Finite Group Databasebeta

← C2×#11738414 #14225808

Subgroups — C2×#11738414 #14225808

Order 1792.

2286 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic
3C2×C7×#474C211yesmaximal, characteristic, complemented
4C2×#89859C211yesmaximal, characteristic, complemented
5C2×#89779C211yesmaximal, characteristic, complemented
6#11738414C2116yesmaximal, direct product factor
7C2×#89654C212yesmaximal, complemented
8C2×#89646C212yesmaximal, complemented
9C2×#89618C211yesmaximal, characteristic, complemented
10C2×#89605C211yesmaximal, characteristic, complemented
11C2×#89546C212yesmaximal, complemented
12C2×#89532C212yesmaximal, complemented
13C22×Q8×D7—21no—
14C22×#1157—21no—
15C2×C7×C4⋊Q8C2211yescharacteristic
16C2×C4×C7×D4C2211yescharacteristic
17C2×#6507—21no—
18C2×#6503C2211yescharacteristic
19C2×#6501C2211yescharacteristic
20C2×C4×C22⋊D7—21no—
21D7×C4⋊Q8—24no—
22D7×C4⋊Q8C2218yescomplemented
23#90239—24no—
24#90239C2218yes—
25C2×#6458C2211yescharacteristic
26C2×D7×C4⋊C4—21no—
27C2×D7×C4⋊C4C2212yes—
28C2×#6451—21no—
29C2×#6451C2211yescharacteristic
30C2×#6451C2212yes—
31C2×#6448—21no—
32C2×#6447—21no—
33C2×C4×D28C2211yescharacteristic
34C2×C42×D7C2211yescharacteristic
35C2×#6432C2211yescharacteristic
36C7×#474C2218yescomplemented
37C2×C7×#107C2212yes—
38C2×C7×C4⋊C8C2211yescharacteristic
39C2×C7×#102C2212yes—
40C2×#6406C2212yes—
41C2×#6395C2212yes—
42C2×(C2×D7)⋊C8C2212yes—
43C2×#6392C2212yes—
44C2×C8×Dic7C2212yes—
45#89859C2218yescomplemented
46#89779C2218yescomplemented
47C2×#6383C2212yes—
48C2×#6381C2212yes—
49C2×#6381C2212yes—
50C2×C4⋊(C7⋊C8)C2211yescharacteristic
51#89654C22116yescomplemented
52#89646C22116yescomplemented
53#89618C2218yescomplemented
54#89605C2218yescomplemented
55#89546C22116yescomplemented
56#89532C22116yescomplemented
57C2×#3226—71nomaximal, Sylow
58C22×C7×Q8—21no—
59C22×C7×D4C2311yescharacteristic
60C23×C4×C7—21no—
61C22×C22⋊D7—21no—
62C22×C22⋊D7—21no—
63C22×C22⋊D7—21no—
64C2×Q8×D7—28no—
65C2×Q8×D7—48no—
66C2×#1157—28no—
67C2×#1157—48no—
68C22×D28—21no—
69C22×D28C2311yescharacteristic
70C22×C4×D7—22no—
71C22×C4×D7—21no—
72C22×C4×D7D411yescharacteristic
73C22×C4×D7D411yescharacteristic
74C22×C4×D7C2311yescharacteristic
75C22×Dic14—21no—
76C22×Dic14—21no—
77C22×Dic14—22no—
78C22×C7×C8C2312yes—
79C7×C4⋊Q8—22no—
80C7×C4⋊Q8C2314yes—
81C4×C7×D4—22no—
82C4×C7×D4C2314yes—
83C2×C7×C4⋊C4—21no—
84C2×C7×C4⋊C4C2312yes—
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C22⋊C4—21no—
87C2×C42×C7C2311yescharacteristic
88C2×C22⋊Dic7—21no—
89#6507—28no—
90#6503—22no—
91#6503C2314yes—
92#6501—22no—
93#6501C2314yes—
94C4×C22⋊D7—28no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7C2311yescharacteristic
99C2×C4⋊Dic7C2312yes—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×C4×Dic7D411yescharacteristic
104C2×C4×Dic7D411yescharacteristic
105C2×C4×Dic7C2311yescharacteristic
106C22×C7⋊C8C2312yes—
107#6458—22no—
108#6458C2314yes—
109D7×C4⋊C4—24no—
110D7×C4⋊C4—28no—
111D7×C4⋊C4C2318yes—
112#6451—24no—
113#6451—28no—
114#6451—22no—
115#6451C2314yes—
116#6451C2318yes—
117#6448—28no—
118#6447—28no—
119C4×D28—22no—
120C4×D28C2314yes—
121C42×D7D414yes—
122C42×D7C2314yes—
123#6432—22no—
124#6432C2314yes—
125C7×#107C2318yes—
126C7×C4⋊C8C2314yes—
127C7×#102C2318yes—
128#6406C2318yes—
129#6395C2318yes—
130(C2×D7)⋊C8C2318yes—
131#6392C2318yes—
132C8×Dic7C2318yes—
133#6383C2318yes—
134#6381C2318yes—
135#6381C2318yes—
136C4⋊(C7⋊C8)C2314yes—
137C2×#532—71no—
138C22×C4⋊Q8—71no—
139#3226—716no—
140C2×#500—72no—
141C2×#486—72no—
142C2×#480—72no—
143C2×#480—72no—
144C2×#474—71no—
145C2×#474—71no—
146C2×#474—71no—
147C2×#474D711yescharacteristic, complemented
148C2×#431—71no—
149C24×C7—21no—
150C23×D7—21no—
151C23×D7C2×D411yescharacteristic
152C2×C7×Q8—24no—
153C2×C7×Q8—44no—
154C2×C7×D4—21no—
155C2×C7×D4—22no—
156C2×C7×D4—22no—
157C2×C7×D4C2412yes—
158C22×C4×C7—22no—
159C22×C4×C7—21no—
160C22×C4×C7—24no—
161C22×C4×C7—44no—
162C22×C4×C7C2×D411yescharacteristic
163C22×C4×C7C2×D411yescharacteristic
164C22×C4×C7C2411yescharacteristic
165C2×C22⋊D7—24no—
166C2×C22⋊D7—24no—
167C2×C22⋊D7—24no—
168C2×C22⋊D7—44no—
169C2×C22⋊D7—44no—
170C2×C22⋊D7—44no—
171C22×Dic7—22no—
172C22×Dic7—21no—
173C22×Dic7C2×D411yescharacteristic
174C22×Dic7C2×D411yescharacteristic
175C22×Dic7C2×D411yescharacteristic
176Q8×D7—432no—
177#1157—432no—
178C2×D28—22no—
179C2×D28—22no—
180C2×D28—24no—
181C2×D28—21no—
182C2×D28—44no—
183C2×D28C2412yes—
184C2×C4×D7—22no—
185C2×C4×D7—22no—
186C2×C4×D7—24no—
187C2×C4×D7—28no—
188C2×C4×D7—24no—
189C2×C4×D7—48no—
190C2×C4×D7—44no—
191C2×C4×D7D818yes—
192C2×C4×D7C2×D412yes—
193C2×C4×D7C2×D414yes—
194C2×C4×D7C2×D414yes—
195C2×C4×D7C2412yes—
196C2×Dic14—24no—
197C2×Dic14—24no—
198C2×Dic14—28no—
199C2×Dic14—44no—
200C2×Dic14—44no—
201C2×Dic14—48no—
202C2×C7×C8—24no—
203C2×C7×C8C2414yes—
204C7×C4⋊C4—24no—
205C7×C4⋊C4—22no—
206C7×C4⋊C4—21no—
207C7×C4⋊C4C2414yes—
208C7×C4⋊C4C2412yes—
209C7×C22⋊C4—24no—
210C42×C7C2×D412yes—
211C42×C7C2412yes—
212C22⋊Dic7—24no—
213(C2×D7)⋊C4—24no—
214(C2×D7)⋊C4—24no—
215C4⋊Dic7—22no—
216C4⋊Dic7—24no—
217C4⋊Dic7—21no—
218C4⋊Dic7C2414yes—
219C4⋊Dic7C2412yes—
220Dic7⋊C4—24no—
221Dic7⋊C4—28no—
222Dic7⋊C4—28no—
223C4×Dic7C2×D412yes—
224C4×Dic7C2×D414yes—
225C4×Dic7C2×D414yes—
226C4×Dic7C2412yes—
227C2×C7⋊C8—24no—
228C2×C7⋊C8C2414yes—
229C22×#41—141no—
230C23×Q8—141no—
231#532—78no—
232#532—144no—
233C2×C4⋊Q8—78no—
234C2×C4⋊Q8—72no—
235C2×C4⋊Q8—71no—
236C2×C4⋊Q8—71no—
237C2×C4⋊Q8—141no—
238C2×C4⋊Q8—144no—
239C2×C4⋊Q8—141no—
240C2×C4⋊Q8C2×D711yescharacteristic
241C2×#127—71no—
242C2×#124—141no—
243C2×#121—71no—
244C2×#121—71no—
245C2×#121—141no—
246C2×C4×D4—71no—
247C2×C4×D4—141no—
248C2×C4×D4C2×D711yescharacteristic
249C22×C4⋊C4—72no—
250C22×C4⋊C4—141no—
251C22×C42—71no—
252#500—716no—
253#486—716no—
254#480—716no—
255#480—716no—
256#474—78no—
257#474—78no—
258#474—78no—
259#474C2×D718yescomplemented
260#431—78no—
261C2×#107—72no—
262C2×#107—72no—
263C2×#107—72no—
264C2×#107C2×D712yes—
265C2×C4⋊C8—71no—
266C2×C4⋊C8C2×D711yescharacteristic
267C2×#102—72no—
268C2×#102—72no—
269C2×#102—72no—
270C2×#102C2×D712yes—
271C2×C22⋊C8—72no—
272C2×C4×C8—72no—
273C23×C7—22no—
274C23×C7—42no—
275C23×C7—42no—
276C23×C7—42no—
277C23×C7C22×D411yescharacteristic
278C22×D7—22no—
279C22×D7—22no—
280C22×D7—22no—
281C22×D7—42no—
282C22×D7—42no—
283C22×D7—42no—
284C22×D7C2×D814yes—
285C22×D7C22×D412yes—
286C7×Q8—48no—
287C7×D4—22no—
288C7×D4—22no—
289C7×D4—42no—
290C2×C4×C7—22no—
291C2×C4×C7—24no—
292C2×C4×C7—22no—
293C2×C4×C7—44no—
294C2×C4×C7—42no—
295C2×C4×C7—48no—
296C2×C4×C7C2×D814yes—
297C2×C4×C7C22×D412yes—
298C2×C4×C7C22×D411yescharacteristic
299C2×C4×C7C22×D412yes—
300C2×C4×C72−1+412yes—
301C2×C4×C72−1+412yes—
302C2×C4×C7C2511yescharacteristic
303C22⋊D7—48no—
304C22⋊D7—48no—
305C22⋊D7—48no—
306C2×Dic7—22no—
307C2×Dic7—24no—
308C2×Dic7—22no—
309C2×Dic7—44no—
310C2×Dic7—42no—
311C2×Dic7C2×D814yes—
312C2×Dic7#13714yes—
313C2×Dic7C22×D412yes—
314C2×Dic7C22×D412yes—
315C2×Dic7C22×D412yes—
316D28—22no—
317D28—22no—
318D28—48no—
319D28—42no—
320C4×D7—24no—
321C4×D7—22no—
322C4×D7—22no—
323C4×D7—28no—
324C4×D7—416no—
325C4×D7—48no—
326C4×D7C2×D8116yes—
327Dic14—48no—
328Dic14—48no—
329Dic14—416no—
330C7×C8—24no—
331C7⋊C8—24no—
332C2×#41—148no—
333C2×#41—288no—
334C22×Q8—21no—
335C22×Q8—141no—
336C22×Q8—142no—
337C22×Q8—148no—
338C22×Q8—141no—
339C22×Q8—288no—
340C22×D4—71no—
341C22×D4—141no—
342C22×D4—141no—
343C22×D4—141no—
344C22×D4—141no—
345C22×D4C22×D711yescharacteristic
346C23×C4—21no—
347C23×C4—71no—
348C23×C4—71no—
349C23×C4—71no—
350C23×C4—142no—
351C23×C4—141no—
352C22×C8—72no—
353C22×C8C22×D712yes—
354C4⋊Q8—22no—
355C4⋊Q8—78no—
356C4⋊Q8—74no—
357C4⋊Q8—74no—
358C4⋊Q8—148no—
359C4⋊Q8—144no—
360C4⋊Q8—142no—
361C4⋊Q8—148no—
362C4⋊Q8—142no—
363C4⋊Q8C22×D714yes—
364#127—74no—
365#127—142no—
366#124—148no—
367#121—74no—
368#121—74no—
369#121—148no—
370#121—142no—
371#121—142no—
372C4×D4—22no—
373C4×D4—74no—
374C4×D4—148no—
375C4×D4—142no—
376C4×D4C22×D714yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—72no—
379C2×C4⋊C4—71no—
380C2×C4⋊C4—78no—
381C2×C4⋊C4—144no—
382C2×C4⋊C4—148no—
383C2×C4⋊C4—142no—
384C2×C4⋊C4—142no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4C22×D712yes—
388C2×C4⋊C4C22×D711yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—141no—
391C2×C22⋊C4—141no—
392C2×C22⋊C4—141no—
393C2×C42—71no—
394C2×C42—71no—
395C2×C42—71no—
396C2×C42—74no—
397C2×C42—74no—
398C2×C42C22×D711yescharacteristic
399#107—78no—
400#107—78no—
401#107—78no—
402#107C22×D718yes—
403C4⋊C8—74no—
404C4⋊C8C22×D714yes—
405#102—78no—
406#102—78no—
407#102—78no—
408#102C22×D718yes—
409C22⋊C8—78no—
410C4×C8—78no—
411C22×C7—42no—
412C22×C7—42no—
413C22×C7—42no—
414C22×C7—84no—
415C22×C7#53612yes—
416C22×C7C22×D812yes—
417C22×C7C2×#13712yes—
418C22×C7C23×D411yescharacteristic
419C2×D7—22no—
420C2×D7—28no—
421C2×D7—22no—
422C2×D7—42no—
423C2×D7—42no—
424C2×D7—42no—
425C2×D7—84no—
426C2×D7C22×D814yes—
427C4×C7—22no—
428C4×C7—44no—
429C4×C7—42no—
430C4×C7#53612yes—
431C4×C7C22×D814yes—
432C4×C7C2×2−1+411yescharacteristic
433C4×C7C2×2−1+411yescharacteristic
434Dic7—22no—
435Dic7—44no—
436Dic7—42no—
437Dic7C22×D814yes—
438Dic7C2×#13714yes—
439C24—21no—
440C24—71no—
441C24—141no—
442#41—2832no—
443C2×Q8—24no—
444C2×Q8—44no—
445C2×Q8—144no—
446C2×Q8—148no—
447C2×Q8—144no—
448C2×Q8—288no—
449C2×Q8—284no—
450C2×Q8—2832no—
451C2×Q8—284no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—72no—
456C2×D4—144no—
457C2×D4—144no—
458C2×D4—144no—
459C2×D4—144no—
460C2×D4—141no—
461C2×D4—142no—
462C2×D4—142no—
463C2×D4—284no—
464C2×D4—284no—
465C2×D4—284no—
466C2×D4—284no—
467C2×D4C23×D712yes—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—44no—
472C22×C4—71no—
473C22×C4—71no—
474C22×C4—78no—
475C22×C4—74no—
476C22×C4—71no—
477C22×C4—74no—
478C22×C4—72no—
479C22×C4—72no—
480C22×C4—144no—
481C22×C4—148no—
482C22×C4—142no—
483C22×C4—142no—
484C22×C4—141no—
485C22×C4—142no—
486C22×C4—144no—
487C22×C4—288no—
488C22×C4—284no—
489C22×C4D4×D711yescharacteristic
490C22×C4D4×D711yescharacteristic
491C22×C4C23×D711yescharacteristic
492C2×C8—24no—
493C2×C8—74no—
494C2×C8—144no—
495C2×C8C23×D714yes—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—74no—
500C4⋊C4—72no—
501C4⋊C4—148no—
502C4⋊C4—148no—
503C4⋊C4—144no—
504C4⋊C4—142no—
505C4⋊C4—141no—
506C4⋊C4—144no—
507C4⋊C4C23×D714yes—
508C4⋊C4C23×D712yes—
509C22⋊C4—24no—
510C22⋊C4—144no—
511C22⋊C4—144no—
512C22⋊C4—144no—
513C42—74no—
514C42—74no—
515C42—72no—
516C42—72no—
517C42D4×D712yes—
518C42C23×D712yes—
519C2×C7—82no—
520C2×C7#322614yescomplemented
521C2×C7C2×#53611yescharacteristic
522C2×C7C23×D811yescharacteristic
523C2×C7C22×#13711yescharacteristic
524D7—24no—
525D7—82no—
526C23—22no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—74no—
531C23—72no—
532C23—142no—
533C23—142no—
534C23—142no—
535C23—282no—
536C23—282no—
537C23—282no—
538C23C2×D4×D711yescharacteristic
539Q8—48no—
540Q8—2816no—
541Q8—288no—
542Q8—288no—
543D4—22no—
544D4—22no—
545D4—42no—
546D4—142no—
547D4—142no—
548D4—288no—
549D4—288no—
550D4—288no—
551D4—288no—
552D4—282no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—48no—
559C2×C4—74no—
560C2×C4—74no—
561C2×C4—72no—
562C2×C4—72no—
563C2×C4—716no—
564C2×C4—72no—
565C2×C4—148no—
566C2×C4—142no—
567C2×C4—144no—
568C2×C4—142no—
569C2×C4—142no—
570C2×C4—142no—
571C2×C4—144no—
572C2×C4—2816no—
573C2×C4—282no—
574C2×C4—284no—
575C2×C4—288no—
576C2×C4D7×D814yes—
577C2×C4C2×D4×D712yes—
578C2×C4C2×D4×D712yes—
579C2×C4C2×D4×D711yescharacteristic
580C2×C4#655112yes—
581C2×C4#655412yes—
582C2×C4C24×D711yescharacteristic
583C8—24no—
584C8—144no—
585C7C2×#322611yescharacteristic, complemented, Sylow
586C22—42no—
587C22—42no—
588C22—42no—
589C22—74no—
590C22—84no—
591C22—142no—
592C22—148no—
593C22—142no—
594C22—282no—
595C22—282no—
596C22—282no—
597C22—564no—
598C22#9031912yes—
599C22C2×D7×D812yes—
600C22D7×#13712yes—
601C22C22×D4×D711yescharacteristic
602C4—22no—
603C4—42no—
604C4—44no—
605C4—74no—
606C4—74no—
607C4—142no—
608C4—282no—
609C4—284no—
610C4#9031912yes—
611C4C2×D7×D814yes—
612C4C2×#655111yescharacteristic
613C4C2×#655411yescharacteristic
614C2—82no—
615C2—144no—
616C2—562no—
617C2#1173841414yesdirect product factor
618C2C2×#9031911yescharacteristic
619C2C22×D7×D811yescharacteristic
620C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#474C2
socleC23×C7C22×D4
prime radicalC2×#90239C2
hypercenterC2×#474D7
hypocenterC7C2×#3226
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×D7×C4⋊Q8C2semidirect
3. C2×C7×#474C2semidirect
4. C2×#89859C2semidirect
5. C2×#89779C2semidirect
6. #11738414C2direct (N × H)
7. C2×#89654C2semidirect
8. C2×#89646C2semidirect
9. C2×#89618C2semidirect
10. C2×#89605C2semidirect
11. C2×#89546C2semidirect
12. C2×#89532C2semidirect
22. D7×C4⋊Q8C22semidirect
36. C7×#474C22semidirect
45. #89859C22semidirect
46. #89779C22semidirect
51. #89654C22semidirect
52. #89646C22semidirect
53. #89618C22semidirect
54. #89605C22semidirect
55. #89546C22semidirect
56. #89532C22semidirect
147. C2×#474D7semidirect
259. #474C2×D7semidirect
520. C2×C7#3226semidirect
585. C7C2×#3226semidirect
617. C2#11738414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D7×C4⋊Q82
C2×#902392
C2×C7×#4742
C2×#898592
C2×#897792
#117384142
C2×#896542
C2×#896462
C2×#896182
C2×#896052
C2×#895462
C2×#895322
C2×#32267