Finite Group Databasebeta

← C2×#11738719 #14225807

Subgroups — C2×#11738719 #14225807

Order 1792.

2286 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90287C211yesmaximal, characteristic
2C22×#6451C211yesmaximal, characteristic, complemented
3C2×C7×#480C211yesmaximal, characteristic, complemented
4C2×#89805C211yesmaximal, characteristic, complemented
5C2×#89739C211yesmaximal, characteristic, complemented
6#11738719C2116yesmaximal, direct product factor
7C2×#89662C212yesmaximal, complemented
8C2×#89646C212yesmaximal, complemented
9C2×#89532C212yesmaximal, complemented
10C2×#89531C212yesmaximal, complemented
11C2×#89508C211yesmaximal, characteristic, complemented
12C2×#89490C211yesmaximal, characteristic, complemented
13C22×#1159—21no—
14C23×Dic14—21no—
15C2×C7×#121C2211yescharacteristic
16C22×C7×C4⋊C4C2211yescharacteristic
17C2×#6503C2211yescharacteristic
18C2×#6502—21no—
19C2×D4×Dic7C2211yescharacteristic
20C2×#6493C2211yescharacteristic
21C22×C4⋊Dic7C2211yescharacteristic
22C22×Dic7⋊C4—21no—
23C22×C4×Dic7C2211yescharacteristic
24#90287—24no—
25#90287C2218yes—
26C2×#6456C2211yescharacteristic
27C2×#6451—24no—
28C2×#6451—21no—
29C2×#6451—21no—
30C2×#6451C2211yescharacteristic
31C2×#6451C2212yes—
32C2×#6451C2212yes—
33C2×#6451C2218yescomplemented
34C2×#6448—21no—
35C2×(C22⋊D7)⋊C4—21no—
36C7×#480C2218yescomplemented
37C2×C7×#107C2212yes—
38C2×C7×#102C2212yes—
39C2×C7×C22⋊C8C2211yescharacteristic
40C2×#6406C2212yes—
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42C2×#6395C2212yes—
43C2×#6392C2212yes—
44C2×Dic7⋊C8C2212yes—
45C2×C8×Dic7C2212yes—
46#89805C2218yescomplemented
47#89739C2218yescomplemented
48C2×#6383C2212yes—
49C2×#6381C2212yes—
50C2×#6381C2212yes—
51#89662C22116yescomplemented
52#89646C22116yescomplemented
53#89532C22116yescomplemented
54#89531C22116yescomplemented
55#89508C2218yescomplemented
56#89490C2218yescomplemented
57C2×#3226—71nomaximal, Sylow
58C22×C7×D4—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C23×C4×C7C2311yescharacteristic
62C22×C22⋊D7—21no—
63C22×C22⋊D7—21no—
64C22×C22⋊D7—21no—
65C23×Dic7—21no—
66C23×Dic7—21no—
67C23×Dic7D411yescharacteristic
68C23×Dic7D411yescharacteristic
69C2×#1159—28no—
70C2×#1159—48no—
71C22×D28C2311yescharacteristic
72C22×C4×D7—21no—
73C22×Dic14—21no—
74C22×Dic14—22no—
75C22×Dic14—22no—
76C22×Dic14—28no—
77C22×Dic14—48no—
78C22×C7×C8C2312yes—
79C7×#121—22no—
80C7×#121C2314yes—
81C2×C7×C4⋊C4—21no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4C2314yes—
84C2×C7×C4⋊C4C2312yes—
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C22⋊C4—21no—
87C2×C22⋊Dic7—21no—
88#6503—22no—
89#6503C2314yes—
90#6502—28no—
91D4×Dic7—22no—
92D4×Dic7C2314yes—
93#6493—22no—
94#6493C2314yes—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7C2311yescharacteristic
100C2×C4⋊Dic7C2312yes—
101C2×C4⋊Dic7C2314yes—
102C2×Dic7⋊C4—21no—
103C2×Dic7⋊C4—22no—
104C2×Dic7⋊C4—22no—
105C2×Dic7⋊C4—28no—
106C2×C4×Dic7D411yescharacteristic
107C2×C4×Dic7D411yescharacteristic
108C2×C4×Dic7D414yes—
109C2×C4×Dic7C2311yescharacteristic
110C2×C4×Dic7C2311yescharacteristic
111C2×C4×Dic7C2314yes—
112C22×C7⋊C8C2312yes—
113#6456—22no—
114#6456C2314yes—
115#6451—24no—
116#6451—24no—
117#6451—28no—
118#6451—28no—
119#6451—22no—
120#6451C2314yes—
121#6451C2318yes—
122#6451C2318yes—
123#6448—28no—
124(C22⋊D7)⋊C4—28no—
125C7×#107C2318yes—
126C7×#102C2318yes—
127C7×C22⋊C8C2314yes—
128#6406C2318yes—
129C22⋊(C7⋊C8)C2314yes—
130#6395C2318yes—
131#6392C2318yes—
132Dic7⋊C8C2318yes—
133C8×Dic7C2318yes—
134#6383C2318yes—
135#6381C2318yes—
136#6381C2318yes—
137C2×#532—71no—
138C22×C4⋊Q8—71no—
139#3226—716no—
140C2×#500—72no—
141C2×#486—72no—
142C2×#480—71no—
143C2×#480—71no—
144C2×#480—71no—
145C2×#480D711yescharacteristic, complemented
146C2×#474—72no—
147C2×#474—72no—
148C2×#431—71no—
149C24×C7—21no—
150C24×C7C2×D411yescharacteristic
151C23×D7—21no—
152C2×C7×D4—24no—
153C2×C7×D4—21no—
154C2×C7×D4—24no—
155C2×C7×D4—44no—
156C2×C7×D4C2412yes—
157C22×C4×C7—24no—
158C22×C4×C7—24no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—44no—
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D412yes—
164C22×C4×C7C2412yes—
165C22×C4×C7C2411yescharacteristic
166C2×C22⋊D7—24no—
167C2×C22⋊D7—24no—
168C2×C22⋊D7—24no—
169C2×C22⋊D7—44no—
170C2×C22⋊D7—44no—
171C2×C22⋊D7—44no—
172C22×Dic7—24no—
173C22×Dic7—24no—
174C22×Dic7—22no—
175C22×Dic7—21no—
176C22×Dic7—24no—
177C22×Dic7—44no—
178C22×Dic7—44no—
179C22×Dic7D818yes—
180C22×Dic7C2×D411yescharacteristic
181C22×Dic7C2×D414yes—
182C22×Dic7C2×D411yescharacteristic
183C22×Dic7C2×D411yescharacteristic
184C22×Dic7C2×D414yes—
185C22×Dic7C2×D411yescharacteristic
186#1159—432no—
187C2×D28—24no—
188C2×D28—21no—
189C2×D28C2412yes—
190C2×C4×D7—24no—
191C2×C4×D7—44no—
192C2×Dic14—24no—
193C2×Dic14—28no—
194C2×Dic14—28no—
195C2×Dic14—48no—
196C2×Dic14—48no—
197C2×Dic14—432no—
198C2×Dic14—44no—
199C2×C7×C8—24no—
200C2×C7×C8C2414yes—
201C7×C4⋊C4—24no—
202C7×C4⋊C4—22no—
203C7×C4⋊C4—21no—
204C7×C4⋊C4C2414yes—
205C7×C4⋊C4C2412yes—
206C7×C22⋊C4—24no—
207C22⋊Dic7—24no—
208(C2×D7)⋊C4—24no—
209(C2×D7)⋊C4—24no—
210C4⋊Dic7—24no—
211C4⋊Dic7—22no—
212C4⋊Dic7—21no—
213C4⋊Dic7C2414yes—
214C4⋊Dic7C2412yes—
215Dic7⋊C4—24no—
216Dic7⋊C4—28no—
217Dic7⋊C4—28no—
218C4×Dic7C2×D414yes—
219C4×Dic7C2×D414yes—
220C4×Dic7C2×D412yes—
221C4×Dic7C2×D412yes—
222C4×Dic7C2412yes—
223C4×Dic7C2412yes—
224C2×C7⋊C8—24no—
225C2×C7⋊C8C2414yes—
226C22×#41—141no—
227C23×Q8—141no—
228#532—78no—
229#532—144no—
230C2×C4⋊Q8—72no—
231C2×C4⋊Q8—71no—
232C2×C4⋊Q8—72no—
233C2×C4⋊Q8—78no—
234C2×C4⋊Q8—141no—
235C2×C4⋊Q8—141no—
236C2×C4⋊Q8—144no—
237C2×#127—71no—
238C2×#124—141no—
239C2×#121—71no—
240C2×#121—141no—
241C2×#121C2×D711yescharacteristic
242C2×C4×D4—71no—
243C2×C4×D4—71no—
244C2×C4×D4—141no—
245C22×C4⋊C4—71no—
246C22×C4⋊C4—141no—
247C22×C4⋊C4C2×D711yescharacteristic
248C22×C42—71no—
249#500—716no—
250#486—716no—
251#480—78no—
252#480—78no—
253#480—78no—
254#480C2×D718yescomplemented
255#474—716no—
256#474—716no—
257#431—78no—
258C2×#107—72no—
259C2×#107—72no—
260C2×#107—72no—
261C2×#107C2×D712yes—
262C2×C4⋊C8—72no—
263C2×#102—72no—
264C2×#102—72no—
265C2×#102—72no—
266C2×#102C2×D712yes—
267C2×C22⋊C8—71no—
268C2×C22⋊C8C2×D711yescharacteristic
269C2×C4×C8—72no—
270C23×C7—22no—
271C23×C7—22no—
272C23×C7—22no—
273C23×C7—42no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7C2×D814yes—
277C23×C7C22×D412yes—
278C23×C7C22×D411yescharacteristic
279C22×D7—22no—
280C22×D7—42no—
281C22×D7—42no—
282C22×D7—42no—
283C7×D4—24no—
284C7×D4—48no—
285C7×D4—42no—
286C2×C4×C7—22no—
287C2×C4×C7—24no—
288C2×C4×C7—24no—
289C2×C4×C7—24no—
290C2×C4×C7—22no—
291C2×C4×C7—48no—
292C2×C4×C7—44no—
293C2×C4×C7—42no—
294C2×C4×C7C22×D412yes—
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C72−1+414yes—
297C2×C4×C7C2511yescharacteristic
298C22⋊D7—48no—
299C22⋊D7—48no—
300C22⋊D7—48no—
301C2×Dic7—22no—
302C2×Dic7—28no—
303C2×Dic7—24no—
304C2×Dic7—22no—
305C2×Dic7—48no—
306C2×Dic7—44no—
307C2×Dic7—42no—
308C2×Dic7—48no—
309C2×Dic7C2×D814yes—
310C2×Dic7C2×D814yes—
311C2×Dic7C2×D8116yes—
312C2×Dic7#13714yes—
313C2×Dic7C22×D412yes—
314C2×Dic7C22×D412yes—
315C2×Dic7C22×D412yes—
316C2×Dic7C22×D412yes—
317D28—24no—
318D28—42no—
319C4×D7—48no—
320Dic14—416no—
321Dic14—416no—
322Dic14—48no—
323C7×C8—24no—
324C7⋊C8—24no—
325C2×#41—148no—
326C2×#41—288no—
327C22×Q8—141no—
328C22×Q8—148no—
329C22×Q8—142no—
330C22×Q8—142no—
331C22×Q8—288no—
332C22×D4—21no—
333C22×D4—71no—
334C22×D4—141no—
335C22×D4—141no—
336C22×D4—141no—
337C22×D4C22×D711yescharacteristic
338C23×C4—21no—
339C23×C4—71no—
340C23×C4—71no—
341C23×C4—141no—
342C23×C4—141no—
343C23×C4—141no—
344C23×C4C22×D711yescharacteristic
345C22×C8—72no—
346C22×C8C22×D712yes—
347C4⋊Q8—78no—
348C4⋊Q8—78no—
349C4⋊Q8—74no—
350C4⋊Q8—144no—
351C4⋊Q8—148no—
352C4⋊Q8—148no—
353C4⋊Q8—144no—
354C4⋊Q8—142no—
355#127—74no—
356#127—142no—
357#124—148no—
358#121—22no—
359#121—74no—
360#121—148no—
361#121—142no—
362#121C22×D714yes—
363C4×D4—74no—
364C4×D4—74no—
365C4×D4—148no—
366C4×D4—142no—
367C4×D4—142no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—72no—
371C2×C4⋊C4—74no—
372C2×C4⋊C4—71no—
373C2×C4⋊C4—148no—
374C2×C4⋊C4—142no—
375C2×C4⋊C4—142no—
376C2×C4⋊C4—141no—
377C2×C4⋊C4—142no—
378C2×C4⋊C4—141no—
379C2×C4⋊C4C22×D712yes—
380C2×C4⋊C4C22×D714yes—
381C2×C4⋊C4C22×D711yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—141no—
384C2×C22⋊C4—141no—
385C2×C22⋊C4—141no—
386C2×C42—71no—
387C2×C42—71no—
388C2×C42—74no—
389C2×C42—71no—
390C2×C42—71no—
391C2×C42—74no—
392#107—78no—
393#107—78no—
394#107—78no—
395#107C22×D718yes—
396C4⋊C8—78no—
397#102—78no—
398#102—78no—
399#102—78no—
400#102C22×D718yes—
401C22⋊C8—74no—
402C22⋊C8C22×D714yes—
403C4×C8—78no—
404C22×C7—22no—
405C22×C7—28no—
406C22×C7—22no—
407C22×C7—42no—
408C22×C7—42no—
409C22×C7—42no—
410C22×C7—84no—
411C22×C7#53612yes—
412C22×C7C22×D814yes—
413C22×C7C22×D812yes—
414C22×C7C2×#13712yes—
415C22×C7C23×D411yescharacteristic
416C2×D7—42no—
417C2×D7—42no—
418C2×D7—42no—
419C2×D7—84no—
420C4×C7—22no—
421C4×C7—44no—
422C4×C7—42no—
423C4×C7#53612yes—
424C4×C7C2×2−1+412yes—
425Dic7—22no—
426Dic7—44no—
427Dic7—42no—
428Dic7C22×D814yes—
429Dic7C22×D814yes—
430Dic7C2×#13714yes—
431C24—21no—
432C24—141no—
433C24D4×D711yescharacteristic
434#41—2832no—
435C2×Q8—144no—
436C2×Q8—148no—
437C2×Q8—148no—
438C2×Q8—288no—
439C2×Q8—288no—
440C2×Q8—2832no—
441C2×Q8—284no—
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—24no—
445C2×D4—44no—
446C2×D4—72no—
447C2×D4—144no—
448C2×D4—144no—
449C2×D4—144no—
450C2×D4—141no—
451C2×D4—144no—
452C2×D4—284no—
453C2×D4—284no—
454C2×D4—284no—
455C2×D4C23×D712yes—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—44no—
461C22×C4—78no—
462C22×C4—74no—
463C22×C4—71no—
464C22×C4—71no—
465C22×C4—71no—
466C22×C4—74no—
467C22×C4—71no—
468C22×C4—144no—
469C22×C4—144no—
470C22×C4—144no—
471C22×C4—144no—
472C22×C4—141no—
473C22×C4—142no—
474C22×C4—284no—
475C22×C4—284no—
476C22×C4—284no—
477C22×C4D4×D712yes—
478C22×C4D4×D711yescharacteristic
479C22×C4C23×D712yes—
480C22×C4C23×D711yescharacteristic
481C2×C8—24no—
482C2×C8—74no—
483C2×C8—144no—
484C2×C8C23×D714yes—
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—74no—
489C4⋊C4—72no—
490C4⋊C4—148no—
491C4⋊C4—148no—
492C4⋊C4—144no—
493C4⋊C4—144no—
494C4⋊C4—142no—
495C4⋊C4—141no—
496C4⋊C4C23×D714yes—
497C4⋊C4C23×D712yes—
498C22⋊C4—24no—
499C22⋊C4—144no—
500C22⋊C4—144no—
501C22⋊C4—144no—
502C42—74no—
503C42—72no—
504C42—74no—
505C42—72no—
506C42—72no—
507C42—72no—
508C2×C7—24no—
509C2×C7—82no—
510C2×C7#322614yescomplemented
511C2×C7C2×#53611yescharacteristic
512C2×C7C23×D811yescharacteristic
513C2×C7C22×#13711yescharacteristic
514D7—82no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—142no—
522C23—282no—
523C23—282no—
524C23—282no—
525C23D7×D814yes—
526C23C2×D4×D712yes—
527C23C2×D4×D711yescharacteristic
528Q8—2816no—
529Q8—2816no—
530Q8—288no—
531D4—24no—
532D4—48no—
533D4—42no—
534D4—144no—
535D4—288no—
536D4—288no—
537D4—288no—
538D4—282no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—74no—
548C2×C4—74no—
549C2×C4—716no—
550C2×C4—74no—
551C2×C4—72no—
552C2×C4—72no—
553C2×C4—72no—
554C2×C4—72no—
555C2×C4—148no—
556C2×C4—142no—
557C2×C4—142no—
558C2×C4—144no—
559C2×C4—288no—
560C2×C4—288no—
561C2×C4—282no—
562C2×C4—288no—
563C2×C4—284no—
564C2×C4C2×D4×D712yes—
565C2×C4C2×D4×D711yescharacteristic
566C2×C4#655414yes—
567C2×C4C24×D711yescharacteristic
568C8—24no—
569C8—144no—
570C7C2×#322611yescharacteristic, complemented, Sylow
571C22—22no—
572C22—22no—
573C22—28no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—282no—
579C22—282no—
580C22—282no—
581C22—564no—
582C22#9033912yes—
583C22C2×D7×D814yes—
584C22C2×D7×D812yes—
585C22D7×#13712yes—
586C22C22×D4×D711yescharacteristic
587C4—22no—
588C4—44no—
589C4—42no—
590C4—74no—
591C4—74no—
592C4—74no—
593C4—142no—
594C4—282no—
595C4—284no—
596C4#9033912yes—
597C4C2×#655412yes—
598C2—24no—
599C2—82no—
600C2—562no—
601C2#1173871914yesdirect product factor
602C2C2×#9033911yescharacteristic
603C2C22×D7×D811yescharacteristic
604C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#480C2
socleC23×C7C22×D4
prime radicalC2×#90287C2
hypercenterC2×#480D7
hypocenterC7C2×#3226
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#6451C2semidirect
3. C2×C7×#480C2semidirect
4. C2×#89805C2semidirect
5. C2×#89739C2semidirect
6. #11738719C2direct (N × H)
7. C2×#89662C2semidirect
8. C2×#89646C2semidirect
9. C2×#89532C2semidirect
10. C2×#89531C2semidirect
11. C2×#89508C2semidirect
12. C2×#89490C2semidirect
33. C2×#6451C22semidirect
36. C7×#480C22semidirect
46. #89805C22semidirect
47. #89739C22semidirect
51. #89662C22semidirect
52. #89646C22semidirect
53. #89532C22semidirect
54. #89531C22semidirect
55. #89508C22semidirect
56. #89490C22semidirect
145. C2×#480D7semidirect
254. #480C2×D7semidirect
510. C2×C7#3226semidirect
570. C7C2×#3226semidirect
601. C2#11738719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902872
C22×#64512
C2×C7×#4802
C2×#898052
C2×#897392
#117387192
C2×#896622
C2×#896462
C2×#895322
C2×#895312
C2×#895082
C2×#894902
C2×#32267