Finite Group Databasebeta

← C2×#11727458 #13325973

Subgroups — C2×#11727458 #13325973

Order 1792.

1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90191C211yesmaximal, characteristic, complemented
2C2×C7×#394C211yesmaximal, characteristic
3C2×#89990C212yesmaximal
4C2×#89323C211yesmaximal, characteristic, complemented
5#11727458C218yesmaximal, direct product factor
6C2×#89247C212yesmaximal, complemented
7C23×C7×D4C2211yescharacteristic
8C22×C7×C4⋊C4C2211yescharacteristic
9C22×C7×C22⋊C4—21no—
10C22×C7×C22⋊C4—21no—
11C22×#1142—22no—
12C2×#6489—21no—
13C2×#6487—21no—
14C2×#6487C2212yes—
15#90191—22no—
16#90191—24no—
17#90191C2214yescomplemented
18C2×#6453—22no—
19C2×#6451—22no—
20C7×#394—22no—
21C7×#394C2214yes—
22C2×C7×#95C2211yescharacteristic
23#89990—24no—
24#89990C2218yes—
25C2×#6406—22no—
26C2×C22⋊(C7⋊C8)C2212yes—
27#89323C2214yescomplemented
28#89247C2218yescomplemented
29C2×#1599—71nomaximal, Sylow
30C25×C7—21no—
31C22×C7×D4—22no—
32C22×C7×D4—22no—
33C22×C7×D4—21no—
34C22×C7×D4—44no—
35C22×C7×D4C2312yes—
36C23×C4×C7—21no—
37C23×C4×C7D411yescharacteristic
38C23×C4×C7D411yescharacteristic
39C23×C4×C7C2311yescharacteristic
40C22×Dic14—21no—
41C22×Dic14D412yes—
42C2×C7×C4⋊C4—22no—
43C2×C7×C4⋊C4—22no—
44C2×C7×C4⋊C4D412yes—
45C2×C7×C4⋊C4C2312yes—
46C2×C7×C22⋊C4—24no—
47C2×C7×C22⋊C4—24no—
48C2×C7×C22⋊C4—44no—
49C2×C7×C22⋊C4—44no—
50C2×C22⋊Dic7—22no—
51C2×#1142—28no—
52C2×#1142—48no—
53#6489—24no—
54#6489—24no—
55C2×C4⋊Dic7—21no—
56C2×C4⋊Dic7—21no—
57C2×C4⋊Dic7—21no—
58C2×C4⋊Dic7D412yes—
59#6487—24no—
60#6487—22no—
61#6487—22no—
62#6487—24no—
63#6487D414yes—
64#6487C2314yes—
65C2×Dic7⋊C4—22no—
66C2×Dic7⋊C4—22no—
67C2×C4×Dic7—22no—
68C22×C7⋊C8—22no—
69#6453—28no—
70#6453—28no—
71#6451—28no—
72#6451—28no—
73C7×#95—21no—
74C7×#95C2312yes—
75#6406—28no—
76C22⋊(C7⋊C8)—22no—
77C22⋊(C7⋊C8)C2314yes—
78C2×#544—71no—
79C2×#450—72no—
80C2×#394D711yescharacteristic
81#1599—78no—
82C2×#328—72no—
83C2×#324—71no—
84C24×C7—24no—
85C24×C7—22no—
86C24×C7—42no—
87C24×C7—42no—
88C24×C7—42no—
89C24×C7—41no—
90C24×C7—41no—
91C24×C7—42no—
92C24×C7—42no—
93C24×C7C2×D411yescharacteristic
94C2×C7×D4—28no—
95C2×C7×D4—24no—
96C2×C7×D4—44no—
97C2×C7×D4—44no—
98C2×C7×D4—48no—
99C2×C7×D4—44no—
100C2×C7×D4—42no—
101C22×C4×C7—21no—
102C22×C4×C7—21no—
103C22×C4×C7—22no—
104C22×C4×C7—21no—
105C22×C4×C7—21no—
106C22×C4×C7—22no—
107C22×C4×C7—42no—
108C22×C4×C7—42no—
109C22×C4×C7—42no—
110C22×C4×C7—42no—
111C22×C4×C7—42no—
112C22×C4×C7SD1614yescomplemented
113C22×C4×C7C2×D412yes—
114C22×C4×C7C2×D412yes—
115C22×C4×C7C2×D412yes—
116C22×C4×C7C2×D411yescharacteristic
117C22×C4×C7C2×D412yes—
118C22×C4×C7C2411yescharacteristic
119C22×Dic7—22no—
120C22×Dic7—22no—
121C2×Dic14—24no—
122C2×Dic14—22no—
123C2×Dic14—44no—
124C2×Dic14—82no—
125C2×Dic14C2×D414yes—
126C7×C4⋊C4—24no—
127C7×C4⋊C4—24no—
128C7×C22⋊C4—48no—
129C7×C22⋊C4—48no—
130C22⋊Dic7—24no—
131C22⋊Dic7—24no—
132#1142—416no—
133C4⋊Dic7—24no—
134C4⋊Dic7—24no—
135C4⋊Dic7—24no—
136C4⋊Dic7—22no—
137C4⋊Dic7C2×D414yes—
138Dic7⋊C4—28no—
139Dic7⋊C4—24no—
140Dic7⋊C4—24no—
141C4×Dic7—28no—
142C2×C7⋊C8—24no—
143C2×C7⋊C8—44no—
144C23×D4C2×D711yescharacteristic
145C22×SD16—142no—
146#544—74no—
147#544—144no—
148#544—142no—
149C2×C4⋊Q8—142no—
150C2×#125—142no—
151C2×C22⋊Q8—72no—
152C2×C22⋊Q8—141no—
153C2×#117—141no—
154C22×C4⋊C4C2×D711yescharacteristic
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157#450—78no—
158#450—144no—
159C2×#102—142no—
160C2×C22⋊C8—72no—
161#394—22no—
162#394C2×D714yes—
163C2×#95C2×D711yescharacteristic
164#328—78no—
165#324—74no—
166C23×C7—22no—
167C23×C7—22no—
168C23×C7—24no—
169C23×C7—42no—
170C23×C7—44no—
171C23×C7—48no—
172C23×C7—48no—
173C23×C7—42no—
174C23×C7—42no—
175C23×C7—42no—
176C23×C7—42no—
177C23×C7—42no—
178C23×C7—44no—
179C23×C7—84no—
180C23×C7—84no—
181C23×C7—82no—
182C23×C7—82no—
183C23×C7—82no—
184C23×C7—82no—
185C23×C7#12011yescharacteristic
186C23×C7#12011yescharacteristic
187C23×C7C2×SD1612yes—
188C23×C7#13712yes—
189C23×C7C22×D411yescharacteristic
190C7×D4—28no—
191C7×D4—44no—
192C7×D4—48no—
193C2×C4×C7—22no—
194C2×C4×C7—22no—
195C2×C4×C7—24no—
196C2×C4×C7—24no—
197C2×C4×C7—24no—
198C2×C4×C7—22no—
199C2×C4×C7—42no—
200C2×C4×C7—41no—
201C2×C4×C7—41no—
202C2×C4×C7—42no—
203C2×C4×C7—42no—
204C2×C4×C7—42no—
205C2×C4×C7—42no—
206C2×C4×C7—42no—
207C2×C4×C7—81no—
208C2×C4×C7—84no—
209C2×C4×C7#12012yes—
210C2×C4×C7C2×SD1614yescomplemented
211C2×C4×C7C22×D412yes—
212C2×Dic7—24no—
213C2×Dic7—24no—
214C2×Dic7—44no—
215C2×Dic7—44no—
216Dic14—44no—
217Dic14—82no—
218Dic14—84no—
219C7⋊C8—44no—
220C25—21no—
221C22×Q8—72no—
222C22×Q8—141no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—21no—
226C22×D4—44no—
227C22×D4C22×D712yes—
228C23×C4—21no—
229C23×C4C22⋊D711yescharacteristic
230C23×C4C22⋊D711yescharacteristic
231C23×C4C22×D711yescharacteristic
232C2×SD16—148no—
233C2×SD16—288no—
234C22×C8—142no—
235C4⋊Q8—148no—
236C4⋊Q8—148no—
237#125—148no—
238#125—148no—
239C22⋊Q8—74no—
240C22⋊Q8—74no—
241C22⋊Q8—144no—
242C22⋊Q8—142no—
243C22⋊Q8—142no—
244C22⋊Q8—144no—
245#117—144no—
246#117—144no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—72no—
250C2×C4⋊C4—141no—
251C2×C4⋊C4—141no—
252C2×C4⋊C4—141no—
253C2×C4⋊C4—142no—
254C2×C4⋊C4—142no—
255C2×C4⋊C4C22⋊D712yes—
256C2×C4⋊C4C22×D712yes—
257C2×C22⋊C4—24no—
258C2×C22⋊C4—24no—
259C2×C22⋊C4—44no—
260C2×C22⋊C4—44no—
261C2×C22⋊C4—142no—
262C2×C42—142no—
263#102—148no—
264C22⋊C8—74no—
265C22⋊C8—142no—
266#95—21no—
267#95C22×D712yes—
268C22×C7—24no—
269C22×C7—24no—
270C22×C7—21no—
271C22×C7—21no—
272C22×C7—21no—
273C22×C7—21no—
274C22×C7—44no—
275C22×C7—44no—
276C22×C7—44no—
277C22×C7—82no—
278C22×C7—82no—
279C22×C7—88no—
280C22×C7—88no—
281C22×C7—82no—
282C22×C7—82no—
283C22×C7#44812yes—
284C22×C7#44812yes—
285C22×C7#45412yes—
286C22×C7B(4,𝔽2)12yes—
287C22×C7C2×#12011yescharacteristic
288C22×C7C22×SD1611yescharacteristic
289C22×C7C2×#13711yescharacteristic
290C4×C7—24no—
291C4×C7—22no—
292C4×C7—22no—
293C4×C7—42no—
294C4×C7—82no—
295Dic7—44no—
296Dic7—44no—
297C24—24no—
298C24—22no—
299C24—42no—
300C24—42no—
301C24—42no—
302C24—42no—
303C24—41no—
304C24—41no—
305C24—42no—
306C24C2×C22⋊D711yescharacteristic
307C2×Q8—74no—
308C2×Q8—144no—
309C2×Q8—142no—
310C2×Q8—284no—
311C2×Q8—562no—
312C2×D4—28no—
313C2×D4—24no—
314C2×D4—44no—
315C2×D4—44no—
316C2×D4—48no—
317C2×D4—44no—
318C2×D4—42no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—142no—
331C22×C4—142no—
332C22×C4#114214yescomplemented
333C22×C4D4×D712yes—
334C22×C4D4×D712yes—
335C22×C4C2×C22⋊D712yes—
336C22×C4C2×C22⋊D712yes—
337C22×C4C2×C22⋊D711yescharacteristic
338C22×C4C23×D711yescharacteristic
339SD16—2816no—
340C2×C8—144no—
341C2×C8—284no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—74no—
345C4⋊C4—148no—
346C4⋊C4—144no—
347C4⋊C4—144no—
348C4⋊C4—144no—
349C4⋊C4—144no—
350C4⋊C4—142no—
351C4⋊C4—144no—
352C22⋊C4—48no—
353C22⋊C4—48no—
354C22⋊C4—144no—
355C22⋊C4—144no—
356C42—148no—
357C2×C7—21no—
358C2×C7—21no—
359C2×C7—22no—
360C2×C7—84no—
361C2×C7#159914yescomplemented
362C2×C7C2×#44811yescharacteristic
363C2×C7C2×#45411yescharacteristic
364C2×C7C2×B(4,𝔽2)11yescharacteristic
365C23—22no—
366C23—22no—
367C23—24no—
368C23—42no—
369C23—44no—
370C23—48no—
371C23—48no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—42no—
376C23—42no—
377C23—44no—
378C23—84no—
379C23—84no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C2×#114212yes—
385C23#650011yescharacteristic
386C23#650011yescharacteristic
387C23#651412yes—
388C23C22×C22⋊D711yescharacteristic
389Q8—284no—
390Q8—562no—
391Q8—564no—
392D4—28no—
393D4—44no—
394D4—48no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—84no—
411C2×C4—144no—
412C2×C4—144no—
413C2×C4—284no—
414C2×C4—284no—
415C2×C4C2×#114214yescomplemented
416C2×C4#650012yes—
417C2×C4C2×D4×D712yes—
418C8—284no—
419C7C2×#159911yescharacteristic, complemented, Sylow
420C22—24no—
421C22—24no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—82no—
430C22—82no—
431C22—88no—
432C22—88no—
433C22—82no—
434C22—82no—
435C22#8980412yes—
436C22#8981212yes—
437C22#8981212yes—
438C22#8983412yes—
439C22C22×#114211yescharacteristic
440C22C2×#650011yescharacteristic
441C22C2×#651411yescharacteristic
442C4—22no—
443C4—22no—
444C4—24no—
445C4—42no—
446C4—82no—
447C4—284no—
448C4—284no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—84no—
453C2#1172745814yesdirect product factor
454C2C2×#8980411yescharacteristic
455C2C2×#8981211yescharacteristic
456C2C2×#8983411yescharacteristic
subgroupG/H
centerC23#6500
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#394C2
socleC23×C7#120
prime radicalC23×C7×D4C22
hypercenterC2×#394D7
hypocenterC7C2×#1599
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C2×#90191C2semidirect
4. C2×#89323C2semidirect
5. #11727458C2direct (N × H)
6. C2×#89247C2semidirect
17. #90191C22semidirect
27. #89323C22semidirect
28. #89247C22semidirect
112. C22×C4×C7SD16semidirect
210. C2×C4×C7C2×SD16semidirect
332. C22×C4#1142semidirect
361. C2×C7#1599semidirect
415. C2×C4C2×#1142semidirect
419. C7C2×#1599semidirect
453. C2#11727458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#901912
C2×C7×#3942
C2×#899902
C2×#893232
#117274582
C2×#892472
C2×#15997