Finite Group Databasebeta

← C2×#11740900 #14226027

Subgroups — C2×#11740900 #14226027

Order 1792.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2C2×#90210C211yesmaximal, characteristic, complemented
3#11740900C2116yesmaximal, direct product factor
4C2×#89852C211yesmaximal, characteristic, complemented
5C2×#89851C211yesmaximal, characteristic, complemented
6C2×#89827C211yesmaximal, characteristic, complemented
7C2×#89828C211yesmaximal, characteristic, complemented
8C2×#89817C211yesmaximal, characteristic, complemented
9C2×#89815C211yesmaximal, characteristic, complemented
10C2×#89806C211yesmaximal, characteristic
11C2×#89807C211yesmaximal, characteristic
12C2×#89794C211yesmaximal, characteristic, complemented
13C2×#89792C211yesmaximal, characteristic, complemented
14C2×#89781C211yesmaximal, characteristic, complemented
15C2×#89780C211yesmaximal, characteristic, complemented
16C2×#89772C211yesmaximal, characteristic, complemented
17C7×#542—24no—
18C7×#542C2218yes—
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#124—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#123—21no—
24C2×C7×C22⋊Q8—21no—
25C2×C7×C22⋊Q8C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C2×#6489C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32#90210—24no—
33#90210C2218yescomplemented
34C2×#6453—21no—
35C2×#6451—21no—
36C2×#6441—21no—
37C2×#6441—21no—
38C2×#6433C2211yescharacteristic
39C2×#6433C2211yescharacteristic
40C2×#6432C2211yescharacteristic
41C2×#6432C2211yescharacteristic
42C2×#6409C2211yescharacteristic
43C2×#6409C2211yescharacteristic
44C2×#6409C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6406C2211yescharacteristic
47C2×#6406C2211yescharacteristic
48C2×#6406C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×C22⋊(C7⋊C8)C2211yescharacteristic
51C2×C22⋊(C7⋊C8)C2211yescharacteristic
52#89852C2218yescomplemented
53#89851C2218yescomplemented
54#89828C2218yescomplemented
55#89827C2218yescomplemented
56#89817C2218yescomplemented
57#89815C2218yescomplemented
58#89807C2218yes—
59#89806C2218yes—
60#89794C2218yescomplemented
61#89792C2218yescomplemented
62#89781C2218yescomplemented
63#89780C2218yescomplemented
64#89772C2218yescomplemented
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3244—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4—21no—
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C23×C4×C7C2311yescharacteristic
84C23×Dic7—21no—
85C22×Dic14—21no—
86C22×Dic14—21no—
87C7×C4⋊Q8—22no—
88C7×C4⋊Q8C2314yes—
89C7×#126—28no—
90C7×#124—28no—
91C7×#124—22no—
92C7×#124C2314yes—
93C7×#123—28no—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—28no—
96C7×C22⋊Q8C2314yes—
97C7×#121—22no—
98C7×#121C2314yes—
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C4×C7×D4—22no—
102C4×C7×D4C2314yes—
103C7×#117D414yes—
104C7×#117C2314yes—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4D411yescharacteristic
109C2×C7×C4⋊C4D411yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4D411yescharacteristic
118C2×C7×C22⋊C4D411yescharacteristic
119C2×C42×C7—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C2×C22⋊Dic7—21no—
123#6489—22no—
124#6489C2314yes—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7—21no—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—22no—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2314yes—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×C4×Dic7—21no—
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143#6453—28no—
144#6451—28no—
145#6441—28no—
146#6441—28no—
147#6433—22no—
148#6433—22no—
149#6433C2314yes—
150#6433C2314yes—
151#6432—22no—
152#6432—22no—
153#6432C2314yes—
154#6432C2314yes—
155#6409C2314yes—
156#6409C2314yes—
157#6409C2314yes—
158#6409C2314yes—
159#6406C2314yes—
160#6406C2314yes—
161#6406C2314yes—
162#6406C2314yes—
163C22⋊(C7⋊C8)C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165#6382C2314yes—
166#6382C2314yes—
167#6382C2314yes—
168#6382C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6381C2314yes—
172#6381C2314yes—
173C4⋊(C7⋊C8)C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175#6377C2314yes—
176C4×C7⋊C8C2314yes—
177C2×#544—71no—
178C2×#542D711yescharacteristic
179#3244—716no—
180C2×#501—71no—
181C2×#498—71no—
182C2×#489—71no—
183C2×#488—71no—
184C2×#481—71no—
185C2×#485—71no—
186C2×#482—71no—
187C2×#483—71no—
188C2×#479—71no—
189C2×#475—71no—
190C2×#478—71no—
191C2×#476—71no—
192C2×#433—71no—
193C24×C7—21no—
194C24×C7C2×D411yescharacteristic
195C2×C7×Q8—21no—
196C2×C7×Q8—24no—
197C2×C7×Q8—22no—
198C2×C7×Q8—22no—
199C2×C7×Q8—82no—
200C2×C7×Q8C2412yes—
201C2×C7×D4—24no—
202C2×C7×D4—21no—
203C2×C7×D4—22no—
204C2×C7×D4—22no—
205C2×C7×D4—82no—
206C2×C7×D4C2412yes—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—24no—
213C22×C4×C7—82no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2411yescharacteristic
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—24no—
227C22×Dic7—82no—
228C2×Dic14—24no—
229C2×Dic14—24no—
230C2×Dic14—82no—
231C2×Dic14—82no—
232C7×C4⋊C4—24no—
233C7×C4⋊C4—24no—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—21no—
237C7×C4⋊C4C2×D414yes—
238C7×C4⋊C4C2×D414yes—
239C7×C4⋊C4C2412yes—
240C7×C4⋊C4C2412yes—
241C7×C22⋊C4—24no—
242C7×C22⋊C4—24no—
243C7×C22⋊C4—24no—
244C7×C22⋊C4—24no—
245C7×C22⋊C4—24no—
246C7×C22⋊C4C2×D414yes—
247C7×C22⋊C4C2×D414yes—
248C42×C7—24no—
249C42×C7C2×D412yes—
250C42×C7C2×D412yes—
251C42×C7C2412yes—
252C42×C7C2412yes—
253C22⋊Dic7—24no—
254C4⋊Dic7—21no—
255C4⋊Dic7—21no—
256C4⋊Dic7—21no—
257C4⋊Dic7—24no—
258C4⋊Dic7—24no—
259C4⋊Dic7—21no—
260C4⋊Dic7—24no—
261C4⋊Dic7C2412yes—
262C4⋊Dic7C2412yes—
263C4⋊Dic7C2412yes—
264C4⋊Dic7C2412yes—
265Dic7⋊C4—24no—
266Dic7⋊C4—24no—
267Dic7⋊C4—24no—
268Dic7⋊C4—24no—
269C4×Dic7—24no—
270C2×C7⋊C8—22no—
271C2×C7⋊C8—22no—
272C2×C7⋊C8—22no—
273C2×C7⋊C8—22no—
274C2×C7⋊C8C2412yes—
275C2×C7⋊C8C2412yes—
276C2×C7⋊C8C2412yes—
277C2×C7⋊C8C2412yes—
278#544—78no—
279#544—144no—
280#542—24no—
281#542C2×D718yes—
282C2×C4⋊Q8—71no—
283C2×C4⋊Q8—71no—
284C2×C4⋊Q8—141no—
285C2×C4⋊Q8C2×D711yescharacteristic
286C2×#126—21no—
287C2×#125—71no—
288C2×#125—71no—
289C2×#125—141no—
290C2×#124—21no—
291C2×#124C2×D711yescharacteristic
292C2×#123—21no—
293C2×C22⋊Q8—21no—
294C2×C22⋊Q8—141no—
295C2×C22⋊Q8—141no—
296C2×C22⋊Q8C2×D711yescharacteristic
297C2×#121C2×D711yescharacteristic
298C2×C4×Q8C2×D711yescharacteristic
299C2×C4×D4C2×D711yescharacteristic
300C2×#117—71no—
301C2×#117C2×D711yescharacteristic
302C22×C4⋊C4—71no—
303#501—78no—
304#498—78no—
305#489—78no—
306#488—78no—
307#485—78no—
308#483—78no—
309#482—78no—
310#481—78no—
311#479—78no—
312#478—78no—
313#476—78no—
314#475—78no—
315#433—78no—
316C2×#107—71no—
317C2×#107—71no—
318C2×#106—71no—
319C2×#106—71no—
320C2×#106—71no—
321C2×#106—71no—
322C2×#106—71no—
323C2×#106—71no—
324C2×C4⋊C8—71no—
325C2×C4⋊C8—71no—
326C2×#103—71no—
327C2×#103—71no—
328C2×#103—71no—
329C2×#103—71no—
330C2×#102—71no—
331C2×#102—71no—
332C2×#102—71no—
333C2×#102—71no—
334C2×C22⋊C8—71no—
335C2×C22⋊C8—71no—
336C2×#97—71no—
337C2×C4×C8—71no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7C22×D412yes—
346C23×C7C22×D411yescharacteristic
347C7×Q8—22no—
348C7×Q8—22no—
349C7×Q8—42no—
350C7×Q8—84no—
351C7×D4—22no—
352C7×D4—22no—
353C7×D4—42no—
354C7×D4—84no—
355C2×C4×C7—22no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—24no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—84no—
370C2×C4×C7C22×D412yes—
371C2×C4×C7C22×D412yes—
372C2×C4×C7C22×D412yes—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D411yescharacteristic
376C2×C4×C72−1+412yes—
377C2×C4×C72−1+412yes—
378C2×C4×C7C2511yescharacteristic
379C2×Dic7—22no—
380C2×Dic7—22no—
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—42no—
384C2×Dic7—42no—
385C2×Dic7—42no—
386C2×Dic7—42no—
387C2×Dic7—84no—
388Dic14—84no—
389Dic14—84no—
390C7⋊C8—22no—
391C7⋊C8—22no—
392C7⋊C8—22no—
393C7⋊C8—22no—
394C22×Q8—21no—
395C22×Q8—141no—
396C22×Q8—141no—
397C22×Q8C22×D711yescharacteristic
398C22×D4—21no—
399C22×D4C22×D711yescharacteristic
400C23×C4—21no—
401C23×C4—141no—
402C23×C4C22×D711yescharacteristic
403C22×C8—71no—
404C22×C8—71no—
405C22×C8—71no—
406C22×C8—71no—
407C4⋊Q8—22no—
408C4⋊Q8—74no—
409C4⋊Q8—74no—
410C4⋊Q8—148no—
411C4⋊Q8—142no—
412C4⋊Q8—142no—
413C4⋊Q8C22×D714yes—
414#126—28no—
415#125—74no—
416#125—74no—
417#125—148no—
418#125—142no—
419#125—142no—
420#124—28no—
421#124—22no—
422#124C22×D714yes—
423#123—28no—
424C22⋊Q8—22no—
425C22⋊Q8—28no—
426C22⋊Q8—148no—
427C22⋊Q8—148no—
428C22⋊Q8C22×D714yes—
429#121—22no—
430#121C22×D714yes—
431C4×Q8—22no—
432C4×Q8C22×D714yes—
433C4×D4—22no—
434C4×D4C22×D714yes—
435#117—74no—
436#117—142no—
437#117C22⋊D714yes—
438#117C22×D714yes—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—71no—
443C2×C4⋊C4—71no—
444C2×C4⋊C4—74no—
445C2×C4⋊C4—71no—
446C2×C4⋊C4—71no—
447C2×C4⋊C4—141no—
448C2×C4⋊C4—142no—
449C2×C4⋊C4—141no—
450C2×C4⋊C4—141no—
451C2×C4⋊C4—141no—
452C2×C4⋊C4—141no—
453C2×C4⋊C4—141no—
454C2×C4⋊C4—141no—
455C2×C4⋊C4C22⋊D711yescharacteristic
456C2×C4⋊C4C22⋊D711yescharacteristic
457C2×C4⋊C4C22×D711yescharacteristic
458C2×C4⋊C4C22×D711yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—141no—
465C2×C22⋊C4C22⋊D711yescharacteristic
466C2×C22⋊C4C22⋊D711yescharacteristic
467C2×C42—21no—
468C2×C42—141no—
469C2×C42C22×D711yescharacteristic
470C2×C42C22×D711yescharacteristic
471#107—74no—
472#107—74no—
473#106—74no—
474#106—74no—
475#106—74no—
476#106—74no—
477#106—74no—
478#106—74no—
479C4⋊C8—74no—
480C4⋊C8—74no—
481#103—74no—
482#103—74no—
483#103—74no—
484#103—74no—
485#102—74no—
486#102—74no—
487#102—74no—
488#102—74no—
489C22⋊C8—74no—
490C22⋊C8—74no—
491#97—74no—
492C4×C8—74no—
493C22×C7—22no—
494C22×C7—22no—
495C22×C7—22no—
496C22×C7—44no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—84no—
501C22×C7#53612yes—
502C22×C7#57712yes—
503C22×C7#57712yes—
504C22×C7C23×D411yescharacteristic
505C4×C7—22no—
506C4×C7—22no—
507C4×C7—22no—
508C4×C7—22no—
509C4×C7—22no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—42no—
513C4×C7#53612yes—
514C4×C7C2×2−1+411yescharacteristic
515C4×C7C2×2−1+411yescharacteristic
516Dic7—42no—
517Dic7—42no—
518Dic7—42no—
519Dic7—42no—
520C24—21no—
521C24C2×C22⋊D711yescharacteristic
522C2×Q8—21no—
523C2×Q8—24no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—82no—
527C2×Q8—144no—
528C2×Q8—144no—
529C2×Q8—562no—
530C2×Q8—562no—
531C2×Q8C23×D712yes—
532C2×D4—24no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—21no—
536C2×D4—82no—
537C2×D4C23×D712yes—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—82no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—144no—
550C22×C4—562no—
551C22×C4C2×C22⋊D712yes—
552C22×C4C2×C22⋊D711yescharacteristic
553C22×C4C2×C22⋊D711yescharacteristic
554C22×C4C2×C22⋊D711yescharacteristic
555C22×C4C2×C22⋊D711yescharacteristic
556C22×C4C2×C22⋊D711yescharacteristic
557C22×C4C23×D712yes—
558C22×C4C23×D711yescharacteristic
559C2×C8—72no—
560C2×C8—72no—
561C2×C8—72no—
562C2×C8—72no—
563C2×C8—142no—
564C2×C8—142no—
565C2×C8—142no—
566C2×C8—142no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—72no—
573C4⋊C4—72no—
574C4⋊C4—72no—
575C4⋊C4—72no—
576C4⋊C4—144no—
577C4⋊C4—144no—
578C4⋊C4—144no—
579C4⋊C4—144no—
580C4⋊C4—144no—
581C4⋊C4—141no—
582C4⋊C4—141no—
583C4⋊C4—141no—
584C4⋊C4—141no—
585C4⋊C4—144no—
586C4⋊C4—144no—
587C4⋊C4C2×C22⋊D714yes—
588C4⋊C4C2×C22⋊D714yes—
589C4⋊C4C23×D712yes—
590C4⋊C4C23×D712yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—144no—
597C22⋊C4C2×C22⋊D714yes—
598C22⋊C4C2×C22⋊D714yes—
599C42—24no—
600C42—144no—
601C42C2×C22⋊D712yes—
602C42C2×C22⋊D712yes—
603C42C23×D712yes—
604C42C23×D712yes—
605C2×C7—42no—
606C2×C7—82no—
607C2×C7#324414yescomplemented
608C2×C7C2×#53611yescharacteristic
609C2×C7C2×#57711yescharacteristic
610C2×C7C2×#57711yescharacteristic
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23C22×C22⋊D712yes—
619C23C22×C22⋊D711yescharacteristic
620Q8—22no—
621Q8—22no—
622Q8—42no—
623Q8—84no—
624Q8—564no—
625Q8—564no—
626D4—22no—
627D4—22no—
628D4—42no—
629D4—84no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—84no—
645C2×C4—142no—
646C2×C4—142no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—282no—
650C2×C4—282no—
651C2×C4—282no—
652C2×C4—282no—
653C2×C4—564no—
654C2×C4#655412yes—
655C2×C4#655412yes—
656C2×C4C22×C22⋊D712yes—
657C2×C4C22×C22⋊D712yes—
658C2×C4C22×C22⋊D712yes—
659C2×C4C22×C22⋊D712yes—
660C2×C4C22×C22⋊D712yes—
661C2×C4C22×C22⋊D711yescharacteristic
662C2×C4C24×D711yescharacteristic
663C8—142no—
664C8—142no—
665C8—142no—
666C8—142no—
667C7C2×#324411yescharacteristic, complemented, Sylow
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#9051612yes—
677C22#9052712yes—
678C22#9052812yes—
679C22C23×C22⋊D711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—282no—
689C4—282no—
690C4—282no—
691C4—282no—
692C4#9051612yes—
693C4C2×#655411yescharacteristic
694C4C2×#655411yescharacteristic
695C2—42no—
696C2—82no—
697C2#1174090014yesdirect product factor
698C2C2×#9051611yescharacteristic
699C2C2×#9052711yescharacteristic
700C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#542C2
socleC23×C7C22×D4
prime radicalC2×C7×#121C22
hypercenterC2×#542D7
hypocenterC7C2×#3244
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
2. C2×#90210C2semidirect
3. #11740900C2direct (N × H)
4. C2×#89852C2semidirect
5. C2×#89851C2semidirect
6. C2×#89827C2semidirect
7. C2×#89828C2semidirect
8. C2×#89817C2semidirect
9. C2×#89815C2semidirect
12. C2×#89794C2semidirect
13. C2×#89792C2semidirect
14. C2×#89781C2semidirect
15. C2×#89780C2semidirect
16. C2×#89772C2semidirect
33. #90210C22semidirect
52. #89852C22semidirect
53. #89851C22semidirect
54. #89828C22semidirect
55. #89827C22semidirect
56. #89817C22semidirect
57. #89815C22semidirect
60. #89794C22semidirect
61. #89792C22semidirect
62. #89781C22semidirect
63. #89780C22semidirect
64. #89772C22semidirect
607. C2×C7#3244semidirect
667. C7C2×#3244semidirect
697. C2#11740900direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
C2×#902102
#117409002
C2×#898522
C2×#898512
C2×#898272
C2×#898282
C2×#898172
C2×#898152
C2×#898062
C2×#898072
C2×#897942
C2×#897922
C2×#897812
C2×#897802
C2×#897722
C2×#32447