Finite Group Databasebeta

← C73×#9348 #32918752

Subgroups — C73×#9348 #32918752

Order 18688.

470 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3094C211yesmaximal, characteristic
2C73×#2924C211yesmaximal, characteristic, complemented
3C73×#1825C211yesmaximal, characteristic, complemented
4C73×#1519C211yesmaximal, characteristic
5C73×#1471C211yesmaximal, characteristic
6C73×#1305C211yesmaximal, characteristic, complemented
7C73×#1298C211yesmaximal, characteristic, complemented
8C2×#121×C73C2211yescharacteristic
9C2×#117×C73C2211yescharacteristic
10#482×C73—21no—
11#482×C73—21no—
12#481×C73—21no—
13#480×C73—21no—
14#433×C73—22no—
15#432×C73—21no—
16#431×C73—21no—
17#428×C73C411yescharacteristic, complemented
18#428×C73C411yescharacteristic, complemented
19#424×C73—21no—
20#418×C73C411yescharacteristic, complemented
21#418×C73C411yescharacteristic, complemented
22#407×C73C2211yescharacteristic
23#407×C73C2211yescharacteristic
24C2×C22⋊C8×C73C2211yescharacteristic
25C2×C22⋊C8×C73C2211yescharacteristic
26#405×C73—21no—
27#380×C73C2211yescharacteristic
28#340×C73—21no—
29#340×C73—21no—
30#327×C73—21no—
31#327×C73—21no—
32#323×C73—22no—
33C22×D4×C73—21no—
34C22×D4×C73C2×C411yescharacteristic
35C23×C4×C73C2311yescharacteristic
36C2×M16×C73—21no—
37C2×M16×C73C2×C411yescharacteristic
38C2×M16×C73C2×C411yescharacteristic
39C22×C8×C73—21no—
40C22×C8×C73—21no—
41#121×C73—21no—
42#121×C73—21no—
43#121×C73—21no—
44#121×C73—21no—
45#117×C73—21no—
46#117×C73—21no—
47#117×C73C2×C411yescharacteristic
48#117×C73C2×C411yescharacteristic
49#117×C73D411yescharacteristic
50#117×C73D411yescharacteristic
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C4⋊C4×C73D411yescharacteristic
54C2×C4⋊C4×C73D411yescharacteristic
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—21no—
57C2×C22⋊C4×C73—21no—
58C2×C42×C73—21no—
59#107×C73—21no—
60#107×C73—21no—
61#106×C73—21no—
62#106×C73—21no—
63C4⋊C8×C73—22no—
64C4⋊C8×C73—22no—
65#102×C73—21no—
66#102×C73—21no—
67#102×C73—21no—
68#102×C73—21no—
69C22⋊C8×C73—21no—
70C22⋊C8×C73—21no—
71C22⋊C8×C73—21no—
72C22⋊C8×C73—21no—
73C22⋊C8×C73—21no—
74C22⋊C8×C73—21no—
75C22⋊C8×C73D411yescharacteristic
76C22⋊C8×C73D411yescharacteristic
77C22⋊C8×C73D412yes—
78#97×C73—22no—
79C4×C8×C73—22no—
80#95×C73—21no—
81C24×C73—21no—
82C24×C73#4111yescharacteristic
83C2×D4×C73—21no—
84C2×D4×C73—21no—
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—21no—
94C22×C4×C73—41no—
95C22×C4×C73—41no—
96C22×C4×C73—41no—
97C22×C4×C73C22×C411yescharacteristic
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D411yescharacteristic
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73#4111yescharacteristic
103M16×C73—41no—
104M16×C73—41no—
105M16×C73—41no—
106M16×C73—41no—
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73—21no—
110C2×C8×C73—22no—
111C2×C8×C73—21no—
112C2×C8×C73—41no—
113C2×C8×C73—41no—
114C2×C8×C73—41no—
115C2×C8×C73—41no—
116C2×C8×C73—41no—
117C4⋊C4×C73—21no—
118C4⋊C4×C73—21no—
119C4⋊C4×C73—21no—
120C4⋊C4×C73—21no—
121C4⋊C4×C73—41no—
122C4⋊C4×C73—41no—
123C4⋊C4×C73C22⋊C411yescharacteristic
124C4⋊C4×C73C22⋊C411yescharacteristic
125C4⋊C4×C73C22⋊C411yescharacteristic
126C4⋊C4×C73C22⋊C411yescharacteristic
127C22⋊C4×C73—21no—
128C22⋊C4×C73—21no—
129C22⋊C4×C73—21no—
130C22⋊C4×C73—21no—
131C22⋊C4×C73—41no—
132C22⋊C4×C73—41no—
133C22⋊C4×C73—81no—
134C42×C73—21no—
135C42×C73—21no—
136C42×C73—21no—
137C42×C73—21no—
138C23×C73—21no—
139C23×C73—21no—
140C23×C73—41no—
141C23×C73—41no—
142C23×C73—42no—
143C23×C73—41no—
144C23×C73—81no—
145C23×C73—81no—
146C23×C73C4×D411yescharacteristic
147C23×C73#12111yescharacteristic
148C23×C73#12311yescharacteristic
149D4×C73—41no—
150D4×C73—41no—
151D4×C73—81no—
152D4×C73—82no—
153D4×C73—81no—
154D4×C73—81no—
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—21no—
160C2×C4×C73—21no—
161C2×C4×C73—21no—
162C2×C4×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73—41no—
168C2×C4×C73—41no—
169C2×C4×C73—41no—
170C2×C4×C73—41no—
171C2×C4×C73—81no—
172C2×C4×C73—81no—
173C2×C4×C73—81no—
174C2×C4×C73—81no—
175C2×C4×C73—81no—
176C2×C4×C73C2×C22⋊C411yescharacteristic
177C2×C4×C73C4×D411yescharacteristic
178C2×C4×C73#12011yescharacteristic
179C2×C4×C73#12111yescharacteristic
180C8×C73—41no—
181C8×C73—41no—
182C8×C73—42no—
183C8×C73—41no—
184C8×C73—41no—
185C8×C73—81no—
186C22×C73—21no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—21no—
192C22×C73—21no—
193C22×C73—21no—
194C22×C73—81no—
195C22×C73—81no—
196C22×C73—81no—
197C22×C73—81no—
198C22×C73—81no—
199C22×C73—162no—
200C22×C73#38611yescharacteristic
201C22×C73#47111yescharacteristic
202C22×C73#47211yescharacteristic
203C4×C73—21no—
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—41no—
207C4×C73—41no—
208C4×C73—41no—
209C4×C73—41no—
210C4×C73—81no—
211C4×C73—161no—
212C4×C73#41011yescharacteristic
213C4×C73#41011yescharacteristic
214#9348C7311yesmaximal, characteristic, direct product factor, Sylow
215C2×C73—21no—
216C2×C73—21no—
217C2×C73—41no—
218C2×C73—41no—
219C2×C73—161no—
220C2×C73#188111yescharacteristic
221C2×C73#189911yescharacteristic
222C2×C73#190711yescharacteristic
223#3094C2×C7311yescharacteristic
224#2924C2×C7311yescharacteristic, complemented
225#1825C2×C7311yescharacteristic, complemented
226#1519C2×C7311yescharacteristic
227#1471C2×C7311yescharacteristic
228#1305C2×C7311yescharacteristic, complemented
229#1298C2×C7311yescharacteristic, complemented
230C73#934811yescharacteristic, direct product factor, Sylow
231C2×#121C22×C7311yescharacteristic
232C2×#117C22×C7311yescharacteristic
233#482—21no—
234#482—21no—
235#481—21no—
236#480—21no—
237#433—22no—
238#432—21no—
239#431—21no—
240#428C4×C7311yescharacteristic, complemented
241#428C4×C7311yescharacteristic, complemented
242#424—21no—
243#418C4×C7311yescharacteristic, complemented
244#418C4×C7311yescharacteristic, complemented
245#407C22×C7311yescharacteristic
246#407C22×C7311yescharacteristic
247C2×C22⋊C8C22×C7311yescharacteristic
248C2×C22⋊C8C22×C7311yescharacteristic
249#405—21no—
250#380C22×C7311yescharacteristic
251#340—21no—
252#340—21no—
253#327—21no—
254#327—21no—
255#323—22no—
256C22×D4—21no—
257C22×D4C2×C4×C7311yescharacteristic
258C23×C4C23×C7311yescharacteristic
259C2×M16—21no—
260C2×M16C2×C4×C7311yescharacteristic
261C2×M16C2×C4×C7311yescharacteristic
262C22×C8—21no—
263C22×C8—21no—
264#121—21no—
265#121—21no—
266#121—21no—
267#121—21no—
268#117—21no—
269#117—21no—
270#117C2×C4×C7311yescharacteristic
271#117C2×C4×C7311yescharacteristic
272#117D4×C7311yescharacteristic
273#117D4×C7311yescharacteristic
274C2×C4⋊C4—21no—
275C2×C4⋊C4C2×C4×C7311yescharacteristic
276C2×C4⋊C4D4×C7311yescharacteristic
277C2×C4⋊C4D4×C7311yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C42—21no—
282#107—21no—
283#107—21no—
284#106—21no—
285#106—21no—
286C4⋊C8—22no—
287C4⋊C8—22no—
288#102—21no—
289#102—21no—
290#102—21no—
291#102—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8D4×C7312yes—
299C22⋊C8D4×C7311yescharacteristic
300C22⋊C8D4×C7311yescharacteristic
301#97—22no—
302C4×C8—22no—
303#95—21no—
304C24—21no—
305C24#41×C7311yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—81no—
313C2×D4—81no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C22×C4×C7311yescharacteristic
321C22×C4C2×D4×C7311yescharacteristic
322C22×C4C2×D4×C7311yescharacteristic
323C22×C4C2×D4×C7311yescharacteristic
324C22×C4C2×D4×C7311yescharacteristic
325C22×C4#41×C7311yescharacteristic
326M16—41no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4C22⋊C4×C7311yescharacteristic
347C4⋊C4C22⋊C4×C7311yescharacteristic
348C4⋊C4C22⋊C4×C7311yescharacteristic
349C4⋊C4C22⋊C4×C7311yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—81no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23C4×D4×C7311yescharacteristic
370C23#121×C7311yescharacteristic
371C23#123×C7311yescharacteristic
372D4—41no—
373D4—41no—
374D4—81no—
375D4—82no—
376D4—81no—
377D4—81no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C2×C22⋊C4×C7311yescharacteristic
400C2×C4C4×D4×C7311yescharacteristic
401C2×C4#120×C7311yescharacteristic
402C2×C4#121×C7311yescharacteristic
403C8—41no—
404C8—41no—
405C8—42no—
406C8—41no—
407C8—41no—
408C8—81no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—162no—
423C22#386×C7311yescharacteristic
424C22#471×C7311yescharacteristic
425C22#472×C7311yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—81no—
434C4—161no—
435C4#410×C7311yescharacteristic
436C4#410×C7311yescharacteristic
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2C73×#188111yescharacteristic
443C2C73×#189911yescharacteristic
444C2C73×#190711yescharacteristic
subgroupG/H
center, socleC22×C73#386
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2924C2semidirect
3. C73×#1825C2semidirect
6. C73×#1305C2semidirect
7. C73×#1298C2semidirect
17. #428×C73C4semidirect
18. #428×C73C4semidirect
20. #418×C73C4semidirect
21. #418×C73C4semidirect
214. #9348C73direct (N × H)
224. #2924C2×C73semidirect
225. #1825C2×C73semidirect
228. #1305C2×C73semidirect
229. #1298C2×C73semidirect
230. C73#9348direct (N × H)
240. #428C4×C73semidirect
241. #428C4×C73semidirect
243. #418C4×C73semidirect
244. #418C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30942
C73×#29242
C73×#18252
C73×#15192
C73×#14712
C73×#13052
C73×#12982
#934873