Finite Group Databasebeta

← C73×#10537 #32919941

Subgroups — C73×#10537 #32919941

Order 18688.

554 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#492×C73C211yesmaximal, characteristic
2C73×#1988C211yesmaximal, characteristic, complemented
3C73×#1982C211yesmaximal, characteristic
4C73×#1939C211yesmaximal, characteristic, complemented
5C2×#332×C73C211yesmaximal, characteristic, complemented
6C2×#331×C73C211yesmaximal, characteristic
7C73×#1277C211yesmaximal, characteristic, complemented
8C22×SD16×C73—21no—
9C22×SD16×C73—21no—
10C2×C4⋊Q8×C73C2211yescharacteristic
11C2×#127×C73C2211yescharacteristic
12#492×C73—22no—
13#492×C73—22no—
14C2×C4⋊C8×C73—21no—
15C2×C4⋊C8×C73C2211yescharacteristic
16C2×C4⋊C8×C73C2211yescharacteristic
17C2×C4⋊C8×C73C2211yescharacteristic
18C2×#102×C73—21no—
19C2×#102×C73—21no—
20C2×C4×C8×C73C2211yescharacteristic
21C4×C4⋊C4×C73C2211yescharacteristic
22#340×C73—21no—
23#340×C73—21no—
24#336×C73—21no—
25#332×C73—22no—
26#331×C73—22no—
27C22×Q8×C73—21no—
28C22×D4×C73—21no—
29C22×D4×C73—21no—
30C22×D4×C73—21no—
31C2×SD16×C73—24no—
32C2×SD16×C73—24no—
33C2×SD16×C73—42no—
34C2×SD16×C73—42no—
35C2×SD16×C73—42no—
36C2×SD16×C73—42no—
37C22×C8×C73—21no—
38C22×C8×C73—21no—
39C22×C8×C73—21no—
40C22×C8×C73D411yescharacteristic
41C22×C8×C73D411yescharacteristic
42C4⋊Q8×C73—21no—
43C4⋊Q8×C73—21no—
44C4⋊Q8×C73—21no—
45C4⋊Q8×C73D412yes—
46#127×C73—21no—
47#127×C73—21no—
48#127×C73—21no—
49#127×C73D412yes—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73D411yescharacteristic
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C42×C73—21no—
55C2×C42×C73C2311yescharacteristic
56C4⋊C8×C73—21no—
57C4⋊C8×C73—21no—
58C4⋊C8×C73—21no—
59C4⋊C8×C73—21no—
60C4⋊C8×C73—21no—
61C4⋊C8×C73—21no—
62C4⋊C8×C73—42no—
63#102×C73—42no—
64#102×C73—42no—
65C4×C8×C73—21no—
66C4×C8×C73—21no—
67#95×C73—21no—
68C24×C73—41no—
69C2×Q8×C73—22no—
70C2×Q8×C73—41no—
71C2×Q8×C73—41no—
72C2×Q8×C73—41no—
73C2×Q8×C73—41no—
74C2×Q8×C73—41no—
75C2×D4×C73—22no—
76C2×D4×C73—22no—
77C2×D4×C73—22no—
78C2×D4×C73—41no—
79C2×D4×C73—41no—
80C2×D4×C73—41no—
81C2×D4×C73—41no—
82C2×D4×C73—41no—
83C2×D4×C73—41no—
84C2×D4×C73—41no—
85C2×D4×C73—41no—
86C2×D4×C73—41no—
87C2×D4×C73—41no—
88C2×D4×C73—41no—
89C2×D4×C73—81no—
90C2×D4×C73—81no—
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73—41no—
94C22×C4×C73C2×D411yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
96C22×C4×C73#4111yescharacteristic
97SD16×C73—48no—
98SD16×C73—48no—
99C2×C8×C73—21no—
100C2×C8×C73—21no—
101C2×C8×C73—21no—
102C2×C8×C73—21no—
103C2×C8×C73—41no—
104C2×C8×C73—41no—
105C2×C8×C73—41no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C2×C8×C73—41no—
112C2×C8×C73D812yes—
113C2×C8×C73SD1612yes—
114C4⋊C4×C73—21no—
115C4⋊C4×C73—22no—
116C4⋊C4×C73—22no—
117C4⋊C4×C73—21no—
118C4⋊C4×C73—21no—
119C4⋊C4×C73—41no—
120C4⋊C4×C73—41no—
121C4⋊C4×C73SD1612yescomplemented
122C42×C73—41no—
123C42×C73—41no—
124C42×C73C2×D411yescharacteristic
125C42×C73C2×D411yescharacteristic
126C42×C73#4111yescharacteristic
127C42×C73#4111yescharacteristic
128C23×C73—42no—
129C23×C73—81no—
130C23×C73—81no—
131C23×C73—81no—
132C23×C73—81no—
133C23×C73—81no—
134C23×C73—81no—
135C23×C73#12111yescharacteristic
136Q8×C73—42no—
137Q8×C73—42no—
138Q8×C73—81no—
139Q8×C73—81no—
140D4×C73—42no—
141D4×C73—42no—
142D4×C73—42no—
143D4×C73—42no—
144D4×C73—82no—
145D4×C73—82no—
146D4×C73—81no—
147D4×C73—81no—
148D4×C73—81no—
149D4×C73—81no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—22no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—42no—
156C2×C4×C73—41no—
157C2×C4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73—81no—
160C2×C4×C73—81no—
161C2×C4×C73#12011yescharacteristic
162C2×C4×C73#12111yescharacteristic
163C2×C4×C73#12111yescharacteristic
164C2×C4×C73#12311yescharacteristic
165C2×C4×C73#12311yescharacteristic
166C2×C4×C73#12411yescharacteristic
167C2×C4×C73C2×D811yescharacteristic
168C2×C4×C73C2×SD1611yescharacteristic
169C2×C4×C73C2×SD1611yescharacteristic
170C2×C4×C73#13511yescharacteristic
171C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C73#13711yescharacteristic
175C8×C73—22no—
176C8×C73—22no—
177C8×C73—81no—
178C8×C73—81no—
179C8×C73—81no—
180C22×C73—82no—
181C22×C73—82no—
182C22×C73—82no—
183C22×C73—161no—
184C22×C73—161no—
185C22×C73—161no—
186C22×C73—161no—
187C22×C73#39411yescharacteristic
188C22×C73#45911yescharacteristic
189C22×C73#46011yescharacteristic
190C22×C73#46511yescharacteristic
191C22×C73#46811yescharacteristic
192C22×C73#47111yescharacteristic
193C22×C73#47111yescharacteristic
194C4×C73—21no—
195C4×C73—21no—
196C4×C73—42no—
197C4×C73—81no—
198C4×C73—82no—
199C4×C73#44711yescharacteristic
200C4×C73#45011yescharacteristic
201C4×C73#46011yescharacteristic
202C4×C73#46111yescharacteristic
203C4×C73#46311yescharacteristic
204C4×C73#46411yescharacteristic
205C4×C73#48611yescharacteristic
206C4×C73#49011yescharacteristic
207#10537C7311yesmaximal, characteristic, direct product factor, Sylow
208C2×C73—162no—
209C2×C73#166511yescharacteristic
210C2×C73#166611yescharacteristic
211C2×C73#168511yescharacteristic
212C2×C73#168611yescharacteristic
213C2×C73#204111yescharacteristic
214C2×C73#204611yescharacteristic
215C2×C73#205511yescharacteristic
216C2×#492C2×C7311yescharacteristic
217#1988C2×C7311yescharacteristic, complemented
218#1982C2×C7311yescharacteristic
219#1939C2×C7311yescharacteristic, complemented
220C2×#332C2×C7311yescharacteristic, complemented
221C2×#331C2×C7311yescharacteristic
222#1277C2×C7311yescharacteristic, complemented
223C73#1053711yescharacteristic, direct product factor, Sylow
224C22×SD16—21no—
225C22×SD16—21no—
226C2×C4⋊Q8C22×C7311yescharacteristic
227C2×#127C22×C7311yescharacteristic
228#492—22no—
229#492—22no—
230C2×C4⋊C8—21no—
231C2×C4⋊C8C22×C7311yescharacteristic
232C2×C4⋊C8C22×C7311yescharacteristic
233C2×C4⋊C8C22×C7311yescharacteristic
234C2×#102—21no—
235C2×#102—21no—
236C2×C4×C8C22×C7311yescharacteristic
237C4×C4⋊C4C22×C7311yescharacteristic
238#340—21no—
239#340—21no—
240#336—21no—
241#332—22no—
242#331—22no—
243C22×Q8—21no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4—21no—
247C2×SD16—24no—
248C2×SD16—24no—
249C2×SD16—42no—
250C2×SD16—42no—
251C2×SD16—42no—
252C2×SD16—42no—
253C22×C8—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8D4×C7311yescharacteristic
257C22×C8D4×C7311yescharacteristic
258C4⋊Q8—21no—
259C4⋊Q8—21no—
260C4⋊Q8—21no—
261C4⋊Q8D4×C7312yes—
262#127—21no—
263#127—21no—
264#127—21no—
265#127D4×C7312yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4D4×C7311yescharacteristic
269C2×C4⋊C4D4×C7311yescharacteristic
270C2×C42—21no—
271C2×C42C23×C7311yescharacteristic
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—42no—
279#102—42no—
280#102—42no—
281C4×C8—21no—
282C4×C8—21no—
283#95—21no—
284C24—41no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—81no—
306C2×D4—81no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4C2×D4×C7311yescharacteristic
311C22×C4C2×D4×C7311yescharacteristic
312C22×C4#41×C7311yescharacteristic
313SD16—48no—
314SD16—48no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8D8×C7312yes—
329C2×C8SD16×C7312yes—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4SD16×C7312yescomplemented
338C42—41no—
339C42—41no—
340C42C2×D4×C7311yescharacteristic
341C42C2×D4×C7311yescharacteristic
342C42#41×C7311yescharacteristic
343C42#41×C7311yescharacteristic
344C23—42no—
345C23—81no—
346C23—81no—
347C23—81no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23#121×C7311yescharacteristic
352Q8—42no—
353Q8—42no—
354Q8—81no—
355Q8—81no—
356D4—42no—
357D4—42no—
358D4—42no—
359D4—42no—
360D4—82no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4#120×C7311yescharacteristic
378C2×C4#121×C7311yescharacteristic
379C2×C4#121×C7311yescharacteristic
380C2×C4#123×C7311yescharacteristic
381C2×C4#123×C7311yescharacteristic
382C2×C4#124×C7311yescharacteristic
383C2×C4C2×D8×C7311yescharacteristic
384C2×C4C2×SD16×C7311yescharacteristic
385C2×C4C2×SD16×C7311yescharacteristic
386C2×C4#135×C7311yescharacteristic
387C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
388C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
389C2×C4AGL(1,ℤ/8)×C7311yescharacteristic
390C2×C4#137×C7311yescharacteristic
391C8—22no—
392C8—22no—
393C8—81no—
394C8—81no—
395C8—81no—
396C22—82no—
397C22—82no—
398C22—82no—
399C22—161no—
400C22—161no—
401C22—161no—
402C22—161no—
403C22#394×C7311yescharacteristic
404C22#459×C7311yescharacteristic
405C22#460×C7311yescharacteristic
406C22#465×C7311yescharacteristic
407C22#468×C7311yescharacteristic
408C22#471×C7311yescharacteristic
409C22#471×C7311yescharacteristic
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—82no—
415C4#447×C7311yescharacteristic
416C4#450×C7311yescharacteristic
417C4#460×C7311yescharacteristic
418C4#461×C7311yescharacteristic
419C4#463×C7311yescharacteristic
420C4#464×C7311yescharacteristic
421C4#486×C7311yescharacteristic
422C4#490×C7311yescharacteristic
423C2—162no—
424C2C73×#166511yescharacteristic
425C2C73×#166611yescharacteristic
426C2C73×#168511yescharacteristic
427C2C73×#168611yescharacteristic
428C2C73×#204111yescharacteristic
429C2C73×#204611yescharacteristic
430C2C73×#205511yescharacteristic
subgroupG/H
center, socleC23×C73#121
commutator, Frattini, cosocleC2×C42C23×C73
prime radicalC2×#127×C73C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#1988C2semidirect
4. C73×#1939C2semidirect
5. C2×#332×C73C2semidirect
7. C73×#1277C2semidirect
121. C4⋊C4×C73SD16semidirect
207. #10537C73direct (N × H)
217. #1988C2×C73semidirect
219. #1939C2×C73semidirect
220. C2×#332C2×C73semidirect
222. #1277C2×C73semidirect
223. C73#10537direct (N × H)
337. C4⋊C4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#492×C732
C73×#19882
C73×#19822
C73×#19392
C2×#332×C732
C2×#331×C732
C73×#12772
#1053773