Finite Group Databasebeta

← #32978718

Subgroups — #32978718

Order 18688.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556565C211yesmaximal, characteristic
2C2×#17988322C212yesmaximal
3#22608158C211yesmaximal, characteristic, complemented
4#22607811C212yesmaximal, complemented
5C73×#1797C211yesmaximal, characteristic, complemented
6C2×#14556565C2211yescharacteristic
7C2×C4×D292C411yescharacteristic, complemented
8C2×C4×C22⋊D73—21no—
9#17988489C411yescharacteristic, complemented
10#17988485C411yescharacteristic, complemented
11#17988478—21no—
12#17988466—21no—
13#17988447C2211yescharacteristic
14C4×C4⋊Dic73C411yescharacteristic, complemented
15C4×#11924005—21no—
16C2×#14556498—21no—
17C2×#14556498—21no—
18C2×#14556498C2212yes—
19#17988322—24no—
20C22×C42×C73C2211yescharacteristic
21C2×C4⋊C8×C73—21no—
22C2×C22⋊C8×C73C2212yes—
23#336×C73—21no—
24C22×D292C2×C411yescharacteristic
25C22×C22⋊D73—21no—
26C23×Dic73—22no—
27C22×C4×D73—21no—
28#14556565—21no—
29#14556565—21no—
30#14556565D412yes—
31#14556565Q812yes—
32C4×D292—42no—
33C4×C22⋊D73—44no—
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×C4⋊Dic73C2×C411yescharacteristic
37C2×#11924007—21no—
38C2×C22⋊Dic73—21no—
39C2×#11924005—21no—
40C2×#11924005—21no—
41C2×#11924005—21no—
42C2×#11924005—21no—
43C2×C4×Dic73—21no—
44#14556498—24no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—22no—
49#14556498—22no—
50#14556498—42no—
51C23×C4×C73D411yescharacteristic
52C23×C4×C73D411yescharacteristic
53C23×C4×C73C2311yescharacteristic
54C22×C8×C73—22no—
55C2×C42×C73—42no—
56C2×C42×C73C2×C411yescharacteristic
57C2×C42×C73C2×C411yescharacteristic
58C2×C42×C73D411yescharacteristic
59C2×C42×C73D411yescharacteristic
60C4⋊C8×C73—42no—
61C22⋊C8×C73—22no—
62C22⋊C8×C73—22no—
63C23×D73—21no—
64C2×D292—21no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292C4⋊C412yes—
68C2×C22⋊D73—22no—
69C2×C22⋊D73—22no—
70C2×C22⋊D73—42no—
71C2×C22⋊D73—42no—
72C22×Dic73—21no—
73C22×Dic73—24no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C22×Dic73—42no—
77C22×Dic73—42no—
78C22×Dic73—42no—
79C22×Dic73—42no—
80C22×Dic73—42no—
81C22×Dic73—42no—
82C2×C4×D73—42no—
83C2×C4×D73—42no—
84C2×C4×D73—42no—
85C4⋊Dic73—21no—
86C4⋊Dic73—41no—
87C4⋊Dic73—41no—
88C4⋊Dic73C4⋊C412yes—
89#11924007—42no—
90C22⋊Dic73—42no—
91#11924005—22no—
92#11924005—22no—
93#11924005—42no—
94#11924005—42no—
95#11924005—42no—
96C4×Dic73—42no—
97C24×C73C2×D411yescharacteristic
98C22×C4×C73—22no—
99C22×C4×C73—22no—
100C22×C4×C73—22no—
101C22×C4×C73—22no—
102C22×C4×C73—41no—
103C22×C4×C73—41no—
104C22×C4×C73—41no—
105C22×C4×C73—41no—
106C22×C4×C73C22⋊C411yescharacteristic
107C22×C4×C73C22⋊C411yescharacteristic
108C22×C4×C73C22⋊C411yescharacteristic
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C22×C411yescharacteristic
111C22×C4×C73C2×D411yescharacteristic
112C22×C4×C73C2×D411yescharacteristic
113C22×C4×C73C2×Q811yescharacteristic
114C22×C4×C73#4111yescharacteristic
115C22×C4×C73#4111yescharacteristic
116C2×C8×C73—42no—
117C2×C8×C73—42no—
118C2×C8×C73—42no—
119C42×C73—22no—
120C42×C73—22no—
121C42×C73—41no—
122C42×C73—41no—
123C23×C73—21no—
124C23×C73—21no—
125C23×C73—21no—
126C23×C73—21no—
127C23×C73C2×C22⋊C411yescharacteristic
128C23×C73#12111yescharacteristic
129C23×C73C22⋊Q811yescharacteristic
130C23×C73#13512yes—
131C23×C73AGL(1,ℤ/8)12yes—
132C22×D73—22no—
133C22×D73—41no—
134C22×D73—41no—
135C22×D73—41no—
136C22×D73—41no—
137C22×D73—41no—
138C22×D73—41no—
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—21no—
149C2×C4×C73—21no—
150C2×C4×C73—21no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—44no—
158C2×C4×C73—44no—
159C2×C4×C73#9912yes—
160C2×C4×C73#10412yes—
161C2×C4×C73C2×C4⋊C411yescharacteristic
162C2×C4×C73#11711yescharacteristic
163C2×C4×C73#12111yescharacteristic
164C2×C4×C73C22⋊Q811yescharacteristic
165C22⋊D73—44no—
166C22⋊D73—44no—
167C2×Dic73—22no—
168C2×Dic73—41no—
169C2×Dic73—41no—
170C2×Dic73—44no—
171C2×Dic73—44no—
172C2×Dic73—44no—
173C2×Dic73—41no—
174C2×Dic73—41no—
175C2×Dic73—41no—
176C2×Dic73—41no—
177C2×Dic73—41no—
178C2×Dic73—41no—
179C2×Dic73—82no—
180C2×Dic73—82no—
181C2×Dic73—82no—
182C2×Dic73—82no—
183D292—42no—
184D292—42no—
185C4×D73—84no—
186C8×C73—82no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—22no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—22no—
195C22×C73#38011yescharacteristic
196C22×C73C2×#9911yescharacteristic
197C22×C73#41011yescharacteristic
198C22×C73#41611yescharacteristic
199C22×C73#41811yescharacteristic
200C22×C73C2×#10411yescharacteristic
201C22×C73#42111yescharacteristic
202C22×C73#46312yes—
203C22×C73#47812yes—
204C2×D73—42no—
205C2×D73—42no—
206C2×D73—42no—
207C2×D73—81no—
208C2×D73—81no—
209C2×D73—81no—
210C2×D73—81no—
211C4×C73—21no—
212C4×C73—21no—
213C4×C73—21no—
214C4×C73—21no—
215C4×C73—22no—
216C4×C73—22no—
217C4×C73—41no—
218C4×C73—41no—
219Dic73—42no—
220Dic73—84no—
221Dic73—81no—
222Dic73—81no—
223#8573—731nomaximal, Sylow
224C2×C73—22no—
225C2×C73—22no—
226C2×C73#150011yescharacteristic
227C2×C73#150711yescharacteristic
228C2×C73#151411yescharacteristic
229C2×C73#151611yescharacteristic
230C2×C73#179911yescharacteristic
231C2×C73#180411yescharacteristic
232C2×C73#180611yescharacteristic
233D73—82no—
234C4×#121—731no—
235#1797D7311yescharacteristic, complemented
236C2×#327—732no—
237#1434—731no—
238#1294—732no—
239C73#857311yescharacteristic, complemented, Sylow
240C2×#121—731no—
241C2×C4×D4—731no—
242C2×C4×D4—1461no—
243C22×C42C2×D7311yescharacteristic
244C2×C4⋊C8—21no—
245C2×C22⋊C8C2×D7312yes—
246#390—731no—
247#389—731no—
248#388—1461no—
249#386—1461no—
250#380—731no—
251C4×C4⋊C4—731no—
252C4×C22⋊C4—1461no—
253C2×#95—732no—
254C2×#95—1461no—
255C2×#95—1461no—
256#336—21no—
257#327—1464no—
258C22×D4—731no—
259C22×D4—1461no—
260C23×C4—1462no—
261C23×C4—1461no—
262C23×C4D29211yescharacteristic
263C23×C4D29211yescharacteristic
264C23×C4C22×D7311yescharacteristic
265C22×C8—22no—
266#121—732no—
267#121—732no—
268#121—1461no—
269#121—1461no—
270C4×D4—2922no—
271C4×D4—2924no—
272C2×C4⋊C4—731no—
273C2×C4⋊C4—731no—
274C2×C4⋊C4—731no—
275C2×C4⋊C4—1461no—
276C2×C22⋊C4—1461no—
277C2×C22⋊C4—1461no—
278C2×C22⋊C4—1461no—
279C2×C22⋊C4—1461no—
280C2×C22⋊C4—1461no—
281C2×C42—42no—
282C2×C42—1461no—
283C2×C42C4×D7311yescharacteristic
284C2×C42C4×D7311yescharacteristic
285C2×C42C22⋊D7311yescharacteristic
286C2×C42C22⋊D7311yescharacteristic
287C4⋊C8—42no—
288C22⋊C8—22no—
289C22⋊C8—22no—
290#95—2922no—
291#95—1464no—
292#95—1462no—
293#95—1462no—
294#95—1461no—
295#95—1461no—
296#95—1461no—
297C24—1461no—
298C24C2×D29211yescharacteristic
299C2×D4—2921no—
300C2×D4—2921no—
301C2×D4—2922no—
302C2×D4—2922no—
303C2×D4—732no—
304C2×D4—1462no—
305C2×D4—1462no—
306C2×D4—1461no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—2922no—
316C22×C4—2922no—
317C22×C4—2922no—
318C22×C4—2922no—
319C22×C4—2922no—
320C22×C4—2922no—
321C22×C4—2922no—
322C22×C4—2922no—
323C22×C4—2922no—
324C22×C4—1464no—
325C22×C4—1461no—
326C22×C4—1461no—
327C22×C4—1461no—
328C22×C4#1192400511yescharacteristic
329C22×C4#1192400511yescharacteristic
330C22×C4#1192400511yescharacteristic
331C22×C4#1192400511yescharacteristic
332C22×C4C2×C4×D7311yescharacteristic
333C22×C4D4×D7311yescharacteristic
334C22×C4C2×C22⋊D7311yescharacteristic
335C22×C4Q8×D7311yescharacteristic
336C22×C4#1192402711yescharacteristic
337C22×C4#1192402911yescharacteristic
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—42no—
341C4⋊C4—2921no—
342C4⋊C4—2921no—
343C4⋊C4—2922no—
344C4⋊C4—732no—
345C4⋊C4—1461no—
346C22⋊C4—2922no—
347C22⋊C4—2922no—
348C22⋊C4—2922no—
349C22⋊C4—2922no—
350C22⋊C4—1462no—
351C22⋊C4—1462no—
352C42—22no—
353C42—22no—
354C42—41no—
355C42—41no—
356C42—2922no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—2921no—
362C23—2921no—
363C23—2921no—
364C23—2921no—
365C23—2921no—
366C23—2921no—
367C23—1462no—
368C23C2×#1192400511yescharacteristic
369C23#1455656611yescharacteristic
370C23#1455657111yescharacteristic
371C23#1455661312yes—
372C23#1455661912yes—
373D4—2922no—
374D4—2922no—
375D4—2924no—
376D4—2924no—
377C2×C4—21no—
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—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—2921no—
398C2×C4—2921no—
399C2×C4—2924no—
400C2×C4—2924no—
401C2×C4—2924no—
402C2×C4—2921no—
403C2×C4—2921no—
404C2×C4—2921no—
405C2×C4—2921no—
406C2×C4—2921no—
407C2×C4—2921no—
408C2×C4—5844no—
409C2×C4—5842no—
410C2×C4—5842no—
411C2×C4—5842no—
412C2×C4—5842no—
413C2×C4—1462no—
414C2×C4#1455650512yes—
415C2×C4#1455651712yes—
416C2×C4C4⋊C4×D7311yescharacteristic
417C2×C4#1455654911yescharacteristic
418C2×C4#1455656211yescharacteristic
419C2×C4#1455656711yescharacteristic
420C8—82no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—21no—
428C22—21no—
429C22—2922no—
430C22—2922no—
431C22—2922no—
432C22—5841no—
433C22—5841no—
434C22—5841no—
435C22—5841no—
436C22#1798844411yescharacteristic
437C22C2×#1455650511yescharacteristic
438C22#1798856011yescharacteristic
439C22#1798858411yescharacteristic
440C22#1798859311yescharacteristic
441C22C2×#1455651711yescharacteristic
442C22#1798860311yescharacteristic
443C22#1798880312yes—
444C22#1798888812yes—
445C4—22no—
446C4—22no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—41no—
452C4—41no—
453C4—2922no—
454C4—5844no—
455C4—5841no—
456C4—5841no—
457C2—22no—
458C2—22no—
459C2—5842no—
460C2#2260841811yescharacteristic
461C2#2260844811yescharacteristic
462C2#2260847911yescharacteristic
463C2#2260848811yescharacteristic
464C2#2260991611yescharacteristic
465C2#2260994211yescharacteristic
466C2#2260994811yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1797C2
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556565C22
cosocleC23×C4×C73C23
hypercenter#1797D73
hypocenterC73#8573
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #22608158C2semidirect
4. #22607811C2semidirect
5. C73×#1797C2semidirect
7. C2×C4×D292C4semidirect
9. #17988489C4semidirect
10. #17988485C4semidirect
14. C4×C4⋊Dic73C4semidirect
235. #1797D73semidirect
239. C73#8573semidirect

Maximal subgroups

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

subgroupindex
C4×#145565652
C2×#179883222
#226081582
#226078112
C73×#17972
#857373