Finite Group Databasebeta

← #13320071

Subgroups — #13320071

Order 1792.

1060 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#551C211yesmaximal, characteristic
2#11739748C212yesmaximal, complemented
3#11729499C212yesmaximal, complemented
4#11729456C212yesmaximal, complemented
5#11729445C212yesmaximal, complemented
6#11729356C211yesmaximal, characteristic, complemented
7#11729354C211yesmaximal, characteristic, complemented
8#11729326C211yesmaximal, characteristic, complemented
9#11729325C211yesmaximal, characteristic, complemented
10#11729293C211yesmaximal, characteristic, complemented
11C2×#89320C211yesmaximal, characteristic, complemented
12C7×#551—22no—
13C7×#551—22no—
14C7×#551—22no—
15C7×#551—22no—
16C2×C7×#126C411yescharacteristic
17C2×C7×#126C2211yescharacteristic
18C2×C7×#124C411yescharacteristic
19C2×C7×#123C411yescharacteristic
20C2×C7×#123C411yescharacteristic
21C2×C7×#123C2211yescharacteristic
22C2×C7×C22⋊Q8C411yescharacteristic
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×#120C411yescharacteristic
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117C411yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×C7×C22⋊C4C411yescharacteristic
30C22×C7×C22⋊C4C2211yescharacteristic
31#89979C2212yes—
32#89979C2212yescomplemented
33C2×C22⋊(C7⋊C8)C2212yes—
34C2×C22⋊(C7⋊C8)C2212yescomplemented
35#89784—22no—
36#89783—22no—
37#89783—22no—
38D4×C7⋊C8—22no—
39#89698C2212yescomplemented
40#89697C2212yescomplemented
41#89323C2212yescomplemented
42#89323C2212yescomplemented
43#89323C2212yescomplemented
44#89323C2212yescomplemented
45#89320C2212yes—
46#89320C2212yes—
47#89320C2211yescharacteristic
48#89320C2211yescharacteristic
49#89320C2211yescharacteristic
50#89320C2211yescharacteristic
51#17422—71nomaximal, Sylow
52C25×C7C2×C411yescharacteristic
53C22×C7×Q8C2×C411yescharacteristic
54C22×C7×D4C2×C411yescharacteristic
55C22×C7×D4C2×C411yescharacteristic
56C22×C7×D4C2×C411yescharacteristic
57C23×C4×C7C2×C411yescharacteristic
58C23×C4×C7C2×C411yescharacteristic
59C23×C4×C7C2×C411yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C7×#126—22no—
63C7×#126—22no—
64C7×#126—22no—
65C7×#126—22no—
66C7×#124—22no—
67C7×#124—22no—
68C7×#123—22no—
69C7×#123—22no—
70C7×#123—22no—
71C7×#123—22no—
72C7×#123—22no—
73C7×#123—22no—
74C7×C22⋊Q8—22no—
75C7×C22⋊Q8—22no—
76C7×C22⋊Q8—22no—
77C7×C22⋊Q8—22no—
78C7×#120—22no—
79C7×#120—22no—
80C4×C7×D4—22no—
81C4×C7×D4—22no—
82C4×C7×D4D412yes—
83C4×C7×D4D412yes—
84C4×C7×D4D412yes—
85C4×C7×D4D412yes—
86C7×#117—21no—
87C7×#117—21no—
88C7×#117—21no—
89C7×#117—21no—
90C7×#117—22no—
91C7×#117—22no—
92C2×C7×C4⋊C4C2×C411yescharacteristic
93C2×C7×C4⋊C4C2×C411yescharacteristic
94C2×C7×C4⋊C4C2×C411yescharacteristic
95C2×C7×C4⋊C4C2×C411yescharacteristic
96C2×C7×C4⋊C4C2×C411yescharacteristic
97C2×C7×C4⋊C4C2×C411yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4C2×C411yescharacteristic
107C2×C7×C22⋊C4C2×C411yescharacteristic
108C2×C7×C22⋊C4C2×C411yescharacteristic
109C2×C7×C22⋊C4C2×C411yescharacteristic
110C2×C7×C22⋊C4C2×C411yescharacteristic
111C2×C7×C22⋊C4C2×C411yescharacteristic
112C2×C7×C22⋊C4C2×C411yescharacteristic
113C2×C7×C22⋊C4C2×C411yescharacteristic
114C2×C7×C22⋊C4C2×C411yescharacteristic
115C2×C7×C22⋊C4C2×C411yescharacteristic
116C2×C7×C22⋊C4C2×C411yescharacteristic
117C2×C7×C22⋊C4C2×C411yescharacteristic
118C2×C7×C22⋊C4C2311yescharacteristic
119C2×C7×C22⋊C4C2311yescharacteristic
120C2×C42×C7C2×C411yescharacteristic
121C2×C42×C7C2×C411yescharacteristic
122C2×C42×C7C2311yescharacteristic
123C2×#1136—22no—
124C2×#1136—22no—
125C22×C7⋊C8—22no—
126C22×C7⋊C8—22no—
127C22⋊(C7⋊C8)—22no—
128C22⋊(C7⋊C8)—22no—
129C22⋊(C7⋊C8)—22no—
130C22⋊(C7⋊C8)—22no—
131C22⋊(C7⋊C8)C2312yes—
132C22⋊(C7⋊C8)C2312yes—
133C22⋊(C7⋊C8)C2312yes—
134C22⋊(C7⋊C8)C2312yes—
135C4⋊(C7⋊C8)—22no—
136C4⋊(C7⋊C8)—22no—
137#6377—22no—
138C4×C7⋊C8—22no—
139C2×#551D711yescharacteristic
140#2974—72no—
141#1473—72no—
142#1472—72no—
143#1468—72no—
144#1465—71no—
145#1464—71no—
146#1462—71no—
147#1459—71no—
148#1458—71no—
149C2×#323—71no—
150C24×C7—21no—
151C24×C7—21no—
152C24×C7—22no—
153C24×C7—41no—
154C24×C7—42no—
155C24×C7—81no—
156C24×C7C22×C411yescharacteristic
157C24×C7C22×C411yescharacteristic
158C24×C7C22×C411yescharacteristic
159C24×C7C22×C411yescharacteristic
160C2×C7×Q8—22no—
161C2×C7×Q8—81no—
162C2×C7×D4—22no—
163C2×C7×D4—22no—
164C2×C7×D4—22no—
165C2×C7×D4—41no—
166C2×C7×D4—42no—
167C2×C7×D4—81no—
168C2×C7×D4C22⋊C412yes—
169C2×C7×D4C22⋊C412yes—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—22no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
176C22×C4×C7—21no—
177C22×C4×C7—41no—
178C22×C4×C7—42no—
179C22×C4×C7—81no—
180C22×C4×C7—81no—
181C22×C4×C7—81no—
182C22×C4×C7C22×C411yescharacteristic
183C22×C4×C7C22×C411yescharacteristic
184C22×C4×C7C22×C411yescharacteristic
185C22×C4×C7C22×C411yescharacteristic
186C22×C4×C7C22×C411yescharacteristic
187C22×C4×C7C22×C411yescharacteristic
188C22×C4×C7C22×C411yescharacteristic
189C22×C4×C7C22×C411yescharacteristic
190C22×C4×C7C22×C411yescharacteristic
191C22×C4×C7C22×C411yescharacteristic
192C22×C4×C7C2×D412yes—
193C22×C4×C7C2×D412yes—
194C22×C4×C7C2×D412yes—
195C22×C4×C7C2×D412yes—
196C22×C4×C7C2411yescharacteristic
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
199C7×C4⋊C4—22no—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—21no—
202C7×C4⋊C4—22no—
203C7×C4⋊C4—22no—
204C7×C4⋊C4—22no—
205C7×C4⋊C4—22no—
206C7×C4⋊C4C22⋊C412yes—
207C7×C4⋊C4C22⋊C412yes—
208C7×C22⋊C4—21no—
209C7×C22⋊C4—21no—
210C7×C22⋊C4—21no—
211C7×C22⋊C4—21no—
212C7×C22⋊C4—22no—
213C7×C22⋊C4—22no—
214C7×C22⋊C4—22no—
215C7×C22⋊C4—21no—
216C7×C22⋊C4—21no—
217C7×C22⋊C4—22no—
218C7×C22⋊C4—21no—
219C7×C22⋊C4—21no—
220C7×C22⋊C4—22no—
221C7×C22⋊C4—22no—
222C7×C22⋊C4—22no—
223C7×C22⋊C4—22no—
224C7×C22⋊C4C22⋊C411yescharacteristic
225C7×C22⋊C4C22⋊C411yescharacteristic
226C7×C22⋊C4C22⋊C411yescharacteristic
227C7×C22⋊C4C22⋊C411yescharacteristic
228C7×C22⋊C4C22⋊C412yes—
229C7×C22⋊C4C22⋊C412yes—
230C42×C7—21no—
231C42×C7—21no—
232C42×C7—21no—
233C42×C7—21no—
234C42×C7C2×D412yes—
235C42×C7C2×D412yes—
236#1136—82no—
237#1136—82no—
238C2×C7⋊C8—22no—
239C2×C7⋊C8—22no—
240C2×C7⋊C8—22no—
241C2×C7⋊C8—22no—
242C2×C7⋊C8—82no—
243C2×C7⋊C8—82no—
244#551—22no—
245#551—22no—
246#551—22no—
247#551—22no—
248C2×#126Dic711yescharacteristic
249C2×#126C2×D711yescharacteristic
250C2×#124Dic711yescharacteristic
251C2×#123Dic711yescharacteristic
252C2×#123Dic711yescharacteristic
253C2×#123C2×D711yescharacteristic
254C2×C22⋊Q8Dic711yescharacteristic
255C2×C22⋊Q8C2×D711yescharacteristic
256C2×#120Dic711yescharacteristic
257C2×C4×D4C2×D711yescharacteristic
258C2×C4×D4C2×D711yescharacteristic
259C2×#117Dic711yescharacteristic
260C2×#117C2×D711yescharacteristic
261C22×C22⋊C4Dic711yescharacteristic
262C22×C22⋊C4C2×D711yescharacteristic
263#436—142no—
264#435—142no—
265#435—142no—
266C8×D4—142no—
267#432—72no—
268#431—72no—
269#407—72no—
270#407—72no—
271C2×C22⋊C8—72no—
272C2×C22⋊C8—72no—
273#324—72no—
274#324—72no—
275#324—72no—
276#324—72no—
277#323—71no—
278#323—71no—
279#323—72no—
280#323—71no—
281#323—71no—
282#323—72no—
283C23×C7—21no—
284C23×C7—21no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—22no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—21no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7—41no—
294C23×C7—41no—
295C23×C7—41no—
296C23×C7—42no—
297C23×C7—42no—
298C23×C7—41no—
299C23×C7—41no—
300C23×C7—42no—
301C23×C7—41no—
302C23×C7—41no—
303C23×C7—42no—
304C23×C7—81no—
305C23×C7—81no—
306C23×C7—84no—
307C23×C7—84no—
308C23×C7C2×C22⋊C411yescharacteristic
309C23×C7C2×C22⋊C412yes—
310C23×C7C2×C22⋊C411yescharacteristic
311C23×C7#13112yes—
312C23×C7C23×C411yescharacteristic
313C7×Q8—82no—
314C7×D4—24no—
315C7×D4—42no—
316C7×D4—44no—
317C7×D4—82no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—21no—
325C2×C4×C7—21no—
326C2×C4×C7—21no—
327C2×C4×C7—21no—
328C2×C4×C7—21no—
329C2×C4×C7—21no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—41no—
335C2×C4×C7—41no—
336C2×C4×C7—41no—
337C2×C4×C7—41no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7—42no—
341C2×C4×C7—42no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—81no—
347C2×C4×C7—81no—
348C2×C4×C7C2×C22⋊C411yescharacteristic
349C2×C4×C7C2×C22⋊C411yescharacteristic
350C2×C4×C7C2×C22⋊C411yescharacteristic
351C2×C4×C7C2×C22⋊C411yescharacteristic
352C2×C4×C7C2×C22⋊C412yes—
353C2×C4×C7C2×C22⋊C412yes—
354C2×C4×C7C22×D412yes—
355C7⋊C8—42no—
356C7⋊C8—42no—
357C7⋊C8—42no—
358C7⋊C8—42no—
359C25C2×Dic711yescharacteristic
360C22×Q8C2×Dic711yescharacteristic
361C22×D4C2×Dic711yescharacteristic
362C22×D4C2×Dic711yescharacteristic
363C22×D4C2×Dic711yescharacteristic
364C23×C4C2×Dic711yescharacteristic
365C23×C4C2×Dic711yescharacteristic
366C23×C4C2×Dic711yescharacteristic
367C23×C4C22×D711yescharacteristic
368C23×C4C22×D711yescharacteristic
369C2×M16—142no—
370C2×M16—142no—
371C22×C8—142no—
372C22×C8—142no—
373#126—22no—
374#126—22no—
375#126—22no—
376#126—22no—
377#124—22no—
378#124—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389#120—22no—
390#120—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4C22⋊D712yes—
394C4×D4C22⋊D712yes—
395C4×D4C22⋊D712yes—
396C4×D4C22⋊D712yes—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4C2×Dic711yescharacteristic
404C2×C4⋊C4C2×Dic711yescharacteristic
405C2×C4⋊C4C2×Dic711yescharacteristic
406C2×C4⋊C4C2×Dic711yescharacteristic
407C2×C4⋊C4C2×Dic711yescharacteristic
408C2×C4⋊C4C2×Dic711yescharacteristic
409C2×C4⋊C4C22×D711yescharacteristic
410C2×C4⋊C4C22×D711yescharacteristic
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4C2×Dic711yescharacteristic
418C2×C22⋊C4C2×Dic711yescharacteristic
419C2×C22⋊C4C2×Dic711yescharacteristic
420C2×C22⋊C4C2×Dic711yescharacteristic
421C2×C22⋊C4C2×Dic711yescharacteristic
422C2×C22⋊C4C2×Dic711yescharacteristic
423C2×C22⋊C4C2×Dic711yescharacteristic
424C2×C22⋊C4C2×Dic711yescharacteristic
425C2×C22⋊C4C2×Dic711yescharacteristic
426C2×C22⋊C4C2×Dic711yescharacteristic
427C2×C22⋊C4C2×Dic711yescharacteristic
428C2×C22⋊C4C2×Dic711yescharacteristic
429C2×C22⋊C4C22×D711yescharacteristic
430C2×C22⋊C4C22×D711yescharacteristic
431C2×C42C2×Dic711yescharacteristic
432C2×C42C2×Dic711yescharacteristic
433C2×C42C22×D711yescharacteristic
434C4⋊C8—142no—
435C4⋊C8—142no—
436C22⋊C8—72no—
437C22⋊C8—72no—
438C22⋊C8—72no—
439C22⋊C8—72no—
440C22⋊C8—142no—
441C22⋊C8—142no—
442C22⋊C8—142no—
443C22⋊C8—142no—
444#97—142no—
445C4×C8—142no—
446C22×C7—21no—
447C22×C7—21no—
448C22×C7—21no—
449C22×C7—21no—
450C22×C7—22no—
451C22×C7—22no—
452C22×C7—21no—
453C22×C7—22no—
454C22×C7—21no—
455C22×C7—21no—
456C22×C7—22no—
457C22×C7—42no—
458C22×C7—42no—
459C22×C7—42no—
460C22×C7—42no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—81no—
467C22×C7—81no—
468C22×C7—84no—
469C22×C7—81no—
470C22×C7—81no—
471C22×C7—84no—
472C22×C7#41312yes—
473C22×C7C22×C22⋊C411yescharacteristic
474C22×C7C2×#13111yescharacteristic
475C22×C7#56811yescharacteristic
476C4×C7—21no—
477C4×C7—21no—
478C4×C7—22no—
479C4×C7—21no—
480C4×C7—21no—
481C4×C7—22no—
482C4×C7—22no—
483C4×C7—41no—
484C4×C7—41no—
485C4×C7—41no—
486C4×C7—41no—
487C4×C7—41no—
488C4×C7—41no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—41no—
493C24—42no—
494C24—81no—
495C24C22×Dic711yescharacteristic
496C24C22×Dic711yescharacteristic
497C24C22×Dic711yescharacteristic
498C24C22×Dic711yescharacteristic
499C2×Q8—22no—
500C2×Q8—81no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—41no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4C22⋊Dic712yes—
508C2×D4C22⋊Dic712yes—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—41no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4C22×Dic711yescharacteristic
522C22×C4C22×Dic711yescharacteristic
523C22×C4C22×Dic711yescharacteristic
524C22×C4C22×Dic711yescharacteristic
525C22×C4C22×Dic711yescharacteristic
526C22×C4C22×Dic711yescharacteristic
527C22×C4C22×Dic711yescharacteristic
528C22×C4C22×Dic711yescharacteristic
529C22×C4C22×Dic711yescharacteristic
530C22×C4C22×Dic711yescharacteristic
531C22×C4C2×C22⋊D712yes—
532C22×C4C2×C22⋊D712yes—
533C22×C4C2×C22⋊D712yes—
534C22×C4C2×C22⋊D712yes—
535C22×C4C23×D711yescharacteristic
536M16—562no—
537M16—562no—
538C2×C8—142no—
539C2×C8—142no—
540C2×C8—142no—
541C2×C8—142no—
542C2×C8—562no—
543C2×C8—562no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4C22⋊Dic712yes—
554C4⋊C4C22⋊Dic712yes—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4C22⋊Dic711yescharacteristic
572C22⋊C4C22⋊Dic711yescharacteristic
573C22⋊C4C22⋊Dic711yescharacteristic
574C22⋊C4C22⋊Dic711yescharacteristic
575C22⋊C4C22⋊Dic712yes—
576C22⋊C4C22⋊Dic712yes—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42C2×C22⋊D712yes—
582C42C2×C22⋊D712yes—
583C2×C7—21no—
584C2×C7—21no—
585C2×C7—22no—
586C2×C7—41no—
587C2×C7—42no—
588C2×C7—42no—
589C2×C7—81no—
590C2×C7#288011yescharacteristic
591C2×C7#288311yescharacteristic
592C2×C7C2×#41311yescharacteristic
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—42no—
607C23—42no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—81no—
615C23—81no—
616C23—84no—
617C23—84no—
618C23#651112yes—
619C23C2×C22⋊Dic711yescharacteristic
620C23C2×C22⋊Dic712yes—
621C23C2×C22⋊Dic711yescharacteristic
622C23C23×Dic711yescharacteristic
623Q8—82no—
624D4—24no—
625D4—42no—
626D4—44no—
627D4—82no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4C2×C22⋊Dic711yescharacteristic
659C2×C4C2×C22⋊Dic711yescharacteristic
660C2×C4C2×C22⋊Dic711yescharacteristic
661C2×C4C2×C22⋊Dic711yescharacteristic
662C2×C4C2×C22⋊Dic712yes—
663C2×C4C2×C22⋊Dic712yes—
664C2×C4C22×C22⋊D712yes—
665C8—282no—
666C8—282no—
667C8—282no—
668C8—282no—
669C7#1742211yescharacteristic, complemented, Sylow
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—22no—
675C22—22no—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—22no—
680C22—21no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—81no—
691C22—81no—
692C22—84no—
693C22—81no—
694C22—81no—
695C22—84no—
696C22#9000912yes—
697C22C2×#651111yescharacteristic
698C22#9051011yescharacteristic
699C22C22×C22⋊Dic711yescharacteristic
700C4—21no—
701C4—21no—
702C4—22no—
703C4—22no—
704C4—21no—
705C4—21no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C2—21no—
714C2—21no—
715C2—22no—
716C2—41no—
717C2—42no—
718C2—42no—
719C2—81no—
720C2#1174152011yescharacteristic
721C2C2×#9000911yescharacteristic
722C2#1174155211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic7
commutatorC23×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#551C2
socleC22×C7C22×C22⋊C4
prime radicalC2×C7×#120C4
cosocleC22×C4×C7C24
hypercenterC2×#551D7
hypocenterC7#17422
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
2. #11739748C2semidirect
3. #11729499C2semidirect
4. #11729456C2semidirect
5. #11729445C2semidirect
6. #11729356C2semidirect
7. #11729354C2semidirect
8. #11729326C2semidirect
9. #11729325C2semidirect
10. #11729293C2semidirect
11. C2×#89320C2semidirect
32. #89979C22semidirect
34. C2×C22⋊(C7⋊C8)C22semidirect
39. #89698C22semidirect
40. #89697C22semidirect
41. #89323C22semidirect
42. #89323C22semidirect
43. #89323C22semidirect
44. #89323C22semidirect
669. C7#17422semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5512
#117397482
#117294992
#117294562
#117294452
#117293562
#117293542
#117293262
#117293252
#117292932
C2×#893202
#174227