Finite Group Databasebeta

← C73×#12962 #32922366

Subgroups — C73×#12962 #32922366

Order 18688.

426 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2977C211yesmaximal, characteristic
2C73×#2120C211yesmaximal, characteristic
3C73×#1891C211yesmaximal, characteristic
4C73×#1868C211yesmaximal, characteristic, complemented
5C73×#1858C211yesmaximal, characteristic, complemented
6C73×#1395C211yesmaximal, characteristic, complemented
7C73×#1392C211yesmaximal, characteristic, complemented
8#568×C73C2211yescharacteristic
9#525×C73C2211yescharacteristic
10#435×C73—21no—
11#435×C73—21no—
12C8×D4×C73—21no—
13C8×D4×C73—21no—
14#433×C73—21no—
15#430×C73—21no—
16#424×C73—21no—
17#413×C73C2211yescharacteristic
18#413×C73C2211yescharacteristic
19#410×C73C2211yescharacteristic
20#408×C73C2211yescharacteristic
21#408×C73C2211yescharacteristic
22#407×C73—21no—
23C2×C22⋊C8×C73—21no—
24#352×C73C412yes—
25AΣL(1,𝔽16)×C73C412yes—
26#344×C73—21no—
27#344×C73—21no—
28#341×C73—21no—
29C2×#41×C73C2311yescharacteristic
30C23×C4×C73D411yescharacteristic
31#131×C73—42no—
32C2×M16×C73—21no—
33C2×M16×C73—21no—
34C2×M16×C73—21no—
35C2×M16×C73—21no—
36C2×M16×C73—21no—
37C2×M16×C73D411yescharacteristic
38C2×M16×C73D411yescharacteristic
39C22×C8×C73—21no—
40C22×C8×C73—21no—
41C22×C8×C73D411yescharacteristic
42C22×C8×C73D411yescharacteristic
43#123×C73C2×C411yescharacteristic
44#123×C73Q811yescharacteristic
45C22⋊Q8×C73—21no—
46#121×C73—21no—
47#120×C73C2×C411yescharacteristic
48#120×C73Q811yescharacteristic
49C4×D4×C73—21no—
50C4×D4×C73—21no—
51#117×C73—21no—
52#117×C73D411yescharacteristic
53#108×C73—42no—
54C4⋊C8×C73—21no—
55C4⋊C8×C73—21no—
56C4⋊C8×C73—42no—
57#101×C73—21no—
58#101×C73—21no—
59#100×C73—21no—
60#100×C73C2×C412yes—
61#99×C73—21no—
62#99×C73C2×C412yes—
63C22⋊C8×C73—21no—
64C22⋊C8×C73—21no—
65C22⋊C8×C73—21no—
66C22⋊C8×C73—21no—
67C22⋊C8×C73—21no—
68C22⋊C8×C73—21no—
69C22⋊C8×C73—42no—
70#97×C73—21no—
71C4×C8×C73—21no—
72C24×C73C4⋊C411yescharacteristic
73#41×C73—41no—
74#41×C73—41no—
75C2×Q8×C73#4111yescharacteristic
76C2×D4×C73—21no—
77C2×D4×C73—21no—
78C2×D4×C73C22×C411yescharacteristic
79C2×D4×C73C2×Q811yescharacteristic
80C2×D4×C73#4111yescharacteristic
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73C4⋊C411yescharacteristic
86C22×C4×C73C2×D411yescharacteristic
87C22×C4×C73C2×D411yescharacteristic
88C22×C4×C73C2×D411yescharacteristic
89M16×C73—22no—
90M16×C73—22no—
91M16×C73—41no—
92M16×C73—41no—
93M16×C73—41no—
94M16×C73—41no—
95M16×C73—41no—
96M16×C73—41no—
97M16×C73—41no—
98M16×C73—41no—
99C2×C8×C73—22no—
100C2×C8×C73—22no—
101C2×C8×C73—21no—
102C2×C8×C73—21no—
103C2×C8×C73—21no—
104C2×C8×C73—21no—
105C2×C8×C73—41no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C2×C8×C73—41no—
110C2×C8×C73—81no—
111C2×C8×C73—81no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73—21no—
114C4⋊C4×C73—21no—
115C4⋊C4×C73—41no—
116C22⋊C4×C73—21no—
117C22⋊C4×C73—21no—
118C22⋊C4×C73—21no—
119C22⋊C4×C73—21no—
120C22⋊C4×C73—22no—
121C22⋊C4×C73C4⋊C411yescharacteristic
122C22⋊C4×C73C4⋊C411yescharacteristic
123C42×C73—21no—
124C42×C73—41no—
125C23×C73—21no—
126C23×C73—41no—
127C23×C73—42no—
128C23×C73C2×C4⋊C411yescharacteristic
129C23×C73C4×D411yescharacteristic
130C23×C73C22⋊Q811yescharacteristic
131Q8×C73—41no—
132D4×C73—41no—
133D4×C73—41no—
134D4×C73—41no—
135D4×C73—42no—
136D4×C73—42no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—21no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—21no—
143C2×C4×C73—21no—
144C2×C4×C73—21no—
145C2×C4×C73—21no—
146C2×C4×C73—41no—
147C2×C4×C73—41no—
148C2×C4×C73—41no—
149C2×C4×C73—42no—
150C2×C4×C73—81no—
151C2×C4×C73C4×D411yescharacteristic
152C2×C4×C73#12011yescharacteristic
153C2×C4×C73C22⋊Q811yescharacteristic
154C2×C4×C73#12311yescharacteristic
155C8×C73—42no—
156C8×C73—42no—
157C8×C73—41no—
158C8×C73—41no—
159C8×C73—41no—
160C8×C73—41no—
161C8×C73—81no—
162C22×C73—22no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—42no—
171C22×C73—41no—
172C22×C73—81no—
173C22×C73#38511yescharacteristic
174C4×C73—21no—
175C4×C73—21no—
176C4×C73—21no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73—41no—
180C4×C73—82no—
181C4×C73B(4,𝔽2)11yescharacteristic
182C4×C73#45811yescharacteristic
183#12962C7311yesmaximal, characteristic, direct product factor, Sylow
184C2×C73—21no—
185C2×C73—41no—
186C2×C73—41no—
187C2×C73—42no—
188C2×C73—41no—
189C2×C73#186711yescharacteristic
190#2977C2×C7311yescharacteristic
191#2120C2×C7311yescharacteristic
192#1891C2×C7311yescharacteristic
193#1868C2×C7311yescharacteristic, complemented
194#1858C2×C7311yescharacteristic, complemented
195#1395C2×C7311yescharacteristic, complemented
196#1392C2×C7311yescharacteristic, complemented
197C73#1296211yescharacteristic, direct product factor, Sylow
198#568C22×C7311yescharacteristic
199#525C22×C7311yescharacteristic
200#435—21no—
201#435—21no—
202C8×D4—21no—
203C8×D4—21no—
204#433—21no—
205#430—21no—
206#424—21no—
207#413C22×C7311yescharacteristic
208#413C22×C7311yescharacteristic
209#410C22×C7311yescharacteristic
210#408C22×C7311yescharacteristic
211#408C22×C7311yescharacteristic
212#407—21no—
213C2×C22⋊C8—21no—
214#352C4×C7312yes—
215AΣL(1,𝔽16)C4×C7312yes—
216#344—21no—
217#344—21no—
218#341—21no—
219C2×#41C23×C7311yescharacteristic
220C23×C4D4×C7311yescharacteristic
221#131—42no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16D4×C7311yescharacteristic
228C2×M16D4×C7311yescharacteristic
229C22×C8—21no—
230C22×C8—21no—
231C22×C8D4×C7311yescharacteristic
232C22×C8D4×C7311yescharacteristic
233#123C2×C4×C7311yescharacteristic
234#123Q8×C7311yescharacteristic
235C22⋊Q8—21no—
236#121—21no—
237#120C2×C4×C7311yescharacteristic
238#120Q8×C7311yescharacteristic
239C4×D4—21no—
240C4×D4—21no—
241#117—21no—
242#117D4×C7311yescharacteristic
243#108—42no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—42no—
247#101—21no—
248#101—21no—
249#100—21no—
250#100C2×C4×C7312yes—
251#99—21no—
252#99C2×C4×C7312yes—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—42no—
260#97—21no—
261C4×C8—21no—
262C24C4⋊C4×C7311yescharacteristic
263#41—41no—
264#41—41no—
265C2×Q8#41×C7311yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4C22×C4×C7311yescharacteristic
269C2×D4C2×Q8×C7311yescharacteristic
270C2×D4#41×C7311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4C4⋊C4×C7311yescharacteristic
276C22×C4C2×D4×C7311yescharacteristic
277C22×C4C2×D4×C7311yescharacteristic
278C22×C4C2×D4×C7311yescharacteristic
279M16—22no—
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—81no—
301C2×C8—81no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—22no—
311C22⋊C4C4⋊C4×C7311yescharacteristic
312C22⋊C4C4⋊C4×C7311yescharacteristic
313C42—21no—
314C42—41no—
315C23—21no—
316C23—41no—
317C23—42no—
318C23C2×C4⋊C4×C7311yescharacteristic
319C23C4×D4×C7311yescharacteristic
320C23C22⋊Q8×C7311yescharacteristic
321Q8—41no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4C4×D4×C7311yescharacteristic
342C2×C4#120×C7311yescharacteristic
343C2×C4C22⋊Q8×C7311yescharacteristic
344C2×C4#123×C7311yescharacteristic
345C8—42no—
346C8—42no—
347C8—41no—
348C8—41no—
349C8—41no—
350C8—41no—
351C8—81no—
352C22—22no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—41no—
362C22—81no—
363C22#385×C7311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—82no—
371C4B(4,𝔽2)×C7311yescharacteristic
372C4#458×C7311yescharacteristic
373C2—21no—
374C2—41no—
375C2—42no—
376C2—41no—
377C2—41no—
378C2C73×#186711yescharacteristic
subgroupG/H
centerC4×C73B(4,𝔽2)
commutatorC2×D4C22×C4×C73
Frattini, cosocleC2×#41C23×C73
socleC2×C73#1867
prime radical#525×C73C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
4. C73×#1868C2semidirect
5. C73×#1858C2semidirect
6. C73×#1395C2semidirect
7. C73×#1392C2semidirect
183. #12962C73direct (N × H)
193. #1868C2×C73semidirect
194. #1858C2×C73semidirect
195. #1395C2×C73semidirect
196. #1392C2×C73semidirect
197. C73#12962direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#29772
C73×#21202
C73×#18912
C73×#18682
C73×#18582
C73×#13952
C73×#13922
#1296273