Finite Group Databasebeta

← C73×#33944 #32943348

Subgroups — C73×#33944 #32943348

Order 18688.

468 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3393C211yesmaximal, characteristic
2C73×#3383C211yesmaximal, characteristic, complemented
3C73×#2245C211yesmaximal, characteristic, complemented
4C73×#2243C211yesmaximal, characteristic
5C73×#2242C211yesmaximal, characteristic
6C73×#2229C211yesmaximal, characteristic, complemented
7C73×#2228C211yesmaximal, characteristic
8C73×#2227C211yesmaximal, characteristic, complemented
9C73×#2211C211yesmaximal, characteristic
10C73×#2211C211yesmaximal, characteristic
11C73×#2209C211yesmaximal, characteristic, complemented
12C73×#2183C211yesmaximal, characteristic, complemented
13C73×#2176C211yesmaximal, characteristic, complemented
14C73×#2175C211yesmaximal, characteristic
15C4×Q32×C73C211yesmaximal, characteristic, complemented
16#557×C73—21no—
17#556×C73—21no—
18C2×Q32×C73C2211yescharacteristic
19C2×Q32×C73C2211yescharacteristic
20C2×SD32×C73C2211yescharacteristic
21#500×C73C2211yescharacteristic
22#499×C73C2211yescharacteristic
23#499×C73C2211yescharacteristic
24#495×C73C2211yescharacteristic
25#495×C73C2211yescharacteristic
26#494×C73C2211yescharacteristic
27#479×C73—21no—
28#479×C73—21no—
29#475×C73—21no—
30#464×C73—21no—
31#464×C73—21no—
32#461×C73—21no—
33C8×Q8×C73C2211yescharacteristic
34C4×Q16×C73C2211yescharacteristic
35C4×Q16×C73C2211yescharacteristic
36C4×Q16×C73C2211yescharacteristic
37C4×Q16×C73C2211yescharacteristic
38C4×Q16×C73C2211yescharacteristic
39C4×D8×C73C2211yescharacteristic
40#367×C73C2211yescharacteristic
41#366×C73C2211yescharacteristic
42#366×C73C2211yescharacteristic
43C4⋊C16×C73C2211yescharacteristic
44C4⋊C16×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic
46#358×C73C2211yescharacteristic
47#358×C73C2211yescharacteristic
48#358×C73C2211yescharacteristic
49#358×C73C2211yescharacteristic
50#358×C73C2211yescharacteristic
51#358×C73C2211yescharacteristic
52#358×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55#357×C73C2211yescharacteristic
56#346×C73C2211yescharacteristic
57#346×C73C2211yescharacteristic
58C4×C16×C73C2211yescharacteristic
59C2×Q16×C73—21no—
60C2×Q16×C73C2311yescharacteristic
61C2×Q16×C73C2311yescharacteristic
62C2×Q16×C73C2311yescharacteristic
63C2×SD16×C73—21no—
64C2×SD16×C73—21no—
65C2×D8×C73C2311yescharacteristic
66C4⋊Q8×C73—21no—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73—41no—
69#126×C73—41no—
70#126×C73—41no—
71#125×C73—21no—
72#125×C73—21no—
73#125×C73—41no—
74#125×C73—41no—
75#124×C73—21no—
76#124×C73—21no—
77C22⋊Q8×C73—41no—
78C4×Q8×C73—21no—
79C4×Q8×C73—21no—
80C4×Q8×C73—21no—
81C4×Q8×C73—21no—
82C4×Q8×C73—21no—
83C4×Q8×C73—41no—
84C4×Q8×C73D411yescharacteristic
85C4×D4×C73—21no—
86#117×C73—41no—
87Q32×C73—22no—
88Q32×C73—22no—
89SD32×C73—22no—
90C2×C16×C73C2311yescharacteristic
91C2×C16×C73C2311yescharacteristic
92C2×C16×C73C2311yescharacteristic
93C2×C16×C73C2311yescharacteristic
94#107×C73—21no—
95#107×C73C2311yescharacteristic
96#107×C73C2311yescharacteristic
97#107×C73C2311yescharacteristic
98#107×C73C2311yescharacteristic
99#106×C73—21no—
100#106×C73—21no—
101C4⋊C8×C73D411yescharacteristic
102C4⋊C8×C73D411yescharacteristic
103C4⋊C8×C73D411yescharacteristic
104#103×C73—21no—
105#103×C73—21no—
106#103×C73—21no—
107#103×C73—21no—
108#103×C73—21no—
109#102×C73—21no—
110C4×C8×C73C2311yescharacteristic
111C4×C8×C73C2311yescharacteristic
112C4×C8×C73C2311yescharacteristic
113C2×Q8×C73—21no—
114C2×Q8×C73—21no—
115C2×Q8×C73—21no—
116C2×Q8×C73—41no—
117C2×Q8×C73D811yescharacteristic
118C2×D4×C73—21no—
119C22×C4×C73—41no—
120Q16×C73—21no—
121Q16×C73—21no—
122Q16×C73—21no—
123Q16×C73—21no—
124Q16×C73—21no—
125Q16×C73—81no—
126Q16×C73#4112yes—
127SD16×C73—81no—
128SD16×C73—81no—
129D8×C73—21no—
130D8×C73—21no—
131C2×C8×C73C2×D411yescharacteristic
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2411yescharacteristic
135C4⋊C4×C73—21no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—21no—
138C4⋊C4×C73—21no—
139C4⋊C4×C73—41no—
140C4⋊C4×C73—41no—
141C4⋊C4×C73—41no—
142C4⋊C4×C73—41no—
143C4⋊C4×C73—41no—
144C4⋊C4×C73—41no—
145C4⋊C4×C73—41no—
146C4⋊C4×C73—41no—
147C4⋊C4×C73—41no—
148C4⋊C4×C73—41no—
149C4⋊C4×C73—41no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73D811yescharacteristic
152C4⋊C4×C73D811yescharacteristic
153C4⋊C4×C73D811yescharacteristic
154C22⋊C4×C73—41no—
155C22⋊C4×C73—41no—
156C22⋊C4×C73—41no—
157C22⋊C4×C73—41no—
158C22⋊C4×C73—41no—
159C42×C73—41no—
160C42×C73—41no—
161C42×C73—41no—
162C42×C73—41no—
163C42×C73—41no—
164C42×C73C2×D411yescharacteristic
165C42×C73C2×D411yescharacteristic
166C42×C73C2×D411yescharacteristic
167C16×C73—21no—
168C16×C73—21no—
169C16×C73—21no—
170C16×C73—21no—
171C23×C73—41no—
172Q8×C73—22no—
173Q8×C73—41no—
174Q8×C73—41no—
175Q8×C73—41no—
176Q8×C73—41no—
177Q8×C73—41no—
178Q8×C73—41no—
179Q8×C73—82no—
180D4×C73—41no—
181D4×C73—41no—
182C2×C4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—41no—
185C2×C4×C73—41no—
186C2×C4×C73—41no—
187C2×C4×C73—41no—
188C2×C4×C73—41no—
189C2×C4×C73—82no—
190C2×C4×C73C2×D811yescharacteristic
191C2×C4×C73C2×D811yescharacteristic
192C2×C4×C73C2×D811yescharacteristic
193C2×C4×C73C2×D811yescharacteristic
194C2×C4×C73C2×D811yescharacteristic
195C2×C4×C73C2×D811yescharacteristic
196C2×C4×C73C22×D411yescharacteristic
197C8×C73—21no—
198C8×C73—21no—
199C8×C73—21no—
200C8×C73C2×#4111yescharacteristic
201C8×C732−1+411yescharacteristic
202C22×C73—81no—
203C22×C73—81no—
204C22×C73—81no—
205C22×C73C22×D811yescharacteristic
206C4×C73—21no—
207C4×C73—21no—
208C4×C73—21no—
209C4×C73—21no—
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—42no—
213C4×C73—81no—
214C4×C73—81no—
215C4×C73—81no—
216C4×C73—81no—
217C4×C73—81no—
218C4×C73—81no—
219C4×C73#54811yescharacteristic
220C4×C73#57711yescharacteristic
221#33944C7311yesmaximal, characteristic, direct product factor, Sylow
222C2×C73—161no—
223C2×C73#335811yescharacteristic
224C2×C73#341411yescharacteristic
225C2×C73#341711yescharacteristic
226#3393C2×C7311yescharacteristic
227#3383C2×C7311yescharacteristic, complemented
228#2245C2×C7311yescharacteristic, complemented
229#2243C2×C7311yescharacteristic
230#2242C2×C7311yescharacteristic
231#2229C2×C7311yescharacteristic, complemented
232#2228C2×C7311yescharacteristic
233#2227C2×C7311yescharacteristic, complemented
234#2211C2×C7311yescharacteristic
235#2211C2×C7311yescharacteristic
236#2209C2×C7311yescharacteristic, complemented
237#2183C2×C7311yescharacteristic, complemented
238#2176C2×C7311yescharacteristic, complemented
239#2175C2×C7311yescharacteristic
240C4×Q32C2×C7311yescharacteristic, complemented
241C73#3394411yescharacteristic, direct product factor, Sylow
242#557—21no—
243#556—21no—
244C2×Q32C22×C7311yescharacteristic
245C2×Q32C22×C7311yescharacteristic
246C2×SD32C22×C7311yescharacteristic
247#500C22×C7311yescharacteristic
248#499C22×C7311yescharacteristic
249#499C22×C7311yescharacteristic
250#495C22×C7311yescharacteristic
251#495C22×C7311yescharacteristic
252#494C22×C7311yescharacteristic
253#479—21no—
254#479—21no—
255#475—21no—
256#464—21no—
257#464—21no—
258#461—21no—
259C8×Q8C22×C7311yescharacteristic
260C4×Q16C22×C7311yescharacteristic
261C4×Q16C22×C7311yescharacteristic
262C4×Q16C22×C7311yescharacteristic
263C4×Q16C22×C7311yescharacteristic
264C4×Q16C22×C7311yescharacteristic
265C4×D8C22×C7311yescharacteristic
266#367C22×C7311yescharacteristic
267#366C22×C7311yescharacteristic
268#366C22×C7311yescharacteristic
269C4⋊C16C22×C7311yescharacteristic
270C4⋊C16C22×C7311yescharacteristic
271C4⋊C16C22×C7311yescharacteristic
272#358C22×C7311yescharacteristic
273#358C22×C7311yescharacteristic
274#358C22×C7311yescharacteristic
275#358C22×C7311yescharacteristic
276#358C22×C7311yescharacteristic
277#358C22×C7311yescharacteristic
278#358C22×C7311yescharacteristic
279#357C22×C7311yescharacteristic
280#357C22×C7311yescharacteristic
281#357C22×C7311yescharacteristic
282#346C22×C7311yescharacteristic
283#346C22×C7311yescharacteristic
284C4×C16C22×C7311yescharacteristic
285C2×Q16—21no—
286C2×Q16C23×C7311yescharacteristic
287C2×Q16C23×C7311yescharacteristic
288C2×Q16C23×C7311yescharacteristic
289C2×SD16—21no—
290C2×SD16—21no—
291C2×D8C23×C7311yescharacteristic
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—41no—
295#126—41no—
296#126—41no—
297#125—21no—
298#125—21no—
299#125—41no—
300#125—41no—
301#124—21no—
302#124—21no—
303C22⋊Q8—41no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—41no—
310C4×Q8D4×C7311yescharacteristic
311C4×D4—21no—
312#117—41no—
313Q32—22no—
314Q32—22no—
315SD32—22no—
316C2×C16C23×C7311yescharacteristic
317C2×C16C23×C7311yescharacteristic
318C2×C16C23×C7311yescharacteristic
319C2×C16C23×C7311yescharacteristic
320#107—21no—
321#107C23×C7311yescharacteristic
322#107C23×C7311yescharacteristic
323#107C23×C7311yescharacteristic
324#107C23×C7311yescharacteristic
325#106—21no—
326#106—21no—
327C4⋊C8D4×C7311yescharacteristic
328C4⋊C8D4×C7311yescharacteristic
329C4⋊C8D4×C7311yescharacteristic
330#103—21no—
331#103—21no—
332#103—21no—
333#103—21no—
334#103—21no—
335#102—21no—
336C4×C8C23×C7311yescharacteristic
337C4×C8C23×C7311yescharacteristic
338C4×C8C23×C7311yescharacteristic
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8D8×C7311yescharacteristic
344C2×D4—21no—
345C22×C4—41no—
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350Q16—21no—
351Q16—81no—
352Q16#41×C7312yes—
353SD16—81no—
354SD16—81no—
355D8—21no—
356D8—21no—
357C2×C8C2×D4×C7311yescharacteristic
358C2×C8C2×D4×C7311yescharacteristic
359C2×C8C2×D4×C7311yescharacteristic
360C2×C8C24×C7311yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4D8×C7311yescharacteristic
378C4⋊C4D8×C7311yescharacteristic
379C4⋊C4D8×C7311yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42—41no—
390C42C2×D4×C7311yescharacteristic
391C42C2×D4×C7311yescharacteristic
392C42C2×D4×C7311yescharacteristic
393C16—21no—
394C16—21no—
395C16—21no—
396C16—21no—
397C23—41no—
398Q8—22no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—41no—
403Q8—41no—
404Q8—41no—
405Q8—82no—
406D4—41no—
407D4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—82no—
416C2×C4C2×D8×C7311yescharacteristic
417C2×C4C2×D8×C7311yescharacteristic
418C2×C4C2×D8×C7311yescharacteristic
419C2×C4C2×D8×C7311yescharacteristic
420C2×C4C2×D8×C7311yescharacteristic
421C2×C4C2×D8×C7311yescharacteristic
422C2×C4C22×D4×C7311yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8C2×#41×C7311yescharacteristic
427C82−1+4×C7311yescharacteristic
428C22—81no—
429C22—81no—
430C22—81no—
431C22C22×D8×C7311yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4#548×C7311yescharacteristic
446C4#577×C7311yescharacteristic
447C2—161no—
448C2C73×#335811yescharacteristic
449C2C73×#341411yescharacteristic
450C2C73×#341711yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC2×D8×C73C23
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C4×Q8×C73 ◁ C8×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3383C2semidirect
3. C73×#2245C2semidirect
6. C73×#2229C2semidirect
8. C73×#2227C2semidirect
11. C73×#2209C2semidirect
12. C73×#2183C2semidirect
13. C73×#2176C2semidirect
15. C4×Q32×C73C2semidirect
221. #33944C73direct (N × H)
227. #3383C2×C73semidirect
228. #2245C2×C73semidirect
231. #2229C2×C73semidirect
233. #2227C2×C73semidirect
236. #2209C2×C73semidirect
237. #2183C2×C73semidirect
238. #2176C2×C73semidirect
240. C4×Q32C2×C73semidirect
241. C73#33944direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33932
C73×#33832
C73×#22452
C73×#22432
C73×#22422
C73×#22292
C73×#22282
C73×#22272
C73×#22112
C73×#22092
C73×#21832
C73×#21762
C73×#21752
C4×Q32×C732
#3394473