Finite Group Databasebeta

← C73×#19245 #32928649

Subgroups — C73×#19245 #32928649

Order 18688.

606 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3246C211yesmaximal, characteristic
2C73×#3209C211yesmaximal, characteristic, complemented
3C73×#3141C211yesmaximal, characteristic
4C73×#2962C211yesmaximal, characteristic, complemented
5C73×#1702C212yesmaximal, complemented
6C73×#1700C212yesmaximal, complemented
7C73×#1682C212yesmaximal, complemented
8C73×#1680C212yesmaximal, complemented
9C73×#1565C211yesmaximal, characteristic, complemented
10C73×#1540C211yesmaximal, characteristic
11C2×#332×C73C211yesmaximal, characteristic, complemented
12#533×C73C2211yescharacteristic
13#532×C73C2211yescharacteristic
14C2×C4⋊Q8×C73C2211yescharacteristic
15#494×C73—21no—
16#489×C73—22no—
17#487×C73—21no—
18#487×C73C2212yes—
19#486×C73C2212yes—
20#476×C73—21no—
21#475×C73C2212yes—
22#465×C73—22no—
23#462×C73C2212yes—
24#462×C73C2212yes—
25#461×C73—21no—
26#460×C73C2212yes—
27#451×C73—22no—
28#446×C73—22no—
29#446×C73C2212yes—
30C8×Q8×C73C2212yes—
31#431×C73C2211yescharacteristic
32#424×C73—21no—
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35#417×C73—21no—
36#417×C73—21no—
37#405×C73—21no—
38C4×M16×C73C2211yescharacteristic
39#335×C73C2212yes—
40#334×C73C2212yes—
41#332×C73C2211yescharacteristic
42#332×C73C2212yes—
43#332×C73C2211yescharacteristic
44#332×C73C2212yes—
45#331×C73C2211yescharacteristic
46#331×C73C2211yescharacteristic
47C2×#41×C73—21no—
48C22×Q8×C73—21no—
49C2×Q16×C73—22no—
50C2×Q16×C73—22no—
51C2×SD16×C73—22no—
52C2×M16×C73D411yescharacteristic
53C2×M16×C73D411yescharacteristic
54C22×C8×C73—21no—
55C22×C8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73D411yescharacteristic
60C4⋊Q8×C73D411yescharacteristic
61C4⋊Q8×C73C2312yes—
62C4⋊Q8×C73C2311yescharacteristic
63#127×C73C2311yescharacteristic
64#125×C73—21no—
65#124×C73—21no—
66C22⋊Q8×C73—21no—
67C22⋊Q8×C73D412yes—
68#121×C73—21no—
69#121×C73—21no—
70C4×Q8×C73—21no—
71C4×Q8×C73C2312yes—
72C4×D4×C73—21no—
73C4×D4×C73—21no—
74#117×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C42×C73C2311yescharacteristic
78#106×C73—22no—
79C4⋊C8×C73—22no—
80C4⋊C8×C73—22no—
81C4⋊C8×C73—21no—
82C4⋊C8×C73—21no—
83C4⋊C8×C73C2311yescharacteristic
84C4⋊C8×C73C2311yescharacteristic
85C4⋊C8×C73C2312yes—
86C4⋊C8×C73C2311yescharacteristic
87C4⋊C8×C73C2311yescharacteristic
88#103×C73—22no—
89#103×C73—22no—
90#103×C73—22no—
91#103×C73—22no—
92#103×C73—22no—
93#102×C73—22no—
94#102×C73—22no—
95#102×C73—22no—
96C22⋊C8×C73—21no—
97#97×C73—22no—
98#97×C73D412yes—
99C4×C8×C73—22no—
100C4×C8×C73—21no—
101C4×C8×C73C2312yes—
102#41×C73—42no—
103#41×C73—42no—
104C2×Q8×C73—21no—
105C2×Q8×C73—21no—
106C2×Q8×C73—22no—
107C2×Q8×C73—41no—
108C2×Q8×C73—81no—
109C2×Q8×C73—81no—
110C2×Q8×C73C2×D412yes—
111C2×D4×C73—21no—
112C2×D4×C73—21no—
113C2×D4×C73—21no—
114C2×D4×C73—41no—
115C22×C4×C73—41no—
116C22×C4×C73—41no—
117C22×C4×C73C2×D411yescharacteristic
118C22×C4×C73C2×D411yescharacteristic
119C22×C4×C73#4111yescharacteristic
120Q16×C73—82no—
121Q16×C73—82no—
122SD16×C73—82no—
123M16×C73—22no—
124M16×C73—22no—
125C2×C8×C73—21no—
126C2×C8×C73—21no—
127C2×C8×C73—21no—
128C2×C8×C73—21no—
129C2×C8×C73—22no—
130C2×C8×C73—42no—
131C2×C8×C73—81no—
132C2×C8×C73C2×D412yes—
133C2×C8×C73C2×D412yes—
134C4⋊C4×C73—21no—
135C4⋊C4×C73—21no—
136C4⋊C4×C73—21no—
137C4⋊C4×C73—22no—
138C4⋊C4×C73—22no—
139C4⋊C4×C73—22no—
140C4⋊C4×C73—21no—
141C4⋊C4×C73—22no—
142C4⋊C4×C73—21no—
143C4⋊C4×C73—41no—
144C4⋊C4×C73—41no—
145C4⋊C4×C73C2×D412yes—
146C22⋊C4×C73—22no—
147C22⋊C4×C73—41no—
148C22⋊C4×C73—41no—
149C42×C73—22no—
150C42×C73C2×D411yescharacteristic
151C42×C73C2×D411yescharacteristic
152C42×C73#4111yescharacteristic
153C42×C73C2411yescharacteristic
154C23×C73—41no—
155C23×C73#12111yescharacteristic
156Q8×C73—22no—
157Q8×C73—22no—
158Q8×C73—41no—
159Q8×C73—41no—
160Q8×C73—42no—
161Q8×C73—42no—
162Q8×C73—81no—
163Q8×C73—82no—
164D4×C73—41no—
165D4×C73—41no—
166D4×C73—41no—
167D4×C73—41no—
168D4×C73—81no—
169D4×C73—82no—
170C2×C4×C73—21no—
171C2×C4×C73—21no—
172C2×C4×C73—22no—
173C2×C4×C73—22no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—42no—
177C2×C4×C73—82no—
178C2×C4×C73—82no—
179C2×C4×C73#12111yescharacteristic
180C2×C4×C73#12111yescharacteristic
181C2×C4×C73#12111yescharacteristic
182C2×C4×C73#13512yes—
183C2×C4×C73#13712yes—
184C2×C4×C73C22×D411yescharacteristic
185C2×C4×C73C22×D411yescharacteristic
186C2×C4×C73C2×#4111yescharacteristic
187C8×C73—22no—
188C8×C73—22no—
189C8×C73—41no—
190C8×C73—41no—
191C8×C73—42no—
192C8×C73—41no—
193C8×C73—41no—
194C22×C73—21no—
195C22×C73—21no—
196C22×C73—81no—
197C22×C73—81no—
198C22×C73—81no—
199C22×C73#46412yes—
200C22×C73C2×#12111yescharacteristic
201C4×C73—21no—
202C4×C73—21no—
203C4×C73—21no—
204C4×C73—42no—
205C4×C73—42no—
206C4×C73—81no—
207C4×C73—82no—
208C4×C73#46412yes—
209C4×C73C2×#13511yescharacteristic
210C4×C73C2×#13711yescharacteristic
211C4×C73#57611yescharacteristic
212C4×C73#57711yescharacteristic
213#19245C7311yesmaximal, characteristic, direct product factor, Sylow
214C2×C73—22no—
215C2×C73—161no—
216C2×C73C2×#46411yescharacteristic
217C2×C73#306211yescharacteristic
218C2×C73#306911yescharacteristic
219#3246C2×C7311yescharacteristic
220#3209C2×C7311yescharacteristic, complemented
221#3141C2×C7311yescharacteristic
222#2962C2×C7311yescharacteristic, complemented
223#1702C2×C7312yescomplemented
224#1700C2×C7312yescomplemented
225#1682C2×C7312yescomplemented
226#1680C2×C7312yescomplemented
227#1565C2×C7311yescharacteristic, complemented
228#1540C2×C7311yescharacteristic
229C2×#332C2×C7311yescharacteristic, complemented
230C73#1924511yescharacteristic, direct product factor, Sylow
231#533C22×C7311yescharacteristic
232#532C22×C7311yescharacteristic
233C2×C4⋊Q8C22×C7311yescharacteristic
234#494—21no—
235#489—22no—
236#487—21no—
237#487C22×C7312yes—
238#486C22×C7312yes—
239#476—21no—
240#475C22×C7312yes—
241#465—22no—
242#462C22×C7312yes—
243#462C22×C7312yes—
244#461—21no—
245#460C22×C7312yes—
246#451—22no—
247#446—22no—
248#446C22×C7312yes—
249C8×Q8C22×C7312yes—
250#431C22×C7311yescharacteristic
251#424—21no—
252C2×C4⋊C8C22×C7311yescharacteristic
253C2×C4⋊C8C22×C7311yescharacteristic
254#417—21no—
255#417—21no—
256#405—21no—
257C4×M16C22×C7311yescharacteristic
258#335C22×C7312yes—
259#334C22×C7312yes—
260#332C22×C7312yes—
261#332C22×C7312yes—
262#332C22×C7311yescharacteristic
263#332C22×C7311yescharacteristic
264#331C22×C7311yescharacteristic
265#331C22×C7311yescharacteristic
266C2×#41—21no—
267C22×Q8—21no—
268C2×Q16—22no—
269C2×Q16—22no—
270C2×SD16—22no—
271C2×M16D4×C7311yescharacteristic
272C2×M16D4×C7311yescharacteristic
273C22×C8—21no—
274C22×C8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8D4×C7311yescharacteristic
279C4⋊Q8D4×C7311yescharacteristic
280C4⋊Q8C23×C7312yes—
281C4⋊Q8C23×C7311yescharacteristic
282#127C23×C7311yescharacteristic
283#125—21no—
284#124—21no—
285C22⋊Q8—21no—
286C22⋊Q8D4×C7312yes—
287#121—21no—
288#121—21no—
289C4×Q8—21no—
290C4×Q8C23×C7312yes—
291C4×D4—21no—
292C4×D4—21no—
293#117—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C42C23×C7311yescharacteristic
297#106—22no—
298C4⋊C8—22no—
299C4⋊C8—22no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8C23×C7311yescharacteristic
303C4⋊C8C23×C7311yescharacteristic
304C4⋊C8C23×C7311yescharacteristic
305C4⋊C8C23×C7311yescharacteristic
306C4⋊C8C23×C7312yes—
307#103—22no—
308#103—22no—
309#103—22no—
310#103—22no—
311#103—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315C22⋊C8—21no—
316#97—22no—
317#97D4×C7312yes—
318C4×C8—22no—
319C4×C8—21no—
320C4×C8C23×C7312yes—
321#41—42no—
322#41—42no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—41no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×Q8C2×D4×C7312yes—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4C2×D4×C7311yescharacteristic
337C22×C4C2×D4×C7311yescharacteristic
338C22×C4#41×C7311yescharacteristic
339Q16—82no—
340Q16—82no—
341SD16—82no—
342M16—22no—
343M16—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—42no—
350C2×C8—81no—
351C2×C8C2×D4×C7312yes—
352C2×C8C2×D4×C7312yes—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C7312yes—
365C22⋊C4—22no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—22no—
369C42C2×D4×C7311yescharacteristic
370C42C2×D4×C7311yescharacteristic
371C42#41×C7311yescharacteristic
372C42C24×C7311yescharacteristic
373C23—41no—
374C23#121×C7311yescharacteristic
375Q8—22no—
376Q8—22no—
377Q8—41no—
378Q8—41no—
379Q8—42no—
380Q8—42no—
381Q8—81no—
382Q8—82no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4#121×C7311yescharacteristic
399C2×C4#121×C7311yescharacteristic
400C2×C4#121×C7311yescharacteristic
401C2×C4#135×C7312yes—
402C2×C4#137×C7312yes—
403C2×C4C22×D4×C7311yescharacteristic
404C2×C4C22×D4×C7311yescharacteristic
405C2×C4C2×#41×C7311yescharacteristic
406C8—22no—
407C8—22no—
408C8—41no—
409C8—41no—
410C8—42no—
411C8—41no—
412C8—41no—
413C22—21no—
414C22—21no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22#464×C7312yes—
419C22C2×#121×C7311yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—81no—
426C4—82no—
427C4#464×C7312yes—
428C4C2×#135×C7311yescharacteristic
429C4C2×#137×C7311yescharacteristic
430C4#576×C7311yescharacteristic
431C4#577×C7311yescharacteristic
432C2—22no—
433C2—161no—
434C2C2×#464×C7311yescharacteristic
435C2C73×#306211yescharacteristic
436C2C73×#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
2. C73×#3209C2semidirect
4. C73×#2962C2semidirect
5. C73×#1702C2semidirect
6. C73×#1700C2semidirect
7. C73×#1682C2semidirect
8. C73×#1680C2semidirect
9. C73×#1565C2semidirect
11. C2×#332×C73C2semidirect
213. #19245C73direct (N × H)
220. #3209C2×C73semidirect
222. #2962C2×C73semidirect
223. #1702C2×C73semidirect
224. #1700C2×C73semidirect
225. #1682C2×C73semidirect
226. #1680C2×C73semidirect
227. #1565C2×C73semidirect
229. C2×#332C2×C73semidirect
230. C73#19245direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32462
C73×#32092
C73×#31412
C73×#29622
C73×#17022
C73×#17002
C73×#16822
C73×#16802
C73×#15652
C73×#15402
C2×#332×C732
#1924573