Finite Group Databasebeta

← C2×#11741074 #14234235

Subgroups — C2×#11741074 #14234235

Order 1792.

1842 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic
2C2×#90258C211yesmaximal, characteristic, complemented
3#11741074C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89851C211yesmaximal, characteristic, complemented
6C2×#89835C212yesmaximal, complemented
7C2×#89836C212yesmaximal, complemented
8C2×Q8×C7⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×#1142C212yesmaximal
10C2×C4×#1142C211yesmaximal, characteristic
11C2×#89781C212yesmaximal
12C2×#89779C211yesmaximal, characteristic
13C7×#554—24no—
14C7×#554C2218yes—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C7×#125C2212yes—
17C2×C7×C22⋊Q8—21no—
18C2×C7×C22⋊Q8—22no—
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×C4×C7×D4C2212yes—
22C22×C7×C4⋊C4—21no—
23C2×#6507—21no—
24C22×#1142C2211yescharacteristic
25#90258—24no—
26#90258C2218yescomplemented
27C2×#6452—22no—
28C2×#6450—21no—
29C2×#6433C2212yes—
30C2×#6432C2211yescharacteristic
31C2×C4×Dic14C2212yes—
32C2×C4×Dic14C2211yescharacteristic
33C2×#6406C2212yes—
34C2×#6406C2211yescharacteristic
35#89863C2218yescomplemented
36#89851C2218yescomplemented
37#89836C22116yescomplemented
38#89835C22116yescomplemented
39Q8×C7⋊C8C2218yescomplemented
40C4×#1142C22116yes—
41C4×#1142C2218yes—
42#89781C22116yes—
43#89779C2218yes—
44C2×#6384C2211yescharacteristic
45C2×#6384C2212yes—
46C2×#6382C2211yescharacteristic
47C2×#6382C2212yes—
48C2×#6382C2212yes—
49C2×#6381C2212yes—
50C2×#6381C2212yes—
51C2×C4⋊(C7⋊C8)C2212yes—
52C2×C4⋊(C7⋊C8)C2211yescharacteristic
53C2×C4×C7⋊C8C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3381—71nomaximal, Sylow
56C22×C7×Q8—21no—
57C22×C7×Q8D411yescharacteristic
58C22×C7×D4C2311yescharacteristic
59C23×C4×C7—21no—
60C23×C4×C7—22no—
61C22×Dic14—21no—
62C22×Dic14C2311yescharacteristic
63C7×C4⋊Q8—22no—
64C7×C4⋊Q8C2314yes—
65C7×#125—24no—
66C7×#125C2318yes—
67C7×C22⋊Q8—28no—
68C7×C22⋊Q8—216no—
69C4×C7×Q8D414yes—
70C4×C7×Q8C2314yes—
71C4×C7×D4—22no—
72C4×C7×D4—24no—
73C4×C7×D4C2314yes—
74C4×C7×D4C2318yes—
75C2×C7×C4⋊C4—22no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—28no—
79C2×C7×C4⋊C4D411yescharacteristic
80C2×C7×C4⋊C4D412yes—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2312yes—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—22no—
85C2×C42×C7C2311yescharacteristic
86C2×C42×C7C2312yes—
87#6507—28no—
88C2×#1142Q818yescomplemented
89C2×#1142C2314yes—
90C2×C4⋊Dic7—21no—
91C2×C4⋊Dic7C2312yes—
92C2×C4⋊Dic7C2311yescharacteristic
93C2×Dic7⋊C4—21no—
94C2×Dic7⋊C4—22no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×C4×Dic7—22no—
98C2×C4×Dic7—21no—
99C22×C7⋊C8C2312yes—
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2311yescharacteristic
102#6452—216no—
103#6450—28no—
104#6433—24no—
105#6433C2318yes—
106#6432—22no—
107#6432C2314yes—
108C4×Dic14—24no—
109C4×Dic14—22no—
110C4×Dic14C2314yes—
111C4×Dic14C2318yes—
112#6406C2318yes—
113#6406C2314yes—
114#6384C2318yes—
115#6384C2314yes—
116#6382C2318yes—
117#6382C2314yes—
118#6382C2318yes—
119#6381C2318yes—
120#6381C2318yes—
121C4⋊(C7⋊C8)C2314yes—
122C4⋊(C7⋊C8)C2318yes—
123C4×C7⋊C8C2318yes—
124C4×C7⋊C8C2314yes—
125C2×#557—71no—
126C2×#554D711yescharacteristic
127#3381—716no—
128C2×#499—72no—
129C2×#498—71no—
130C2×#479—72no—
131C2×#477—71no—
132C2×#478—72no—
133C2×#474—71no—
134C2×C8×Q8—71no—
135C2×C4×SD16—72no—
136C2×C4×SD16—71no—
137C24×C7—21no—
138C2×C7×Q8—24no—
139C2×C7×Q8—24no—
140C2×C7×Q8—82no—
141C2×C7×Q8C2×D414yes—
142C2×C7×D4—21no—
143C2×C7×D4—22no—
144C2×C7×D4C2×Q814yes—
145C2×C7×D4C2412yes—
146C22×C4×C7—21no—
147C22×C4×C7—22no—
148C22×C4×C7—24no—
149C22×C4×C7—28no—
150C22×C4×C7—44no—
151C22×C4×C7—84no—
152C22×C4×C7C2×D412yes—
153C22×C4×C7C2×D412yes—
154C22×C4×C7C2×D411yescharacteristic
155C22×C4×C7C2×D411yescharacteristic
156C22×C4×C7C2411yescharacteristic
157C22×Dic7—21no—
158C22×Dic7—21no—
159C22×Dic7—22no—
160C2×Dic14—21no—
161C2×Dic14—22no—
162C2×Dic14—24no—
163C2×Dic14—44no—
164C2×Dic14C2×Q814yes—
165C2×Dic14C2412yes—
166C7×C4⋊C4—28no—
167C7×C4⋊C4—24no—
168C7×C4⋊C4—28no—
169C7×C4⋊C4—21no—
170C7×C4⋊C4—22no—
171C7×C4⋊C4C2×D414yes—
172C7×C4⋊C4C2×D418yes—
173C7×C4⋊C4C2412yes—
174C7×C4⋊C4C2414yes—
175C7×C22⋊C4—24no—
176C7×C22⋊C4—28no—
177C42×C7C2×D412yes—
178C42×C7C2×D414yes—
179C42×C7C2412yes—
180C42×C7C2414yes—
181#1142C2×Q8116yescomplemented
182C4⋊Dic7—22no—
183C4⋊Dic7—21no—
184C4⋊Dic7—24no—
185C4⋊Dic7C2414yes—
186C4⋊Dic7C2412yes—
187Dic7⋊C4—24no—
188Dic7⋊C4—28no—
189Dic7⋊C4—28no—
190Dic7⋊C4—28no—
191C4×Dic7—28no—
192C4×Dic7—24no—
193C2×C7⋊C8—24no—
194C2×C7⋊C8—22no—
195C2×C7⋊C8C2×Q814yes—
196C2×C7⋊C8C2414yes—
197C2×C7⋊C8C2412yes—
198C2×C7⋊C8C2412yes—
199C22×SD16—71no—
200#557—78no—
201#557—144no—
202#554—24no—
203#554C2×D718yes—
204C2×C4⋊Q8—71no—
205C2×C4⋊Q8—141no—
206C2×C4⋊Q8C2×D711yescharacteristic
207C2×#125—72no—
208C2×#125—142no—
209C2×#125C2×D712yes—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—22no—
212C2×C4×Q8—71no—
213C2×C4×Q8—72no—
214C2×C4×Q8—141no—
215C2×C4×Q8C2×D711yescharacteristic
216C2×C4×D4C2×D712yes—
217C2×C4×D4C2×D711yescharacteristic
218C22×C4⋊C4—21no—
219#499—716no—
220#498—78no—
221#479—716no—
222#478—716no—
223#477—78no—
224#474—78no—
225C8×Q8—78no—
226C4×SD16—78no—
227C4×SD16—716no—
228C2×#107—72no—
229C2×#107—72no—
230C2×#106—72no—
231C2×#106—72no—
232C2×#106—71no—
233C2×C4⋊C8—72no—
234C2×C4⋊C8—71no—
235C2×#103—72no—
236C2×#103—71no—
237C2×#102—71no—
238C2×#102—72no—
239C2×C4×C8—71no—
240C2×C4×C8—72no—
241C23×C7—24no—
242C23×C7—22no—
243C23×C7—42no—
244C23×C7—42no—
245C23×C7C22×D411yescharacteristic
246C7×Q8—28no—
247C7×Q8—84no—
248C7×D4—24no—
249C7×D4—22no—
250C7×D4C22×Q814yes—
251C2×C4×C7—24no—
252C2×C4×C7—24no—
253C2×C4×C7—22no—
254C2×C4×C7—22no—
255C2×C4×C7—24no—
256C2×C4×C7—42no—
257C2×C4×C7—44no—
258C2×C4×C7—48no—
259C2×C4×C7—88no—
260C2×C4×C7#13514yes—
261C2×C4×C7C22×D414yes—
262C2×C4×C7C22×D414yes—
263C2×C4×C7C22×D412yes—
264C2×C4×C7C22×D411yescharacteristic
265C2×C4×C7C22×D412yes—
266C2×C4×C7C22×Q812yes—
267C2×C4×C72−1+412yes—
268C2×C4×C7C2511yescharacteristic
269C2×Dic7—24no—
270C2×Dic7—22no—
271C2×Dic7—22no—
272C2×Dic7—24no—
273C2×Dic7—44no—
274C2×Dic7—42no—
275Dic14—24no—
276Dic14—22no—
277Dic14—48no—
278Dic14C22×Q814yes—
279C7⋊C8—24no—
280C7⋊C8—22no—
281C7⋊C8C22×Q814yes—
282C22×Q8—21no—
283C22×Q8—71no—
284C22×Q8—141no—
285C22×Q8C22⋊D711yescharacteristic
286C22×D4C22×D711yescharacteristic
287C23×C4—21no—
288C23×C4—22no—
289C2×SD16—78no—
290C2×SD16—74no—
291C22×C8—71no—
292C22×C8—71no—
293C22×C8—72no—
294C4⋊Q8—22no—
295C4⋊Q8—74no—
296C4⋊Q8—148no—
297C4⋊Q8—142no—
298C4⋊Q8C22×D714yes—
299#125—24no—
300#125—78no—
301#125—1416no—
302#125—144no—
303#125C22×D718yes—
304C22⋊Q8—28no—
305C22⋊Q8—216no—
306C4×Q8—74no—
307C4×Q8—78no—
308C4×Q8—148no—
309C4×Q8—144no—
310C4×Q8—142no—
311C4×Q8C22⋊D714yes—
312C4×Q8C22×D714yes—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4C22×D714yes—
316C4×D4C22×D718yes—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—71no—
322C2×C4⋊C4—72no—
323C2×C4⋊C4—141no—
324C2×C4⋊C4—142no—
325C2×C4⋊C4—142no—
326C2×C4⋊C4—142no—
327C2×C4⋊C4—141no—
328C2×C4⋊C4C22⋊D711yescharacteristic
329C2×C4⋊C4C22⋊D712yes—
330C2×C4⋊C4C22×D711yescharacteristic
331C2×C4⋊C4C22×D712yes—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C42—142no—
335C2×C42—141no—
336C2×C42C22×D712yes—
337C2×C42C22×D711yescharacteristic
338#107—78no—
339#107—78no—
340#106—78no—
341#106—74no—
342#106—78no—
343C4⋊C8—74no—
344C4⋊C8—78no—
345#103—78no—
346#103—74no—
347#102—78no—
348#102—74no—
349C4×C8—74no—
350C4×C8—78no—
351C22×C7—24no—
352C22×C7—48no—
353C22×C7—42no—
354C22×C7—42no—
355C22×C7D4×Q812yes—
356C22×C7C2×#13512yes—
357C22×C7#57712yes—
358C22×C7C23×D411yescharacteristic
359C4×C7—24no—
360C4×C7—24no—
361C4×C7—22no—
362C4×C7—42no—
363C4×C7—44no—
364C4×C7D4×Q812yes—
365C4×C7C2×#13514yes—
366C4×C7C23×Q811yescharacteristic
367C4×C7C2×2−1+411yescharacteristic
368Dic7—24no—
369Dic7—44no—
370Dic7—42no—
371C24—21no—
372C2×Q8—24no—
373C2×Q8—24no—
374C2×Q8—74no—
375C2×Q8—72no—
376C2×Q8—82no—
377C2×Q8—142no—
378C2×Q8—141no—
379C2×Q8—144no—
380C2×Q8—284no—
381C2×Q8C2×C22⋊D714yes—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4Q8×D714yes—
385C2×D4C23×D712yes—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—44no—
391C22×C4—84no—
392C22×C4—141no—
393C22×C4—141no—
394C22×C4—142no—
395C22×C4C2×C22⋊D712yes—
396C22×C4C2×C22⋊D712yes—
397C22×C4C2×C22⋊D711yescharacteristic
398C22×C4C2×C22⋊D711yescharacteristic
399C22×C4C23×D711yescharacteristic
400SD16—716no—
401C2×C8—74no—
402C2×C8—72no—
403C2×C8—72no—
404C2×C8—74no—
405C2×C8—142no—
406C2×C8—144no—
407C4⋊C4—28no—
408C4⋊C4—24no—
409C4⋊C4—28no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—74no—
413C4⋊C4—72no—
414C4⋊C4—144no—
415C4⋊C4—148no—
416C4⋊C4—148no—
417C4⋊C4—148no—
418C4⋊C4—141no—
419C4⋊C4—142no—
420C4⋊C4—144no—
421C4⋊C4C2×C22⋊D714yes—
422C4⋊C4C2×C22⋊D718yes—
423C4⋊C4C23×D714yes—
424C4⋊C4C23×D712yes—
425C22⋊C4—24no—
426C22⋊C4—28no—
427C42—148no—
428C42—144no—
429C42C2×C22⋊D714yes—
430C42C2×C22⋊D712yes—
431C42C23×D714yes—
432C42C23×D712yes—
433C2×C7—44no—
434C2×C7#338114yescomplemented
435C2×C7C2×D4×Q811yescharacteristic
436C2×C7C22×#13511yescharacteristic
437C2×C7C2×#57711yescharacteristic
438C23—24no—
439C23—22no—
440C23—42no—
441C23—42no—
442C23C22×C22⋊D711yescharacteristic
443Q8—28no—
444Q8—74no—
445Q8—84no—
446Q8—144no—
447Q8—142no—
448Q8—288no—
449D4—24no—
450D4—22no—
451D4C2×Q8×D714yes—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—48no—
460C2×C4—88no—
461C2×C4—144no—
462C2×C4—142no—
463C2×C4—142no—
464C2×C4—144no—
465C2×C4—284no—
466C2×C4—282no—
467C2×C4#651314yes—
468C2×C4C2×Q8×D712yes—
469C2×C4#655112yes—
470C2×C4C22×C22⋊D714yes—
471C2×C4C22×C22⋊D714yes—
472C2×C4C22×C22⋊D712yes—
473C2×C4C22×C22⋊D711yescharacteristic
474C2×C4C22×C22⋊D712yes—
475C2×C4C24×D711yescharacteristic
476C8—74no—
477C8—142no—
478C8—144no—
479C7C2×#338111yescharacteristic, complemented, Sylow
480C22—24no—
481C22—42no—
482C22—42no—
483C22—48no—
484C22Q8×C22⋊D712yes—
485C22C2×#651312yes—
486C22#9052712yes—
487C22C23×C22⋊D711yescharacteristic
488C4—24no—
489C4—24no—
490C4—22no—
491C4—42no—
492C4—44no—
493C4—144no—
494C4—284no—
495C4—282no—
496C4Q8×C22⋊D712yes—
497C4C2×#651314yes—
498C4C22×Q8×D711yescharacteristic
499C4C2×#655111yescharacteristic
500C2—44no—
501C2#1174107414yesdirect product factor
502C2C2×Q8×C22⋊D711yescharacteristic
503C2C22×#651311yescharacteristic
504C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×#554D7
hypocenterC7C2×#3381
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. C2×#90258C2semidirect
3. #11741074C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89851C2semidirect
6. C2×#89835C2semidirect
7. C2×#89836C2semidirect
8. C2×Q8×C7⋊C8C2semidirect
26. #90258C22semidirect
35. #89863C22semidirect
36. #89851C22semidirect
37. #89836C22semidirect
38. #89835C22semidirect
39. Q8×C7⋊C8C22semidirect
88. C2×#1142Q8semidirect
181. #1142C2×Q8semidirect
434. C2×C7#3381semidirect
479. C7C2×#3381semidirect
501. C2#11741074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×#902582
#117410742
C2×#898632
C2×#898512
C2×#898352
C2×#898362
C2×Q8×C7⋊C82
C2×C4×#11422
C2×#897812
C2×#897792
C2×#33817