Finite Group Databasebeta

← C2×#11738475 #14232340

Subgroups — C2×#11738475 #14232340

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90421C211yesmaximal, characteristic
2C2×#90272C211yesmaximal, characteristic
3C2×C7×#475C211yesmaximal, characteristic, complemented
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89802C211yesmaximal, characteristic, complemented
6#11738475C2116yesmaximal, direct product factor
7C2×#89634C211yesmaximal, characteristic, complemented
8C2×#89633C211yesmaximal, characteristic, complemented
9C2×D7×#106C211yesmaximal, characteristic, complemented
10C2×#89639C211yesmaximal, characteristic, complemented
11C2×#89601C211yesmaximal, characteristic, complemented
12C2×#89608C211yesmaximal, characteristic
13C2×#89581C211yesmaximal, characteristic, complemented
14C2×#89577C211yesmaximal, characteristic, complemented
15C2×#89588C211yesmaximal, characteristic, complemented
16C2×#89585C211yesmaximal, characteristic, complemented
17C2×C7×C4⋊Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×#6509—21no—
20C2×#6509—21no—
21C2×#6509C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C22×#1144C2211yescharacteristic
24C22×#1131C2211yescharacteristic
25C22×C8×D7C2211yescharacteristic
26#90421—24no—
27#90421C2218yes—
28#90272—24no—
29#90272C2218yes—
30C2×#6460C2211yescharacteristic
31C2×#6460C2211yescharacteristic
32C2×#6457—21no—
33C2×#6456—21no—
34C2×#6455C2211yescharacteristic
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×D7×C4⋊C4C2211yescharacteristic
38C2×#6453—21no—
39C2×#6452—21no—
40C2×#6439—21no—
41C2×C4×D28C2211yescharacteristic
42C2×#6435—21no—
43C2×#6433C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C7×#475C2218yescomplemented
46C2×C7×#106C2211yescharacteristic
47C2×C7×#106C2211yescharacteristic
48C2×C7×C4⋊C8C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×#6392C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6390C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58#89852C2218yescomplemented
59#89802C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6382C2211yescharacteristic
62C2×#6382C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6377C2211yescharacteristic
67#89639C2218yescomplemented
68#89634C2218yescomplemented
69#89633C2218yescomplemented
70D7×#106C2218yescomplemented
71#89608C2218yes—
72#89601C2218yescomplemented
73#89588C2218yescomplemented
74#89585C2218yescomplemented
75#89581C2218yescomplemented
76#89577C2218yescomplemented
77C2×#3344—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×D28D411yescharacteristic
81C22×C4×D7—21no—
82C22×C4×D7—21no—
83C22×C4×D7—21no—
84C22×C4×D7C2311yescharacteristic
85C22×C4×D7C2311yescharacteristic
86C22×Dic14C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89C7×C4⋊Q8—22no—
90C7×C4⋊Q8C2314yes—
91C4×C7×Q8—22no—
92C4×C7×Q8C2314yes—
93C2×C7×C4⋊C4—21no—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4C2311yescharacteristic
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C42×C7—21no—
99C2×C42×C7C2311yescharacteristic
100#6509—22no—
101#6509—22no—
102#6509—28no—
103#6509—28no—
104#6509C2314yes—
105#6509C2314yes—
106C2×#1144—24no—
107C2×#1144C2314yes—
108C2×(C2×D7)⋊C4—21no—
109C2×(C2×D7)⋊C4—21no—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4D411yescharacteristic
114C2×(C2×D7)⋊C4D411yescharacteristic
115C2×C4⋊Dic7—21no—
116C2×C4⋊Dic7—21no—
117C2×C4⋊Dic7D411yescharacteristic
118C2×C4⋊Dic7C2311yescharacteristic
119C2×C4⋊Dic7C2311yescharacteristic
120C2×C4⋊Dic7C2311yescharacteristic
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×Dic7⋊C4—21no—
127C2×Dic7⋊C4—21no—
128C2×Dic7⋊C4—21no—
129C2×C4×Dic7—21no—
130C2×C4×Dic7—21no—
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133C2×#1131—24no—
134C2×#1131C2314yes—
135C2×C8×D7—24no—
136C2×C8×D7C2314yes—
137#6460—22no—
138#6460—22no—
139#6460C2314yes—
140#6460C2314yes—
141#6457—28no—
142#6456—28no—
143#6455—22no—
144#6455C2314yes—
145D7×C4⋊C4—22no—
146D7×C4⋊C4—22no—
147D7×C4⋊C4—22no—
148D7×C4⋊C4C2314yes—
149D7×C4⋊C4C2314yes—
150D7×C4⋊C4C2314yes—
151#6453—28no—
152#6452—28no—
153#6439—28no—
154C4×D28D414yes—
155C4×D28C2314yes—
156#6435—28no—
157#6433—22no—
158#6433C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×C4⋊C8C2314yes—
164C7×#103C2314yes—
165C7×#103C2314yes—
166#6409C2314yes—
167(C2×D7)⋊C8C2314yes—
168(C2×D7)⋊C8C2314yes—
169#6392C2314yes—
170#6391C2314yes—
171#6390C2314yes—
172#6390C2314yes—
173#6384C2314yes—
174#6382C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6377C2314yes—
180C2×#554—71no—
181C2×#552—71no—
182#3344—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#483—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475D711yescharacteristic, complemented
190C2×#470—71no—
191C2×#467—71no—
192C2×#441—71no—
193C2×#435—71no—
194C2×#428—71no—
195C22×#106—71no—
196C23×D7C2×D411yescharacteristic
197C23×D7C2×D411yescharacteristic
198C2×C7×Q8—21no—
199C2×C7×Q8—24no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—82no—
203C2×C7×Q8C2412yes—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2411yescharacteristic
211C22×Dic7—21no—
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7C2×D411yescharacteristic
216C22×Dic7C2×D411yescharacteristic
217C2×D28—24no—
218C2×D28C2×D414yes—
219C2×C4×D7—22no—
220C2×C4×D7—22no—
221C2×C4×D7—22no—
222C2×C4×D7—22no—
223C2×C4×D7—24no—
224C2×C4×D7—24no—
225C2×C4×D7—24no—
226C2×C4×D7—44no—
227C2×C4×D7—82no—
228C2×C4×D7—82no—
229C2×C4×D7C2×D412yes—
230C2×C4×D7C2×D412yes—
231C2×C4×D7C2412yes—
232C2×C4×D7C2412yes—
233C2×Dic14—22no—
234C2×Dic14—22no—
235C2×Dic14—21no—
236C2×Dic14C2412yes—
237C2×C7×C8—22no—
238C2×C7×C8—22no—
239C2×C7×C8C2412yes—
240C2×C7×C8C2412yes—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—21no—
244C7×C4⋊C4—21no—
245C7×C4⋊C4—21no—
246C7×C4⋊C4C2412yes—
247C7×C4⋊C4C2412yes—
248C7×C4⋊C4C2412yes—
249C42×C7—24no—
250C42×C7C2×D412yes—
251C42×C7C2412yes—
252#1144—28no—
253(C2×D7)⋊C4—24no—
254(C2×D7)⋊C4—24no—
255(C2×D7)⋊C4—24no—
256(C2×D7)⋊C4—24no—
257(C2×D7)⋊C4—24no—
258(C2×D7)⋊C4C2×D414yes—
259(C2×D7)⋊C4C2×D414yes—
260C4⋊Dic7—21no—
261C4⋊Dic7—21no—
262C4⋊Dic7—21no—
263C4⋊Dic7—24no—
264C4⋊Dic7—24no—
265C4⋊Dic7C2×D414yes—
266C4⋊Dic7C2412yes—
267C4⋊Dic7C2412yes—
268C4⋊Dic7C2412yes—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277C4×Dic7—24no—
278C4×Dic7—24no—
279C2×C7⋊C8—22no—
280C2×C7⋊C8#4114yes—
281C2×C7⋊C8C2412yes—
282C2×C7⋊C8C2412yes—
283#1131—28no—
284C8×D7—28no—
285C22×Q16—71no—
286C22×M16—71no—
287C23×C8—71no—
288#554—78no—
289#554—144no—
290#552—78no—
291#552—144no—
292C2×C4⋊Q8C2×D711yescharacteristic
293C2×#126—141no—
294C2×#125—71no—
295C2×#125—141no—
296C2×#125—141no—
297C2×#123—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8—71no—
301C2×C22⋊Q8—71no—
302C2×C22⋊Q8—141no—
303C2×C22⋊Q8—141no—
304C2×C4×Q8—71no—
305C2×C4×Q8C2×D711yescharacteristic
306C2×C4×D4—71no—
307C2×C4×D4—141no—
308C2×#117—71no—
309C2×#117—141no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313#501—78no—
314#485—78no—
315#484—78no—
316#483—78no—
317#483—78no—
318#479—78no—
319#475C2×D718yescomplemented
320#470—78no—
321#467—78no—
322#441—78no—
323#435—78no—
324#428—78no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#106—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—78no—
333C2×#106C2×D711yescharacteristic
334C2×#106C2×D711yescharacteristic
335C2×C4⋊C8C2×D711yescharacteristic
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×#103C2×D711yescharacteristic
341C2×#103C2×D711yescharacteristic
342C2×C22⋊C8—71no—
343C2×C22⋊C8—71no—
344C2×#97—71no—
345C23×C7C22×D411yescharacteristic
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7#13714yes—
352C22×D7C22×D412yes—
353C22×D7C22×D412yes—
354C7×Q8—22no—
355C7×Q8—22no—
356C7×Q8—42no—
357C7×Q8—84no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7C22×D412yes—
369C2×C4×C7C22×D412yes—
370C2×C4×C7C22×D411yescharacteristic
371C2×C4×C7C2×#4112yes—
372C2×C4×C72−1+412yes—
373C2×C4×C7C2511yescharacteristic
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7—42no—
381C2×Dic7—42no—
382C2×Dic7—42no—
383C2×Dic7—42no—
384C2×Dic7C22×D412yes—
385C2×Dic7C22×D412yes—
386D28—28no—
387C4×D7—24no—
388C4×D7—24no—
389C4×D7—22no—
390C4×D7—22no—
391C4×D7—22no—
392C4×D7—22no—
393C4×D7—48no—
394C4×D7—84no—
395C4×D7—84no—
396Dic14—22no—
397Dic14—22no—
398Dic14—42no—
399C7×C8—22no—
400C7×C8—22no—
401C7⋊C8—22no—
402C7⋊C8C2×#4114yes—
403C22×Q8—21no—
404C22×Q8—71no—
405C22×Q8C22×D711yescharacteristic
406C22×D4—71no—
407C23×C4—71no—
408C23×C4—71no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4—141no—
412C2×Q16—74no—
413C2×Q16—144no—
414C2×M16—74no—
415C2×M16—144no—
416C22×C8—71no—
417C22×C8—71no—
418C22×C8—74no—
419C22×C8—144no—
420C22×C8C22×D711yescharacteristic
421C22×C8C22×D711yescharacteristic
422C4⋊Q8—22no—
423C4⋊Q8C22×D714yes—
424#126—148no—
425#125—74no—
426#125—148no—
427#125—148no—
428#125—142no—
429#123—148no—
430C22⋊Q8—74no—
431C22⋊Q8—74no—
432C22⋊Q8—74no—
433C22⋊Q8—74no—
434C22⋊Q8—148no—
435C22⋊Q8—148no—
436C22⋊Q8—142no—
437C22⋊Q8—142no—
438C22⋊Q8—142no—
439C22⋊Q8—142no—
440C4×Q8—22no—
441C4×Q8—74no—
442C4×Q8—142no—
443C4×Q8C22×D714yes—
444C4×D4—74no—
445C4×D4—74no—
446C4×D4—148no—
447#117—74no—
448#117—148no—
449#117—142no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—74no—
457C2×C4⋊C4—74no—
458C2×C4⋊C4—74no—
459C2×C4⋊C4—142no—
460C2×C4⋊C4—142no—
461C2×C4⋊C4—142no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4—141no—
464C2×C4⋊C4—141no—
465C2×C4⋊C4—141no—
466C2×C4⋊C4—141no—
467C2×C4⋊C4—141no—
468C2×C4⋊C4—141no—
469C2×C4⋊C4—141no—
470C2×C4⋊C4—141no—
471C2×C4⋊C4—141no—
472C2×C4⋊C4C22×D711yescharacteristic
473C2×C4⋊C4C22×D711yescharacteristic
474C2×C4⋊C4C22×D711yescharacteristic
475C2×C22⋊C4—71no—
476C2×C22⋊C4—71no—
477C2×C22⋊C4—141no—
478C2×C22⋊C4—141no—
479C2×C22⋊C4—141no—
480C2×C22⋊C4—141no—
481C2×C22⋊C4—141no—
482C2×C42—21no—
483C2×C42—141no—
484C2×C42—141no—
485C2×C42C22×D711yescharacteristic
486#107—74no—
487#107—74no—
488#107—74no—
489#106—74no—
490#106—74no—
491#106—74no—
492#106—74no—
493#106C22×D714yes—
494#106C22×D714yes—
495C4⋊C8C22×D714yes—
496#103—74no—
497#103—74no—
498#103—74no—
499#103—74no—
500#103C22×D714yes—
501#103C22×D714yes—
502C22⋊C8—74no—
503C22⋊C8—74no—
504#97—74no—
505C22×C7#54712yes—
506C22×C7C2×#13712yes—
507C22×C7#57712yes—
508C22×C7C23×D411yescharacteristic
509C2×D7—28no—
510C2×D7—22no—
511C2×D7—22no—
512C2×D7—22no—
513C2×D7—22no—
514C2×D7—22no—
515C2×D7—44no—
516C2×D7C2×#13714yes—
517C4×C7—22no—
518C4×C7—22no—
519C4×C7—42no—
520C4×C7—42no—
521C4×C7—42no—
522C4×C7—42no—
523C4×C7#54712yes—
524C4×C7C22×#4111yescharacteristic
525C4×C7C2×2−1+411yescharacteristic
526Dic7—22no—
527Dic7—22no—
528Dic7—42no—
529Dic7—42no—
530Dic7—42no—
531Dic7—42no—
532C24—71no—
533C24—71no—
534C2×Q8—21no—
535C2×Q8—24no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—72no—
539C2×Q8—82no—
540C2×Q8—141no—
541C2×Q8—142no—
542C2×Q8—142no—
543C2×Q8C23×D712yes—
544C2×D4—74no—
545C2×D4—144no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—71no—
551C22×C4—71no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—144no—
557C22×C4—144no—
558C22×C4—144no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—141no—
566C22×C4—141no—
567C22×C4—284no—
568C22×C4—562no—
569C22×C4—562no—
570C22×C4D4×D711yescharacteristic
571C22×C4D4×D711yescharacteristic
572C22×C4C23×D711yescharacteristic
573Q16—148no—
574M16—148no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—74no—
578C2×C8—72no—
579C2×C8—72no—
580C2×C8—148no—
581C2×C8—142no—
582C2×C8C23×D712yes—
583C2×C8C23×D712yes—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—74no—
590C4⋊C4—72no—
591C4⋊C4—72no—
592C4⋊C4—72no—
593C4⋊C4—144no—
594C4⋊C4—144no—
595C4⋊C4—144no—
596C4⋊C4—144no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—144no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4C23×D712yes—
607C4⋊C4C23×D712yes—
608C4⋊C4C23×D712yes—
609C22⋊C4—74no—
610C22⋊C4—74no—
611C22⋊C4—144no—
612C22⋊C4—144no—
613C22⋊C4—144no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C42—24no—
617C42—144no—
618C42—144no—
619C42D4×D712yes—
620C42C23×D712yes—
621C2×C7#334414yescomplemented
622C2×C7C2×#54711yescharacteristic
623C2×C7C22×#13711yescharacteristic
624C2×C7C2×#57711yescharacteristic
625D7—24no—
626D7—42no—
627C23—74no—
628C23—72no—
629C23—72no—
630C23—142no—
631C23—142no—
632C23—142no—
633C23—142no—
634C23—142no—
635C23C2×D4×D711yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—42no—
639Q8—84no—
640Q8—142no—
641Q8—142no—
642Q8—282no—
643D4—148no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—72no—
655C2×C4—72no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—144no—
659C2×C4—144no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—288no—
669C2×C4—282no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—282no—
673C2×C4—564no—
674C2×C4—564no—
675C2×C4C2×D4×D712yes—
676C2×C4C2×D4×D712yes—
677C2×C4C2×D4×D711yescharacteristic
678C2×C4#655112yes—
679C2×C4D7×#4112yes—
680C2×C4C24×D711yescharacteristic
681C8—22no—
682C8—22no—
683C8—74no—
684C8—142no—
685C7C2×#334411yescharacteristic, complemented, Sylow
686C22—74no—
687C22—142no—
688C22—148no—
689C22—142no—
690C22—142no—
691C22—142no—
692C22—142no—
693C22—284no—
694C22#9032212yes—
695C22#9045312yes—
696C22D7×#13712yes—
697C22C22×D4×D711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—142no—
705C4—142no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C4#9032212yes—
711C4C2×#655111yescharacteristic
712C4C2×D7×#4111yescharacteristic
713C2—144no—
714C2—282no—
715C2#1173847514yesdirect product factor
716C2C2×#9032211yescharacteristic
717C2C2×#9045311yescharacteristic
718C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#475C2
socleC23×C7C22×D4
prime radicalC22×D28D4
hypercenterC2×#475D7
hypocenterC7C2×#3344
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. C2×C7×#475C2semidirect
4. C2×#89852C2semidirect
5. C2×#89802C2semidirect
6. #11738475C2direct (N × H)
7. C2×#89634C2semidirect
8. C2×#89633C2semidirect
9. C2×D7×#106C2semidirect
10. C2×#89639C2semidirect
11. C2×#89601C2semidirect
13. C2×#89581C2semidirect
14. C2×#89577C2semidirect
15. C2×#89588C2semidirect
16. C2×#89585C2semidirect
45. C7×#475C22semidirect
58. #89852C22semidirect
59. #89802C22semidirect
67. #89639C22semidirect
68. #89634C22semidirect
69. #89633C22semidirect
70. D7×#106C22semidirect
72. #89601C22semidirect
73. #89588C22semidirect
74. #89585C22semidirect
75. #89581C22semidirect
76. #89577C22semidirect
189. C2×#475D7semidirect
319. #475C2×D7semidirect
621. C2×C7#3344semidirect
685. C7C2×#3344semidirect
715. C2#11738475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904212
C2×#902722
C2×C7×#4752
C2×#898522
C2×#898022
#117384752
C2×#896342
C2×#896332
C2×D7×#1062
C2×#896392
C2×#896012
C2×#896082
C2×#895812
C2×#895772
C2×#895882
C2×#895852
C2×#33447