Finite Group Databasebeta

← C2×#11737079 #14234283

Subgroups — C2×#11737079 #14234283

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic14C211yesmaximal, characteristic, complemented
2C2×#90234C211yesmaximal, characteristic
3C2×C4×C7×SD16C211yesmaximal, characteristic
4C2×#89936C212yesmaximal
5C2×#89793C211yesmaximal, characteristic, complemented
6C2×#89780C211yesmaximal, characteristic
7#11737079C2116yesmaximal, direct product factor
8C2×#89628C212yesmaximal, complemented
9C2×#89568C212yesmaximal, complemented
10C2×#89531C212yesmaximal
11C2×#89451C211yesmaximal, characteristic, complemented
12C2×#89454C211yesmaximal, characteristic, complemented
13C22×C7×SD16C2211yescharacteristic
14C2×C4×C7×Q8C2211yescharacteristic
15C2×C4×C7×D4C2211yescharacteristic
16C2×Q8×Dic7C2212yes—
17C2×D4×Dic7C2212yes—
18C22×C4⋊Dic7—21no—
19C2×#6487—21no—
20Q8×Dic14—24no—
21Q8×Dic14C2218yescomplemented
22#90234—24no—
23#90234C2218yes—
24C2×#6453C2212yes—
25C2×#6451—22no—
26C2×#6451C2212yes—
27C2×#6441—22no—
28C2×#6432—21no—
29C2×#6432C2211yescharacteristic
30C2×#6432C2211yescharacteristic
31C2×C4×Dic14—21no—
32C2×C4×Dic14C2211yescharacteristic
33C4×C7×SD16C2218yes—
34C2×C7×#106C2211yescharacteristic
35C2×C7×#103C2211yescharacteristic
36C2×C7×#102C2211yescharacteristic
37C2×C4×C7×C8C2211yescharacteristic
38C2×#6409C2212yes—
39C2×#6406C2212yes—
40#89936C22116yes—
41C2×#6392C2212yes—
42C2×#6392C2212yes—
43C2×#6389C2212yes—
44C2×Dic7⋊C8C2212yes—
45#89793C2218yescomplemented
46#89780C2218yes—
47C2×#6382C2212yes—
48C2×#6381C2212yes—
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50#89628C22116yescomplemented
51#89568C22116yescomplemented
52#89531C22116yes—
53#89454C2218yescomplemented
54#89451C2218yescomplemented
55C2×#3385—71nomaximal, Sylow
56C22×C7×Q8C2311yescharacteristic
57C22×C7×D4C2311yescharacteristic
58C23×C4×C7—21no—
59C23×Dic7—22no—
60C22×Dic14—21no—
61C22×Dic14—21no—
62C22×Dic14—22no—
63C22×Dic14D411yescharacteristic
64C2×C7×SD16Q818yescomplemented
65C2×C7×SD16C2314yes—
66C22×C7×C8C2311yescharacteristic
67C22×C7×C8C2311yescharacteristic
68C4×C7×Q8—22no—
69C4×C7×Q8C2314yes—
70C4×C7×D4—22no—
71C4×C7×D4C2314yes—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4C2311yescharacteristic
74C2×C7×C4⋊C4C2311yescharacteristic
75C2×C7×C22⋊C4—21no—
76C2×C42×C7—21no—
77C2×C42×C7C2311yescharacteristic
78C2×C22⋊Dic7—22no—
79Q8×Dic7—24no—
80Q8×Dic7C2318yes—
81D4×Dic7—24no—
82D4×Dic7C2318yes—
83C2×C4⋊Dic7—21no—
84C2×C4⋊Dic7—21no—
85C2×C4⋊Dic7—22no—
86C2×C4⋊Dic7—22no—
87C2×C4⋊Dic7—28no—
88C2×C4⋊Dic7D411yescharacteristic
89C2×C4⋊Dic7C2312yes—
90C2×C4⋊Dic7C2312yes—
91#6487—28no—
92C2×Dic7⋊C4—22no—
93C2×Dic7⋊C4—22no—
94C2×Dic7⋊C4D412yes—
95C2×C4×Dic7—22no—
96C2×C4×Dic7C2312yes—
97C22×C7⋊C8C2312yes—
98#6453—24no—
99#6453C2318yes—
100#6451—216no—
101#6451—24no—
102#6451C2318yes—
103#6441—216no—
104#6432—22no—
105#6432—22no—
106#6432—28no—
107#6432C2314yes—
108#6432C2314yes—
109C4×Dic14—28no—
110C4×Dic14D414yes—
111C4×Dic14C2314yes—
112C7×#106C2314yes—
113C7×#103C2314yes—
114C7×#102C2314yes—
115C4×C7×C8C2314yes—
116#6409C2318yes—
117#6406C2318yes—
118#6392C2318yes—
119#6392C2318yes—
120#6389C2318yes—
121Dic7⋊C8C2318yes—
122#6382C2318yes—
123#6381C2318yes—
124C4⋊(C7⋊C8)C2314yes—
125C2×Q82—71no—
126C2×#554—71no—
127#3385—716no—
128C2×#501—72no—
129C2×#500—71no—
130C2×#479—72no—
131C2×#477—71no—
132C2×#476—71no—
133C2×#474—72no—
134C2×#446—71no—
135C2×#440—72no—
136C2×C4×SD16D711yescharacteristic
137C24×C7—21no—
138C2×C7×Q8—21no—
139C2×C7×Q8—22no—
140C2×C7×Q8C2×Q814yes—
141C2×C7×Q8C2412yes—
142C2×C7×D4—21no—
143C2×C7×D4—22no—
144C2×C7×D4C2×Q814yes—
145C2×C7×D4C2412yes—
146C22×C4×C7—21no—
147C22×C4×C7—21no—
148C22×C4×C7—21no—
149C22×C4×C7—24no—
150C22×C4×C7—44no—
151C22×C4×C7C2×D411yescharacteristic
152C22×C4×C7C2×D411yescharacteristic
153C22×C4×C7C2411yescharacteristic
154C22×Dic7—22no—
155C22×Dic7—22no—
156C22×Dic7—28no—
157C22×Dic7—84no—
158C22×Dic7C2×D412yes—
159C22×Dic7C2×D412yes—
160C2×Dic14—24no—
161C2×Dic14—24no—
162C2×Dic14—24no—
163C2×Dic14—28no—
164C2×Dic14—84no—
165C2×Dic14—82no—
166C2×Dic14—82no—
167C2×Dic14C2×D414yes—
168C7×SD16C2×Q8116yescomplemented
169C2×C7×C8—22no—
170C2×C7×C8C2×Q814yes—
171C2×C7×C8C2412yes—
172C2×C7×C8C2412yes—
173C7×C4⋊C4—24no—
174C7×C4⋊C4—21no—
175C7×C4⋊C4—21no—
176C7×C4⋊C4C2412yes—
177C7×C4⋊C4C2412yes—
178C7×C22⋊C4—24no—
179C42×C7—24no—
180C42×C7C2×D412yes—
181C42×C7C2412yes—
182C22⋊Dic7—28no—
183C4⋊Dic7—24no—
184C4⋊Dic7—22no—
185C4⋊Dic7—22no—
186C4⋊Dic7—24no—
187C4⋊Dic7—28no—
188C4⋊Dic7—28no—
189C4⋊Dic7C2×D414yes—
190C4⋊Dic7C2414yes—
191C4⋊Dic7C2414yes—
192Dic7⋊C4—28no—
193Dic7⋊C4—28no—
194Dic7⋊C4C2×D418yes—
195C4×Dic7—28no—
196C4×Dic7C2×D414yes—
197C4×Dic7C2414yes—
198C2×C7⋊C8—24no—
199C2×C7⋊C8C2414yes—
200C22×SD16C2×D711yescharacteristic
201Q82—78no—
202Q82—144no—
203#554—78no—
204#554—144no—
205C2×C4⋊Q8—72no—
206C2×C4⋊Q8—71no—
207C2×C4⋊Q8—71no—
208C2×C4⋊Q8—141no—
209C2×C4⋊Q8—142no—
210C2×#125—72no—
211C2×C22⋊Q8—142no—
212C2×C22⋊Q8—141no—
213C2×C4×Q8—71no—
214C2×C4×Q8—72no—
215C2×C4×Q8—141no—
216C2×C4×Q8C2×D711yescharacteristic
217C2×C4×D4—72no—
218C2×C4×D4C2×D711yescharacteristic
219C22×C4⋊C4—141no—
220#501—716no—
221#500—78no—
222#479—716no—
223#477—78no—
224#476—78no—
225#474—716no—
226#446—78no—
227#440—716no—
228C4×SD16C2×D718yes—
229C2×#107—72no—
230C2×#107—72no—
231C2×#107—72no—
232C2×#106—72no—
233C2×#106C2×D711yescharacteristic
234C2×C4⋊C8—72no—
235C2×C4⋊C8—71no—
236C2×#103—72no—
237C2×#103C2×D711yescharacteristic
238C2×#102—72no—
239C2×#102C2×D711yescharacteristic
240C2×#97—72no—
241C2×C4×C8C2×D711yescharacteristic
242C23×C7—24no—
243C23×C7—22no—
244C23×C7—42no—
245C23×C7—42no—
246C23×C7C22×D411yescharacteristic
247C7×Q8—24no—
248C7×Q8—22no—
249C7×Q8C22×Q814yes—
250C7×D4—24no—
251C7×D4—22no—
252C7×D4C22×Q814yes—
253C2×C4×C7—24no—
254C2×C4×C7—22no—
255C2×C4×C7—22no—
256C2×C4×C7—22no—
257C2×C4×C7—22no—
258C2×C4×C7—42no—
259C2×C4×C7—42no—
260C2×C4×C7—48no—
261C2×C4×C7#13714yes—
262C2×C4×C7C22×D412yes—
263C2×C4×C7C22×D411yescharacteristic
264C2×C4×C7C22×D412yes—
265C2×C4×C7C22×Q812yes—
266C2×C4×C72−1+412yes—
267C2×C4×C7C2511yescharacteristic
268C2×Dic7—24no—
269C2×Dic7—24no—
270C2×Dic7—24no—
271C2×Dic7—24no—
272C2×Dic7—44no—
273C2×Dic7—44no—
274C2×Dic7—88no—
275C2×Dic7C22×D414yes—
276C2×Dic7C22×D414yes—
277Dic14—28no—
278Dic14—88no—
279Dic14—84no—
280Dic14—84no—
281C7×C8—22no—
282C7×C8C22×Q814yes—
283C7⋊C8—24no—
284C22×Q8—71no—
285C22×Q8—142no—
286C22×Q8—141no—
287C22×Q8—141no—
288C22×Q8C22×D711yescharacteristic
289C22×D4C22×D711yescharacteristic
290C23×C4—21no—
291C23×C4—142no—
292C2×SD16Dic1418yescomplemented
293C2×SD16C22×D714yes—
294C22×C8—72no—
295C22×C8C22×D711yescharacteristic
296C22×C8C22×D711yescharacteristic
297C4⋊Q8—78no—
298C4⋊Q8—74no—
299C4⋊Q8—74no—
300C4⋊Q8—148no—
301C4⋊Q8—144no—
302C4⋊Q8—1416no—
303C4⋊Q8—142no—
304C4⋊Q8—142no—
305#125—78no—
306#125—144no—
307C22⋊Q8—1416no—
308C22⋊Q8—148no—
309C4×Q8—22no—
310C4×Q8—74no—
311C4×Q8—74no—
312C4×Q8—78no—
313C4×Q8—148no—
314C4×Q8—144no—
315C4×Q8C22×D714yes—
316C4×D4—22no—
317C4×D4—78no—
318C4×D4—144no—
319C4×D4C22×D714yes—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—71no—
322C2×C4⋊C4—72no—
323C2×C4⋊C4—72no—
324C2×C4⋊C4—72no—
325C2×C4⋊C4—148no—
326C2×C4⋊C4—142no—
327C2×C4⋊C4—142no—
328C2×C4⋊C4—142no—
329C2×C4⋊C4—142no—
330C2×C4⋊C4—141no—
331C2×C4⋊C4—141no—
332C2×C4⋊C4C22×D711yescharacteristic
333C2×C4⋊C4C22×D711yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—142no—
336C2×C42—21no—
337C2×C42—72no—
338C2×C42—142no—
339C2×C42C22×D711yescharacteristic
340#107—78no—
341#107—78no—
342#107—78no—
343#106—78no—
344#106C22×D714yes—
345C4⋊C8—78no—
346C4⋊C8—74no—
347#103—78no—
348#103C22×D714yes—
349#102—78no—
350#102C22×D714yes—
351#97—78no—
352C4×C8C22×D714yes—
353C22×C7—24no—
354C22×C7—48no—
355C22×C7—42no—
356C22×C7—42no—
357C22×C7D4×Q812yes—
358C22×C7C2×#13712yes—
359C22×C7#57612yes—
360C22×C7C23×D411yescharacteristic
361C4×C7—24no—
362C4×C7—22no—
363C4×C7—42no—
364C4×C7—42no—
365C4×C7D4×Q812yes—
366C4×C7C2×#13714yes—
367C4×C7C23×Q811yescharacteristic
368C4×C7C2×2−1+411yescharacteristic
369Dic7—24no—
370Dic7—24no—
371Dic7—44no—
372Dic7—44no—
373C24—21no—
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8—74no—
377C2×Q8—148no—
378C2×Q8—144no—
379C2×Q8—144no—
380C2×Q8—144no—
381C2×Q8—562no—
382C2×Q8—562no—
383C2×Q8—564no—
384C2×Q8C2×Dic1414yes—
385C2×Q8C23×D712yes—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4C2×Dic1414yes—
389C2×D4C23×D712yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—24no—
394C22×C4—44no—
395C22×C4—72no—
396C22×C4—72no—
397C22×C4—148no—
398C22×C4—142no—
399C22×C4—142no—
400C22×C4—564no—
401C22×C4D4×D711yescharacteristic
402C22×C4D4×D711yescharacteristic
403C22×C4C23×D711yescharacteristic
404SD16C2×Dic14116yescomplemented
405C2×C8—22no—
406C2×C8—74no—
407C2×C8—144no—
408C2×C8C2×Dic1414yes—
409C2×C8C23×D712yes—
410C2×C8C23×D712yes—
411C4⋊C4—24no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—78no—
415C4⋊C4—74no—
416C4⋊C4—74no—
417C4⋊C4—74no—
418C4⋊C4—148no—
419C4⋊C4—148no—
420C4⋊C4—148no—
421C4⋊C4—148no—
422C4⋊C4—142no—
423C4⋊C4—142no—
424C4⋊C4—144no—
425C4⋊C4—144no—
426C4⋊C4C23×D712yes—
427C4⋊C4C23×D712yes—
428C22⋊C4—24no—
429C22⋊C4—148no—
430C42—24no—
431C42—74no—
432C42—74no—
433C42—148no—
434C42D4×D712yes—
435C42C23×D712yes—
436C2×C7—44no—
437C2×C7#338514yescomplemented
438C2×C7C2×D4×Q811yescharacteristic
439C2×C7C22×#13711yescharacteristic
440C2×C7C2×#57611yescharacteristic
441C23—24no—
442C23—22no—
443C23—42no—
444C23—42no—
445C23C2×D4×D711yescharacteristic
446Q8—24no—
447Q8—22no—
448Q8—148no—
449Q8—564no—
450Q8—564no—
451Q8—568no—
452Q8C22×Dic1414yes—
453D4—24no—
454D4—22no—
455D4C22×Dic1414yes—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—48no—
464C2×C4—74no—
465C2×C4—74no—
466C2×C4—144no—
467C2×C4—144no—
468C2×C4—144no—
469C2×C4—144no—
470C2×C4—284no—
471C2×C4—284no—
472C2×C4—568no—
473C2×C4#647814yes—
474C2×C4C22×Dic1412yes—
475C2×C4C2×D4×D712yes—
476C2×C4C2×D4×D712yes—
477C2×C4C2×D4×D711yescharacteristic
478C2×C4#655412yes—
479C2×C4C24×D711yescharacteristic
480C8—22no—
481C8—144no—
482C8C22×Dic1414yes—
483C7C2×#338511yescharacteristic, complemented, Sylow
484C22—24no—
485C22—42no—
486C22—48no—
487C22—42no—
488C22D4×Dic1412yes—
489C22C2×#647812yes—
490C22#9046012yes—
491C22C22×D4×D711yescharacteristic
492C4—24no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—144no—
497C4—144no—
498C4—284no—
499C4—284no—
500C4D4×Dic1412yes—
501C4C2×#647814yes—
502C4C23×Dic1411yescharacteristic
503C4C2×#655411yescharacteristic
504C2—44no—
505C2#1173707914yesdirect product factor
506C2C2×D4×Dic1411yescharacteristic
507C2C22×#647811yescharacteristic
508C2C2×#9046011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C4×C7×SD16C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
hypercenterC2×C4×SD16D7
hypocenterC7C2×#3385
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic14C2semidirect
5. C2×#89793C2semidirect
7. #11737079C2direct (N × H)
8. C2×#89628C2semidirect
9. C2×#89568C2semidirect
11. C2×#89451C2semidirect
12. C2×#89454C2semidirect
21. Q8×Dic14C22semidirect
45. #89793C22semidirect
50. #89628C22semidirect
51. #89568C22semidirect
53. #89454C22semidirect
54. #89451C22semidirect
64. C2×C7×SD16Q8semidirect
168. C7×SD16C2×Q8semidirect
292. C2×SD16Dic14semidirect
404. SD16C2×Dic14semidirect
437. C2×C7#3385semidirect
483. C7C2×#3385semidirect
505. C2#11737079direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic142
C2×#902342
C2×C4×C7×SD162
C2×#899362
C2×#897932
C2×#897802
#117370792
C2×#896282
C2×#895682
C2×#895312
C2×#894512
C2×#894542
C2×#33857