Finite Group Databasebeta

← #32981554

Subgroups — #32981554

Order 18688.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618262C211yesmaximal, characteristic
2C2×#17988322C212yesmaximal
3#22608158C211yesmaximal, characteristic, complemented
4#22607811C212yesmaximal, complemented
5C2×#431×C73C211yesmaximal, characteristic, complemented
6C2×#14556574—21no—
7C2×#14556565C2211yescharacteristic
8#17988489C411yescharacteristic, complemented
9#17988489C411yescharacteristic, complemented
10#17988485C411yescharacteristic, complemented
11#17988485C411yescharacteristic, complemented
12#17988478—21no—
13#17988478—21no—
14#17988466—21no—
15#17988447C2211yescharacteristic
16C2×#14556498—21no—
17C2×#14556498—21no—
18C2×#14556498C2212yes—
19#17988322—24no—
20C22×C42×C73C2211yescharacteristic
21#431×C73—24no—
22C2×C4⋊C8×C73—21no—
23C2×C22⋊C8×C73C2212yes—
24C2×C4×C8×C73—21no—
25C22×D292C2×C411yescharacteristic
26C22×C22⋊D73—21no—
27C23×Dic73—22no—
28#14556574—42no—
29#14556574—42no—
30#14556565—22no—
31#14556565—22no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×#11924005—21no—
39C2×#11924005—21no—
40C2×#11924005—21no—
41C2×#11924005—21no—
42C2×#11924005—21no—
43#14556498—24no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—22no—
48#14556498—22no—
49#14556498—42no—
50C23×C4×C73D411yescharacteristic
51C23×C4×C73D411yescharacteristic
52C23×C4×C73C2311yescharacteristic
53C22×C8×C73—22no—
54C2×C42×C73—22no—
55C2×C42×C73—22no—
56C2×C42×C73C2×C411yescharacteristic
57C2×C42×C73C2×C411yescharacteristic
58C2×C42×C73D411yescharacteristic
59C2×C42×C73D411yescharacteristic
60C4⋊C8×C73—24no—
61C22⋊C8×C73—22no—
62C22⋊C8×C73D414yes—
63C4×C8×C73—24no—
64C23×D73—21no—
65C2×D292—22no—
66C2×D292—41no—
67C2×D292—41no—
68C2×C22⋊D73—42no—
69C2×C22⋊D73—41no—
70C2×C22⋊D73—41no—
71C2×C22⋊D73—42no—
72C22×Dic73—24no—
73C22×Dic73—21no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C22×Dic73—42no—
77C22×Dic73—42no—
78C22×Dic73—42no—
79C22×Dic73—42no—
80C22×Dic73—42no—
81C22×Dic73—42no—
82C4⋊Dic73—22no—
83C4⋊Dic73—41no—
84C4⋊Dic73—41no—
85#11924007—42no—
86#11924007—42no—
87C22⋊Dic73—41no—
88C22⋊Dic73—41no—
89#11924005—42no—
90#11924005—42no—
91#11924005—42no—
92#11924005—42no—
93#11924005—41no—
94#11924005—41no—
95C24×C73C2×D411yescharacteristic
96C22×C4×C73—22no—
97C22×C4×C73—22no—
98C22×C4×C73—22no—
99C22×C4×C73—22no—
100C22×C4×C73—41no—
101C22×C4×C73—41no—
102C22×C4×C73—41no—
103C22×C4×C73C22⋊C411yescharacteristic
104C22×C4×C73C22⋊C411yescharacteristic
105C22×C4×C73C22⋊C411yescharacteristic
106C22×C4×C73C22⋊C411yescharacteristic
107C22×C4×C73D812yes—
108C22×C4×C73SD1612yes—
109C22×C4×C73C22×C411yescharacteristic
110C22×C4×C73C2×D411yescharacteristic
111C22×C4×C73C2×D412yes—
112C22×C4×C73#4112yes—
113C2×C8×C73—24no—
114C2×C8×C73—42no—
115C2×C8×C73—42no—
116C42×C73—22no—
117C42×C73—22no—
118C42×C73—21no—
119C42×C73—21no—
120C42×C73—21no—
121C42×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73C2×C22⋊C411yescharacteristic
127C23×C73#12112yes—
128C23×C73C2×D811yescharacteristic
129C23×C73C2×SD1611yescharacteristic
130C23×C73#13512yes—
131C22×D73—41no—
132C22×D73—41no—
133C22×D73—41no—
134C22×D73—41no—
135C22×D73—41no—
136C22×D73—41no—
137C22×D73—41no—
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—21no—
147C2×C4×C73—21no—
148C2×C4×C73—24no—
149C2×C4×C73—24no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—42no—
154C2×C4×C73—42no—
155C2×C4×C73—44no—
156C2×C4×C73#10212yes—
157C2×C4×C73#10212yes—
158C2×C4×C73#10412yes—
159C2×C4×C73C4×D412yes—
160C2×C4×C73#12011yescharacteristic
161C2×C4×C73#12311yescharacteristic
162C22⋊D73—82no—
163C22⋊D73—82no—
164C2×Dic73—44no—
165C2×Dic73—44no—
166C2×Dic73—44no—
167C2×Dic73—41no—
168C2×Dic73—41no—
169C2×Dic73—41no—
170C2×Dic73—41no—
171C2×Dic73—41no—
172C2×Dic73—41no—
173C2×Dic73—41no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C2×Dic73—82no—
177C2×Dic73—82no—
178C2×Dic73—82no—
179C2×Dic73—82no—
180D292—82no—
181C8×C73—44no—
182C22×C73—22no—
183C22×C73—22no—
184C22×C73—22no—
185C22×C73—21no—
186C22×C73—21no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—22no—
190C22×C73#38611yescharacteristic
191C22×C73#41011yescharacteristic
192C22×C73#41011yescharacteristic
193C22×C73C2×#10211yescharacteristic
194C22×C73#41611yescharacteristic
195C22×C73C2×#10411yescharacteristic
196C22×C73#42111yescharacteristic
197C22×C73#46512yes—
198C22×C73#46612yes—
199C2×D73—81no—
200C2×D73—81no—
201C2×D73—81no—
202C2×D73—81no—
203C2×D73—81no—
204C2×D73—81no—
205C2×D73—81no—
206C4×C73—22no—
207C4×C73—22no—
208C4×C73—22no—
209C4×C73—21no—
210C4×C73—22no—
211C4×C73—21no—
212C4×C73—41no—
213Dic73—84no—
214Dic73—81no—
215Dic73—81no—
216Dic73—81no—
217#9114—731nomaximal, Sylow
218C2×C73—22no—
219C2×C73—22no—
220C2×C73#150011yescharacteristic
221C2×C73#150211yescharacteristic
222C2×C73#151711yescharacteristic
223C2×C73#152111yescharacteristic
224C2×C73#187111yescharacteristic
225C2×C73#189311yescharacteristic
226C2×C73#189911yescharacteristic
227D73—161no—
228C2×#431D7311yescharacteristic, complemented
229#2854—731no—
230C2×#327—732no—
231#1434—731no—
232#1294—732no—
233C73#911411yescharacteristic, complemented, Sylow
234C2×#123—1461no—
235C2×#121—731no—
236C22×C42C2×D7311yescharacteristic
237#431—24no—
238C2×C4⋊C8—21no—
239C2×C22⋊C8C2×D7312yes—
240C2×C4×C8—21no—
241#390—731no—
242#390—731no—
243#389—731no—
244#389—731no—
245#388—1461no—
246#388—1461no—
247#386—1461no—
248#380—731no—
249C2×#95—732no—
250C2×#95—1461no—
251C2×#95—1461no—
252#327—1464no—
253C22×D4—731no—
254C22×D4—1461no—
255C23×C4—1462no—
256C23×C4D29211yescharacteristic
257C23×C4D29211yescharacteristic
258C23×C4C22×D7311yescharacteristic
259C22×C8—22no—
260#123—2922no—
261#123—2922no—
262#121—1462no—
263#121—1462no—
264C2×C4⋊C4—731no—
265C2×C4⋊C4—731no—
266C2×C4⋊C4—731no—
267C2×C4⋊C4—1461no—
268C2×C4⋊C4—1461no—
269C2×C22⋊C4—1461no—
270C2×C22⋊C4—1461no—
271C2×C22⋊C4—1461no—
272C2×C22⋊C4—1461no—
273C2×C22⋊C4—1461no—
274C2×C22⋊C4—1461no—
275C2×C42—22no—
276C2×C42—22no—
277C2×C42C4×D7311yescharacteristic
278C2×C42C4×D7311yescharacteristic
279C2×C42C22⋊D7311yescharacteristic
280C2×C42C22⋊D7311yescharacteristic
281C4⋊C8—24no—
282C22⋊C8—22no—
283C22⋊C8C22⋊D7314yes—
284C4×C8—24no—
285#95—2922no—
286#95—1464no—
287#95—1462no—
288#95—1462no—
289#95—1461no—
290#95—1461no—
291#95—1461no—
292C24—1461no—
293C24C2×D29211yescharacteristic
294C2×D4—2921no—
295C2×D4—2921no—
296C2×D4—2922no—
297C2×D4—2921no—
298C2×D4—2921no—
299C2×D4—2922no—
300C2×D4—1462no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—2922no—
309C22×C4—2922no—
310C22×C4—2922no—
311C22×C4—2922no—
312C22×C4—2922no—
313C22×C4—2922no—
314C22×C4—1464no—
315C22×C4—1461no—
316C22×C4—1461no—
317C22×C4—1461no—
318C22×C4#1192400511yescharacteristic
319C22×C4#1192400511yescharacteristic
320C22×C4#1192400511yescharacteristic
321C22×C4#1192400511yescharacteristic
322C22×C4D58412yes—
323C22×C4#1192401712yes—
324C22×C4C2×C4×D7311yescharacteristic
325C22×C4C2×C22⋊D7311yescharacteristic
326C22×C4C2×C22⋊D7312yes—
327C22×C4#1192402812yes—
328C2×C8—24no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—2921no—
332C4⋊C4—2921no—
333C4⋊C4—2922no—
334C4⋊C4—2922no—
335C4⋊C4—1462no—
336C22⋊C4—2922no—
337C22⋊C4—2921no—
338C22⋊C4—2921no—
339C22⋊C4—2922no—
340C22⋊C4—2922no—
341C22⋊C4—2922no—
342C22⋊C4—2921no—
343C22⋊C4—2921no—
344C42—22no—
345C42—22no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—2921no—
355C23—2921no—
356C23—2921no—
357C23—2921no—
358C23—2921no—
359C23—2921no—
360C23—2921no—
361C23C2×#1192400511yescharacteristic
362C23#1455656512yes—
363C23C2×D58411yescharacteristic
364C23C2×#1192401711yescharacteristic
365C23#1455661312yes—
366D4—5842no—
367D4—5842no—
368D4—5842no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—2924no—
388C2×C4—2924no—
389C2×C4—2924no—
390C2×C4—2921no—
391C2×C4—2921no—
392C2×C4—2921no—
393C2×C4—2921no—
394C2×C4—2921no—
395C2×C4—2921no—
396C2×C4—2921no—
397C2×C4—2921no—
398C2×C4—2921no—
399C2×C4—5842no—
400C2×C4—5842no—
401C2×C4—5842no—
402C2×C4—5842no—
403C2×C4#1455651312yes—
404C2×C4#1455651312yes—
405C2×C4#1455651712yes—
406C2×C4C4×C22⋊D7312yes—
407C2×C4#1455656011yescharacteristic
408C2×C4#1455657411yescharacteristic
409C8—44no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—5841no—
419C22—5841no—
420C22—5841no—
421C22—5841no—
422C22—5841no—
423C22—5841no—
424C22—5841no—
425C22#1798846611yescharacteristic
426C22#1798856011yescharacteristic
427C22#1798856011yescharacteristic
428C22C2×#1455651311yescharacteristic
429C22#1798858411yescharacteristic
430C22C2×#1455651711yescharacteristic
431C22#1798860311yescharacteristic
432C22#1798881612yes—
433C22#1798882312yes—
434C4—22no—
435C4—22no—
436C4—22no—
437C4—21no—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—5844no—
442C4—5841no—
443C4—5841no—
444C4—5841no—
445C2—22no—
446C2—22no—
447C2—11681no—
448C2#2260841811yescharacteristic
449C2#2260842711yescharacteristic
450C2#2260849211yescharacteristic
451C2#2260850911yescharacteristic
452C2#2261023311yescharacteristic
453C2#2261035911yescharacteristic
454C2#2261038911yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC2×#431×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556565C22
cosocleC23×C4×C73C23
hypercenterC2×#431D73
hypocenterC73#9114
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #22608158C2semidirect
4. #22607811C2semidirect
5. C2×#431×C73C2semidirect
8. #17988489C4semidirect
9. #17988489C4semidirect
10. #17988485C4semidirect
11. #17988485C4semidirect
228. C2×#431D73semidirect
233. C73#9114semidirect

Maximal subgroups

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

subgroupindex
#226182622
C2×#179883222
#226081582
#226078112
C2×#431×C732
#911473