Finite Group Databasebeta

← C2×#11726709 #13358434

Subgroups — C2×#11726709 #13358434

Order 1792.

1698 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6441C211yesmaximal, characteristic
2C2×#89714C211yesmaximal, characteristic
3C2×C22⋊C4×Dic7C211yesmaximal, characteristic
4C2×C7×#342C211yesmaximal, characteristic
5C2×#89322C211yesmaximal, characteristic
6C2×#89322C211yesmaximal, characteristic
7C2×#89321C211yesmaximal, characteristic
8#11726709C218yesmaximal, direct product factor
9C24×Dic7C2211yescharacteristic
10C23×Dic14C411yescharacteristic, complemented
11C22×C7×C22⋊C4C2211yescharacteristic
12C22×C7×C22⋊C4C2211yescharacteristic
13C22×C7×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic7C2211yescharacteristic
15C22×C22⋊Dic7C2211yescharacteristic
16C22×C22⋊Dic7C2211yescharacteristic
17C22×C4⋊Dic7C411yescharacteristic, complemented
18C22×Dic7⋊C4—21no—
19C22×Dic7⋊C4C411yescharacteristic, complemented
20C22×Dic7⋊C4C411yescharacteristic, complemented
21C22×C4×Dic7—21no—
22C2×#6441—21no—
23C2×#6441—21no—
24C2×#6441—22no—
25C2×#6441—22no—
26C2×#6441—21no—
27C2×#6441—21no—
28C2×#6441C414yescomplemented
29C2×#6441C2214yes—
30C2×C7⋊#95—21no—
31C2×C7⋊#95—21no—
32#89714—22no—
33#89714C2214yes—
34C22⋊C4×Dic7—22no—
35C22⋊C4×Dic7C2214yes—
36C7×#342C2214yes—
37#89322C2214yes—
38#89322C2214yes—
39#89321C2214yes—
40C2×#1996—71nomaximal, Sylow
41C25×C7C2311yescharacteristic
42C23×C4×C7—21no—
43C23×C4×C7—21no—
44C23×C4×C7C2×C411yescharacteristic
45C23×C4×C7C2×C411yescharacteristic
46C23×Dic7—21no—
47C23×Dic7—21no—
48C23×Dic7—44no—
49C23×Dic7C2×C411yescharacteristic
50C23×Dic7C2×C411yescharacteristic
51C23×Dic7C2×C411yescharacteristic
52C23×Dic7C2×C412yes—
53C23×Dic7C2×C411yescharacteristic
54C23×Dic7D411yescharacteristic
55C23×Dic7D411yescharacteristic
56C23×Dic7D412yes—
57C23×Dic7D412yes—
58C23×Dic7D411yescharacteristic
59C23×Dic7D411yescharacteristic
60C23×Dic7C2312yes—
61C22×Dic14—21no—
62C22×Dic14—22no—
63C22×Dic14—21no—
64C22×Dic14—44no—
65C22×Dic14C2×C414yescomplemented
66C2×C7×C22⋊C4—21no—
67C2×C7×C22⋊C4—21no—
68C2×C7×C22⋊C4—21no—
69C2×C7×C22⋊C4—21no—
70C2×C7×C22⋊C4—21no—
71C2×C7×C22⋊C4—22no—
72C2×C7×C22⋊C4—22no—
73C2×C7×C22⋊C4—22no—
74C2×C7×C22⋊C4—21no—
75C2×C7×C22⋊C4C2×C412yes—
76C2×C7×C22⋊C4Q814yescomplemented
77C2×C7×C22⋊C4C2312yes—
78C2×C7×C22⋊C4C2312yes—
79C2×C7×C22⋊C4C2312yes—
80C2×C22⋊Dic7—21no—
81C2×C22⋊Dic7—21no—
82C2×C22⋊Dic7—21no—
83C2×C22⋊Dic7—21no—
84C2×C22⋊Dic7—21no—
85C2×C22⋊Dic7—22no—
86C2×C22⋊Dic7—22no—
87C2×C22⋊Dic7—22no—
88C2×C22⋊Dic7—21no—
89C2×C22⋊Dic7C2×C412yes—
90C2×C22⋊Dic7Q814yescomplemented
91C2×C22⋊Dic7C2312yes—
92C2×C22⋊Dic7C2312yes—
93C2×C22⋊Dic7C2312yes—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7—21no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7C2×C414yescomplemented
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×Dic7⋊C4—22no—
102C2×Dic7⋊C4—22no—
103C2×Dic7⋊C4—21no—
104C2×Dic7⋊C4—24no—
105C2×Dic7⋊C4—44no—
106C2×Dic7⋊C4C2×C414yescomplemented
107C2×Dic7⋊C4C2×C414yescomplemented
108C2×C4×Dic7—24no—
109C2×C4×Dic7—44no—
110#6441—24no—
111#6441—24no—
112#6441—24no—
113#6441—24no—
114#6441—24no—
115#6441—24no—
116#6441—24no—
117#6441—24no—
118C7⋊#95—24no—
119C7⋊#95—24no—
120C22×C22⋊Q8—71no—
121C2×#380—71no—
122C2×C4×C22⋊C4—71no—
123#1996—78no—
124C2×#342—71no—
125C2×#342—71no—
126C2×#342—71no—
127C2×#342D711yescharacteristic
128C24×C7—42no—
129C24×C7—42no—
130C24×C7C22×C411yescharacteristic
131C24×C7C22×C411yescharacteristic
132C24×C7C2×D411yescharacteristic
133C24×C7C2×D411yescharacteristic
134C24×C7C2×D411yescharacteristic
135C24×C7C2×D411yescharacteristic
136C24×C7C2×Q812yes—
137C24×C7C2×Q812yes—
138C24×C7#4112yes—
139C24×C7#4112yes—
140C24×C7C2411yescharacteristic
141C22×C4×C7—21no—
142C22×C4×C7—21no—
143C22×C4×C7—21no—
144C22×C4×C7—21no—
145C22×C4×C7—24no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—42no—
149C22×C4×C7—42no—
150C22×C4×C7—42no—
151C22×C4×C7—42no—
152C22×C4×C7—42no—
153C22×C4×C7—42no—
154C22×C4×C7—42no—
155C22×C4×C7C22×C412yes—
156C22×C4×C7C22×C412yes—
157C22×Dic7—24no—
158C22×Dic7—24no—
159C22×Dic7—24no—
160C22×Dic7—21no—
161C22×Dic7—21no—
162C22×Dic7—21no—
163C22×Dic7—21no—
164C22×Dic7—24no—
165C22×Dic7—22no—
166C22×Dic7—22no—
167C22×Dic7—44no—
168C22×Dic7—44no—
169C22×Dic7—44no—
170C22×Dic7—44no—
171C22×Dic7—42no—
172C22×Dic7—42no—
173C22×Dic7—42no—
174C22×Dic7—42no—
175C22×Dic7—42no—
176C22×Dic7—42no—
177C22×Dic7—42no—
178C22×Dic7—42no—
179C22×Dic7—42no—
180C22×Dic7—42no—
181C22×Dic7C22⋊C412yes—
182C22×Dic7C22⋊C412yes—
183C22×Dic7C22⋊C411yescharacteristic
184C22×Dic7C22⋊C411yescharacteristic
185C22×Dic7C22⋊C411yescharacteristic
186C22×Dic7C22⋊C412yes—
187C22×Dic7C22⋊C412yes—
188C22×Dic7C22⋊C412yes—
189C22×Dic7C22⋊C412yes—
190C22×Dic7C22⋊C411yescharacteristic
191C22×Dic7C22×C412yes—
192C22×Dic7C22×C412yes—
193C22×Dic7C22×C412yes—
194C22×Dic7C22×C412yes—
195C22×Dic7C2×D412yes—
196C22×Dic7C2×D412yes—
197C22×Dic7C2×D412yes—
198C22×Dic7C2×D412yes—
199C2×Dic14—24no—
200C2×Dic14—24no—
201C2×Dic14—44no—
202C2×Dic14—48no—
203C2×Dic14—44no—
204C2×Dic14—48no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—22no—
207C7×C22⋊C4—24no—
208C7×C22⋊C4—22no—
209C7×C22⋊C4—22no—
210C7×C22⋊C4—22no—
211C7×C22⋊C4—22no—
212C7×C22⋊C4—22no—
213C7×C22⋊C4—42no—
214C7×C22⋊C4C2×Q814yescomplemented
215C22⋊Dic7—22no—
216C22⋊Dic7—22no—
217C22⋊Dic7—24no—
218C22⋊Dic7—22no—
219C22⋊Dic7—22no—
220C22⋊Dic7—22no—
221C22⋊Dic7—22no—
222C22⋊Dic7—22no—
223C22⋊Dic7—42no—
224C22⋊Dic7C2×Q814yescomplemented
225C4⋊Dic7—24no—
226C4⋊Dic7—24no—
227Dic7⋊C4—24no—
228Dic7⋊C4—24no—
229Dic7⋊C4—24no—
230Dic7⋊C4—24no—
231Dic7⋊C4—48no—
232C4×Dic7—48no—
233C23×Q8—71no—
234C24×C4—71no—
235C2×C22⋊Q8—74no—
236C2×C22⋊Q8—74no—
237C2×C22⋊Q8—141no—
238C2×C22⋊Q8—141no—
239C2×C22⋊Q8—141no—
240C2×C22⋊Q8—141no—
241C2×C22⋊Q8—142no—
242C2×C22⋊Q8—142no—
243C22×C4⋊C4—71no—
244C22×C4⋊C4—71no—
245C22×C4⋊C4—71no—
246C22×C4⋊C4—141no—
247C22×C22⋊C4—71no—
248C22×C22⋊C4—71no—
249C22×C22⋊C4—71no—
250C22×C22⋊C4C2×D711yescharacteristic
251C22×C22⋊C4C2×D711yescharacteristic
252C22×C22⋊C4C2×D711yescharacteristic
253C22×C42—141no—
254#380—74no—
255#380—142no—
256C4×C22⋊C4—74no—
257C4×C22⋊C4—142no—
258C2×#95—141no—
259C2×#95—141no—
260#342—74no—
261#342—74no—
262#342—74no—
263#342C2×D714yes—
264C23×C7—22no—
265C23×C7—22no—
266C23×C7—22no—
267C23×C7—22no—
268C23×C7—22no—
269C23×C7—22no—
270C23×C7—41no—
271C23×C7—41no—
272C23×C7—41no—
273C23×C7—41no—
274C23×C7—41no—
275C23×C7—41no—
276C23×C7—41no—
277C23×C7—44no—
278C23×C7—44no—
279C23×C7—44no—
280C23×C7—44no—
281C23×C7—41no—
282C23×C7C2×C22⋊C411yescharacteristic
283C23×C7C2×C22⋊C411yescharacteristic
284C23×C7C2×C22⋊C411yescharacteristic
285C23×C7C2×C22⋊C411yescharacteristic
286C23×C7C4×Q812yes—
287C23×C7C4×Q812yes—
288C23×C7C4×Q812yes—
289C23×C7C4×Q812yes—
290C23×C7C22⋊Q812yes—
291C23×C7C22⋊Q812yes—
292C23×C7C22⋊Q812yes—
293C23×C7C22⋊Q812yes—
294C23×C7#12412yes—
295C23×C7#12412yes—
296C23×C7C4⋊Q812yes—
297C23×C7C4⋊Q812yes—
298C23×C7C23×C411yescharacteristic
299C23×C7C22×D411yescharacteristic
300C23×C7C22×D411yescharacteristic
301C23×C7C22×Q811yescharacteristic
302C23×C7C22×Q811yescharacteristic
303C23×C7C2×#4111yescharacteristic
304C23×C7C2×#4111yescharacteristic
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—42no—
309C2×C4×C7—42no—
310C2×C4×C7—42no—
311C2×C4×C7—48no—
312C2×C4×C7—42no—
313C2×C4×C7—42no—
314C2×C4×C7—42no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—42no—
318C2×C4×C7—42no—
319C2×C4×C7—42no—
320C2×C4×C7—84no—
321C2×Dic7—22no—
322C2×Dic7—22no—
323C2×Dic7—22no—
324C2×Dic7—24no—
325C2×Dic7—24no—
326C2×Dic7—24no—
327C2×Dic7—24no—
328C2×Dic7—24no—
329C2×Dic7—24no—
330C2×Dic7—22no—
331C2×Dic7—22no—
332C2×Dic7—24no—
333C2×Dic7—42no—
334C2×Dic7—42no—
335C2×Dic7—42no—
336C2×Dic7—42no—
337C2×Dic7—42no—
338C2×Dic7—42no—
339C2×Dic7—42no—
340C2×Dic7—42no—
341C2×Dic7—42no—
342C2×Dic7—48no—
343C2×Dic7—42no—
344C2×Dic7—42no—
345C2×Dic7—42no—
346C2×Dic7—42no—
347C2×Dic7—42no—
348C2×Dic7—42no—
349C2×Dic7—42no—
350C2×Dic7—42no—
351C2×Dic7—84no—
352C2×Dic7#9914yes—
353C2×Dic7C2×C22⋊C412yes—
354C2×Dic7C2×C22⋊C412yes—
355C2×Dic7C2×C22⋊C412yes—
356C2×Dic7C2×C22⋊C412yes—
357Dic14—48no—
358Dic14—48no—
359C25C22×D711yescharacteristic
360C22×Q8—74no—
361C22×Q8—142no—
362C22×Q8—141no—
363C22×Q8—141no—
364C22×Q8—284no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—71no—
368C23×C4—71no—
369C23×C4—71no—
370C23×C4—71no—
371C23×C4—72no—
372C23×C4—71no—
373C23×C4—71no—
374C23×C4—72no—
375C23×C4—72no—
376C23×C4—72no—
377C23×C4—71no—
378C23×C4—71no—
379C23×C4—141no—
380C23×C4—141no—
381C23×C4—284no—
382C23×C4C4×D711yescharacteristic
383C23×C4C4×D711yescharacteristic
384C22⋊Q8—144no—
385C22⋊Q8—144no—
386C22⋊Q8—144no—
387C22⋊Q8—144no—
388C22⋊Q8—144no—
389C22⋊Q8—144no—
390C22⋊Q8—144no—
391C22⋊Q8—144no—
392C2×C4⋊C4—74no—
393C2×C4⋊C4—74no—
394C2×C4⋊C4—74no—
395C2×C4⋊C4—142no—
396C2×C4⋊C4—142no—
397C2×C4⋊C4—141no—
398C2×C4⋊C4—141no—
399C2×C4⋊C4—141no—
400C2×C4⋊C4—141no—
401C2×C4⋊C4—142no—
402C2×C4⋊C4—141no—
403C2×C4⋊C4—141no—
404C2×C4⋊C4—144no—
405C2×C4⋊C4—284no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—74no—
416C2×C22⋊C4—72no—
417C2×C22⋊C4—72no—
418C2×C22⋊C4—72no—
419C2×C22⋊C4—72no—
420C2×C22⋊C4—142no—
421C2×C22⋊C4—141no—
422C2×C22⋊C4—141no—
423C2×C22⋊C4—141no—
424C2×C22⋊C4—141no—
425C2×C22⋊C4—141no—
426C2×C22⋊C4—142no—
427C2×C22⋊C4—142no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4Dic1414yescomplemented
430C2×C22⋊C4C4×D712yes—
431C2×C22⋊C4C22×D712yes—
432C2×C22⋊C4C22×D712yes—
433C2×C22⋊C4C22×D712yes—
434C2×C42—144no—
435C2×C42—284no—
436#95—144no—
437#95—144no—
438C22×C7—21no—
439C22×C7—21no—
440C22×C7—21no—
441C22×C7—21no—
442C22×C7—21no—
443C22×C7—21no—
444C22×C7—21no—
445C22×C7—21no—
446C22×C7—21no—
447C22×C7—21no—
448C22×C7—21no—
449C22×C7—21no—
450C22×C7—24no—
451C22×C7—24no—
452C22×C7—24no—
453C22×C7—24no—
454C22×C7—24no—
455C22×C7—24no—
456C22×C7—42no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
461C22×C7—42no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7#39112yes—
467C22×C7#39112yes—
468C22×C7#39112yes—
469C22×C7#39112yes—
470C22×C7C2×#9912yes—
471C22×C7#41012yes—
472C22×C7C22×C22⋊C411yescharacteristic
473C22×C7C2×C4×Q811yescharacteristic
474C22×C7C2×C4×Q811yescharacteristic
475C22×C7C2×C22⋊Q811yescharacteristic
476C22×C7C2×C22⋊Q811yescharacteristic
477C22×C7C2×#12411yescharacteristic
478C22×C7C2×C4⋊Q811yescharacteristic
479C4×C7—44no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—82no—
483Dic7—22no—
484Dic7—22no—
485Dic7—22no—
486Dic7—44no—
487Dic7—42no—
488Dic7—42no—
489Dic7—82no—
490Dic7C2×#9914yes—
491C24—42no—
492C24—42no—
493C24C2×Dic1412yes—
494C24C2×C4×D711yescharacteristic
495C24C2×C4×D711yescharacteristic
496C24#115712yes—
497C24D4×D711yescharacteristic
498C24D4×D711yescharacteristic
499C24D4×D711yescharacteristic
500C24D4×D711yescharacteristic
501C24#115912yes—
502C24Q8×D712yes—
503C24C23×D711yescharacteristic
504C2×Q8—144no—
505C2×Q8—144no—
506C2×Q8—284no—
507C2×Q8—288no—
508C2×Q8—288no—
509C2×Q8—284no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—71no—
525C22×C4—72no—
526C22×C4—72no—
527C22×C4—72no—
528C22×C4—71no—
529C22×C4—71no—
530C22×C4—71no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—72no—
539C22×C4—72no—
540C22×C4—72no—
541C22×C4—72no—
542C22×C4—144no—
543C22×C4—144no—
544C22×C4—144no—
545C22×C4—141no—
546C22×C4—141no—
547C22×C4—141no—
548C22×C4—141no—
549C22×C4—144no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—284no—
553C22×C4—284no—
554C22×C4—284no—
555C22×C4—284no—
556C22×C4—282no—
557C22×C4—282no—
558C22×C4—282no—
559C22×C4—282no—
560C22×C4—282no—
561C22×C4—282no—
562C22×C4—282no—
563C22×C4—282no—
564C22×C4—282no—
565C22×C4—282no—
566C22×C4C2×C4×D712yes—
567C22×C4C2×C4×D712yes—
568C4⋊C4—144no—
569C4⋊C4—144no—
570C4⋊C4—144no—
571C4⋊C4—144no—
572C4⋊C4—144no—
573C4⋊C4—144no—
574C4⋊C4—288no—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—42no—
584C22⋊C4—74no—
585C22⋊C4—142no—
586C22⋊C4—142no—
587C22⋊C4—144no—
588C22⋊C4—142no—
589C22⋊C4—142no—
590C22⋊C4—142no—
591C22⋊C4—142no—
592C22⋊C4—142no—
593C22⋊C4—282no—
594C22⋊C4C2×Dic1414yescomplemented
595C42—288no—
596C2×C7—21no—
597C2×C7—21no—
598C2×C7—21no—
599C2×C7—21no—
600C2×C7—21no—
601C2×C7—21no—
602C2×C7—22no—
603C2×C7—22no—
604C2×C7—22no—
605C2×C7#199614yescomplemented
606C2×C7C2×#39111yescharacteristic
607C2×C7C22×#9911yescharacteristic
608C2×C7C2×#41011yescharacteristic
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—44no—
620C23—41no—
621C23—44no—
622C23—41no—
623C23—41no—
624C23—44no—
625C23—44no—
626C23—41no—
627C23C4×Dic1412yes—
628C23C4×Dic1412yes—
629C23#644112yes—
630C23#644112yes—
631C23D7×C22⋊C411yescharacteristic
632C23D7×C22⋊C411yescharacteristic
633C23D7×C22⋊C411yescharacteristic
634C23D7×C22⋊C411yescharacteristic
635C23#644812yes—
636C23#644812yes—
637C23#645012yes—
638C23#645012yes—
639C23#645112yes—
640C23#645112yes—
641C23#645912yes—
642C23#645912yes—
643C23C22×Dic1411yescharacteristic
644C23C22×C4×D711yescharacteristic
645C23C2×#115711yescharacteristic
646C23C2×D4×D711yescharacteristic
647C23C2×D4×D711yescharacteristic
648C23C2×#115911yescharacteristic
649C23C2×Q8×D711yescharacteristic
650Q8—288no—
651Q8—288no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—48no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—72no—
668C2×C4—74no—
669C2×C4—72no—
670C2×C4—72no—
671C2×C4—72no—
672C2×C4—84no—
673C2×C4—144no—
674C2×C4—144no—
675C2×C4—144no—
676C2×C4—144no—
677C2×C4—144no—
678C2×C4—144no—
679C2×C4—142no—
680C2×C4—142no—
681C2×C4—142no—
682C2×C4—142no—
683C2×C4—142no—
684C2×C4—144no—
685C2×C4—282no—
686C2×C4—282no—
687C2×C4—282no—
688C2×C4—282no—
689C2×C4—282no—
690C2×C4—282no—
691C2×C4—282no—
692C2×C4—282no—
693C2×C4—288no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4—282no—
699C2×C4—282no—
700C2×C4—282no—
701C2×C4—282no—
702C2×C4—282no—
703C2×C4—564no—
704C7C2×#199611yescharacteristic, complemented, Sylow
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—24no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22#8941812yes—
734C22#8941812yes—
735C22#8941812yes—
736C22#8941812yes—
737C22#8951212yes—
738C22D7×#9912yes—
739C22C2×C4×Dic1411yescharacteristic
740C22C2×#644111yescharacteristic
741C22C2×D7×C22⋊C411yescharacteristic
742C22C2×#644811yescharacteristic
743C22C2×#645011yescharacteristic
744C22C2×#645111yescharacteristic
745C22C2×#645911yescharacteristic
746C4—44no—
747C4—42no—
748C4—42no—
749C4—74no—
750C4—82no—
751C4—142no—
752C4—142no—
753C4—142no—
754C4—284no—
755C4—282no—
756C4—282no—
757C4—562no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—22no—
763C2—22no—
764C2—22no—
765C2—21no—
766C2—21no—
767C2#1172670914yesdirect product factor
768C2C2×#8941811yescharacteristic
769C2C2×#8951211yescharacteristic
770C2C2×D7×#9911yescharacteristic
subgroupG/H
centerC23D7×C22⋊C4
commutatorC23×C7C23×C4
FrattiniC24C23×D7
FittingC2×C7×#342C2
socleC23×C7C2×C22⋊C4
prime radicalC25×C7C23
cosocleC24×C7C24
hypercenterC2×#342D7
hypocenterC7C2×#1996
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
8. #11726709C2direct (N × H)
10. C23×Dic14C4semidirect
17. C22×C4⋊Dic7C4semidirect
19. C22×Dic7⋊C4C4semidirect
20. C22×Dic7⋊C4C4semidirect
28. C2×#6441C4semidirect
65. C22×Dic14C2×C4semidirect
76. C2×C7×C22⋊C4Q8semidirect
90. C2×C22⋊Dic7Q8semidirect
97. C2×C4⋊Dic7C2×C4semidirect
106. C2×Dic7⋊C4C2×C4semidirect
107. C2×Dic7⋊C4C2×C4semidirect
214. C7×C22⋊C4C2×Q8semidirect
224. C22⋊Dic7C2×Q8semidirect
429. C2×C22⋊C4Dic14semidirect
594. C22⋊C4C2×Dic14semidirect
605. C2×C7#1996semidirect
704. C7C2×#1996semidirect
767. C2#11726709direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64412
C2×#897142
C2×C22⋊C4×Dic72
C2×C7×#3422
C2×#893222
C2×#893212
#117267092
C2×#19967