Finite Group Databasebeta

← C73×#19357 #32928761

Subgroups — C73×#19357 #32928761

Order 18688.

596 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3238C211yesmaximal, characteristic
2C73×#3218C211yesmaximal, characteristic
3C2×#498×C73C211yesmaximal, characteristic, complemented
4C73×#2966C211yesmaximal, characteristic
5C73×#1692C212yesmaximal, complemented
6C73×#1691C212yesmaximal, complemented
7C73×#1672C212yesmaximal, complemented
8C73×#1671C212yesmaximal, complemented
9C73×#1568C211yesmaximal, characteristic, complemented
10C73×#1558C211yesmaximal, characteristic, complemented
11C73×#1556C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C73C2211yescharacteristic
13C2×C4⋊Q8×C73C2211yescharacteristic
14#529×C73C2211yescharacteristic
15#501×C73—21no—
16#498×C73—21no—
17#498×C73—21no—
18#498×C73C2212yes—
19#498×C73C2212yes—
20#497×C73—21no—
21#491×C73—21no—
22#489×C73—21no—
23#483×C73—21no—
24#480×C73—21no—
25#477×C73C2212yes—
26#476×C73C2212yes—
27#462×C73C2212yes—
28#461×C73C2212yes—
29#451×C73—21no—
30#448×C73—21no—
31#446×C73C2211yescharacteristic
32C8×Q8×C73C2211yescharacteristic
33#436×C73C2211yescharacteristic
34#435×C73—21no—
35C8×D4×C73—21no—
36C8×D4×C73C2211yescharacteristic
37#433×C73—21no—
38#432×C73C2211yescharacteristic
39#432×C73C2211yescharacteristic
40#432×C73C2211yescharacteristic
41C2×#106×C73—21no—
42C2×#106×C73—21no—
43#405×C73—21no—
44C2×C4×C8×C73C2211yescharacteristic
45#335×C73C2212yes—
46#334×C73C2212yes—
47#333×C73C2212yes—
48#333×C73C2212yes—
49#332×C73C2212yes—
50#332×C73C2212yes—
51C22×Q8×C73—21no—
52C22×Q8×C73—21no—
53C2×Q16×C73—22no—
54C2×SD16×C73—22no—
55C2×M16×C73—21no—
56C22×C8×C73—21no—
57C22×C8×C73D411yescharacteristic
58C22×C8×C73D411yescharacteristic
59C4⋊Q8×C73—21no—
60C4⋊Q8×C73—21no—
61C4⋊Q8×C73—21no—
62C4⋊Q8×C73—21no—
63C4⋊Q8×C73—21no—
64C4⋊Q8×C73—21no—
65C4⋊Q8×C73C2312yes—
66C4⋊Q8×C73C2312yes—
67#126×C73—21no—
68#125×C73D411yescharacteristic
69#124×C73D411yescharacteristic
70#123×C73—21no—
71C22⋊Q8×C73D411yescharacteristic
72#121×C73D411yescharacteristic
73C4×Q8×C73C2311yescharacteristic
74C4×D4×C73—21no—
75C4×D4×C73C2311yescharacteristic
76#117×C73—21no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73—21no—
80C2×C4⋊C4×C73—21no—
81C2×C42×C73C2311yescharacteristic
82#107×C73—22no—
83#106×C73—22no—
84#106×C73—22no—
85#106×C73—22no—
86#106×C73—22no—
87#106×C73—22no—
88C4⋊C8×C73—21no—
89C4⋊C8×C73—21no—
90C4⋊C8×C73C2311yescharacteristic
91C4⋊C8×C73C2311yescharacteristic
92C4⋊C8×C73C2312yes—
93C4⋊C8×C73C2312yes—
94#103×C73—22no—
95#103×C73—22no—
96#103×C73—22no—
97#102×C73—22no—
98C22⋊C8×C73—21no—
99C22⋊C8×C73—21no—
100C22⋊C8×C73—21no—
101C22⋊C8×C73—21no—
102C22⋊C8×C73—21no—
103#97×C73—21no—
104#97×C73—21no—
105#97×C73—21no—
106#97×C73—21no—
107C4×C8×C73—21no—
108C4×C8×C73D411yescharacteristic
109C4×C8×C73D411yescharacteristic
110C4×C8×C73C2311yescharacteristic
111C4×C8×C73C2311yescharacteristic
112C2×Q8×C73—22no—
113C2×Q8×C73—22no—
114C2×Q8×C73—41no—
115C2×Q8×C73—41no—
116C2×Q8×C73—82no—
117C2×Q8×C73—82no—
118C2×Q8×C73C2×D411yescharacteristic
119C2×D4×C73—21no—
120C2×D4×C73C2×D411yescharacteristic
121C22×C4×C73—21no—
122C22×C4×C73—41no—
123C22×C4×C73—41no—
124C22×C4×C73C2×D411yescharacteristic
125C22×C4×C73C2×D411yescharacteristic
126C22×C4×C73#4111yescharacteristic
127Q16×C73—82no—
128SD16×C73—82no—
129M16×C73—42no—
130C2×C8×C73—22no—
131C2×C8×C73—22no—
132C2×C8×C73—21no—
133C2×C8×C73—21no—
134C2×C8×C73—22no—
135C2×C8×C73—22no—
136C2×C8×C73—42no—
137C2×C8×C73C2×D411yescharacteristic
138C2×C8×C73C2×D411yescharacteristic
139C2×C8×C73C2×D411yescharacteristic
140C2×C8×C73C2×D411yescharacteristic
141C4⋊C4×C73—21no—
142C4⋊C4×C73—21no—
143C4⋊C4×C73—21no—
144C4⋊C4×C73—21no—
145C4⋊C4×C73—22no—
146C4⋊C4×C73—22no—
147C4⋊C4×C73—22no—
148C4⋊C4×C73—22no—
149C4⋊C4×C73—41no—
150C4⋊C4×C73—41no—
151C4⋊C4×C73—41no—
152C4⋊C4×C73—41no—
153C4⋊C4×C73C2×D411yescharacteristic
154C4⋊C4×C73C2×D411yescharacteristic
155C22⋊C4×C73—21no—
156C22⋊C4×C73—21no—
157C22⋊C4×C73—21no—
158C22⋊C4×C73—21no—
159C22⋊C4×C73—21no—
160C42×C73—21no—
161C42×C73C2×D411yescharacteristic
162C42×C73C2×D411yescharacteristic
163C42×C73#4111yescharacteristic
164C42×C73C2411yescharacteristic
165C23×C73—21no—
166C23×C73#12111yescharacteristic
167Q8×C73—22no—
168Q8×C73—42no—
169Q8×C73—42no—
170Q8×C73—82no—
171Q8×C73—82no—
172Q8×C73—82no—
173D4×C73—22no—
174D4×C73—42no—
175C2×C4×C73—22no—
176C2×C4×C73—21no—
177C2×C4×C73—21no—
178C2×C4×C73—22no—
179C2×C4×C73—21no—
180C2×C4×C73—21no—
181C2×C4×C73—21no—
182C2×C4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—42no—
185C2×C4×C73—42no—
186C2×C4×C73—82no—
187C2×C4×C73—82no—
188C2×C4×C73#12111yescharacteristic
189C2×C4×C73#12111yescharacteristic
190C2×C4×C73#12111yescharacteristic
191C2×C4×C73C22×D411yescharacteristic
192C2×C4×C73C22×D411yescharacteristic
193C2×C4×C73C2×#4111yescharacteristic
194C8×C73—21no—
195C8×C73—21no—
196C8×C73—41no—
197C8×C73—41no—
198C8×C73—42no—
199C8×C73—42no—
200C8×C73#13712yes—
201C8×C73#13712yes—
202C22×C73—21no—
203C22×C73—21no—
204C22×C73—41no—
205C22×C73—41no—
206C22×C73—41no—
207C22×C73#47112yes—
208C22×C73C2×#12111yescharacteristic
209C4×C73—21no—
210C4×C73—21no—
211C4×C73—21no—
212C4×C73—21no—
213C4×C73—41no—
214C4×C73—41no—
215C4×C73—41no—
216C4×C73—82no—
217C4×C73—82no—
218C4×C73C2×#13711yescharacteristic
219C4×C73C2×#13711yescharacteristic
220C4×C73#57712yes—
221#19357C7311yesmaximal, characteristic, direct product factor, Sylow
222C2×C73—22no—
223C2×C73—81no—
224C2×C73#303911yescharacteristic
225C2×C73#305711yescharacteristic
226C2×C73C2×#47111yescharacteristic
227#3238C2×C7311yescharacteristic
228#3218C2×C7311yescharacteristic
229C2×#498C2×C7311yescharacteristic, complemented
230#2966C2×C7311yescharacteristic
231#1692C2×C7312yescomplemented
232#1691C2×C7312yescomplemented
233#1672C2×C7312yescomplemented
234#1671C2×C7312yescomplemented
235#1568C2×C7311yescharacteristic, complemented
236#1558C2×C7311yescharacteristic, complemented
237#1556C2×C7311yescharacteristic, complemented
238C73#1935711yescharacteristic, direct product factor, Sylow
239C2×C4⋊Q8C22×C7311yescharacteristic
240C2×C4⋊Q8C22×C7311yescharacteristic
241#529C22×C7311yescharacteristic
242#501—21no—
243#498—21no—
244#498—21no—
245#498C22×C7312yes—
246#498C22×C7312yes—
247#497—21no—
248#491—21no—
249#489—21no—
250#483—21no—
251#480—21no—
252#477C22×C7312yes—
253#476C22×C7312yes—
254#462C22×C7312yes—
255#461C22×C7312yes—
256#451—21no—
257#448—21no—
258#446C22×C7311yescharacteristic
259C8×Q8C22×C7311yescharacteristic
260#436C22×C7311yescharacteristic
261#435—21no—
262C8×D4—21no—
263C8×D4C22×C7311yescharacteristic
264#433—21no—
265#432C22×C7311yescharacteristic
266#432C22×C7311yescharacteristic
267#432C22×C7311yescharacteristic
268C2×#106—21no—
269C2×#106—21no—
270#405—21no—
271C2×C4×C8C22×C7311yescharacteristic
272#335C22×C7312yes—
273#334C22×C7312yes—
274#333C22×C7312yes—
275#333C22×C7312yes—
276#332C22×C7312yes—
277#332C22×C7312yes—
278C22×Q8—21no—
279C22×Q8—21no—
280C2×Q16—22no—
281C2×SD16—22no—
282C2×M16—21no—
283C22×C8—21no—
284C22×C8D4×C7311yescharacteristic
285C22×C8D4×C7311yescharacteristic
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C23×C7312yes—
293C4⋊Q8C23×C7312yes—
294#126—21no—
295#125D4×C7311yescharacteristic
296#124D4×C7311yescharacteristic
297#123—21no—
298C22⋊Q8D4×C7311yescharacteristic
299#121D4×C7311yescharacteristic
300C4×Q8C23×C7311yescharacteristic
301C4×D4—21no—
302C4×D4C23×C7311yescharacteristic
303#117—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C42C23×C7311yescharacteristic
309#107—22no—
310#106—22no—
311#106—22no—
312#106—22no—
313#106—22no—
314#106—22no—
315C4⋊C8—21no—
316C4⋊C8—21no—
317C4⋊C8C23×C7311yescharacteristic
318C4⋊C8C23×C7311yescharacteristic
319C4⋊C8C23×C7312yes—
320C4⋊C8C23×C7312yes—
321#103—22no—
322#103—22no—
323#103—22no—
324#102—22no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330#97—21no—
331#97—21no—
332#97—21no—
333#97—21no—
334C4×C8—21no—
335C4×C8D4×C7311yescharacteristic
336C4×C8D4×C7311yescharacteristic
337C4×C8C23×C7311yescharacteristic
338C4×C8C23×C7311yescharacteristic
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—82no—
344C2×Q8—82no—
345C2×Q8C2×D4×C7311yescharacteristic
346C2×D4—21no—
347C2×D4C2×D4×C7311yescharacteristic
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4C2×D4×C7311yescharacteristic
352C22×C4C2×D4×C7311yescharacteristic
353C22×C4#41×C7311yescharacteristic
354Q16—82no—
355SD16—82no—
356M16—42no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8C2×D4×C7311yescharacteristic
365C2×C8C2×D4×C7311yescharacteristic
366C2×C8C2×D4×C7311yescharacteristic
367C2×C8C2×D4×C7311yescharacteristic
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C2×D4×C7311yescharacteristic
381C4⋊C4C2×D4×C7311yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C42—21no—
388C42C2×D4×C7311yescharacteristic
389C42C2×D4×C7311yescharacteristic
390C42#41×C7311yescharacteristic
391C42C24×C7311yescharacteristic
392C23—21no—
393C23#121×C7311yescharacteristic
394Q8—22no—
395Q8—42no—
396Q8—42no—
397Q8—82no—
398Q8—82no—
399Q8—82no—
400D4—22no—
401D4—42no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4#121×C7311yescharacteristic
416C2×C4#121×C7311yescharacteristic
417C2×C4#121×C7311yescharacteristic
418C2×C4C22×D4×C7311yescharacteristic
419C2×C4C22×D4×C7311yescharacteristic
420C2×C4C2×#41×C7311yescharacteristic
421C8—21no—
422C8—21no—
423C8—41no—
424C8—41no—
425C8—42no—
426C8—42no—
427C8#137×C7312yes—
428C8#137×C7312yes—
429C22—21no—
430C22—21no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22#471×C7312yes—
435C22C2×#121×C7311yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—82no—
444C4—82no—
445C4C2×#137×C7311yescharacteristic
446C4C2×#137×C7311yescharacteristic
447C4#577×C7312yes—
448C2—22no—
449C2—81no—
450C2C73×#303911yescharacteristic
451C2C73×#305711yescharacteristic
452C2C2×#471×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radical#121×C73D4
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. C2×#498×C73C2semidirect
5. C73×#1692C2semidirect
6. C73×#1691C2semidirect
7. C73×#1672C2semidirect
8. C73×#1671C2semidirect
9. C73×#1568C2semidirect
10. C73×#1558C2semidirect
11. C73×#1556C2semidirect
221. #19357C73direct (N × H)
229. C2×#498C2×C73semidirect
231. #1692C2×C73semidirect
232. #1691C2×C73semidirect
233. #1672C2×C73semidirect
234. #1671C2×C73semidirect
235. #1568C2×C73semidirect
236. #1558C2×C73semidirect
237. #1556C2×C73semidirect
238. C73#19357direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32382
C73×#32182
C2×#498×C732
C73×#29662
C73×#16922
C73×#16912
C73×#16722
C73×#16712
C73×#15682
C73×#15582
C73×#15562
#1935773