Finite Group Databasebeta

← C73×#19518 #32928922

Subgroups — C73×#19518 #32928922

Order 18688.

580 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3254C211yesmaximal, characteristic
2C73×#3246C211yesmaximal, characteristic
3C73×#3231C211yesmaximal, characteristic, complemented
4C73×#2981C211yesmaximal, characteristic
5C73×#1699C212yesmaximal, complemented
6C73×#1691C212yesmaximal, complemented
7C73×#1683C212yesmaximal, complemented
8C73×#1673C212yesmaximal, complemented
9C73×#1571C211yesmaximal, characteristic, complemented
10C73×#1559C211yesmaximal, characteristic, complemented
11C73×#1552C211yesmaximal, characteristic, complemented
12#533×C73C2211yescharacteristic
13#533×C73C2211yescharacteristic
14#532×C73C2211yescharacteristic
15#500×C73C2211yescharacteristic
16#498×C73C2211yescharacteristic
17#487×C73C2211yescharacteristic
18#487×C73C2211yescharacteristic
19#485×C73—22no—
20#479×C73—22no—
21#477×C73—21no—
22#476×C73C2212yes—
23#475×C73—21no—
24#474×C73C2212yes—
25#468×C73—22no—
26#465×C73—22no—
27#461×C73C2212yes—
28#461×C73C2212yes—
29#460×C73—21no—
30#460×C73—21no—
31#436×C73C2212yes—
32#435×C73—22no—
33C8×D4×C73C2212yes—
34#432×C73C2211yescharacteristic
35#431×C73C2211yescharacteristic
36#423×C73C2211yescharacteristic
37C2×C4⋊C8×C73C2211yescharacteristic
38#408×C73—22no—
39#335×C73C2212yes—
40#335×C73C2212yes—
41#333×C73C2212yes—
42#332×C73C2212yes—
43#332×C73C2212yes—
44#332×C73C2212yes—
45C2×#41×C73—21no—
46C2×SD16×C73—22no—
47C2×SD16×C73—22no—
48C2×M16×C73—21no—
49C2×M16×C73—22no—
50C22×C8×C73—21no—
51C22×C8×C73—22no—
52C4⋊Q8×C73D411yescharacteristic
53C4⋊Q8×C73C2311yescharacteristic
54C4⋊Q8×C73C2311yescharacteristic
55C4⋊Q8×C73C2311yescharacteristic
56C4⋊Q8×C73C2311yescharacteristic
57#127×C73D411yescharacteristic
58#125×C73—21no—
59#125×C73—21no—
60#124×C73—21no—
61C22⋊Q8×C73—21no—
62C22⋊Q8×C73—21no—
63C22⋊Q8×C73—21no—
64C22⋊Q8×C73—21no—
65#121×C73—21no—
66#121×C73D412yes—
67C4×Q8×C73—21no—
68C4×Q8×C73—21no—
69C4×Q8×C73—21no—
70C4×Q8×C73—21no—
71C4×D4×C73—21no—
72C4×D4×C73C2312yes—
73#117×C73—21no—
74#117×C73—21no—
75C2×C42×C73C2311yescharacteristic
76#107×C73—22no—
77#107×C73—22no—
78#106×C73—22no—
79#106×C73—22no—
80C4⋊C8×C73—21no—
81C4⋊C8×C73—21no—
82C4⋊C8×C73D412yes—
83C4⋊C8×C73C2312yes—
84C4⋊C8×C73C2312yes—
85C4⋊C8×C73C2312yes—
86#103×C73—22no—
87#103×C73—22no—
88#103×C73—22no—
89#103×C73—22no—
90#102×C73—22no—
91#102×C73—22no—
92C22⋊C8×C73—21no—
93C22⋊C8×C73—22no—
94C22⋊C8×C73—22no—
95C22⋊C8×C73D412yes—
96#97×C73—21no—
97C4×C8×C73C2311yescharacteristic
98C4×C8×C73C2311yescharacteristic
99#41×C73—82no—
100C2×Q8×C73—21no—
101C2×Q8×C73—21no—
102C2×Q8×C73—21no—
103C2×Q8×C73—21no—
104C2×Q8×C73—21no—
105C2×D4×C73—22no—
106C2×D4×C73—21no—
107C2×D4×C73—21no—
108C2×D4×C73C2×D412yes—
109C22×C4×C73—22no—
110C22×C4×C73C2×D411yescharacteristic
111C22×C4×C73C2×D411yescharacteristic
112C22×C4×C73#4111yescharacteristic
113SD16×C73—82no—
114SD16×C73—82no—
115M16×C73—82no—
116M16×C73—81no—
117C2×C8×C73—22no—
118C2×C8×C73—22no—
119C2×C8×C73—22no—
120C2×C8×C73—82no—
121C2×C8×C73—81no—
122C2×C8×C73C2×D412yes—
123C2×C8×C73C2×D412yes—
124C4⋊C4×C73—21no—
125C4⋊C4×C73—21no—
126C4⋊C4×C73—21no—
127C4⋊C4×C73—21no—
128C4⋊C4×C73—21no—
129C4⋊C4×C73—21no—
130C4⋊C4×C73—21no—
131C4⋊C4×C73—21no—
132C4⋊C4×C73—21no—
133C4⋊C4×C73—41no—
134C4⋊C4×C73—41no—
135C4⋊C4×C73—41no—
136C4⋊C4×C73—41no—
137C4⋊C4×C73C2×D412yes—
138C22⋊C4×C73—22no—
139C22⋊C4×C73—22no—
140C22⋊C4×C73—41no—
141C22⋊C4×C73—41no—
142C42×C73—41no—
143C42×C73—41no—
144C42×C73C2×D411yescharacteristic
145C42×C73C2×D411yescharacteristic
146C42×C73#4111yescharacteristic
147C42×C73C2411yescharacteristic
148C23×C73—22no—
149C23×C73#12111yescharacteristic
150Q8×C73—41no—
151Q8×C73—41no—
152Q8×C73—42no—
153Q8×C73—41no—
154Q8×C73—41no—
155Q8×C73—81no—
156Q8×C73—81no—
157D4×C73—22no—
158D4×C73—22no—
159D4×C73—81no—
160D4×C73—81no—
161D4×C73—82no—
162C2×C4×C73—21no—
163C2×C4×C73—22no—
164C2×C4×C73—21no—
165C2×C4×C73—22no—
166C2×C4×C73—41no—
167C2×C4×C73—42no—
168C2×C4×C73—42no—
169C2×C4×C73—41no—
170C2×C4×C73—41no—
171C2×C4×C73—41no—
172C2×C4×C73—41no—
173C2×C4×C73#12111yescharacteristic
174C2×C4×C73#12111yescharacteristic
175C2×C4×C73#12111yescharacteristic
176C2×C4×C73C22×D411yescharacteristic
177C2×C4×C73C22×D411yescharacteristic
178C2×C4×C73C2×#4111yescharacteristic
179C8×C73—22no—
180C8×C73—22no—
181C8×C73—42no—
182C8×C73—42no—
183C8×C73—42no—
184C22×C73—21no—
185C22×C73—21no—
186C22×C73—21no—
187C22×C73—42no—
188C22×C73—42no—
189C22×C73—42no—
190C22×C73C2×#12111yescharacteristic
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—21no—
195C4×C73—42no—
196C4×C73—81no—
197C4×C73—81no—
198C4×C73—81no—
199C4×C73—81no—
200C4×C73#57611yescharacteristic
201C4×C73#57712yes—
202C4×C73#57811yescharacteristic
203#19518C7311yesmaximal, characteristic, direct product factor, Sylow
204C2×C73—41no—
205C2×C73—82no—
206C2×C73#304211yescharacteristic
207C2×C73#306111yescharacteristic
208C2×C73#306911yescharacteristic
209#3254C2×C7311yescharacteristic
210#3246C2×C7311yescharacteristic
211#3231C2×C7311yescharacteristic, complemented
212#2981C2×C7311yescharacteristic
213#1699C2×C7312yescomplemented
214#1691C2×C7312yescomplemented
215#1683C2×C7312yescomplemented
216#1673C2×C7312yescomplemented
217#1571C2×C7311yescharacteristic, complemented
218#1559C2×C7311yescharacteristic, complemented
219#1552C2×C7311yescharacteristic, complemented
220C73#1951811yescharacteristic, direct product factor, Sylow
221#533C22×C7311yescharacteristic
222#533C22×C7311yescharacteristic
223#532C22×C7311yescharacteristic
224#500C22×C7311yescharacteristic
225#498C22×C7311yescharacteristic
226#487C22×C7311yescharacteristic
227#487C22×C7311yescharacteristic
228#485—22no—
229#479—22no—
230#477—21no—
231#476C22×C7312yes—
232#475—21no—
233#474C22×C7312yes—
234#468—22no—
235#465—22no—
236#461C22×C7312yes—
237#461C22×C7312yes—
238#460—21no—
239#460—21no—
240#436C22×C7312yes—
241#435—22no—
242C8×D4C22×C7312yes—
243#432C22×C7311yescharacteristic
244#431C22×C7311yescharacteristic
245#423C22×C7311yescharacteristic
246C2×C4⋊C8C22×C7311yescharacteristic
247#408—22no—
248#335C22×C7312yes—
249#335C22×C7312yes—
250#333C22×C7312yes—
251#332C22×C7312yes—
252#332C22×C7312yes—
253#332C22×C7312yes—
254C2×#41—21no—
255C2×SD16—22no—
256C2×SD16—22no—
257C2×M16—21no—
258C2×M16—22no—
259C22×C8—21no—
260C22×C8—22no—
261C4⋊Q8D4×C7311yescharacteristic
262C4⋊Q8C23×C7311yescharacteristic
263C4⋊Q8C23×C7311yescharacteristic
264C4⋊Q8C23×C7311yescharacteristic
265C4⋊Q8C23×C7311yescharacteristic
266#127D4×C7311yescharacteristic
267#125—21no—
268#125—21no—
269#124—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274#121—21no—
275#121D4×C7312yes—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×Q8—21no—
280C4×D4—21no—
281C4×D4C23×C7312yes—
282#117—21no—
283#117—21no—
284C2×C42C23×C7311yescharacteristic
285#107—22no—
286#107—22no—
287#106—22no—
288#106—22no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8D4×C7312yes—
292C4⋊C8C23×C7312yes—
293C4⋊C8C23×C7312yes—
294C4⋊C8C23×C7312yes—
295#103—22no—
296#103—22no—
297#103—22no—
298#103—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—21no—
302C22⋊C8—22no—
303C22⋊C8—22no—
304C22⋊C8D4×C7312yes—
305#97—21no—
306C4×C8C23×C7311yescharacteristic
307C4×C8C23×C7311yescharacteristic
308#41—82no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4C2×D4×C7312yes—
318C22×C4—22no—
319C22×C4C2×D4×C7311yescharacteristic
320C22×C4C2×D4×C7311yescharacteristic
321C22×C4#41×C7311yescharacteristic
322SD16—82no—
323SD16—82no—
324M16—82no—
325M16—81no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—82no—
330C2×C8—81no—
331C2×C8C2×D4×C7312yes—
332C2×C8C2×D4×C7312yes—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4C2×D4×C7312yes—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C42—41no—
352C42—41no—
353C42C2×D4×C7311yescharacteristic
354C42C2×D4×C7311yescharacteristic
355C42#41×C7311yescharacteristic
356C42C24×C7311yescharacteristic
357C23—22no—
358C23#121×C7311yescharacteristic
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—41no—
363Q8—41no—
364Q8—81no—
365Q8—81no—
366D4—22no—
367D4—22no—
368D4—81no—
369D4—81no—
370D4—82no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4#121×C7311yescharacteristic
383C2×C4#121×C7311yescharacteristic
384C2×C4#121×C7311yescharacteristic
385C2×C4C22×D4×C7311yescharacteristic
386C2×C4C22×D4×C7311yescharacteristic
387C2×C4C2×#41×C7311yescharacteristic
388C8—22no—
389C8—22no—
390C8—42no—
391C8—42no—
392C8—42no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22C2×#121×C7311yescharacteristic
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4#576×C7311yescharacteristic
410C4#577×C7312yes—
411C4#578×C7311yescharacteristic
412C2—41no—
413C2—82no—
414C2C73×#304211yescharacteristic
415C2C73×#306111yescharacteristic
416C2C73×#306911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radical#532×C73C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#3231C2semidirect
5. C73×#1699C2semidirect
6. C73×#1691C2semidirect
7. C73×#1683C2semidirect
8. C73×#1673C2semidirect
9. C73×#1571C2semidirect
10. C73×#1559C2semidirect
11. C73×#1552C2semidirect
203. #19518C73direct (N × H)
211. #3231C2×C73semidirect
213. #1699C2×C73semidirect
214. #1691C2×C73semidirect
215. #1683C2×C73semidirect
216. #1673C2×C73semidirect
217. #1571C2×C73semidirect
218. #1559C2×C73semidirect
219. #1552C2×C73semidirect
220. C73#19518direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32542
C73×#32462
C73×#32312
C73×#29812
C73×#16992
C73×#16912
C73×#16832
C73×#16732
C73×#15712
C73×#15592
C73×#15522
#1951873