Finite Group Databasebeta

← C2×#11741003 #14234297

Subgroups — C2×#11741003 #14234297

Order 1792.

2006 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×D4×Q8C211yesmaximal, characteristic
2C2×#90258C211yesmaximal, characteristic, complemented
3#11741003C2116yesmaximal, direct product factor
4C2×#89863C212yesmaximal, complemented
5C2×#89866C211yesmaximal, characteristic, complemented
6C2×#89852C212yesmaximal, complemented
7C2×#89850C211yesmaximal, characteristic, complemented
8C2×#89796C211yesmaximal, characteristic, complemented
9C2×C4×#1142C211yesmaximal, characteristic
10C2×#89781C212yesmaximal
11C2×#89779C211yesmaximal, characteristic
12C2×#89790C212yesmaximal
13C23×C7×Q8—21no—
14C7×D4×Q8—24no—
15C7×D4×Q8C2218yes—
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C7×C4⋊Q8C2212yes—
18C2×C7×C22⋊Q8—21no—
19C2×C7×C22⋊Q8—22no—
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2212yes—
22C2×C4×C7×D4C2211yescharacteristic
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#89866C2218yescomplemented
36#89863C22116yescomplemented
37#89852C22116yescomplemented
38#89850C2218yescomplemented
39#89796C2218yescomplemented
40#89790C22116yes—
41C4×#1142C2218yes—
42#89781C22116yes—
43#89779C2218yes—
44C2×#6384C2212yes—
45C2×#6384C2211yescharacteristic
46C2×#6382C2212yes—
47C2×#6382C2211yescharacteristic
48C2×#6381C2212yes—
49C2×#6381C2212yes—
50C2×#6381C2212yes—
51C2×C4⋊(C7⋊C8)C2211yescharacteristic
52C2×C4⋊(C7⋊C8)C2212yes—
53C2×#6377C2212yes—
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×#3386—71nomaximal, Sylow
56C22×C7×Q8—28no—
57C22×C7×Q8—22no—
58C22×C7×Q8—21no—
59C22×C7×Q8—48no—
60C22×C7×Q8D411yescharacteristic
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—22no—
63C23×C4×C7—21no—
64C22×Dic14—21no—
65C22×Dic14C2311yescharacteristic
66C7×C4⋊Q8—22no—
67C7×C4⋊Q8—24no—
68C7×C4⋊Q8C2318yes—
69C7×C4⋊Q8C2314yes—
70C7×C22⋊Q8—28no—
71C7×C22⋊Q8—216no—
72C4×C7×Q8D414yes—
73C4×C7×Q8C2314yes—
74C4×C7×D4—22no—
75C4×C7×D4—24no—
76C4×C7×D4C2314yes—
77C4×C7×D4C2318yes—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—21no—
80C2×C7×C4⋊C4D411yescharacteristic
81C2×C7×C4⋊C4D412yes—
82C2×C7×C4⋊C4C2312yes—
83C2×C7×C4⋊C4C2311yescharacteristic
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—21no—
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2312yes—
88#6507—28no—
89C2×#1142Q818yescomplemented
90C2×#1142C2314yes—
91C2×C4⋊Dic7—21no—
92C2×C4⋊Dic7C2312yes—
93C2×C4⋊Dic7C2311yescharacteristic
94C2×Dic7⋊C4—21no—
95C2×Dic7⋊C4—22no—
96C2×Dic7⋊C4—22no—
97C2×Dic7⋊C4—22no—
98C2×C4×Dic7—22no—
99C2×C4×Dic7—21no—
100C22×C7⋊C8C2311yescharacteristic
101C22×C7⋊C8C2312yes—
102C22×C7⋊C8C2311yescharacteristic
103#6452—216no—
104#6450—28no—
105#6433—24no—
106#6433C2318yes—
107#6432—22no—
108#6432C2314yes—
109C4×Dic14—24no—
110C4×Dic14—22no—
111C4×Dic14C2318yes—
112C4×Dic14C2314yes—
113#6406C2318yes—
114#6406C2314yes—
115#6384C2314yes—
116#6384C2318yes—
117#6382C2318yes—
118#6382C2314yes—
119#6381C2318yes—
120#6381C2318yes—
121#6381C2318yes—
122C4⋊(C7⋊C8)C2318yes—
123C4⋊(C7⋊C8)C2314yes—
124#6377C2318yes—
125C4×C7⋊C8C2314yes—
126C2×#557—71no—
127C2×D4×Q8D711yescharacteristic
128#3386—716no—
129C2×#501—72no—
130C2×#500—71no—
131C2×#477—72no—
132C2×#475—71no—
133C2×#478—72no—
134C2×#474—71no—
135C2×#446—71no—
136C2×#440—72no—
137C2×C4×SD16—71no—
138C24×C7—21no—
139C2×C7×Q8—24no—
140C2×C7×Q8—28no—
141C2×C7×Q8—24no—
142C2×C7×Q8—48no—
143C2×C7×Q8—432no—
144C2×C7×Q8—44no—
145C2×C7×Q8C2×D414yes—
146C2×C7×D4—21no—
147C2×C7×D4—22no—
148C2×C7×D4C2×Q814yes—
149C2×C7×D4C2412yes—
150C22×C4×C7—22no—
151C22×C4×C7—21no—
152C22×C4×C7—28no—
153C22×C4×C7—24no—
154C22×C4×C7—48no—
155C22×C4×C7—44no—
156C22×C4×C7C2×D412yes—
157C22×C4×C7C2×D412yes—
158C22×C4×C7C2×D411yescharacteristic
159C22×C4×C7C2×D411yescharacteristic
160C22×C4×C7C2411yescharacteristic
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—22no—
164C2×Dic14—21no—
165C2×Dic14—22no—
166C2×Dic14—24no—
167C2×Dic14—44no—
168C2×Dic14C2×Q814yescomplemented
169C2×Dic14C2412yes—
170C7×C4⋊C4—28no—
171C7×C4⋊C4—24no—
172C7×C4⋊C4—22no—
173C7×C4⋊C4—21no—
174C7×C4⋊C4C2×D414yes—
175C7×C4⋊C4C2×D418yes—
176C7×C4⋊C4C2412yes—
177C7×C4⋊C4C2414yes—
178C7×C22⋊C4—28no—
179C7×C22⋊C4—24no—
180C42×C7C2×D412yes—
181C42×C7C2×D414yes—
182C42×C7C2412yes—
183C42×C7C2414yes—
184#1142C2×Q8116yescomplemented
185C4⋊Dic7—22no—
186C4⋊Dic7—21no—
187C4⋊Dic7—24no—
188C4⋊Dic7C2414yes—
189C4⋊Dic7C2412yes—
190Dic7⋊C4—24no—
191Dic7⋊C4—28no—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194C4×Dic7—28no—
195C4×Dic7—24no—
196C2×C7⋊C8—22no—
197C2×C7⋊C8—24no—
198C2×C7⋊C8C2×Q814yescomplemented
199C2×C7⋊C8C2412yes—
200C2×C7⋊C8C2414yes—
201C2×C7⋊C8C2412yes—
202C23×Q8—21no—
203C22×SD16—71no—
204#557—78no—
205#557—144no—
206D4×Q8—24no—
207D4×Q8C2×D718yes—
208C2×C4⋊Q8—71no—
209C2×C4⋊Q8—141no—
210C2×C4⋊Q8C2×D711yescharacteristic
211C2×C4⋊Q8C2×D712yes—
212C2×#125—72no—
213C2×#125—142no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—22no—
216C2×C4×Q8—71no—
217C2×C4×Q8—72no—
218C2×C4×Q8—141no—
219C2×C4×Q8C2×D711yescharacteristic
220C2×C4×D4C2×D712yes—
221C2×C4×D4C2×D711yescharacteristic
222#501—716no—
223#500—78no—
224#478—716no—
225#477—716no—
226#475—78no—
227#474—78no—
228#446—78no—
229#440—716no—
230C4×SD16—78no—
231C2×#107—72no—
232C2×#107—72no—
233C2×#107—72no—
234C2×#106—72no—
235C2×#106—71no—
236C2×C4⋊C8—72no—
237C2×C4⋊C8—71no—
238C2×#103—72no—
239C2×#103—71no—
240C2×#102—71no—
241C2×#102—72no—
242C2×#97—72no—
243C2×C4×C8—71no—
244C23×C7—24no—
245C23×C7—22no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7C22×D411yescharacteristic
249C7×Q8—28no—
250C7×Q8—416no—
251C7×Q8—48no—
252C7×D4—24no—
253C7×D4—22no—
254C7×D4C22×Q814yes—
255C2×C4×C7—24no—
256C2×C4×C7—24no—
257C2×C4×C7—22no—
258C2×C4×C7—24no—
259C2×C4×C7—22no—
260C2×C4×C7—416no—
261C2×C4×C7—44no—
262C2×C4×C7—42no—
263C2×C4×C7—48no—
264C2×C4×C7AGL(1,ℤ/8)14yes—
265C2×C4×C7C22×D414yes—
266C2×C4×C7C22×D414yes—
267C2×C4×C7C22×D412yes—
268C2×C4×C7C22×D411yescharacteristic
269C2×C4×C7C22×D412yes—
270C2×C4×C7C22×Q812yes—
271C2×C4×C72−1+412yes—
272C2×C4×C7C2511yescharacteristic
273C2×Dic7—24no—
274C2×Dic7—22no—
275C2×Dic7—22no—
276C2×Dic7—24no—
277C2×Dic7—44no—
278C2×Dic7—42no—
279Dic14—24no—
280Dic14—22no—
281Dic14—48no—
282Dic14C22×Q814yescomplemented
283C7⋊C8—22no—
284C7⋊C8—24no—
285C7⋊C8C22×Q814yescomplemented
286C22×Q8—28no—
287C22×Q8—22no—
288C22×Q8—21no—
289C22×Q8—48no—
290C22×Q8—71no—
291C22×Q8—141no—
292C22×Q8C22⋊D711yescharacteristic
293C22×D4C22×D711yescharacteristic
294C23×C4—22no—
295C23×C4—21no—
296C2×SD16—78no—
297C2×SD16—74no—
298C22×C8—71no—
299C22×C8—71no—
300C22×C8—72no—
301C4⋊Q8—24no—
302C4⋊Q8—22no—
303C4⋊Q8—74no—
304C4⋊Q8—148no—
305C4⋊Q8—142no—
306C4⋊Q8C22×D714yes—
307C4⋊Q8C22×D718yes—
308#125—78no—
309#125—1416no—
310#125—144no—
311C22⋊Q8—28no—
312C22⋊Q8—216no—
313C4×Q8—74no—
314C4×Q8—78no—
315C4×Q8—148no—
316C4×Q8—144no—
317C4×Q8—142no—
318C4×Q8C22⋊D714yes—
319C4×Q8C22×D714yes—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4C22×D714yes—
323C4×D4C22×D718yes—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—71no—
327C2×C4⋊C4—72no—
328C2×C4⋊C4—141no—
329C2×C4⋊C4—142no—
330C2×C4⋊C4—142no—
331C2×C4⋊C4—142no—
332C2×C4⋊C4—141no—
333C2×C4⋊C4C22⋊D711yescharacteristic
334C2×C4⋊C4C22⋊D712yes—
335C2×C4⋊C4C22×D712yes—
336C2×C4⋊C4C22×D711yescharacteristic
337C2×C22⋊C4—22no—
338C2×C22⋊C4—21no—
339C2×C42—142no—
340C2×C42—141no—
341C2×C42C22×D712yes—
342C2×C42C22×D711yescharacteristic
343#107—78no—
344#107—78no—
345#107—78no—
346#106—74no—
347#106—78no—
348C4⋊C8—74no—
349C4⋊C8—78no—
350#103—74no—
351#103—78no—
352#102—74no—
353#102—78no—
354#97—78no—
355C4×C8—74no—
356C22×C7—24no—
357C22×C7—48no—
358C22×C7—42no—
359C22×C7—42no—
360C22×C7D4×Q812yes—
361C22×C7C2×AGL(1,ℤ/8)12yes—
362C22×C7#57812yes—
363C22×C7C23×D411yescharacteristic
364C4×C7—24no—
365C4×C7—24no—
366C4×C7—22no—
367C4×C7—44no—
368C4×C7—42no—
369C4×C7D4×Q812yes—
370C4×C7C2×AGL(1,ℤ/8)14yes—
371C4×C7C23×Q811yescharacteristic
372C4×C7C2×2−1+411yescharacteristic
373Dic7—24no—
374Dic7—44no—
375Dic7—42no—
376C24—21no—
377C2×Q8—24no—
378C2×Q8—28no—
379C2×Q8—24no—
380C2×Q8—48no—
381C2×Q8—432no—
382C2×Q8—44no—
383C2×Q8—74no—
384C2×Q8—72no—
385C2×Q8—142no—
386C2×Q8—141no—
387C2×Q8—144no—
388C2×Q8—284no—
389C2×Q8C2×C22⋊D714yes—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4Q8×D714yes—
393C2×D4C23×D712yes—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—28no—
397C22×C4—24no—
398C22×C4—48no—
399C22×C4—44no—
400C22×C4—141no—
401C22×C4—141no—
402C22×C4—142no—
403C22×C4C2×C22⋊D712yes—
404C22×C4C2×C22⋊D711yescharacteristic
405C22×C4C2×C22⋊D712yes—
406C22×C4C2×C22⋊D711yescharacteristic
407C22×C4C23×D711yescharacteristic
408SD16—716no—
409C2×C8—74no—
410C2×C8—72no—
411C2×C8—72no—
412C2×C8—74no—
413C2×C8—142no—
414C2×C8—144no—
415C4⋊C4—28no—
416C4⋊C4—24no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—72no—
420C4⋊C4—74no—
421C4⋊C4—144no—
422C4⋊C4—148no—
423C4⋊C4—148no—
424C4⋊C4—148no—
425C4⋊C4—141no—
426C4⋊C4—142no—
427C4⋊C4—144no—
428C4⋊C4C2×C22⋊D714yes—
429C4⋊C4C2×C22⋊D718yes—
430C4⋊C4C23×D712yes—
431C4⋊C4C23×D714yes—
432C22⋊C4—28no—
433C22⋊C4—24no—
434C42—148no—
435C42—144no—
436C42C2×C22⋊D714yes—
437C42C2×C22⋊D712yes—
438C42C23×D712yes—
439C42C23×D714yes—
440C2×C7—44no—
441C2×C7#338614yescomplemented
442C2×C7C2×D4×Q811yescharacteristic
443C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
444C2×C7C2×#57811yescharacteristic
445C23—24no—
446C23—22no—
447C23—42no—
448C23—42no—
449C23C22×C22⋊D711yescharacteristic
450Q8—28no—
451Q8—416no—
452Q8—48no—
453Q8—74no—
454Q8—144no—
455Q8—142no—
456Q8—288no—
457D4—24no—
458D4—22no—
459D4C2×Q8×D714yes—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—416no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—48no—
469C2×C4—144no—
470C2×C4—142no—
471C2×C4—142no—
472C2×C4—144no—
473C2×C4—284no—
474C2×C4—282no—
475C2×C4#649514yes—
476C2×C4C2×Q8×D712yes—
477C2×C4#655112yes—
478C2×C4C22×C22⋊D714yes—
479C2×C4C22×C22⋊D712yes—
480C2×C4C22×C22⋊D714yes—
481C2×C4C22×C22⋊D712yes—
482C2×C4C22×C22⋊D711yescharacteristic
483C2×C4C24×D711yescharacteristic
484C8—74no—
485C8—142no—
486C8—144no—
487C7C2×#338611yescharacteristic, complemented, Sylow
488C22—24no—
489C22—42no—
490C22—48no—
491C22—42no—
492C22C2×#649512yes—
493C22Q8×C22⋊D712yes—
494C22#9052912yes—
495C22C23×C22⋊D711yescharacteristic
496C4—24no—
497C4—24no—
498C4—22no—
499C4—44no—
500C4—42no—
501C4—144no—
502C4—284no—
503C4—282no—
504C4C2×#649514yes—
505C4Q8×C22⋊D712yes—
506C4C22×Q8×D711yescharacteristic
507C4C2×#655111yescharacteristic
508C2—44no—
509C2#1174100314yesdirect product factor
510C2C22×#649511yescharacteristic
511C2C2×Q8×C22⋊D711yescharacteristic
512C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×D4×Q8C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×D4×Q8D7
hypocenterC7C2×#3386
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#90258C2semidirect
3. #11741003C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89866C2semidirect
6. C2×#89852C2semidirect
7. C2×#89850C2semidirect
8. C2×#89796C2semidirect
26. #90258C22semidirect
35. #89866C22semidirect
36. #89863C22semidirect
37. #89852C22semidirect
38. #89850C22semidirect
39. #89796C22semidirect
89. C2×#1142Q8semidirect
168. C2×Dic14C2×Q8semidirect
184. #1142C2×Q8semidirect
198. C2×C7⋊C8C2×Q8semidirect
282. Dic14C22×Q8semidirect
285. C7⋊C8C22×Q8semidirect
441. C2×C7#3386semidirect
487. C7C2×#3386semidirect
509. C2#11741003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×D4×Q82
C2×#902582
#117410032
C2×#898632
C2×#898662
C2×#898522
C2×#898502
C2×#897962
C2×C4×#11422
C2×#897812
C2×#897792
C2×#897902
C2×#33867