Finite Group Databasebeta

← #13249678

Subgroups — #13249678

Order 1792.

510 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740654C211yesmaximal, characteristic
2#11736457C211yesmaximal, characteristic
3C2×C7×#332C211yesmaximal, characteristic, complemented
4#11729527C211yesmaximal, characteristic, complemented
5#11728179C211yesmaximal, characteristic
6#11725513C211yesmaximal, characteristic, complemented
7#11725511C211yesmaximal, characteristic, complemented
8C2×C7×C4⋊Q8C2211yescharacteristic
9C2×#6505—21no—
10C2×#6464—21no—
11C4×#1157C2211yescharacteristic
12C2×C7×C4⋊C8C2211yescharacteristic
13C2×C7×C4⋊C8C2211yescharacteristic
14#89997—21no—
15#89874—21no—
16#89862—21no—
17#89862C412yes—
18#89855—21no—
19#89855C412yes—
20#89697C2211yescharacteristic
21#89696C2211yescharacteristic
22#89696C2211yescharacteristic
23#89611—22no—
24#89609—21no—
25D7×C4⋊C8—21no—
26C7×#332—21no—
27C7×#332—21no—
28#89342—22no—
29#89279—21no—
30#89278—21no—
31#9171—71nomaximal, Sylow
32C22×C7×Q8—21no—
33C2×#1157D411yescharacteristic
34C22×C7×C8—21no—
35C22×C7×C8—21no—
36C7×C4⋊Q8—21no—
37C7×C4⋊Q8—21no—
38C7×C4⋊Q8—21no—
39C7×C4⋊Q8C2×C412yes—
40C2×C7×C4⋊C4—21no—
41C2×C7×C4⋊C4—21no—
42C2×C42×C7C2311yescharacteristic
43C2×#1144—22no—
44#6505—42no—
45#6505—42no—
46C2×#1143—22no—
47C4×C22⋊D7—21no—
48C4×C22⋊D7—21no—
49#6489D411yescharacteristic
50C2×#1136—21no—
51C2×#1136—21no—
52#6464—42no—
53#6464—42no—
54C2×#1131—22no—
55C2×C8×D7—22no—
56C4×D28C2×C411yescharacteristic
57C4×D28D411yescharacteristic
58#6435—21no—
59C42×D7—21no—
60C4×Dic14C2×C411yescharacteristic
61C4×Dic14D411yescharacteristic
62C7×C4⋊C8—21no—
63C7×C4⋊C8—21no—
64C7×C4⋊C8—21no—
65C7×C4⋊C8D411yescharacteristic
66C7×C4⋊C8D411yescharacteristic
67#6409—22no—
68#6409—22no—
69C22⋊(C7⋊C8)—21no—
70Dic7⋊C8—22no—
71Dic7⋊C8—22no—
72C4⋊(C7⋊C8)—21no—
73C4⋊(C7⋊C8)—21no—
74C4⋊(C7⋊C8)—21no—
75C4⋊(C7⋊C8)C2×C412yes—
76C4⋊(C7⋊C8)D412yes—
77C4×C7⋊C8—21no—
78#3039—71no—
79#2906—71no—
80#1546—71no—
81C2×#332D711yescharacteristic, complemented
82#1477—71no—
83#1301—71no—
84#1292—71no—
85C2×C7×Q8—22no—
86C2×C7×Q8—41no—
87C2×C7×Q8—41no—
88C2×C7×Q8—41no—
89C2×C7×Q8—41no—
90C2×C7×Q8—41no—
91C22×C4×C7—41no—
92C22×C4×C7C2×D411yescharacteristic
93C22×C4×C7#4111yescharacteristic
94C22×C4×C7#4111yescharacteristic
95C2×C22⋊D7—21no—
96#1157—21no—
97#1157—21no—
98#1157D812yes—
99#1157SD1612yes—
100C2×D28C22⋊C411yescharacteristic
101C2×C4×D7—21no—
102C2×C4×D7—21no—
103C2×C4×D7—21no—
104C2×Dic14C22⋊C411yescharacteristic
105C2×C7×C8—21no—
106C2×C7×C8—21no—
107C2×C7×C8—41no—
108C2×C7×C8—41no—
109C2×C7×C8—41no—
110C2×C7×C8—81no—
111C7×C4⋊C4—22no—
112C7×C4⋊C4—22no—
113C7×C4⋊C4—41no—
114C7×C4⋊C4—41no—
115C42×C7C22×C411yescharacteristic
116C42×C7C2×D411yescharacteristic
117C42×C7C2×D411yescharacteristic
118C42×C7C2×D411yescharacteristic
119C22⋊Dic7—21no—
120#1144—44no—
121#1143—44no—
122(C2×D7)⋊C4—21no—
123(C2×D7)⋊C4—21no—
124C4⋊Dic7C22⋊C411yescharacteristic
125C4⋊Dic7C22⋊C411yescharacteristic
126Dic7⋊C4—21no—
127Dic7⋊C4—21no—
128C4×Dic7—21no—
129C4×Dic7—21no—
130C4×Dic7—21no—
131#1136—41no—
132#1136—41no—
133#1136—41no—
134#1136—41no—
135C2×C7⋊C8—22no—
136C2×C7⋊C8—22no—
137C2×C7⋊C8—41no—
138#1131—44no—
139C8×D7—44no—
140C2×#137—141no—
141C2×#131—141no—
142C2×C4⋊Q8C2×D711yescharacteristic
143C4×#41—71no—
144#462—72no—
145#462—141no—
146#461—72no—
147#461—141no—
148#431—71no—
149#424—142no—
150#424—141no—
151#423—71no—
152#423—71no—
153#423—141no—
154C2×C4⋊C8—141no—
155C2×C4⋊C8C2×D711yescharacteristic
156C2×C4⋊C8C2×D711yescharacteristic
157#419—141no—
158#332—21no—
159#332—21no—
160#332—142no—
161Q8⋊C8—141no—
162D4⋊C8—141no—
163C23×C7#12311yescharacteristic
164C22×D7—21no—
165C7×Q8—42no—
166C7×Q8—42no—
167C7×Q8—81no—
168C7×Q8—81no—
169C2×C4×C7—21no—
170C2×C4×C7—21no—
171C2×C4×C7—41no—
172C2×C4×C7—42no—
173C2×C4×C7—81no—
174C2×C4×C7—81no—
175C2×C4×C7C2×C22⋊C411yescharacteristic
176C2×C4×C7C4×D411yescharacteristic
177C2×C4×C7C4×D411yescharacteristic
178C2×C4×C7#12011yescharacteristic
179C2×C4×C7#12111yescharacteristic
180C2×C4×C7#12111yescharacteristic
181C2×C4×C7C2×D811yescharacteristic
182C2×C4×C7C2×SD1611yescharacteristic
183C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C7#13711yescharacteristic
185C22⋊D7—22no—
186C22⋊D7—22no—
187C2×Dic7—21no—
188C2×Dic7—21no—
189C2×Dic7—21no—
190D28—21no—
191D28#10212yes—
192C4×D7—22no—
193C4×D7—22no—
194C4×D7—41no—
195C4×D7—41no—
196C4×D7—81no—
197Dic14—21no—
198Dic14#10212yes—
199C7×C8—41no—
200C7×C8—41no—
201C7×C8—81no—
202C7⋊C8—42no—
203C7⋊C8—42no—
204C7⋊C8—81no—
205C2×#41—71no—
206C22×Q8—21no—
207#137—282no—
208#137—282no—
209C2×Q16—142no—
210C2×SD16—142no—
211#131—282no—
212#131—282no—
213C2×M16—142no—
214C2×M16—141no—
215C2×M16—141no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—142no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8C4×D712yes—
223C4×Q8—71no—
224C4×Q8—71no—
225C4×D4—71no—
226C4×D4—71no—
227C4×D4—141no—
228C4×D4—141no—
229#117—71no—
230#117—141no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C42—141no—
234C2×C42C22×D711yescharacteristic
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—72no—
239C4⋊C8—72no—
240C4⋊C8—142no—
241C4⋊C8—142no—
242C4⋊C8—141no—
243C4⋊C8—141no—
244C4⋊C8—141no—
245C4⋊C8C22⋊D711yescharacteristic
246C4⋊C8C22⋊D711yescharacteristic
247#103—142no—
248#103—142no—
249C22⋊C8—141no—
250C4×C8—141no—
251C22×C7—21no—
252C22×C7—21no—
253C22×C7#38611yescharacteristic
254C22×C7#48011yescharacteristic
255C22×C7#48111yescharacteristic
256C2×D7—22no—
257C2×D7—41no—
258C2×D7—41no—
259C4×C7—21no—
260C4×C7—21no—
261C4×C7—21no—
262C4×C7—82no—
263C4×C7C2×#10211yescharacteristic
264C4×C7#41711yescharacteristic
265C4×C7#44711yescharacteristic
266C4×C7#44811yescharacteristic
267C4×C7#47111yescharacteristic
268C4×C7#47311yescharacteristic
269Dic7—22no—
270Dic7—41no—
271Dic7—41no—
272#41—72no—
273#41—72no—
274#41—141no—
275#41—141no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—71no—
283C2×D4—71no—
284C2×D4—141no—
285C22×C4—41no—
286C22×C4—141no—
287C22×C4—141no—
288C22×C4—141no—
289C22×C4#115711yescharacteristic
290C22×C4D4×D711yescharacteristic
291C22×C4#115911yescharacteristic
292Q16—284no—
293SD16—284no—
294M16—284no—
295M16—281no—
296M16—281no—
297M16—281no—
298M16—281no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—81no—
305C2×C8—142no—
306C2×C8—142no—
307C2×C8—284no—
308C2×C8—281no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—71no—
314C4⋊C4—71no—
315C4⋊C4—141no—
316C4⋊C4—141no—
317C22⋊C4—141no—
318C22⋊C4—141no—
319C22⋊C4—141no—
320C42—141no—
321C42—141no—
322C42—141no—
323C42C2×C4×D711yescharacteristic
324C42D4×D711yescharacteristic
325C42D4×D711yescharacteristic
326C42C2×C22⋊D711yescharacteristic
327C2×C7—21no—
328C2×C7—21no—
329C2×C7#187411yescharacteristic
330C2×C7#190211yescharacteristic
331C2×C7#190811yescharacteristic
332D7—42no—
333C23—141no—
334C23#644611yescharacteristic
335Q8—42no—
336Q8—42no—
337Q8—72no—
338Q8—81no—
339Q8—81no—
340Q8—141no—
341D4—72no—
342D4—142no—
343D4—142no—
344D4—141no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—141no—
352C2×C4—142no—
353C2×C4—142no—
354C2×C4—141no—
355C2×C4—141no—
356C2×C4—281no—
357C2×C4—281no—
358C2×C4—561no—
359C2×C4D7×C22⋊C411yescharacteristic
360C2×C4(C22⋊D7)⋊C411yescharacteristic
361C2×C4#644711yescharacteristic
362C2×C4D7×D811yescharacteristic
363C2×C4#647411yescharacteristic
364C2×C4D7×SD1611yescharacteristic
365C2×C4#647811yescharacteristic
366C2×C4C4×C22⋊D711yescharacteristic
367C2×C4#650011yescharacteristic
368C2×C4#650111yescharacteristic
369C8—41no—
370C8—41no—
371C8—81no—
372C8—282no—
373C8—282no—
374C8—561no—
375C7#917111yescharacteristic, complemented, Sylow
376C22—21no—
377C22—21no—
378C22—142no—
379C22—281no—
380C22—281no—
381C22#8954611yescharacteristic
382C22#8954911yescharacteristic
383C22#8972811yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—82no—
388C4—142no—
389C4—281no—
390C4—281no—
391C4D7×#10211yescharacteristic
392C4#8954311yescharacteristic
393C4#8992811yescharacteristic
394C4#8994211yescharacteristic
395C4#8994911yescharacteristic
396C4#8996411yescharacteristic
397C2—21no—
398C2—21no—
399C2—282no—
400C2#1172787611yescharacteristic
401C2#1172795411yescharacteristic
402C2#1172804011yescharacteristic
subgroupG/H
centerC22#89728
commutatorC42×C7C22×C4
FrattiniC2×C42C22×D7
FittingC2×C7×#332C2
socleC22×C7#386
prime radicalC2×#1157D4
cosocleC2×C42×C7C23
hypercenterC2×#332D7
hypocenterC7#9171
LCSG ▷ C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. C2×C7×#332C2semidirect
4. #11729527C2semidirect
6. #11725513C2semidirect
7. #11725511C2semidirect
81. C2×#332D7semidirect
375. C7#9171semidirect

Maximal subgroups

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

subgroupindex
#117406542
#117364572
C2×C7×#3322
#117295272
#117281792
#117255132
#117255112
#91717