Finite Group Databasebeta

← #13271969

Subgroups — #13271969

Order 1792.

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×#89900C211yesmaximal, characteristic
2C2×C7×#349C211yesmaximal, characteristic, complemented
3C2×#89348C211yesmaximal, characteristic, complemented
4C2×#89309C211yesmaximal, characteristic, complemented
5C2×#89309C211yesmaximal, characteristic, complemented
6#11729174C211yesmaximal, characteristic, complemented
7Dic7×M32C211yesmaximal, characteristic, complemented
8C22×C7×M16C2211yescharacteristic
9C2×C4×C22⋊D7C411yescharacteristic
10C22×#1131C2211yescharacteristic
11C2×C7×M32C2211yescharacteristic
12C2×C7×M32C2211yescharacteristic
13C2×C22⋊(C7⋊C8)C411yescharacteristic
14#89900—21no—
15#89900—21no—
16#89900—21no—
17#89900—21no—
18C2×(C2×D7)⋊C8C411yescharacteristic
19C2×Dic7⋊C8C411yescharacteristic
20C2×C8×Dic7C2211yescharacteristic
21C2×#6386C2211yescharacteristic
22C2×#6386C2211yescharacteristic
23C7×#349—22no—
24#89348—22no—
25#89309—22no—
26#89309—22no—
27#89297—21no—
28Dic7⋊C16—21no—
29Dic7⋊C16—21no—
30C16×Dic7—21no—
31#13194—71nomaximal, Sylow
32C23×C4×C7C2×C411yescharacteristic
33C22×C22⋊D7C811yescharacteristic
34C22×C4×D7C2×C411yescharacteristic
35C2×C7×M16—21no—
36C2×C7×M16—21no—
37C2×C7×M16—21no—
38C2×C7×M16—21no—
39C2×C7×M16—21no—
40C2×C7×M16—21no—
41C22×C7×C8C2×C411yescharacteristic
42C22×C7×C8C2311yescharacteristic
43C2×C22⋊Dic7C811yescharacteristic
44C4×C22⋊D7—21no—
45C4×C22⋊D7—21no—
46C4×C22⋊D7—21no—
47C4×C22⋊D7—21no—
48C2×(C2×D7)⋊C4C811yescharacteristic
49C2×Dic7⋊C4C811yescharacteristic
50C2×C4×Dic7C2×C411yescharacteristic
51C22×C7⋊C8C2×C411yescharacteristic
52C22×C7⋊C8C2×C411yescharacteristic
53C2×#1131—21no—
54C2×#1131—21no—
55C2×#1131—21no—
56C2×#1131—21no—
57C2×#1131—21no—
58C2×#1131—21no—
59C7×M32—21no—
60C7×M32—21no—
61C7×M32—21no—
62C7×M32D412yescomplemented
63C2×C7×C16—21no—
64C2×C7×C16—21no—
65C22⋊(C7⋊C8)—21no—
66C22⋊(C7⋊C8)—21no—
67(C2×D7)⋊C8—21no—
68(C2×D7)⋊C8—21no—
69Dic7⋊C8—21no—
70Dic7⋊C8—21no—
71C8×Dic7D411yescharacteristic
72C8×Dic7D411yescharacteristic
73C8×Dic7D411yescharacteristic
74C8×Dic7D411yescharacteristic
75#6386—21no—
76#6386—21no—
77#6386—21no—
78#6386D412yescomplemented
79C2×C7⋊C16—21no—
80C2×C7⋊C16—21no—
81C2×#436—71no—
82#2150—71no—
83C2×#349—71no—
84C2×#349—71no—
85C2×#349—71no—
86C2×#349D711yescharacteristic, complemented
87C4×M32—71no—
88C24×C7C2×C811yescharacteristic
89C23×D7C2×C811yescharacteristic
90C22×C4×C7—21no—
91C22×C4×C7—21no—
92C22×C4×C7—21no—
93C22×C4×C7—21no—
94C22×C4×C7—21no—
95C22×C4×C7—21no—
96C22×C4×C7C2×C811yescharacteristic
97C22×C4×C7C22×C411yescharacteristic
98C2×C22⋊D7—21no—
99C2×C22⋊D7—21no—
100C2×C22⋊D7—42no—
101C22×Dic7C2×C811yescharacteristic
102C22×Dic7C2×C811yescharacteristic
103C22×Dic7C2×C811yescharacteristic
104C2×C4×D7—21no—
105C2×C4×D7—21no—
106C2×C4×D7—21no—
107C2×C4×D7—21no—
108C2×C4×D7—21no—
109C2×C4×D7—21no—
110C7×M16—41no—
111C7×M16—41no—
112C7×M16—41no—
113C7×M16—41no—
114C2×C7×C8—21no—
115C2×C7×C8—21no—
116C2×C7×C8—21no—
117C2×C7×C8C2×D411yescharacteristic
118C2×C7×C8C2×D411yescharacteristic
119C2×C7×C8C2×D411yescharacteristic
120C2×C7×C8C2×D411yescharacteristic
121C2×C7×C8#4111yescharacteristic
122C2×C7×C8#4111yescharacteristic
123C22⋊Dic7—21no—
124C22⋊Dic7—21no—
125(C2×D7)⋊C4—21no—
126(C2×D7)⋊C4—21no—
127Dic7⋊C4—21no—
128Dic7⋊C4—21no—
129C4×Dic7C22⋊C411yescharacteristic
130C4×Dic7C22⋊C411yescharacteristic
131C4×Dic7M1611yescharacteristic
132C4×Dic7M1611yescharacteristic
133C2×C7⋊C8—21no—
134C2×C7⋊C8—21no—
135C2×C7⋊C8—21no—
136C2×C7⋊C8—21no—
137C2×C7⋊C8—21no—
138C2×C7⋊C8C22⋊C411yescharacteristic
139C2×C7⋊C8C22⋊C411yescharacteristic
140#1131—41no—
141#1131—41no—
142#1131—41no—
143#1131—41no—
144C7×C16—22no—
145C7×C16—41no—
146C7⋊C16—22no—
147C7⋊C16—41no—
148C22×M16—71no—
149C22×M16C2×D711yescharacteristic
150C2×C4×D4—71no—
151C2×M32—71no—
152C2×M32—71no—
153C2×M32C2×D711yescharacteristic
154C2×M32C2×D711yescharacteristic
155#436—141no—
156#436—141no—
157#436—141no—
158#436—141no—
159C2×C4⋊C8—71no—
160C2×C22⋊C8—71no—
161C2×C22⋊C8—71no—
162C2×C4×C8—71no—
163C4⋊C16—141no—
164C4⋊C16—141no—
165#349—22no—
166#349—142no—
167#349—142no—
168#349—142no—
169#346—141no—
170C4×C16—141no—
171C23×C7—21no—
172C23×C7—21no—
173C23×C7—21no—
174C23×C7—41no—
175C23×C7—41no—
176C23×C7C22×C811yescharacteristic
177C22×D7—21no—
178C22×D7—21no—
179C22×D7—21no—
180C22×D7—41no—
181C22×D7—41no—
182C2×C4×C7—21no—
183C2×C4×C7—21no—
184C2×C4×C7—21no—
185C2×C4×C7—41no—
186C2×C4×C7—41no—
187C2×C4×C7—41no—
188C2×C4×C7—41no—
189C2×C4×C7C2×C22⋊C411yescharacteristic
190C2×C4×C7C4×D411yescharacteristic
191C2×C4×C7C4×D411yescharacteristic
192C2×C4×C7C2×M1611yescharacteristic
193C2×C4×C7#13111yescharacteristic
194C2×C4×C7#13111yescharacteristic
195C22⋊D7—42no—
196C22⋊D7—42no—
197C2×Dic7—22no—
198C2×Dic7—21no—
199C2×Dic7—21no—
200C2×Dic7—21no—
201C2×Dic7—41no—
202C2×Dic7C22⋊C811yescharacteristic
203C2×Dic7C22⋊C811yescharacteristic
204C2×Dic7C22⋊C811yescharacteristic
205C2×Dic7C22⋊C811yescharacteristic
206C4×D7—41no—
207C4×D7—41no—
208C4×D7—41no—
209C4×D7—41no—
210C7×C8—41no—
211C7×C8#12111yescharacteristic
212C7×C8#12111yescharacteristic
213C7×C8#12411yescharacteristic
214C7×C8#12711yescharacteristic
215C7⋊C8—21no—
216C7⋊C8—21no—
217C7⋊C8—41no—
218C22×D4—71no—
219C23×C4—71no—
220C23×C4C4×D711yescharacteristic
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—141no—
228C2×M16—141no—
229C2×M16—141no—
230C2×M16—141no—
231C2×M16—141no—
232C2×M16—141no—
233C22×C8—71no—
234C22×C8—71no—
235C22×C8C4×D711yescharacteristic
236C22×C8C22×D711yescharacteristic
237C4×D4—141no—
238C4×D4—141no—
239C4×D4—141no—
240C4×D4—141no—
241C2×C4⋊C4—71no—
242C2×C22⋊C4—71no—
243C2×C22⋊C4—71no—
244C2×C42—71no—
245M32—21no—
246M32—21no—
247M32—21no—
248M32—72no—
249M32—141no—
250M32—141no—
251M32—141no—
252M32C22⋊D712yescomplemented
253C2×C16—21no—
254C2×C16—21no—
255C2×C16—141no—
256C2×C16—141no—
257C4⋊C8—141no—
258C4⋊C8—141no—
259C22⋊C8—141no—
260C22⋊C8—141no—
261C22⋊C8—141no—
262C22⋊C8—141no—
263C4×C8—71no—
264C4×C8—71no—
265C4×C8—71no—
266C4×C8—71no—
267C22×C7—21no—
268C22×C7—21no—
269C22×C7—41no—
270C22×C7—41no—
271C22×C7—41no—
272C22×C7—81no—
273C22×C7—81no—
274C22×C7C2×C22⋊C811yescharacteristic
275C22×C7C8×D411yescharacteristic
276C22×C7C8×D411yescharacteristic
277C2×D7—41no—
278C2×D7—41no—
279C2×D7—41no—
280C2×D7—81no—
281C2×D7—81no—
282C4×C7—41no—
283C4×C7#39011yescharacteristic
284C4×C7#40811yescharacteristic
285C4×C7#43611yescharacteristic
286C4×C7#43611yescharacteristic
287Dic7—21no—
288Dic7—21no—
289Dic7—21no—
290Dic7—41no—
291Dic7#34912yescomplemented
292C24—71no—
293C24C8×D711yescharacteristic
294C2×D4—141no—
295C2×D4—141no—
296C2×D4—282no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—71no—
304C22×C4—71no—
305C22×C4—71no—
306C22×C4—141no—
307C22×C4—141no—
308C22×C4—141no—
309C22×C4—141no—
310C22×C4—141no—
311C22×C4—141no—
312C22×C4C8×D711yescharacteristic
313C22×C4C2×C4×D711yescharacteristic
314M16—41no—
315M16—41no—
316M16—41no—
317M16—41no—
318M16—281no—
319M16—281no—
320M16—281no—
321M16—281no—
322C2×C8—21no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—71no—
326C2×C8—71no—
327C2×C8—141no—
328C2×C8—141no—
329C2×C8—141no—
330C2×C8—141no—
331C2×C8—141no—
332C2×C8#115711yescharacteristic
333C2×C8D4×D711yescharacteristic
334C2×C8D4×D711yescharacteristic
335C2×C8D4×D711yescharacteristic
336C2×C8#115911yescharacteristic
337C2×C8C2×C22⋊D711yescharacteristic
338C4⋊C4—141no—
339C4⋊C4—141no—
340C22⋊C4—141no—
341C22⋊C4—141no—
342C22⋊C4—141no—
343C22⋊C4—141no—
344C42—71no—
345C42—71no—
346C42—71no—
347C42—71no—
348C16—22no—
349C16—41no—
350C16—142no—
351C16—281no—
352C2×C7—21no—
353C2×C7—21no—
354C2×C7—81no—
355C2×C7#195411yescharacteristic
356C2×C7C2×#34911yescharacteristic
357C2×C7#211511yescharacteristic
358D7—81no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—41no—
363C23—41no—
364C23—141no—
365C23—141no—
366C23—141no—
367C23—281no—
368C23—281no—
369C23C2×C8×D711yescharacteristic
370D4—282no—
371D4—282no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—71no—
380C2×C4—71no—
381C2×C4—71no—
382C2×C4—71no—
383C2×C4—142no—
384C2×C4—141no—
385C2×C4—141no—
386C2×C4—141no—
387C2×C4—281no—
388C2×C4—281no—
389C2×C4—281no—
390C2×C4—281no—
391C2×C4—281no—
392C2×C4D7×C22⋊C411yescharacteristic
393C2×C4(C22⋊D7)⋊C411yescharacteristic
394C2×C4#646411yescharacteristic
395C2×C4D7×M1611yescharacteristic
396C2×C4#647011yescharacteristic
397C2×C4C4×C22⋊D711yescharacteristic
398C8—41no—
399C8—141no—
400C8—141no—
401C8—281no—
402C8#644711yescharacteristic
403C8#644811yescharacteristic
404C8#650211yescharacteristic
405C8#650311yescharacteristic
406C7#1319411yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—81no—
413C22—81no—
414C22—281no—
415C22—281no—
416C22—281no—
417C22—561no—
418C22—561no—
419C22D7×C22⋊C811yescharacteristic
420C22(C22⋊D7)⋊C811yescharacteristic
421C22C8×C22⋊D711yescharacteristic
422C4—41no—
423C4—72no—
424C4—141no—
425C4—141no—
426C4—141no—
427C4—281no—
428C4#8949911yescharacteristic
429C4#8950111yescharacteristic
430C4#8972911yescharacteristic
431C4#8990011yescharacteristic
432C2—21no—
433C2—21no—
434C2—81no—
435C2—561no—
436C2D7×#34911yescharacteristic
437C2#1172687311yescharacteristic
438C2#1172767011yescharacteristic
subgroupG/H
centerC2×C4D7×C22⋊C4
commutatorC23×C7C22×C8
FrattiniC22×C8C22×D7
FittingC2×C7×#349C2
socleC22×C7C2×C22⋊C8
prime radicalC22×C22⋊D7C8
cosocleC22×C7×C8C23
hypercenterC2×#349D7
hypocenterC7#13194
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. C2×C7×#349C2semidirect
3. C2×#89348C2semidirect
4. C2×#89309C2semidirect
5. C2×#89309C2semidirect
6. #11729174C2semidirect
7. Dic7×M32C2semidirect
62. C7×M32D4semidirect
78. #6386D4semidirect
86. C2×#349D7semidirect
252. M32C22⋊D7semidirect
291. Dic7#349semidirect
406. C7#13194semidirect

Maximal subgroups

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

subgroupindex
C2×#899002
C2×C7×#3492
C2×#893482
C2×#893092
#117291742
Dic7×M322
#131947