—21no—
94#11924036—21no—
95#11924036—21no—
96#11924036—21no—
97C2×#10596833—21no—
98C2×#10596833—21no—
99C4×#64408—21no—
100C4×#64408—21no—
101C4×#64408—21no—
102C4×#64408—21no—
103C4×#64408—21no—
104C4×#64408—21no—
105C4×#64408C2×D411yescharacteristic
106C4×#64408C2×D411yescharacteristic
107C4×#64408#4111yescharacteristic
108C4×#64408#4111yescharacteristic
109C23×D73C4⋊C411yescharacteristic
110C22×Dic73M1611yescharacteristic
111C2×C4×D73—21no—
112C2×C4×D73—21no—
113C2×C4×D73—21no—
114C2×C4×D73—21no—
115C2×C4×D73C4⋊C411yescharacteristic
116C2×C4×D73C2×C811yescharacteristic
117C2×C4×D73M1611yescharacteristic
118C2×C4×D73C22×C411yescharacteristic
119C2×#10596831C2×C811yescharacteristic
120C2×#10596831C2×C811yescharacteristic
121C8×D73—21no—
122C8×D73—21no—
123C8×D73—21no—
124C8×D73—21no—
125C22×C4×C73C2×C811yescharacteristic
126C2×C8×C73C2×C811yescharacteristic
127C2×C8×C73C2×C811yescharacteristic
128C23×C73C4⋊C811yescharacteristic
129C22×D73—21no—
130C22×D73—21no—
131C22×D73—21no—
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73C4⋊C811yescharacteristic
136C22×D73C2×C4⋊C411yescharacteristic
137C2×#64408—21no—
138C2×#64408—21no—
139C2×#64408—21no—
140C2×#64408—21no—
141C2×#64408—21no—
142C2×#64408—21no—
143C2×#64408—21no—
144C2×#64408—42no—
145C2×#64408—42no—
146C2×#64408—41no—
147C2×#64408—41no—
148C2×#64408—41no—
149C2×#64408—41no—
150C2×#64408#10812yes—
151C2×#64408#12011yescharacteristic
152C2×#64408C22⋊Q811yescharacteristic
153C2×#64408C22⋊Q811yescharacteristic
154C2×#64408#12311yescharacteristic
155C2×#64408#13511yescharacteristic
156C2×#64408#13511yescharacteristic
157C2×#64408AGL(1,ℤ/8)11yescharacteristic
158C2×#64408#13711yescharacteristic
159#10596842—42no—
160#10596842—42no—
161#10596842—81no—
162#10596842—81no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73C4⋊C811yescharacteristic
166C2×C4×C73C22×C811yescharacteristic
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73C4⋊C811yescharacteristic
170C2×Dic73C2×M1611yescharacteristic
171C4×D73—21no—
172C4×D73—21no—
173C4×D73—21no—
174C4×D73—21no—
175C4×D73—21no—
176C4×D73—21no—
177C4×D73C4×D411yescharacteristic
178C4×D73C4×D411yescharacteristic
179C4×D73#13111yescharacteristic
180C4×D73#13111yescharacteristic
181#10596833—41no—
182#10596833—41no—
183C8×C73—21no—
184C8×C73—21no—
185#10596831—21no—
186#10596831—21no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73C2×C4⋊C811yescharacteristic
191C2×D73—21no—
192C2×D73—21no—
193C2×D73—21no—
194C2×D73—41no—
195C2×D73—41no—
196C2×D73—41no—
197C2×D73—41no—
198C2×D73#38511yescharacteristic
199C2×D73#42411yescharacteristic
200C2×D73#42711yescharacteristic
201C2×D73#42811yescharacteristic
202C2×D73C2×#10811yescharacteristic
203C2×D73#43011yescharacteristic
204#64408—22no—
205#64408—21no—
206#64408—21no—
207#64408—41no—
208#64408#44911yescharacteristic
209#64408#45211yescharacteristic
210#64408#48211yescharacteristic
211#64408#48511yescharacteristic
212C4×C73—21no—
213C4×C73C8×D411yescharacteristic
214C4×C73C8×D411yescharacteristic
215Dic73—21no—
216Dic73#43511yescharacteristic
217Dic73#43511yescharacteristic
218#8831—731nomaximal, Sylow
219C2×C73—41no—
220C2×C73#156411yescharacteristic
221C2×C73#156511yescharacteristic
222C2×C73#185011yescharacteristic
223D73—41no—
224D73#157211yescharacteristic
225D73#157411yescharacteristic
226D73#185411yescharacteristic
227D73#185511yescharacteristic
228C2×#431—731no—
229#1797—731no—
230C4×C22⋊C8—731no—
231C2×#335—731no—
232C2×#334—731no—
233#1277—731no—
234#1277—731no—
235C73#883111yescharacteristic, complemented, Sylow
236C22×C42—731no—
237#431—1462no—
238#431—1462no—
239C2×C4⋊C8—731no—
240C2×C4⋊C8—731no—
241C2×C4⋊C8—731no—
242C2×C4⋊C8—731no—
243C2×C22⋊C8—731no—
244C2×C22⋊C8—731no—
245C2×C22⋊C8—1461no—
246C2×C22⋊C8—1461no—
247C2×C4×C8—731no—
248C2×C4×C8—731no—
249C2×C4×C8—1461no—
250#336—731no—
251#336—731no—
252#336—1461no—
253#335—1462no—
254#334—1462no—
255C23×C4—731no—
256C23×C4—731no—
257C23×C4—731no—
258C22×C8—731no—
259C22×C8—731no—
260C22×C8—731no—
261C22×C8—731no—
262C22×C8—1461no—
263C22×C8—1461no—
264C22×C8—1461no—
265C22×C8—1461no—
266C2×C42—731no—
267C2×C42—731no—
268C2×C42—731no—
269C2×C42—731no—
270C2×C42—1461no—
271C2×C42—1461no—
272C2×C42—1461no—
273C2×C42—1461no—
274C4⋊C8—732no—
275C4⋊C8—732no—
276C4⋊C8—1461no—
277C4⋊C8—1461no—
278C4⋊C8—1461no—
279C4⋊C8—1461no—
280C4⋊C8—1461no—
281C4⋊C8—1461no—
282C22⋊C8—2922no—
283C22⋊C8—731no—
284C22⋊C8—731no—
285C22⋊C8—731no—
286C22⋊C8—1461no—
287C22⋊C8—1461no—
288C22⋊C8—1464no—
289C22⋊C8#1059684211yescharacteristic, complemented
290C4×C8—1461no—
291C4×C8—1461no—
292C4×C8—1461no—
293C4×C8—1461no—
294C4×C8—1464no—
295C24—731no—
296C22×C4—2921no—
297C22×C4—731no—
298C22×C4—731no—
299C22×C4—731no—
300C22×C4—731no—
301C22×C4—731no—
302C22×C4—731no—
303C22×C4—731no—
304C22×C4—731no—
305C22×C4—731no—
306C22×C4—1461no—
307C22×C4—1461no—
308C22×C4—1461no—
309C22×C4—1461no—
310C22×C4—1461no—
311C22×C4—1461no—
312C22×C4—1461no—
313C22×C4—1461no—
314C22×C4—1461no—
315C22×C4—1461no—
316C22×C4—1461no—
317C22×C4—1461no—
318C22×C4—1462no—
319C22×C4C2×#1059684211yescharacteristic
320C2×C8—2921no—
321C2×C8—2921no—
322C2×C8—2921no—
323C2×C8—2921no—
324C2×C8—2921no—
325C2×C8—2921no—
326C2×C8—2921no—
327C2×C8—2921no—
328C2×C8—2921no—
329C2×C8—2921no—
330C2×C8—731no—
331C2×C8—731no—
332C2×C8—1461no—
333C2×C8—1461no—
334C2×C8—1461no—
335C2×C8—1461no—
336C2×C8—1461no—
337C2×C8—1461no—
338C2×C8—1461no—
339C2×C8—1461no—
340C2×C8—1461no—
341C2×C8—1461no—
342C2×C8—1462no—
343C2×C8—1462no—
344C2×C8C2×#1059684211yescharacteristic
345C2×C8C2×#1059684211yescharacteristic
346C42—731no—
347C42—731no—
348C42—731no—
349C42—731no—
350C42—1461no—
351C42—1461no—
352C42—1461no—
353C42—1461no—
354C42—1461no—
355C42—1461no—
356C23—731no—
357C23—731no—
358C23—1461no—
359C23—1461no—
360C23—1461no—
361C23—1461no—
362C23—1461no—
363C23—1461no—
364C23C4⋊#1059684211yescharacteristic
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—2921no—
368C2×C4—2921no—
369C2×C4—2921no—
370C2×C4—2921no—
371C2×C4—2922no—
372C2×C4—2922no—
373C2×C4—731no—
374C2×C4—731no—
375C2×C4—731no—
376C2×C4—731no—
377C2×C4—731no—
378C2×C4—731no—
379C2×C4—731no—
380C2×C4—731no—
381C2×C4—731no—
382C2×C4—731no—
383C2×C4—731no—
384C2×C4—731no—
385C2×C4—731no—
386C2×C4—732no—
387C2×C4—731no—
388C2×C4—1461no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1461no—
393C2×C4—1461no—
394C2×C4—1461no—
395C2×C4—1461no—
396C2×C4—1461no—
397C2×C4—1461no—
398C2×C4—1461no—
399C2×C4—1461no—
400C2×C4—1461no—
401C2×C4—1461no—
402C2×C4—1461no—
403C2×C4C4⋊#1059684211yescharacteristic
404C2×C4C22×#1059684211yescharacteristic
405C8—21no—
406C8—21no—
407C8—2922no—
408C8—2922no—
409C8—2921no—
410C8—2921no—
411C8—5841no—
412C8—5841no—
413C8—1461no—
414C8—1461no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—2921no—
419C22—2921no—
420C22—2921no—
421C22—2921no—
422C22—731no—
423C22—731no—
424C22—731no—
425C22—731no—
426C22—731no—
427C22—731no—
428C22—1461no—
429C22—1461no—
430C22—1461no—
431C22C2×C4⋊#1059684211yescharacteristic
432C4—21no—
433C4—2921no—
434C4—731no—
435C4—731no—
436C4—731no—
437C4—731no—
438C4—731no—
439C4—731no—
440C4—1461no—
441C4—1461no—
442C4—1462no—
443C4—1461no—
444C4D4×#1059684211yescharacteristic
445C4D4×#1059684211yescharacteristic
446C2—41no—
447C2—2921no—
448C2—731no—
449C2—731no—
450C2—731no—
451C2—731no—
452C2#2262705511yescharacteristic
453C2#2262705611yescharacteristic
454C2#2262707611yescharacteristic
subgroupG/H
centerC22C2×C4⋊#10596842
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
FittingC22⋊C8×C73C8
socleC22×C73C2×C4⋊C8
prime radicalC23×D73C4⋊C4
cosocleC2×C4×#64408C23
hypercenterC22⋊C8#10596842
hypocenterC73#8831
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#17989677C2semidirect
4. C2×#17989676C2semidirect
5. #22626937C2semidirect
6. #22626937C2semidirect
63. C22⋊#10596831C8semidirect
64. #14556503C8semidirect
65. #14556503C8semidirect
66. C22⋊C8×C73C8semidirect
235. C73#8831semidirect
289. C22⋊C8#10596842semidirect

Maximal subgroups

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

subgroupindex
C2×#179897002
#226270712
C2×#179896772
C2×#179896762
#226269372
C22⋊C8×#644082
#883173