Finite Group Databasebeta

← #33002887

Subgroups — #33002887

Order 18688.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D73C211yesmaximal, characteristic, complemented
2C2×#17988660C211yesmaximal, characteristic
3C2×#17988368C211yesmaximal, characteristic, complemented
4C2×#17988368C211yesmaximal, characteristic, complemented
5#22611541C211yesmaximal, characteristic, complemented
6#22608015C211yesmaximal, characteristic, complemented
7C73×#1377C211yesmaximal, characteristic, complemented
8C22×#11924011C2211yescharacteristic
9C22×C8×D73C2211yescharacteristic
10C2×C4×D292C411yescharacteristic
11C2×#14556531C2211yescharacteristic
12C2×#14556531C2211yescharacteristic
13C2×#14556530—21no—
14M32×D73—22no—
15M32×D73—22no—
16C2×C16×D73—21no—
17#17988660—21no—
18#17988660—21no—
19#17988660—21no—
20#17988660—21no—
21C2×C4⋊#10596831C411yescharacteristic
22C2×#14556503C411yescharacteristic
23C2×#14556503C411yescharacteristic
24#17988368—22no—
25#17988368—22no—
26#17988366—21no—
27#17988366—21no—
28C2×M32×C73C2211yescharacteristic
29C2×M32×C73C2211yescharacteristic
30C2×#97×C73C2211yescharacteristic
31C22×D292C811yescharacteristic
32C22×C4×D73C2×C411yescharacteristic
33C22×C4×D73C2×C411yescharacteristic
34C2×#11924011—21no—
35C2×#11924011—21no—
36C2×#11924011—21no—
37C2×#11924011—21no—
38C2×#11924011—21no—
39C2×#11924011—21no—
40C22×#10596831C2×C411yescharacteristic
41C22×#10596831C2×C411yescharacteristic
42C2×C8×D73—21no—
43C2×C8×D73—21no—
44C2×C8×D73—21no—
45C2×C8×D73—21no—
46C2×C8×D73D411yescharacteristic
47C2×C8×D73D411yescharacteristic
48C2×C8×D73D411yescharacteristic
49C2×C8×D73D411yescharacteristic
50C4×D292—21no—
51C4×D292—21no—
52C4×D292—21no—
53C4×D292—21no—
54C2×C4⋊Dic73C811yescharacteristic
55C2×#11924005C811yescharacteristic
56C2×#11924005C811yescharacteristic
57#14556531—21no—
58#14556531—21no—
59#14556531—21no—
60#14556531D412yescomplemented
61#14556530—24no—
62C2×#11924003—21no—
63C2×#11924003—21no—
64C16×D73—24no—
65C4⋊#10596831—21no—
66C4⋊#10596831—21no—
67#14556503—21no—
68#14556503—21no—
69#14556503—21no—
70#14556503—21no—
71C22×C8×C73C2×C411yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C2×C42×C73C2×C411yescharacteristic
74M32×C73—21no—
75M32×C73—21no—
76M32×C73—21no—
77M32×C73D412yescomplemented
78C2×C16×C73—21no—
79C2×C16×C73—21no—
80#97×C73—21no—
81#97×C73—21no—
82C23×D73C2×C811yescharacteristic
83C23×D73C2×C811yescharacteristic
84C2×D292—21no—
85C2×D292—21no—
86C2×D292—42no—
87C22×Dic73C2×C811yescharacteristic
88C22×Dic73C2×C811yescharacteristic
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73—21no—
92C2×C4×D73—21no—
93C2×C4×D73—21no—
94C2×C4×D73—21no—
95C2×C4×D73—21no—
96C2×C4×D73—21no—
97C2×C4×D73—21no—
98C2×C4×D73—21no—
99C2×C4×D73C22⋊C411yescharacteristic
100C2×C4×D73C22⋊C411yescharacteristic
101C2×C4×D73M1611yescharacteristic
102C2×C4×D73M1611yescharacteristic
103#11924011—41no—
104#11924011—41no—
105#11924011—41no—
106#11924011—41no—
107C2×#10596831—21no—
108C2×#10596831—21no—
109C2×#10596831—21no—
110C2×#10596831—21no—
111C2×#10596831—21no—
112C2×#10596831C22⋊C411yescharacteristic
113C2×#10596831C22⋊C411yescharacteristic
114C8×D73—21no—
115C8×D73—21no—
116C8×D73—21no—
117C8×D73—21no—
118C8×D73—21no—
119C8×D73—21no—
120C8×D73—21no—
121C8×D73—21no—
122C4⋊Dic73—21no—
123C4⋊Dic73—21no—
124#11924005—21no—
125#11924005—21no—
126#11924005—21no—
127#11924005—21no—
128#11924003—22no—
129#11924003—41no—
130C22×C4×C73C2×C811yescharacteristic
131C22×C4×C73C2×C811yescharacteristic
132C22×C4×C73C22×C411yescharacteristic
133C2×C8×C73—21no—
134C2×C8×C73—21no—
135C2×C8×C73—21no—
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73#4111yescharacteristic
141C2×C8×C73#4111yescharacteristic
142C42×C73—21no—
143C42×C73—21no—
144C16×C73—22no—
145C16×C73—41no—
146C23×C73C22×C811yescharacteristic
147C22×D73—21no—
148C22×D73—21no—
149C22×D73—22no—
150C22×D73—21no—
151C22×D73—21no—
152C22×D73—21no—
153C22×D73—41no—
154C22×D73—41no—
155C22×D73—41no—
156C22×D73C22⋊C811yescharacteristic
157C22×D73C22⋊C811yescharacteristic
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—41no—
161C2×C4×C73—41no—
162C2×C4×C73C2×C22⋊C411yescharacteristic
163C2×C4×C73C4×D411yescharacteristic
164C2×C4×C73C4×D411yescharacteristic
165C2×C4×C73C2×M1611yescharacteristic
166C2×C4×C73#13111yescharacteristic
167C2×C4×C73#13111yescharacteristic
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—21no—
171C2×Dic73—21no—
172C2×Dic73—21no—
173C2×Dic73C22⋊C811yescharacteristic
174C2×Dic73C22⋊C811yescharacteristic
175D292—42no—
176D292—42no—
177C4×D73—21no—
178C4×D73—21no—
179C4×D73—21no—
180C4×D73—21no—
181C4×D73—21no—
182C4×D73—21no—
183C4×D73—21no—
184C4×D73—21no—
185C4×D73—41no—
186C4×D73—41no—
187C4×D73—41no—
188C4×D73—41no—
189C8×C73—41no—
190C8×C73#12011yescharacteristic
191C8×C73#12111yescharacteristic
192C8×C73#12111yescharacteristic
193C8×C73#12311yescharacteristic
194#10596831—21no—
195#10596831—21no—
196#10596831—41no—
197C22×C73—21no—
198C22×C73—21no—
199C22×C73C2×C22⋊C811yescharacteristic
200C22×C73C8×D411yescharacteristic
201C22×C73C8×D411yescharacteristic
202C2×D73—21no—
203C2×D73—21no—
204C2×D73—21no—
205C2×D73—21no—
206C2×D73—21no—
207C2×D73—42no—
208C2×D73—42no—
209C2×D73—41no—
210C2×D73—41no—
211C2×D73—41no—
212C2×D73—81no—
213C2×D73—81no—
214C2×D73#34912yescomplemented
215C4×C73—41no—
216C4×C73—41no—
217C4×C73#38611yescharacteristic
218C4×C73#40811yescharacteristic
219C4×C73#43511yescharacteristic
220C4×C73#43511yescharacteristic
221Dic73—21no—
222Dic73—21no—
223Dic73—41no—
224#12985—731nomaximal, Sylow
225C2×C73—21no—
226C2×C73—21no—
227C2×C73#186911yescharacteristic
228C2×C73C2×#34911yescharacteristic
229C2×C73#211511yescharacteristic
230D73—22no—
231D73—41no—
232D73—81no—
233C22×M32—731no—
234C2×#435—731no—
235C2×#349—731no—
236C2×#349—731no—
237#2112—731no—
238#1377—731no—
239#1377D7311yescharacteristic, complemented
240C73#1298511yescharacteristic, complemented, Sylow
241C22×M16—731no—
242C23×C8—731no—
243C2×C4×D4—731no—
244C2×M32—731no—
245C2×M32—731no—
246C2×M32—1461no—
247C2×M32—1462no—
248C2×M32—1462no—
249C2×M32C2×D7311yescharacteristic
250C2×M32C2×D7311yescharacteristic
251C22×C16—1461no—
252#435—1461no—
253#435—1461no—
254#435—1461no—
255#435—1461no—
256C2×C4⋊C8—731no—
257C2×C22⋊C8—731no—
258C2×C22⋊C8—731no—
259C2×#97C2×D7311yescharacteristic
260#349—1462no—
261#349—1462no—
262C22⋊C16—1461no—
263C22⋊C16—1461no—
264C22×D4—731no—
265C23×C4—731no—
266C23×C4—731no—
267C2×M16—1461no—
268C2×M16—1461no—
269C2×M16—1461no—
270C2×M16—1461no—
271C2×M16—1461no—
272C2×M16—1461no—
273C22×C8—731no—
274C22×C8—731no—
275C22×C8—731no—
276C22×C8—731no—
277C22×C8—731no—
278C22×C8—731no—
279C22×C8—1461no—
280C22×C8—1461no—
281C22×C8—1461no—
282C22×C8—1461no—
283C22×C8C4×D7311yescharacteristic
284C22×C8C22×D7311yescharacteristic
285C4×D4—1461no—
286C4×D4—1461no—
287C4×D4—1461no—
288C4×D4—1461no—
289C2×C4⋊C4—731no—
290C2×C22⋊C4—731no—
291C2×C22⋊C4—731no—
292C2×C42C4×D7311yescharacteristic
293M32—21no—
294M32—21no—
295M32—21no—
296M32—732no—
297M32—1464no—
298M32—1461no—
299M32—1461no—
300M32—1461no—
301M32D29212yescomplemented
302C2×C16—21no—
303C2×C16—21no—
304C2×C16—1464no—
305C2×C16—1461no—
306C2×C16—1461no—
307C4⋊C8—1461no—
308C4⋊C8—1461no—
309C22⋊C8—1461no—
310C22⋊C8—1461no—
311C22⋊C8—1461no—
312C22⋊C8—1461no—
313#97—21no—
314#97—21no—
315C24—731no—
316C24—731no—
317C2×D4—2922no—
318C2×D4—1461no—
319C2×D4—1461no—
320C22×C4—731no—
321C22×C4—731no—
322C22×C4—731no—
323C22×C4—731no—
324C22×C4—731no—
325C22×C4—731no—
326C22×C4—1461no—
327C22×C4—1461no—
328C22×C4—1461no—
329C22×C4—1461no—
330C22×C4—1461no—
331C22×C4—1461no—
332C22×C4—1461no—
333C22×C4—1461no—
334C22×C4—1461no—
335C22×C4—1461no—
336C22×C4C8×D7311yescharacteristic
337C22×C4C8×D7311yescharacteristic
338C22×C4C2×C4×D7311yescharacteristic
339M16—2921no—
340M16—2921no—
341M16—2921no—
342M16—2921no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—731no—
347C2×C8—731no—
348C2×C8—1461no—
349C2×C8—1461no—
350C2×C8—1461no—
351C2×C8—1461no—
352C2×C8—1461no—
353C2×C8—1461no—
354C2×C8—1461no—
355C2×C8—1461no—
356C2×C8—1461no—
357C2×C8—1461no—
358C2×C8—1461no—
359C2×C8—1461no—
360C2×C8—1461no—
361C2×C8D4×D7311yescharacteristic
362C2×C8D4×D7311yescharacteristic
363C2×C8D4×D7311yescharacteristic
364C2×C8C2×D29211yescharacteristic
365C2×C8#1192402811yescharacteristic
366C2×C8#1192402911yescharacteristic
367C4⋊C4—1461no—
368C4⋊C4—1461no—
369C22⋊C4—1461no—
370C22⋊C4—1461no—
371C22⋊C4—1461no—
372C22⋊C4—1461no—
373C42—21no—
374C42—21no—
375C16—22no—
376C16—41no—
377C16—2921no—
378C16—1462no—
379C23—2921no—
380C23—2921no—
381C23—2921no—
382C23—731no—
383C23—731no—
384C23—1462no—
385C23—1461no—
386C23—1461no—
387C23—1461no—
388C23—1461no—
389C23—1461no—
390C23C2×C8×D7311yescharacteristic
391D4—2922no—
392D4—2922no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—2921no—
398C2×C4—2921no—
399C2×C4—2921no—
400C2×C4—2921no—
401C2×C4—731no—
402C2×C4—731no—
403C2×C4—1461no—
404C2×C4—1461no—
405C2×C4—1461no—
406C2×C4—1461no—
407C2×C4—1461no—
408C2×C4—1461no—
409C2×C4—1461no—
410C2×C4—1461no—
411C2×C4—1461no—
412C2×C4—1461no—
413C2×C4—1461no—
414C2×C4—1461no—
415C2×C4—1461no—
416C2×C4C22⋊C4×D7311yescharacteristic
417C2×C4#1455655311yescharacteristic
418C2×C4C4×D29211yescharacteristic
419C2×C4M16×D7311yescharacteristic
420C2×C4#1455659711yescharacteristic
421C2×C4#1455659911yescharacteristic
422C8—41no—
423C8—2921no—
424C8—1461no—
425C8—1461no—
426C8#1455656111yescharacteristic
427C8#1455656411yescharacteristic
428C8#1455656611yescharacteristic
429C8#1455657611yescharacteristic
430C22—21no—
431C22—21no—
432C22—2922no—
433C22—2922no—
434C22—2921no—
435C22—2921no—
436C22—2921no—
437C22—5841no—
438C22—5841no—
439C22—732no—
440C22—1461no—
441C22—1461no—
442C22—1461no—
443C22—1461no—
444C22—1461no—
445C22C22⋊C8×D7311yescharacteristic
446C22#1798865211yescharacteristic
447C22C8×D29211yescharacteristic
448C4—41no—
449C4—41no—
450C4—2921no—
451C4—1461no—
452C4—1461no—
453C4#1798846511yescharacteristic
454C4#1798855211yescharacteristic
455C4#1798865711yescharacteristic
456C4#1798866011yescharacteristic
457C2—21no—
458C2—21no—
459C2—2921no—
460C2—5841no—
461C2—1462no—
462C2#2261022211yescharacteristic
463C2#349×D7311yescharacteristic
464C2#2261155011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D73
commutatorC23×C73C22×C8
FrattiniC22×C8C22×D73
FittingC73×#1377C2
socleC22×C73C2×C22⋊C8
prime radicalC22×D292C8
cosocleC22×C8×C73C23
hypercenter#1377D73
hypocenterC73#12985
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1377

Complements

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

NH ≅ G/Ntype
1. C2×M32×D73C2semidirect
3. C2×#17988368C2semidirect
4. C2×#17988368C2semidirect
5. #22611541C2semidirect
6. #22608015C2semidirect
7. C73×#1377C2semidirect
60. #14556531D4semidirect
77. M32×C73D4semidirect
214. C2×D73#349semidirect
239. #1377D73semidirect
240. C73#12985semidirect
301. M32D292semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D732
C2×#179886602
C2×#179883682
#226115412
#226080152
C73×#13772
#1298573