Finite Group Databasebeta

← #32979352

Subgroups — #32979352

Order 18688.

496 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612327C211yesmaximal, characteristic
2#22609908C211yesmaximal, characteristic
3C4×#14556503C211yesmaximal, characteristic
4#22607772C211yesmaximal, characteristic, complemented
5#22607771C211yesmaximal, characteristic, complemented
6#22607770C211yesmaximal, characteristic, complemented
7C73×#1279C211yesmaximal, characteristic, complemented
8C2×C42×D73C2211yescharacteristic
9C2×C4⋊#10596831C2211yescharacteristic
10C2×#14556503—21no—
11C2×#14556503—21no—
12C2×C4×#10596831C2211yescharacteristic
13#17988454—21no—
14#17988452C411yescharacteristic
15#17988452C411yescharacteristic
16#17988449—21no—
17#17988444C411yescharacteristic
18#17988444C411yescharacteristic
19C4×C4⋊Dic73C2211yescharacteristic
20C4×#11924005—21no—
21#17988433—21no—
22#17988341—21no—
23#17988341—21no—
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4×C8×C73C2211yescharacteristic
26C4×C4⋊C4×C73C2211yescharacteristic
27C22×C4×D73C2×C411yescharacteristic
28C22×C4×D73D411yescharacteristic
29C22×C4×D73D411yescharacteristic
30C22×#10596831—21no—
31C22×#10596831—21no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924005—21no—
35C2×#11924005—21no—
36C2×C4×Dic73—21no—
37C2×C4×Dic73C2×C411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C42×D73—21no—
41C42×D73—21no—
42C42×D73—21no—
43C42×D73—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831—21no—
46#14556503—24no—
47#14556503—42no—
48C4×#10596831—21no—
49C4×#10596831—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53#14556498—21no—
54#14556498—21no—
55#14556498—21no—
56#14556498—21no—
57C22×C8×C73—21no—
58C22×C8×C73—21no—
59C2×C4⋊C4×C73C2×C411yescharacteristic
60C2×C4⋊C4×C73C2×C411yescharacteristic
61C2×C42×C73—21no—
62C2×C42×C73C2311yescharacteristic
63C4⋊C8×C73—21no—
64C4⋊C8×C73—21no—
65C4×C8×C73—21no—
66C4×C8×C73—21no—
67#95×C73—21no—
68C23×D73C22⋊C411yescharacteristic
69C22×Dic73—21no—
70C22×Dic73—21no—
71C22×Dic73C22⋊C411yescharacteristic
72C22×Dic73C22⋊C411yescharacteristic
73C22×Dic73C22⋊C411yescharacteristic
74C2×C4×D73—22no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79C2×C4×D73—21no—
80C2×C4×D73—21no—
81C2×C4×D73—21no—
82C2×C4×D73—21no—
83C2×C4×D73—21no—
84C2×C4×D73—21no—
85C2×C4×D73—21no—
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—41no—
90C2×#10596831—22no—
91C2×#10596831—41no—
92C2×#10596831—41no—
93C2×#10596831—41no—
94C2×#10596831—41no—
95C2×#10596831—41no—
96C4⋊Dic73—21no—
97C4⋊Dic73—21no—
98C4⋊Dic73—21no—
99C4⋊Dic73—21no—
100#11924005—42no—
101#11924005—42no—
102C4×Dic73—21no—
103C4×Dic73—21no—
104C4×Dic73—21no—
105C4×Dic73—21no—
106C4×Dic73—21no—
107C4×Dic73—21no—
108C4×Dic73—41no—
109C4×Dic73—41no—
110C22×C4×C73—21no—
111C22×C4×C73—21no—
112C22×C4×C73C22×C411yescharacteristic
113C22×C4×C73C2×D411yescharacteristic
114C22×C4×C73C2×D411yescharacteristic
115C2×C8×C73—22no—
116C2×C8×C73—41no—
117C2×C8×C73—41no—
118C2×C8×C73—41no—
119C2×C8×C73—41no—
120C2×C8×C73—41no—
121C4⋊C4×C73—21no—
122C4⋊C4×C73—21no—
123C4⋊C4×C73—21no—
124C4⋊C4×C73—21no—
125C42×C73—41no—
126C42×C73—41no—
127C42×C73#4111yescharacteristic
128C42×C73#4111yescharacteristic
129C42×C73#4111yescharacteristic
130C42×C73#4111yescharacteristic
131C23×C73C2×C22⋊C411yescharacteristic
132C22×D73—21no—
133C22×D73—21no—
134C22×D73—21no—
135C22×D73—21no—
136C22×D73—21no—
137C22×D73—21no—
138C22×D73#10412yes—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—41no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—41no—
145C2×C4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73#11711yescharacteristic
148C2×C4×C73#11711yescharacteristic
149C2×C4×C73#12311yescharacteristic
150C2×C4×C73#12311yescharacteristic
151C2×C4×C73#12311yescharacteristic
152C2×C4×C73#12311yescharacteristic
153C2×C4×C73#13111yescharacteristic
154C2×C4×C73#13111yescharacteristic
155C2×C4×C73#13111yescharacteristic
156C2×C4×C73#13111yescharacteristic
157C2×C4×C73#13511yescharacteristic
158C2×C4×C73#13511yescharacteristic
159C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C73#13711yescharacteristic
161C2×Dic73—21no—
162C2×Dic73—21no—
163C2×Dic73—21no—
164C2×Dic73—21no—
165C2×Dic73—21no—
166C2×Dic73—21no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—41no—
171C2×Dic73—41no—
172C2×Dic73—41no—
173C2×Dic73—41no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C4×D73—42no—
177C4×D73—42no—
178C4×D73—41no—
179C4×D73—41no—
180C4×D73—41no—
181C4×D73—41no—
182C4×D73—41no—
183C4×D73—41no—
184C4×D73—41no—
185C4×D73—41no—
186C8×C73—42no—
187C8×C73—81no—
188#10596831—42no—
189#10596831—81no—
190C22×C73#38111yescharacteristic
191C22×C73#40811yescharacteristic
192C22×C73#40811yescharacteristic
193C22×C73#41611yescharacteristic
194C22×C73#41711yescharacteristic
195C22×C73C2×#10411yescharacteristic
196C22×C73#42111yescharacteristic
197C2×D73—22no—
198C2×D73—22no—
199C2×D73—22no—
200C2×D73—41no—
201C2×D73—41no—
202C2×D73—41no—
203C2×D73—41no—
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—81no—
207C4×C73—81no—
208C4×C73#43311yescharacteristic
209C4×C73#43311yescharacteristic
210C4×C73#43311yescharacteristic
211C4×C73#43311yescharacteristic
212C4×C73#48211yescharacteristic
213C4×C73#48211yescharacteristic
214C4×C73#48511yescharacteristic
215C4×C73#48511yescharacteristic
216Dic73—41no—
217Dic73—41no—
218Dic73—41no—
219Dic73—81no—
220Dic73—81no—
221#8711—731nomaximal, Sylow
222C2×C73#148211yescharacteristic
223C2×C73#148311yescharacteristic
224C2×C73#149411yescharacteristic
225C2×C73#149511yescharacteristic
226C2×C73#181811yescharacteristic
227C2×C73#182511yescharacteristic
228C2×C73#182611yescharacteristic
229D73—42no—
230#2283—731no—
231#1797—731no—
232C4×C22⋊C8—731no—
233#1279—731no—
234#1279—731no—
235#1279—731no—
236#1279D7311yescharacteristic, complemented
237C73#871111yescharacteristic, complemented, Sylow
238C22×C42—731no—
239C2×C4⋊C8—731no—
240C2×C4⋊C8C2×D7311yescharacteristic
241C2×C22⋊C8—1461no—
242C2×C22⋊C8—1461no—
243C2×C4×C8—731no—
244C2×C4×C8C2×D7311yescharacteristic
245#383—1461no—
246#382—731no—
247#382—731no—
248#381—1461no—
249#380—731no—
250#380—731no—
251C4×C4⋊C4—731no—
252C4×C4⋊C4C2×D7311yescharacteristic
253C4×C22⋊C4—1461no—
254#376—1461no—
255#336—1461no—
256#336—1461no—
257C23×C4—731no—
258C23×C4—731no—
259C23×C4—731no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—1461no—
263C22×C8—1461no—
264C2×C4⋊C4—731no—
265C2×C4⋊C4—731no—
266C2×C4⋊C4C4×D7311yescharacteristic
267C2×C4⋊C4C4×D7311yescharacteristic
268C2×C22⋊C4—1461no—
269C2×C22⋊C4—1461no—
270C2×C42—21no—
271C2×C42—731no—
272C2×C42—731no—
273C2×C42—731no—
274C2×C42—1461no—
275C2×C42—1461no—
276C2×C42—1461no—
277C2×C42—1461no—
278C2×C42—1461no—
279C2×C42C22×D7311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—1461no—
283C4⋊C8—1461no—
284C22⋊C8—2922no—
285C22⋊C8—1464no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8—1461no—
289C4×C8—1461no—
290#95—21no—
291#95—1461no—
292#95—1461no—
293#95—1461no—
294#95—1461no—
295#95—1461no—
296#95—1461no—
297#95—1461no—
298C24—731no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—2921no—
302C22×C4—731no—
303C22×C4—731no—
304C22×C4—731no—
305C22×C4—1462no—
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—1461no—
319C22×C4—1461no—
320C22×C4—1461no—
321C22×C4—1461no—
322C22×C4C2×C4×D7311yescharacteristic
323C22×C4D4×D7311yescharacteristic
324C22×C4D4×D7311yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—2921no—
332C2×C8—2921no—
333C2×C8—2921no—
334C2×C8—2921no—
335C2×C8—2921no—
336C2×C8—1462no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—1461no—
342C4⋊C4—1461no—
343C4⋊C4—1461no—
344C4⋊C4—1461no—
345C22⋊C4—2922no—
346C22⋊C4—2922no—
347C42—41no—
348C42—41no—
349C42—2921no—
350C42—2921no—
351C42—1461no—
352C42—1461no—
353C42—1461no—
354C42—1461no—
355C42—1461no—
356C42—1461no—
357C42#1192402711yescharacteristic
358C42#1192402811yescharacteristic
359C42#1192402811yescharacteristic
360C42#1192402911yescharacteristic
361C23—732no—
362C23—1461no—
363C23—1461no—
364C23—1461no—
365C23—1461no—
366C23—1461no—
367C23—1461no—
368C23C22⋊C4×D7311yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—2922no—
378C2×C4—2922no—
379C2×C4—2921no—
380C2×C4—2921no—
381C2×C4—2921no—
382C2×C4—2921no—
383C2×C4—2921no—
384C2×C4—2921no—
385C2×C4—2921no—
386C2×C4—2921no—
387C2×C4—2921no—
388C2×C4—2921no—
389C2×C4—2921no—
390C2×C4—2921no—
391C2×C4—2921no—
392C2×C4—2921no—
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#1455654811yescharacteristic
403C2×C4#1455654911yescharacteristic
404C2×C4#1455657311yescharacteristic
405C2×C4#1455657311yescharacteristic
406C2×C4#1455657611yescharacteristic
407C2×C4#1455657611yescharacteristic
408C2×C4#1455659711yescharacteristic
409C2×C4#1455659711yescharacteristic
410C2×C4#1455659911yescharacteristic
411C2×C4#1455659911yescharacteristic
412C2×C4#1455661211yescharacteristic
413C2×C4#1455661411yescharacteristic
414C2×C4#1455661511yescharacteristic
415C2×C4#1455662011yescharacteristic
416C8—42no—
417C8—81no—
418C8—2922no—
419C8—5841no—
420C22—2921no—
421C22—2921no—
422C22—2921no—
423C22—2921no—
424C22—1462no—
425C22—1462no—
426C22—1462no—
427C22#1798844911yescharacteristic
428C22#1798855211yescharacteristic
429C22#1798855211yescharacteristic
430C22#1798858211yescharacteristic
431C22#1798858511yescharacteristic
432C22#104×D7311yescharacteristic
433C22#1798860211yescharacteristic
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—2921no—
439C4—2921no—
440C4—2921no—
441C4—5841no—
442C4—5841no—
443C4#1798864611yescharacteristic
444C4#1798864711yescharacteristic
445C4#1798864711yescharacteristic
446C4#1798864911yescharacteristic
447C4#1798891011yescharacteristic
448C4#1798891411yescharacteristic
449C4#1798892711yescharacteristic
450C4#1798893111yescharacteristic
451C2—2922no—
452C2#2260833811yescharacteristic
453C2#2260834111yescharacteristic
454C2#2260839011yescharacteristic
455C2#2260839311yescharacteristic
456C2#2261000111yescharacteristic
457C2#2261002511yescharacteristic
458C2#2261002911yescharacteristic
subgroupG/H
centerC22×C4D4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1279C2
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1279D73
hypocenterC73#8711
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #22607772C2semidirect
5. #22607771C2semidirect
6. #22607770C2semidirect
7. C73×#1279C2semidirect
236. #1279D73semidirect
237. C73#8711semidirect

Maximal subgroups

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

subgroupindex
#226123272
#226099082
C4×#145565032
#226077722
#226077712
#226077702
C73×#12792
#871173