Finite Group Databasebeta

← #13387614

Subgroups — #13387614

Order 1792.

1084 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#554C211yesmaximal, characteristic
2C2×#89817C211yesmaximal, characteristic, complemented
3#11739817C211yesmaximal, characteristic
4C2×#89736C211yesmaximal, characteristic, complemented
5#11729537C211yesmaximal, characteristic, complemented
6#11729536C211yesmaximal, characteristic, complemented
7#11729451C211yesmaximal, characteristic, complemented
8#11729449C211yesmaximal, characteristic, complemented
9#11729448C211yesmaximal, characteristic, complemented
10#11729383C211yesmaximal, characteristic, complemented
11#11729382C211yesmaximal, characteristic, complemented
12#11729365C211yesmaximal, characteristic
13#11729310C211yesmaximal, characteristic, complemented
14#11729309C211yesmaximal, characteristic, complemented
15#11729307C211yesmaximal, characteristic, complemented
16C7×#554—24no—
17C7×#554—24no—
18C2×C7×C4⋊Q8C2211yescharacteristic
19C2×C7×#125—21no—
20C2×C7×C22⋊Q8—21no—
21C2×C7×C22⋊Q8—21no—
22C2×C7×C22⋊Q8C2211yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C4×C7×Q8C2211yescharacteristic
25C2×C4×C7×D4—21no—
26C2×C4×C7×D4C2211yescharacteristic
27C22×C7×C4⋊C4C2211yescharacteristic
28C22×C7×C4⋊C4C2211yescharacteristic
29C2×#6489C2211yescharacteristic
30C22×#1136C2211yescharacteristic
31C2×#6409C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35#89994—21no—
36#89984C2211yescharacteristic
37#89984C2211yescharacteristic
38#89984C2211yescharacteristic
39C2×C22⋊(C7⋊C8)C2211yescharacteristic
40C2×C22⋊(C7⋊C8)C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89817—24no—
43#89750—21no—
44#89736—24no—
45C2×#6382C2211yescharacteristic
46C2×#6382C2211yescharacteristic
47C2×#6382C2211yescharacteristic
48C2×#6381C2211yescharacteristic
49C2×#6381C2211yescharacteristic
50C2×#6381C2211yescharacteristic
51#89724—21no—
52#89716—21no—
53#89700C2211yescharacteristic
54#89700C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89319C2211yescharacteristic
62#89319C2211yescharacteristic
63#24109—71nomaximal, Sylow
64C22×C7×Q8—21no—
65C22×C7×Q8C2311yescharacteristic
66C22×C7×D4D411yescharacteristic
67C23×C4×C7—21no—
68C23×C4×C7—21no—
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C7×C4⋊Q8—22no—
72C7×C4⋊Q8—22no—
73C7×#125—28no—
74C7×C22⋊Q8—28no—
75C7×C22⋊Q8—28no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—22no—
78C7×C22⋊Q8—22no—
79C7×C22⋊Q8D414yes—
80C4×C7×Q8—22no—
81C4×C7×Q8—22no—
82C4×C7×D4—28no—
83C4×C7×D4—22no—
84C4×C7×D4—22no—
85C2×C7×C4⋊C4—21no—
86C2×C7×C4⋊C4—21no—
87C2×C7×C4⋊C4—22no—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C4⋊C4—21no—
91C2×C7×C4⋊C4—21no—
92C2×C7×C4⋊C4—22no—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4D411yescharacteristic
95C2×C7×C4⋊C4D414yes—
96C2×C7×C4⋊C4C2311yescharacteristic
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C22⋊C4—21no—
100C2×C7×C22⋊C4—21no—
101C2×C7×C22⋊C4D411yescharacteristic
102C2×C7×C22⋊C4D411yescharacteristic
103C2×C42×C7—21no—
104C2×C42×C7C2311yescharacteristic
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109#6489—22no—
110#6489—22no—
111C2×C4⋊Dic7C2311yescharacteristic
112C2×C4⋊Dic7C2311yescharacteristic
113C2×C4⋊Dic7C2311yescharacteristic
114C2×C4⋊Dic7C2311yescharacteristic
115C2×Dic7⋊C4—21no—
116C2×Dic7⋊C4—21no—
117C2×C4×Dic7—21no—
118C2×#1136—22no—
119C2×#1136—22no—
120C2×#1136—22no—
121C22×C7⋊C8C2311yescharacteristic
122C22×C7⋊C8C2311yescharacteristic
123C22×C7⋊C8C2311yescharacteristic
124C22×C7⋊C8C2311yescharacteristic
125#6409—22no—
126#6409—22no—
127#6409—22no—
128#6409—22no—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C7⋊#95—21no—
133C7⋊#95—21no—
134C22⋊(C7⋊C8)—22no—
135C22⋊(C7⋊C8)—22no—
136C22⋊(C7⋊C8)—22no—
137#6382—22no—
138#6382—22no—
139#6382—22no—
140#6381—22no—
141#6381—22no—
142#6381—22no—
143C2×#554D711yescharacteristic
144C2×#485—71no—
145C2×#428—71no—
146#2485—71no—
147#2058—71no—
148#2057—71no—
149#2036—71no—
150#2035—71no—
151#1894—71no—
152#1870—71no—
153#1865—71no—
154#1863—71no—
155#1853—71no—
156#1852—71no—
157#1823—71no—
158C24×C7C2×D411yescharacteristic
159C24×C7C2×D411yescharacteristic
160C2×C7×Q8—24no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—81no—
167C2×C7×Q8—81no—
168C2×C7×Q8C2×D412yes—
169C2×C7×D4—22no—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—24no—
181C22×C4×C7—24no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—81no—
189C22×C4×C7—81no—
190C22×C4×C7—81no—
191C22×C4×C7—81no—
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2×D412yes—
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2411yescharacteristic
199C22×Dic7—21no—
200C22×Dic7—21no—
201C22×Dic7—21no—
202C22×Dic7—21no—
203C7×C4⋊C4—24no—
204C7×C4⋊C4—24no—
205C7×C4⋊C4—24no—
206C7×C4⋊C4—24no—
207C7×C4⋊C4—24no—
208C7×C4⋊C4—24no—
209C7×C4⋊C4—22no—
210C7×C4⋊C4—21no—
211C7×C4⋊C4—21no—
212C7×C4⋊C4—21no—
213C7×C4⋊C4C2×D412yes—
214C7×C4⋊C4C2×D412yes—
215C7×C4⋊C4C2×D412yes—
216C7×C22⋊C4—24no—
217C7×C22⋊C4—24no—
218C7×C22⋊C4—22no—
219C7×C22⋊C4—22no—
220C42×C7—24no—
221C42×C7—21no—
222C42×C7—21no—
223C22⋊Dic7—42no—
224C22⋊Dic7—42no—
225C22⋊Dic7—81no—
226C22⋊Dic7—81no—
227C4⋊Dic7—21no—
228C4⋊Dic7—21no—
229C4⋊Dic7—21no—
230C4⋊Dic7—21no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235Dic7⋊C4—42no—
236Dic7⋊C4—81no—
237C4×Dic7—42no—
238#1136—28no—
239C2×C7⋊C8—21no—
240C2×C7⋊C8—21no—
241C2×C7⋊C8—21no—
242C2×C7⋊C8—21no—
243C2×C7⋊C8—21no—
244C2×C7⋊C8—21no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8#4112yes—
250C2×C7⋊C8#4112yes—
251C22×M16—71no—
252#554—24no—
253#554—24no—
254C2×C4⋊Q8C2×D711yescharacteristic
255C2×#125—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C2×D711yescharacteristic
259C2×C22⋊Q8C2×D711yescharacteristic
260C2×C4×Q8C2×D711yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4C2×D711yescharacteristic
263C2×#117—71no—
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C4⋊C4C2×D711yescharacteristic
266#485—144no—
267#428—144no—
268C2×#107—71no—
269C2×#107—71no—
270C2×#107—71no—
271C2×#106—71no—
272C2×#106—71no—
273C2×#106—71no—
274C2×#103—71no—
275C2×#103—71no—
276C2×#103—71no—
277C2×#103—71no—
278C2×C22⋊C8—71no—
279C2×C22⋊C8—71no—
280C2×C22⋊C8—71no—
281#397—141no—
282#394—141no—
283#389—71no—
284#389—71no—
285#388—141no—
286#387—141no—
287#380—71no—
288#380—71no—
289#380—71no—
290#340—71no—
291#340—71no—
292#340—71no—
293#340—71no—
294#340—71no—
295#340—71no—
296#336—71no—
297#336—71no—
298C23×C7—21no—
299C23×C7—21no—
300C23×C7—21no—
301C23×C7—21no—
302C23×C7—21no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—21no—
308C23×C7—21no—
309C23×C7—21no—
310C23×C7#12012yes—
311C23×C7#13712yes—
312C23×C7C22×D411yescharacteristic
313C7×Q8—22no—
314C7×Q8—22no—
315C7×Q8—41no—
316C7×Q8—41no—
317C7×Q8—84no—
318C7×D4—28no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—22no—
324C2×C4×C7—22no—
325C2×C4×C7—22no—
326C2×C4×C7—22no—
327C2×C4×C7—22no—
328C2×C4×C7—21no—
329C2×C4×C7—22no—
330C2×C4×C7—21no—
331C2×C4×C7—22no—
332C2×C4×C7—22no—
333C2×C4×C7—21no—
334C2×C4×C7—21no—
335C2×C4×C7—21no—
336C2×C4×C7—21no—
337C2×C4×C7—41no—
338C2×C4×C7—41no—
339C2×C4×C7—41no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—84no—
350C2×C4×C7—84no—
351C2×C4×C7#12012yes—
352C2×C4×C7#13712yes—
353C2×C4×C7C22×D411yescharacteristic
354C2×C4×C7C22×D411yescharacteristic
355C2×C4×C7C2×#4111yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C2×C4×C72−1+411yescharacteristic
358C2×C4×C72−1+411yescharacteristic
359C2×Dic7—41no—
360C2×Dic7—41no—
361C2×Dic7—41no—
362C2×Dic7—41no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C7⋊C8—22no—
372C7⋊C8—22no—
373C7⋊C8—41no—
374C7⋊C8—41no—
375C22×Q8—21no—
376C22×Q8C22×D711yescharacteristic
377C22×D4C22⋊D711yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4C22×D711yescharacteristic
381C23×C4C22×D711yescharacteristic
382C2×M16—142no—
383C2×M16—142no—
384C2×M16—142no—
385C22×C8—71no—
386C22×C8—71no—
387C22×C8—71no—
388C22×C8—71no—
389C4⋊Q8—22no—
390C4⋊Q8—22no—
391#125—28no—
392C22⋊Q8—28no—
393C22⋊Q8—28no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8C22⋊D714yes—
398C4×Q8—22no—
399C4×Q8—22no—
400C4×D4—28no—
401C4×D4—22no—
402C4×D4—22no—
403#117—142no—
404#117—142no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—71no—
415C2×C4⋊C4—71no—
416C2×C4⋊C4—71no—
417C2×C4⋊C4—71no—
418C2×C4⋊C4—141no—
419C2×C4⋊C4—141no—
420C2×C4⋊C4C22⋊D711yescharacteristic
421C2×C4⋊C4C22⋊D714yes—
422C2×C4⋊C4C22×D711yescharacteristic
423C2×C4⋊C4C22×D711yescharacteristic
424C2×C4⋊C4C22×D711yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—141no—
428C2×C22⋊C4—141no—
429C2×C22⋊C4—141no—
430C2×C22⋊C4—141no—
431C2×C22⋊C4C22⋊D711yescharacteristic
432C2×C22⋊C4C22⋊D711yescharacteristic
433C2×C42—21no—
434C2×C42—141no—
435C2×C42C22×D711yescharacteristic
436#107—142no—
437#107—142no—
438#107—142no—
439#106—142no—
440#106—142no—
441#106—142no—
442#103—142no—
443#103—142no—
444#103—142no—
445#103—142no—
446C22⋊C8—142no—
447C22⋊C8—142no—
448C22⋊C8—142no—
449#95—141no—
450#95—141no—
451#95—141no—
452#95—141no—
453#95—141no—
454C22×C7—22no—
455C22×C7—22no—
456C22×C7—22no—
457C22×C7—22no—
458C22×C7—22no—
459C22×C7—22no—
460C22×C7—41no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—41no—
467C22×C7—41no—
468C22×C7C2×#12011yescharacteristic
469C22×C7#54711yescharacteristic
470C22×C7#54711yescharacteristic
471C22×C7C2×#13711yescharacteristic
472C22×C7C2×#13711yescharacteristic
473C22×C7#57611yescharacteristic
474C22×C7#57711yescharacteristic
475C4×C7—22no—
476C4×C7—22no—
477C4×C7—41no—
478C4×C7—42no—
479C4×C7—41no—
480C4×C7—42no—
481C4×C7—42no—
482C4×C7—42no—
483C4×C7#52511yescharacteristic
484C4×C7#53611yescharacteristic
485C4×C7#54711yescharacteristic
486C4×C7#54711yescharacteristic
487Dic7—81no—
488Dic7—81no—
489Dic7—81no—
490Dic7—81no—
491C24C2×C22⋊D711yescharacteristic
492C24C2×C22⋊D711yescharacteristic
493C2×Q8—24no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8C2×C22⋊D712yes—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—141no—
526C22×C4—141no—
527C22×C4—141no—
528C22×C4—141no—
529C22×C4C2×C22⋊D711yescharacteristic
530C22×C4C2×C22⋊D711yescharacteristic
531C22×C4C2×C22⋊D711yescharacteristic
532C22×C4C2×C22⋊D711yescharacteristic
533C22×C4C2×C22⋊D712yes—
534C22×C4C2×C22⋊D712yes—
535C22×C4C23×D711yescharacteristic
536M16—148no—
537C2×C8—72no—
538C2×C8—72no—
539C2×C8—141no—
540C2×C8—141no—
541C2×C8—141no—
542C2×C8—141no—
543C2×C8—141no—
544C2×C8—141no—
545C2×C8—141no—
546C2×C8—141no—
547C2×C8—141no—
548C2×C8—141no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—141no—
560C4⋊C4—141no—
561C4⋊C4—141no—
562C4⋊C4—141no—
563C4⋊C4—141no—
564C4⋊C4—141no—
565C4⋊C4—141no—
566C4⋊C4—141no—
567C4⋊C4—282no—
568C4⋊C4—561no—
569C4⋊C4C2×C22⋊D712yes—
570C4⋊C4C2×C22⋊D712yes—
571C4⋊C4C2×C22⋊D712yes—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—282no—
577C22⋊C4—282no—
578C22⋊C4—561no—
579C22⋊C4—561no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—282no—
584C2×C7—42no—
585C2×C7—42no—
586C2×C7#240611yescharacteristic
587C2×C7#300411yescharacteristic
588C2×C7#301211yescharacteristic
589C2×C7#334411yescharacteristic
590C2×C7#334611yescharacteristic
591C2×C7#335611yescharacteristic
592C2×C7#335711yescharacteristic
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23#650512yes—
606C23#651612yes—
607C23C22×C22⋊D711yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—84no—
613D4—28no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4—281no—
647C2×C4—281no—
648C2×C4—281no—
649C2×C4—281no—
650C2×C4—281no—
651C2×C4—281no—
652C2×C4—281no—
653C2×C4—281no—
654C2×C4—281no—
655C2×C4—281no—
656C2×C4—281no—
657C2×C4—281no—
658C2×C4#650512yes—
659C2×C4#651612yes—
660C2×C4D7×#4111yescharacteristic
661C2×C4D7×#4111yescharacteristic
662C2×C4#655411yescharacteristic
663C2×C4#655411yescharacteristic
664C2×C4C22×C22⋊D711yescharacteristic
665C2×C4C22×C22⋊D711yescharacteristic
666C8—142no—
667C8—142no—
668C8—281no—
669C8—281no—
670C7#2410911yescharacteristic, complemented, Sylow
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22C2×#650511yescharacteristic
686C22C2×#650511yescharacteristic
687C22#9051511yescharacteristic
688C22#9051511yescharacteristic
689C22#9052611yescharacteristic
690C22#9052711yescharacteristic
691C22C2×#651611yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—561no—
701C4—561no—
702C4—561no—
703C4—561no—
704C4#9051511yescharacteristic
705C4#9051511yescharacteristic
706C4#9051611yescharacteristic
707C4#9051911yescharacteristic
708C2—42no—
709C2—42no—
710C2#1174106911yescharacteristic
711C2#1174107011yescharacteristic
712C2#1174107111yescharacteristic
713C2#1174107211yescharacteristic
714C2#1174150411yescharacteristic
715C2#1174153511yescharacteristic
716C2#1174154711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC2×C7×#554C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×#554D7
hypocenterC7#24109
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. C2×#89817C2semidirect
4. C2×#89736C2semidirect
5. #11729537C2semidirect
6. #11729536C2semidirect
7. #11729451C2semidirect
8. #11729449C2semidirect
9. #11729448C2semidirect
10. #11729383C2semidirect
11. #11729382C2semidirect
13. #11729310C2semidirect
14. #11729309C2semidirect
15. #11729307C2semidirect
670. C7#24109semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5542
C2×#898172
#117398172
C2×#897362
#117295372
#117295362
#117294512
#117294492
#117294482
#117293832
#117293822
#117293652
#117293102
#117293092
#117293072
#241097