Finite Group Databasebeta

← #33004157

Subgroups — #33004157

Order 18688.

466 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988663C211yesmaximal, characteristic
2#22611686C211yesmaximal, characteristic, complemented
3C2×#17988369C211yesmaximal, characteristic, complemented
4C2×#17988368C211yesmaximal, characteristic, complemented
5C2×#17988368C211yesmaximal, characteristic, complemented
6M32×Dic73C211yesmaximal, characteristic, complemented
7C2×#349×C73C211yesmaximal, characteristic, complemented
8C22×#11924011C2211yescharacteristic
9C2×C4×C22⋊D73C411yescharacteristic
10C2×#14556531C2211yescharacteristic
11C2×#14556531C2211yescharacteristic
12#17988663—21no—
13#17988663—21no—
14#17988663—21no—
15#17988663—21no—
16C2×#14556520C411yescharacteristic
17C2×C22⋊#10596831C411yescharacteristic
18C2×#14556503C411yescharacteristic
19C2×C8×Dic73C2211yescharacteristic
20#17988405—21no—
21#17988405—21no—
22#17988369—22no—
23#17988368—22no—
24#17988368—22no—
25#17988362—21no—
26C16×Dic73—21no—
27C22×M16×C73C2211yescharacteristic
28C2×M32×C73C2211yescharacteristic
29C2×M32×C73C2211yescharacteristic
30#349×C73—22no—
31C22×C22⋊D73C811yescharacteristic
32C22×C4×D73C2×C411yescharacteristic
33C2×#11924011—21no—
34C2×#11924011—21no—
35C2×#11924011—21no—
36C2×#11924011—21no—
37C2×#11924011—21no—
38C2×#11924011—21no—
39C22×#10596831C2×C411yescharacteristic
40C22×#10596831C2×C411yescharacteristic
41C4×C22⋊D73—21no—
42C4×C22⋊D73—21no—
43C4×C22⋊D73—21no—
44C4×C22⋊D73—21no—
45C2×#11924007C811yescharacteristic
46C2×C22⋊Dic73C811yescharacteristic
47C2×#11924005C811yescharacteristic
48C2×C4×Dic73C2×C411yescharacteristic
49#14556531—21no—
50#14556531—21no—
51#14556531—21no—
52#14556531D412yescomplemented
53C2×#11924003—21no—
54C2×#11924003—21no—
55#14556520—21no—
56#14556520—21no—
57C22⋊#10596831—21no—
58C22⋊#10596831—21no—
59#14556503—21no—
60#14556503—21no—
61C8×Dic73D411yescharacteristic
62C8×Dic73D411yescharacteristic
63C8×Dic73D411yescharacteristic
64C8×Dic73D411yescharacteristic
65C23×C4×C73C2×C411yescharacteristic
66C2×M16×C73—21no—
67C2×M16×C73—21no—
68C2×M16×C73—21no—
69C2×M16×C73—21no—
70C2×M16×C73—21no—
71C2×M16×C73—21no—
72C22×C8×C73C2×C411yescharacteristic
73C22×C8×C73C2311yescharacteristic
74M32×C73—21no—
75M32×C73—21no—
76M32×C73—21no—
77M32×C73D412yescomplemented
78C2×C16×C73—21no—
79C2×C16×C73—21no—
80C23×D73C2×C811yescharacteristic
81C2×C22⋊D73—21no—
82C2×C22⋊D73—21no—
83C2×C22⋊D73—42no—
84C22×Dic73C2×C811yescharacteristic
85C22×Dic73C2×C811yescharacteristic
86C22×Dic73C2×C811yescharacteristic
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73—21no—
92C2×C4×D73—21no—
93#11924011—41no—
94#11924011—41no—
95#11924011—41no—
96#11924011—41no—
97C2×#10596831—21no—
98C2×#10596831—21no—
99C2×#10596831—21no—
100C2×#10596831—21no—
101C2×#10596831—21no—
102C2×#10596831C22⋊C411yescharacteristic
103C2×#10596831C22⋊C411yescharacteristic
104#11924007—21no—
105#11924007—21no—
106C22⋊Dic73—21no—
107C22⋊Dic73—21no—
108#11924005—21no—
109#11924005—21no—
110C4×Dic73C22⋊C411yescharacteristic
111C4×Dic73C22⋊C411yescharacteristic
112C4×Dic73M1611yescharacteristic
113C4×Dic73M1611yescharacteristic
114#11924003—22no—
115#11924003—41no—
116C24×C73C2×C811yescharacteristic
117C22×C4×C73—21no—
118C22×C4×C73—21no—
119C22×C4×C73—21no—
120C22×C4×C73—21no—
121C22×C4×C73—21no—
122C22×C4×C73—21no—
123C22×C4×C73C2×C811yescharacteristic
124C22×C4×C73C22×C411yescharacteristic
125M16×C73—41no—
126M16×C73—41no—
127M16×C73—41no—
128M16×C73—41no—
129C2×C8×C73—21no—
130C2×C8×C73—21no—
131C2×C8×C73—21no—
132C2×C8×C73C2×D411yescharacteristic
133C2×C8×C73C2×D411yescharacteristic
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73#4111yescharacteristic
137C2×C8×C73#4111yescharacteristic
138C16×C73—22no—
139C16×C73—41no—
140C23×C73—21no—
141C23×C73—21no—
142C23×C73—21no—
143C23×C73—41no—
144C23×C73—41no—
145C23×C73C22×C811yescharacteristic
146C22×D73—21no—
147C22×D73—21no—
148C22×D73—21no—
149C22×D73—41no—
150C22×D73—41no—
151C2×C4×C73—21no—
152C2×C4×C73—21no—
153C2×C4×C73—21no—
154C2×C4×C73—41no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—41no—
158C2×C4×C73C2×C22⋊C411yescharacteristic
159C2×C4×C73C4×D411yescharacteristic
160C2×C4×C73C4×D411yescharacteristic
161C2×C4×C73C2×M1611yescharacteristic
162C2×C4×C73#13111yescharacteristic
163C2×C4×C73#13111yescharacteristic
164C22⋊D73—42no—
165C22⋊D73—42no—
166C2×Dic73—22no—
167C2×Dic73—21no—
168C2×Dic73—21no—
169C2×Dic73—21no—
170C2×Dic73—41no—
171C2×Dic73C22⋊C811yescharacteristic
172C2×Dic73C22⋊C811yescharacteristic
173C2×Dic73C22⋊C811yescharacteristic
174C2×Dic73C22⋊C811yescharacteristic
175C4×D73—41no—
176C4×D73—41no—
177C4×D73—41no—
178C4×D73—41no—
179C8×C73—41no—
180C8×C73#12111yescharacteristic
181C8×C73#12111yescharacteristic
182C8×C73#12411yescharacteristic
183C8×C73#12711yescharacteristic
184#10596831—21no—
185#10596831—21no—
186#10596831—41no—
187C22×C73—21no—
188C22×C73—21no—
189C22×C73—41no—
190C22×C73—41no—
191C22×C73—41no—
192C22×C73—81no—
193C22×C73—81no—
194C22×C73C2×C22⋊C811yescharacteristic
195C22×C73C8×D411yescharacteristic
196C22×C73C8×D411yescharacteristic
197C2×D73—41no—
198C2×D73—41no—
199C2×D73—41no—
200C2×D73—81no—
201C2×D73—81no—
202C4×C73—41no—
203C4×C73#39011yescharacteristic
204C4×C73#40811yescharacteristic
205C4×C73#43611yescharacteristic
206C4×C73#43611yescharacteristic
207Dic73—21no—
208Dic73—21no—
209Dic73—21no—
210Dic73—41no—
211Dic73#34912yescomplemented
212#13194—731nomaximal, Sylow
213C2×C73—21no—
214C2×C73—21no—
215C2×C73—81no—
216C2×C73#195411yescharacteristic
217C2×C73C2×#34911yescharacteristic
218C2×C73#211511yescharacteristic
219D73—81no—
220C2×#436—731no—
221#2150—731no—
222C2×#349—731no—
223C2×#349—731no—
224C2×#349—731no—
225C2×#349D7311yescharacteristic, complemented
226C4×M32—731no—
227C73#1319411yescharacteristic, complemented, Sylow
228C22×M16—731no—
229C22×M16C2×D7311yescharacteristic
230C2×C4×D4—731no—
231C2×M32—731no—
232C2×M32—731no—
233C2×M32C2×D7311yescharacteristic
234C2×M32C2×D7311yescharacteristic
235#436—1461no—
236#436—1461no—
237#436—1461no—
238#436—1461no—
239C2×C4⋊C8—731no—
240C2×C22⋊C8—731no—
241C2×C22⋊C8—731no—
242C2×C4×C8—731no—
243C4⋊C16—1461no—
244C4⋊C16—1461no—
245#349—22no—
246#349—1462no—
247#349—1462no—
248#349—1462no—
249#346—1461no—
250C4×C16—1461no—
251C22×D4—731no—
252C23×C4—731no—
253C23×C4C4×D7311yescharacteristic
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—1461no—
261C2×M16—1461no—
262C2×M16—1461no—
263C2×M16—1461no—
264C2×M16—1461no—
265C2×M16—1461no—
266C22×C8—731no—
267C22×C8—731no—
268C22×C8C4×D7311yescharacteristic
269C22×C8C22×D7311yescharacteristic
270C4×D4—1461no—
271C4×D4—1461no—
272C4×D4—1461no—
273C4×D4—1461no—
274C2×C4⋊C4—731no—
275C2×C22⋊C4—731no—
276C2×C22⋊C4—731no—
277C2×C42—731no—
278M32—21no—
279M32—21no—
280M32—21no—
281M32—732no—
282M32—1461no—
283M32—1461no—
284M32—1461no—
285M32C22⋊D7312yescomplemented
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—1461no—
289C2×C16—1461no—
290C4⋊C8—1461no—
291C4⋊C8—1461no—
292C22⋊C8—1461no—
293C22⋊C8—1461no—
294C22⋊C8—1461no—
295C22⋊C8—1461no—
296C4×C8—731no—
297C4×C8—731no—
298C4×C8—731no—
299C4×C8—731no—
300C24—731no—
301C24C8×D7311yescharacteristic
302C2×D4—2922no—
303C2×D4—1461no—
304C2×D4—1461no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—731no—
312C22×C4—731no—
313C22×C4—731no—
314C22×C4—1461no—
315C22×C4—1461no—
316C22×C4—1461no—
317C22×C4—1461no—
318C22×C4—1461no—
319C22×C4—1461no—
320C22×C4C8×D7311yescharacteristic
321C22×C4C2×C4×D7311yescharacteristic
322M16—41no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—2921no—
327M16—2921no—
328M16—2921no—
329M16—2921no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—731no—
334C2×C8—731no—
335C2×C8—1461no—
336C2×C8—1461no—
337C2×C8—1461no—
338C2×C8—1461no—
339C2×C8—1461no—
340C2×C8D4×D7311yescharacteristic
341C2×C8D4×D7311yescharacteristic
342C2×C8D4×D7311yescharacteristic
343C2×C8C2×C22⋊D7311yescharacteristic
344C2×C8#1192402711yescharacteristic
345C2×C8#1192402811yescharacteristic
346C4⋊C4—1461no—
347C4⋊C4—1461no—
348C22⋊C4—1461no—
349C22⋊C4—1461no—
350C22⋊C4—1461no—
351C22⋊C4—1461no—
352C42—731no—
353C42—731no—
354C42—731no—
355C42—731no—
356C16—22no—
357C16—41no—
358C16—2921no—
359C16—1462no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—2921no—
366C23—2921no—
367C23—1461no—
368C23—1461no—
369C23—1461no—
370C23C2×C8×D7311yescharacteristic
371D4—2922no—
372D4—2922no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—2921no—
381C2×C4—2921no—
382C2×C4—2921no—
383C2×C4—2921no—
384C2×C4—2921no—
385C2×C4—731no—
386C2×C4—731no—
387C2×C4—731no—
388C2×C4—731no—
389C2×C4—1461no—
390C2×C4—1461no—
391C2×C4—1461no—
392C2×C4—1462no—
393C2×C4C22⋊C4×D7311yescharacteristic
394C2×C4#1455655111yescharacteristic
395C2×C4C4×C22⋊D7311yescharacteristic
396C2×C4M16×D7311yescharacteristic
397C2×C4#1455659711yescharacteristic
398C2×C4#1455659911yescharacteristic
399C8—41no—
400C8—2921no—
401C8—1461no—
402C8—1461no—
403C8#1455656311yescharacteristic
404C8#1455656411yescharacteristic
405C8#1455657711yescharacteristic
406C8#1455658711yescharacteristic
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—81no—
413C22—81no—
414C22—2921no—
415C22—2921no—
416C22—2921no—
417C22—5841no—
418C22—5841no—
419C22C22⋊C8×D7311yescharacteristic
420C22#1798865011yescharacteristic
421C22C8×C22⋊D7311yescharacteristic
422C4—41no—
423C4—2921no—
424C4—732no—
425C4—1461no—
426C4—1461no—
427C4—1461no—
428C4#1798848711yescharacteristic
429C4#1798855211yescharacteristic
430C4#1798866211yescharacteristic
431C4#1798866311yescharacteristic
432C2—21no—
433C2—21no—
434C2—81no—
435C2—5841no—
436C2#2261072311yescharacteristic
437C2#349×D7311yescharacteristic
438C2#2261155011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D73
commutatorC23×C73C22×C8
FrattiniC22×C8C22×D73
FittingC2×#349×C73C2
socleC22×C73C2×C22⋊C8
prime radicalC22×C22⋊D73C8
cosocleC22×C8×C73C23
hypercenterC2×#349D73
hypocenterC73#13194
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #22611686C2semidirect
3. C2×#17988369C2semidirect
4. C2×#17988368C2semidirect
5. C2×#17988368C2semidirect
6. M32×Dic73C2semidirect
7. C2×#349×C73C2semidirect
52. #14556531D4semidirect
77. M32×C73D4semidirect
211. Dic73#349semidirect
225. C2×#349D73semidirect
227. C73#13194semidirect
285. M32C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886632
#226116862
C2×#179883692
C2×#179883682
M32×Dic732
C2×#349×C732
#1319473