Finite Group Databasebeta

← C73×#8971 #32918375

Subgroups — C73×#8971 #32918375

Order 18688.

478 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3107C211yesmaximal, characteristic
2C73×#2990C211yesmaximal, characteristic
3C73×#1994C211yesmaximal, characteristic, complemented
4C4×#104×C73C211yesmaximal, characteristic
5C73×#1485C211yesmaximal, characteristic, complemented
6C73×#1299C211yesmaximal, characteristic, complemented
7C73×#1276C211yesmaximal, characteristic, complemented
8#533×C73C2211yescharacteristic
9C4×#41×C73C2211yescharacteristic
10#485×C73—21no—
11#475×C73C411yescharacteristic, complemented
12#474×C73C411yescharacteristic, complemented
13#462×C73C411yescharacteristic, complemented
14#461×C73C411yescharacteristic, complemented
15#452×C73—21no—
16#446×C73—21no—
17C4×Q16×C73—21no—
18C4×SD16×C73—21no—
19#435×C73—22no—
20C8×D4×C73—21no—
21#432×C73—21no—
22#431×C73C2211yescharacteristic
23#431×C73C2211yescharacteristic
24#423×C73C2211yescharacteristic
25C2×C4⋊C8×C73—21no—
26C2×#104×C73—21no—
27C4×M16×C73C2211yescharacteristic
28C43×C73C2211yescharacteristic
29#339×C73—22no—
30#339×C73—21no—
31Q8⋊C8×C73—21no—
32Q8⋊C8×C73—21no—
33C2×#41×C73D411yescharacteristic
34C2×Q16×C73—21no—
35C2×SD16×C73—21no—
36C2×M16×C73—21no—
37C2×M16×C73D412yes—
38C22×C8×C73—22no—
39C4⋊Q8×C73C2×C411yescharacteristic
40C4⋊Q8×C73C2×C411yescharacteristic
41#125×C73—21no—
42C22⋊Q8×C73—21no—
43C22⋊Q8×C73—21no—
44C4×Q8×C73—21no—
45C4×Q8×C73—21no—
46C4×Q8×C73C2×C411yescharacteristic
47C4×Q8×C73D411yescharacteristic
48C4×D4×C73—21no—
49C4×D4×C73—21no—
50C4×D4×C73C2×C411yescharacteristic
51C4×D4×C73D411yescharacteristic
52#117×C73—21no—
53#117×C73—21no—
54#117×C73D411yescharacteristic
55C2×C42×C73—21no—
56C2×C42×C73—21no—
57C2×C42×C73—21no—
58C2×C42×C73—21no—
59C2×C42×C73C2311yescharacteristic
60#107×C73—21no—
61#106×C73—21no—
62C4⋊C8×C73—22no—
63C4⋊C8×C73—21no—
64C4⋊C8×C73—21no—
65C4⋊C8×C73C2×C411yescharacteristic
66C4⋊C8×C73C2×C411yescharacteristic
67C4⋊C8×C73D411yescharacteristic
68C4⋊C8×C73D411yescharacteristic
69#104×C73—24no—
70#103×C73—21no—
71#103×C73—21no—
72#103×C73—21no—
73#102×C73—21no—
74C22⋊C8×C73—22no—
75C22⋊C8×C73—21no—
76C22⋊C8×C73—21no—
77#97×C73—22no—
78#97×C73—21no—
79C4×C8×C73—21no—
80C4×C8×C73—21no—
81C4×C8×C73—21no—
82#41×C73—22no—
83#41×C73—41no—
84C2×Q8×C73—21no—
85C2×Q8×C73—21no—
86C2×Q8×C73C22⋊C411yescharacteristic
87C2×D4×C73—21no—
88C2×D4×C73C22⋊C411yescharacteristic
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—41no—
93C22×C4×C73C2×D411yescharacteristic
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73#4111yescharacteristic
96Q16×C73—42no—
97SD16×C73—42no—
98M16×C73—22no—
99M16×C73—41no—
100M16×C73—42no—
101C2×C8×C73—21no—
102C2×C8×C73—21no—
103C2×C8×C73—21no—
104C2×C8×C73—21no—
105C2×C8×C73—22no—
106C2×C8×C73—41no—
107C2×C8×C73—82no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—21no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73—21no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—41no—
116C4⋊C4×C73C22⋊C411yescharacteristic
117C4⋊C4×C73C22⋊C411yescharacteristic
118C22⋊C4×C73—21no—
119C22⋊C4×C73—21no—
120C22⋊C4×C73—21no—
121C22⋊C4×C73—41no—
122C42×C73—21no—
123C42×C73—21no—
124C42×C73—21no—
125C42×C73—22no—
126C42×C73—22no—
127C42×C73—22no—
128C42×C73—41no—
129C42×C73—41no—
130C42×C73—41no—
131C42×C73—41no—
132C42×C73C22×C411yescharacteristic
133C42×C73C2×D411yescharacteristic
134C42×C73C2×D411yescharacteristic
135C42×C73#4111yescharacteristic
136C23×C73—21no—
137C23×C73#12111yescharacteristic
138Q8×C73—21no—
139Q8×C73—21no—
140Q8×C73—41no—
141Q8×C73—41no—
142Q8×C73—41no—
143Q8×C73—41no—
144D4×C73—21no—
145D4×C73—42no—
146D4×C73#10412yes—
147C2×C4×C73—21no—
148C2×C4×C73—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—21no—
155C2×C4×C73—21no—
156C2×C4×C73—42no—
157C2×C4×C73—42no—
158C2×C4×C73—42no—
159C2×C4×C73—42no—
160C2×C4×C73—41no—
161C2×C4×C73—41no—
162C2×C4×C73—41no—
163C2×C4×C73—41no—
164C2×C4×C73—41no—
165C2×C4×C73—41no—
166C2×C4×C73C2×C22⋊C411yescharacteristic
167C2×C4×C73C4×D411yescharacteristic
168C2×C4×C73C4×D411yescharacteristic
169C2×C4×C73#12011yescharacteristic
170C2×C4×C73#12111yescharacteristic
171C2×C4×C73#12311yescharacteristic
172C8×C73—42no—
173C8×C73—41no—
174C8×C73—41no—
175C8×C73—41no—
176C8×C73—42no—
177C8×C73—41no—
178C22×C73—21no—
179C22×C73—22no—
180C22×C73—21no—
181C22×C73—21no—
182C22×C73—41no—
183C22×C73—41no—
184C22×C73#38611yescharacteristic
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—44no—
189C4×C73—41no—
190C4×C73—41no—
191C4×C73—41no—
192C4×C73—81no—
193C4×C73—81no—
194C4×C73C2×#10411yescharacteristic
195C4×C73#42111yescharacteristic
196C4×C73#44311yescharacteristic
197C4×C73#44411yescharacteristic
198C4×C73#45511yescharacteristic
199C4×C73#45611yescharacteristic
200#8971C7311yesmaximal, characteristic, direct product factor, Sylow
201C2×C73—41no—
202C2×C73—42no—
203C2×C73#187111yescharacteristic
204C2×C73#187611yescharacteristic
205C2×C73#188211yescharacteristic
206#3107C2×C7311yescharacteristic
207#2990C2×C7311yescharacteristic
208#1994C2×C7311yescharacteristic, complemented
209C4×#104C2×C7311yescharacteristic
210#1485C2×C7311yescharacteristic, complemented
211#1299C2×C7311yescharacteristic, complemented
212#1276C2×C7311yescharacteristic, complemented
213C73#897111yescharacteristic, direct product factor, Sylow
214#533C22×C7311yescharacteristic
215C4×#41C22×C7311yescharacteristic
216#485—21no—
217#475C4×C7311yescharacteristic, complemented
218#474C4×C7311yescharacteristic, complemented
219#462C4×C7311yescharacteristic, complemented
220#461C4×C7311yescharacteristic, complemented
221#452—21no—
222#446—21no—
223C4×Q16—21no—
224C4×SD16—21no—
225#435—22no—
226C8×D4—21no—
227#432—21no—
228#431C22×C7311yescharacteristic
229#431C22×C7311yescharacteristic
230#423C22×C7311yescharacteristic
231C2×C4⋊C8—21no—
232C2×#104—21no—
233C4×M16C22×C7311yescharacteristic
234C43C22×C7311yescharacteristic
235#339—22no—
236#339—21no—
237Q8⋊C8—21no—
238Q8⋊C8—21no—
239C2×#41D4×C7311yescharacteristic
240C2×Q16—21no—
241C2×SD16—21no—
242C2×M16—21no—
243C2×M16D4×C7312yes—
244C22×C8—22no—
245C4⋊Q8C2×C4×C7311yescharacteristic
246C4⋊Q8C2×C4×C7311yescharacteristic
247#125—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8C2×C4×C7311yescharacteristic
253C4×Q8D4×C7311yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C2×C4×C7311yescharacteristic
257C4×D4D4×C7311yescharacteristic
258#117—21no—
259#117—21no—
260#117D4×C7311yescharacteristic
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42C23×C7311yescharacteristic
266#107—21no—
267#106—21no—
268C4⋊C8—22no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8C2×C4×C7311yescharacteristic
272C4⋊C8C2×C4×C7311yescharacteristic
273C4⋊C8D4×C7311yescharacteristic
274C4⋊C8D4×C7311yescharacteristic
275#104—24no—
276#103—21no—
277#103—21no—
278#103—21no—
279#102—21no—
280C22⋊C8—22no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283#97—22no—
284#97—21no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8—21no—
288#41—22no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8C22⋊C4×C7311yescharacteristic
293C2×D4—21no—
294C2×D4C22⋊C4×C7311yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4C2×D4×C7311yescharacteristic
300C22×C4C2×D4×C7311yescharacteristic
301C22×C4#41×C7311yescharacteristic
302Q16—42no—
303SD16—42no—
304M16—22no—
305M16—41no—
306M16—42no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—82no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C7311yescharacteristic
323C4⋊C4C22⋊C4×C7311yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—22no—
332C42—22no—
333C42—22no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42C22×C4×C7311yescharacteristic
339C42C2×D4×C7311yescharacteristic
340C42C2×D4×C7311yescharacteristic
341C42#41×C7311yescharacteristic
342C23—21no—
343C23#121×C7311yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—41no—
347Q8—41no—
348Q8—41no—
349Q8—41no—
350D4—21no—
351D4—42no—
352D4#104×C7312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4C2×C22⋊C4×C7311yescharacteristic
373C2×C4C4×D4×C7311yescharacteristic
374C2×C4C4×D4×C7311yescharacteristic
375C2×C4#120×C7311yescharacteristic
376C2×C4#121×C7311yescharacteristic
377C2×C4#123×C7311yescharacteristic
378C8—42no—
379C8—41no—
380C8—41no—
381C8—41no—
382C8—42no—
383C8—41no—
384C22—21no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22#386×C7311yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—44no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—81no—
399C4—81no—
400C4C2×#104×C7311yescharacteristic
401C4#421×C7311yescharacteristic
402C4#443×C7311yescharacteristic
403C4#444×C7311yescharacteristic
404C4#455×C7311yescharacteristic
405C4#456×C7311yescharacteristic
406C2—41no—
407C2—42no—
408C2C73×#187111yescharacteristic
409C2C73×#187611yescharacteristic
410C2C73×#188211yescharacteristic
subgroupG/H
centerC2×C4×C73#120
commutatorC42C22×C4×C73
Frattini, cosocleC2×C42C23×C73
socleC22×C73#386
prime radicalC2×#41×C73D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#1994C2semidirect
5. C73×#1485C2semidirect
6. C73×#1299C2semidirect
7. C73×#1276C2semidirect
11. #475×C73C4semidirect
12. #474×C73C4semidirect
13. #462×C73C4semidirect
14. #461×C73C4semidirect
200. #8971C73direct (N × H)
208. #1994C2×C73semidirect
210. #1485C2×C73semidirect
211. #1299C2×C73semidirect
212. #1276C2×C73semidirect
213. C73#8971direct (N × H)
217. #475C4×C73semidirect
218. #474C4×C73semidirect
219. #462C4×C73semidirect
220. #461C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#31072
C73×#29902
C73×#19942
C4×#104×C732
C73×#14852
C73×#12992
C73×#12762
#897173