Finite Group Databasebeta

← #32979347

Subgroups — #32979347

Order 18688.

540 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612335C211yesmaximal, characteristic
2#22609908C211yesmaximal, characteristic
3C4×#14556503C211yesmaximal, characteristic
4#22607772C211yesmaximal, characteristic, complemented
5#22607771C211yesmaximal, characteristic, complemented
6#22607770C211yesmaximal, characteristic, complemented
7C73×#1279C211yesmaximal, characteristic, complemented
8C2×#14556548—21no—
9C2×C42×D73C2211yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556503—21no—
12C2×#14556503—21no—
13C2×C4×#10596831C2211yescharacteristic
14#17988456C411yescharacteristic
15#17988456C411yescharacteristic
16#17988451—21no—
17#17988446—21no—
18#17988444C411yescharacteristic
19#17988444C411yescharacteristic
20C4×#11924007—21no—
21C4×C4⋊Dic73C2211yescharacteristic
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—
32#14556548—42no—
33#14556548—42no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×#11924007—21no—
39C2×#11924007—21no—
40C2×#11924005—21no—
41C2×#11924005—21no—
42C2×C4×Dic73—21no—
43C2×C4×Dic73C2×C411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73D411yescharacteristic
46C42×D73—21no—
47C42×D73—21no—
48C42×D73—21no—
49C42×D73—21no—
50C4⋊#10596831—21no—
51C4⋊#10596831—21no—
52#14556503—24no—
53#14556503—42no—
54C4×#10596831—21no—
55C4×#10596831—21no—
56#14556498—21no—
57#14556498—21no—
58#14556498—21no—
59C22×C8×C73—21no—
60C22×C8×C73—21no—
61C2×C4⋊C4×C73C2×C411yescharacteristic
62C2×C4⋊C4×C73C2×C411yescharacteristic
63C2×C42×C73—21no—
64C2×C42×C73C2311yescharacteristic
65C4⋊C8×C73—21no—
66C4⋊C8×C73—21no—
67C4×C8×C73—21no—
68C4×C8×C73—21no—
69#95×C73—21no—
70C23×D73C22⋊C411yescharacteristic
71C22×Dic73—21no—
72C22×Dic73—21no—
73C22×Dic73C22⋊C411yescharacteristic
74C22×Dic73C22⋊C411yescharacteristic
75C22×Dic73C22⋊C411yescharacteristic
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—22no—
89C2×C4×D73—41no—
90C2×C4×D73SD1612yes—
91C2×C4×D73Q1612yes—
92C2×#10596831—22no—
93C2×#10596831—41no—
94C2×#10596831—41no—
95C2×#10596831—41no—
96C2×#10596831—41no—
97C2×#10596831—41no—
98C4⋊Dic73—21no—
99C4⋊Dic73—21no—
100C4⋊Dic73—21no—
101C4⋊Dic73—21no—
102#11924007—42no—
103#11924007—42no—
104#11924007—42no—
105#11924007—42no—
106#11924005—42no—
107#11924005—42no—
108C4×Dic73—21no—
109C4×Dic73—21no—
110C4×Dic73—21no—
111C4×Dic73—21no—
112C4×Dic73—21no—
113C4×Dic73—21no—
114C4×Dic73—41no—
115C4×Dic73—41no—
116C22×C4×C73—21no—
117C22×C4×C73—21no—
118C22×C4×C73C22×C411yescharacteristic
119C22×C4×C73C2×D411yescharacteristic
120C22×C4×C73C2×D411yescharacteristic
121C2×C8×C73—22no—
122C2×C8×C73—41no—
123C2×C8×C73—41no—
124C2×C8×C73—41no—
125C2×C8×C73—41no—
126C2×C8×C73—41no—
127C4⋊C4×C73—21no—
128C4⋊C4×C73—21no—
129C4⋊C4×C73—21no—
130C4⋊C4×C73—21no—
131C42×C73—41no—
132C42×C73—41no—
133C42×C73#4111yescharacteristic
134C42×C73#4111yescharacteristic
135C42×C73#4111yescharacteristic
136C42×C73#4111yescharacteristic
137C23×C73C2×C22⋊C411yescharacteristic
138C22×D73—21no—
139C22×D73—21no—
140C22×D73—21no—
141C22×D73—21no—
142C22×D73—21no—
143C22×D73—21no—
144C22×D73#10312yes—
145C2×C4×C73—21no—
146C2×C4×C73—21no—
147C2×C4×C73—41no—
148C2×C4×C73—41no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73—41no—
152C2×C4×C73—41no—
153C2×C4×C73#11711yescharacteristic
154C2×C4×C73#11711yescharacteristic
155C2×C4×C73#12311yescharacteristic
156C2×C4×C73#12311yescharacteristic
157C2×C4×C73#12311yescharacteristic
158C2×C4×C73#12311yescharacteristic
159C2×C4×C73#13111yescharacteristic
160C2×C4×C73#13111yescharacteristic
161C2×C4×C73#13111yescharacteristic
162C2×C4×C73#13111yescharacteristic
163C2×C4×C73C2×SD1611yescharacteristic
164C2×C4×C73C2×Q1611yescharacteristic
165C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73—21no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C2×Dic73—41no—
177C2×Dic73—41no—
178C2×Dic73—41no—
179C2×Dic73—41no—
180C2×Dic73#10312yes—
181C2×Dic73#10412yes—
182C4×D73—22no—
183C4×D73—22no—
184C4×D73—22no—
185C4×D73—22no—
186C4×D73—42no—
187C4×D73—42no—
188C4×D73—41no—
189C4×D73—41no—
190C4×D73—41no—
191C4×D73—41no—
192C8×C73—42no—
193C8×C73—81no—
194#10596831—42no—
195#10596831—81no—
196C22×C73#38111yescharacteristic
197C22×C73#40811yescharacteristic
198C22×C73#40811yescharacteristic
199C22×C73C2×#10311yescharacteristic
200C22×C73#41811yescharacteristic
201C22×C73C2×#10411yescharacteristic
202C22×C73#42111yescharacteristic
203C2×D73—22no—
204C2×D73—22no—
205C2×D73—22no—
206C2×D73—41no—
207C2×D73—41no—
208C2×D73—41no—
209C2×D73—41no—
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—81no—
213C4×C73—81no—
214C4×C73#43311yescharacteristic
215C4×C73#43311yescharacteristic
216C4×C73#43311yescharacteristic
217C4×C73#43311yescharacteristic
218C4×C73#48111yescharacteristic
219C4×C73#48111yescharacteristic
220C4×C73#48411yescharacteristic
221C4×C73#48411yescharacteristic
222Dic73—22no—
223Dic73—22no—
224Dic73—41no—
225Dic73—81no—
226Dic73—81no—
227#8710—731nomaximal, Sylow
228C2×C73#148111yescharacteristic
229C2×C73#148411yescharacteristic
230C2×C73#149311yescharacteristic
231C2×C73#149611yescharacteristic
232C2×C73#181811yescharacteristic
233C2×C73#182411yescharacteristic
234C2×C73#182611yescharacteristic
235D73—42no—
236#2285—731no—
237#1797—731no—
238C4×C22⋊C8—731no—
239#1279—731no—
240#1279—731no—
241#1279—731no—
242#1279D7311yescharacteristic, complemented
243C73#871011yescharacteristic, complemented, Sylow
244C2×#117—1461no—
245C22×C42—731no—
246C2×C4⋊C8—731no—
247C2×C4⋊C8C2×D7311yescharacteristic
248C2×C22⋊C8—1461no—
249C2×C22⋊C8—1461no—
250C2×C4×C8—731no—
251C2×C4×C8C2×D7311yescharacteristic
252#384—731no—
253#384—731no—
254#382—1461no—
255#380—731no—
256#380—731no—
257#380—1461no—
258C4×C4⋊C4—731no—
259C4×C4⋊C4—1461no—
260C4×C4⋊C4C2×D7311yescharacteristic
261#336—1461no—
262#336—1461no—
263C23×C4—731no—
264C23×C4—731no—
265C23×C4—731no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—1461no—
269C22×C8—1461no—
270#117—2922no—
271#117—2922no—
272C2×C4⋊C4—731no—
273C2×C4⋊C4—731no—
274C2×C4⋊C4—1461no—
275C2×C4⋊C4—1461no—
276C2×C4⋊C4—1461no—
277C2×C4⋊C4—1461no—
278C2×C4⋊C4C4×D7311yescharacteristic
279C2×C4⋊C4C4×D7311yescharacteristic
280C2×C22⋊C4—1461no—
281C2×C22⋊C4—1461no—
282C2×C42—21no—
283C2×C42—731no—
284C2×C42—731no—
285C2×C42—731no—
286C2×C42—1461no—
287C2×C42—1461no—
288C2×C42—1461no—
289C2×C42—1461no—
290C2×C42—1461no—
291C2×C42C22×D7311yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1461no—
295C4⋊C8—1461no—
296C22⋊C8—2922no—
297C22⋊C8—1464no—
298C4×C8—21no—
299C4×C8—21no—
300C4×C8—1461no—
301C4×C8—1461no—
302#95—21no—
303#95—1461no—
304#95—1461no—
305#95—1461no—
306C24—731no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—2921no—
310C22×C4—731no—
311C22×C4—731no—
312C22×C4—732no—
313C22×C4—732no—
314C22×C4—731no—
315C22×C4—1462no—
316C22×C4—1461no—
317C22×C4—1461no—
318C22×C4—1461no—
319C22×C4—1461no—
320C22×C4—1461no—
321C22×C4—1461no—
322C22×C4—1461no—
323C22×C4—1461no—
324C22×C4—1461no—
325C22×C4—1461no—
326C22×C4—1461no—
327C22×C4—1461no—
328C22×C4—1461no—
329C22×C4—1461no—
330C22×C4C2×C4×D7311yescharacteristic
331C22×C4D4×D7311yescharacteristic
332C22×C4D4×D7311yescharacteristic
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—2921no—
340C2×C8—2921no—
341C2×C8—2921no—
342C2×C8—2921no—
343C2×C8—2921no—
344C2×C8—1462no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—2922no—
350C4⋊C4—2922no—
351C4⋊C4—2922no—
352C4⋊C4—2922no—
353C4⋊C4—1461no—
354C4⋊C4—1461no—
355C4⋊C4—1461no—
356C4⋊C4—1461no—
357C22⋊C4—2922no—
358C22⋊C4—2922no—
359C42—41no—
360C42—41no—
361C42—2921no—
362C42—2921no—
363C42—1461no—
364C42—1461no—
365C42—1461no—
366C42—1461no—
367C42—1461no—
368C42—1461no—
369C42#1192402711yescharacteristic
370C42#1192402811yescharacteristic
371C42#1192402811yescharacteristic
372C42#1192402911yescharacteristic
373C23—732no—
374C23—1461no—
375C23—1461no—
376C23—1461no—
377C23—1461no—
378C23—1461no—
379C23—1461no—
380C23C22⋊C4×D7311yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—2922no—
390C2×C4—2922no—
391C2×C4—2921no—
392C2×C4—2921no—
393C2×C4—2921no—
394C2×C4—2921no—
395C2×C4—2921no—
396C2×C4—2921no—
397C2×C4—2921no—
398C2×C4—2921no—
399C2×C4—2921no—
400C2×C4—2921no—
401C2×C4—732no—
402C2×C4—732no—
403C2×C4—1461no—
404C2×C4—1461no—
405C2×C4—1461no—
406C2×C4—1461no—
407C2×C4—1461no—
408C2×C4—1461no—
409C2×C4—1461no—
410C2×C4—1462no—
411C2×C4—1462no—
412C2×C4—1462no—
413C2×C4—1462no—
414C2×C4#1455654811yescharacteristic
415C2×C4#1455654911yescharacteristic
416C2×C4#1455657311yescharacteristic
417C2×C4#1455657311yescharacteristic
418C2×C4#1455657611yescharacteristic
419C2×C4#1455657611yescharacteristic
420C2×C4#1455659711yescharacteristic
421C2×C4#1455659711yescharacteristic
422C2×C4#1455659911yescharacteristic
423C2×C4#1455659911yescharacteristic
424C2×C4SD16×D7311yescharacteristic
425C2×C4Q16×D7311yescharacteristic
426C2×C4#1455661511yescharacteristic
427C2×C4#1455661811yescharacteristic
428C8—42no—
429C8—81no—
430C8—2922no—
431C8—5841no—
432C22—2921no—
433C22—2921no—
434C22—2921no—
435C22—2921no—
436C22—1462no—
437C22—1462no—
438C22—1462no—
439C22#1798844911yescharacteristic
440C22#1798855211yescharacteristic
441C22#1798855211yescharacteristic
442C22#103×D7311yescharacteristic
443C22#1798859011yescharacteristic
444C22#104×D7311yescharacteristic
445C22#1798860211yescharacteristic
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—2921no—
451C4—5841no—
452C4—5841no—
453C4—1462no—
454C4—1462no—
455C4#1798864611yescharacteristic
456C4#1798864711yescharacteristic
457C4#1798864711yescharacteristic
458C4#1798864911yescharacteristic
459C4#1798890411yescharacteristic
460C4#1798890711yescharacteristic
461C4#1798892111yescharacteristic
462C4#1798892411yescharacteristic
463C2—2922no—
464C2#2260833211yescharacteristic
465C2#2260834611yescharacteristic
466C2#2260838411yescharacteristic
467C2#2260839811yescharacteristic
468C2#2261000111yescharacteristic
469C2#2261002011yescharacteristic
470C2#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#8710
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
242. #1279D73semidirect
243. C73#8710semidirect

Maximal subgroups

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

subgroupindex
#226123352
#226099082
C4×#145565032
#226077722
#226077712
#226077702
C73×#12792
#871073