Finite Group Databasebeta

← C2×#11736002 #14218255

Subgroups — C2×#11736002 #14218255

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90219C211yesmaximal, characteristic
2C2×C7×#405C211yesmaximal, characteristic, complemented
3C2×#89899C211yesmaximal, characteristic, complemented
4C2×#89900C211yesmaximal, characteristic, complemented
5C2×#89883C211yesmaximal, characteristic, complemented
6C2×#89883C211yesmaximal, characteristic, complemented
7C2×#89772C211yesmaximal, characteristic, complemented
8#11736002C2116yesmaximal, direct product factor
9C2×#89478C211yesmaximal, characteristic, complemented
10C2×#89481C211yesmaximal, characteristic, complemented
11C2×#89477C211yesmaximal, characteristic, complemented
12C2×#89473C211yesmaximal, characteristic, complemented
13C2×#89460C211yesmaximal, characteristic, complemented
14C2×#89461C211yesmaximal, characteristic, complemented
15C2×C4×#1131C211yesmaximal, characteristic, complemented
16C2×#89451C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×C4×C22⋊D7C2211yescharacteristic
21C2×C4×C22⋊D7C2211yescharacteristic
22C22×#1131C2211yescharacteristic
23C22×#1131C2211yescharacteristic
24C22×#1131C2211yescharacteristic
25C22×C8×D7C2211yescharacteristic
26#90219C418yes—
27#90219C2218yes—
28C2×#6461C411yescharacteristic
29C2×#6459C411yescharacteristic
30C2×#6457C411yescharacteristic
31C2×#6452C411yescharacteristic
32C2×#6448C411yescharacteristic
33C2×#6447C411yescharacteristic
34C2×#6446C411yescharacteristic
35C2×#6442C411yescharacteristic
36C2×C4×D28C2211yescharacteristic
37C2×#6435C2211yescharacteristic
38C2×C42×D7C2211yescharacteristic
39C2×C4×Dic14C2211yescharacteristic
40C7×#405C2218yescomplemented
41C2×C7×#97C2211yescharacteristic
42C2×C7×#97C2211yescharacteristic
43C2×C4×C7×C8C2211yescharacteristic
44C2×C4×C7×C8C2211yescharacteristic
45C2×C22⋊(C7⋊C8)C2211yescharacteristic
46C2×C22⋊(C7⋊C8)C2211yescharacteristic
47#89900C2218yescomplemented
48#89899C2218yescomplemented
49#89883C2218yescomplemented
50#89883C2218yescomplemented
51C2×(C2×D7)⋊C8C2211yescharacteristic
52C2×(C2×D7)⋊C8C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6389C2211yescharacteristic
56C2×#6389C2211yescharacteristic
57C2×#6389C2211yescharacteristic
58C2×Dic7⋊C8C2211yescharacteristic
59C2×Dic7⋊C8C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C2×C8×Dic7C2211yescharacteristic
63#89772C2218yescomplemented
64C2×C4⋊(C7⋊C8)C2211yescharacteristic
65C2×C4⋊(C7⋊C8)C2211yescharacteristic
66C2×#6377C2211yescharacteristic
67C2×C4×C7⋊C8C2211yescharacteristic
68#89481C2218yescomplemented
69#89478C2218yescomplemented
70#89477C2218yescomplemented
71#89473C2218yescomplemented
72#89461C2218yescomplemented
73#89460C2218yescomplemented
74C4×#1131C2218yescomplemented
75#89451C2218yescomplemented
76C2×#2967—71nomaximal, Sylow
77C23×C4×C7C2311yescharacteristic
78C22×C22⋊D7C2×C411yescharacteristic
79C22×C22⋊D7C2×C411yescharacteristic
80C22×D28C2×C411yescharacteristic
81C22×C4×D7C2×C411yescharacteristic
82C22×C4×D7C2×C411yescharacteristic
83C22×C4×D7C2311yescharacteristic
84C22×C4×D7C2311yescharacteristic
85C22×Dic14C2×C411yescharacteristic
86C2×C7×M16—24no—
87C2×C7×M16C2314yes—
88C22×C7×C8—24no—
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C22×C7×C8C2314yes—
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2311yescharacteristic
94C7×#117C2×C414yes—
95C7×#117C2314yes—
96C2×C7×C4⋊C4C2×C411yescharacteristic
97C2×C7×C4⋊C4C2×C411yescharacteristic
98C2×C7×C22⋊C4C2×C411yescharacteristic
99C2×C7×C22⋊C4C2×C411yescharacteristic
100C2×C42×C7C2311yescharacteristic
101C2×C42×C7C2311yescharacteristic
102C2×C22⋊Dic7C2×C411yescharacteristic
103C2×C22⋊Dic7C2×C411yescharacteristic
104C4×C22⋊D7C2×C414yes—
105C4×C22⋊D7C2×C414yes—
106C4×C22⋊D7C2314yes—
107C4×C22⋊D7C2314yes—
108C2×(C2×D7)⋊C4C2×C411yescharacteristic
109C2×(C2×D7)⋊C4C2×C411yescharacteristic
110C2×(C2×D7)⋊C4C2×C411yescharacteristic
111C2×(C2×D7)⋊C4C2×C411yescharacteristic
112C2×(C2×D7)⋊C4C2×C411yescharacteristic
113C2×(C2×D7)⋊C4C2×C411yescharacteristic
114C2×C4⋊Dic7C2×C411yescharacteristic
115C2×C4⋊Dic7C2×C411yescharacteristic
116C2×Dic7⋊C4C2×C411yescharacteristic
117C2×Dic7⋊C4C2×C411yescharacteristic
118C2×Dic7⋊C4C2×C411yescharacteristic
119C2×Dic7⋊C4C2×C411yescharacteristic
120C2×Dic7⋊C4C2×C411yescharacteristic
121C2×Dic7⋊C4C2×C411yescharacteristic
122C2×C4×Dic7C2×C411yescharacteristic
123C2×C4×Dic7C2×C411yescharacteristic
124C2×C4×Dic7C2311yescharacteristic
125C2×C4×Dic7C2311yescharacteristic
126C22×C7⋊C8C2311yescharacteristic
127C22×C7⋊C8C2311yescharacteristic
128C22×C7⋊C8C2311yescharacteristic
129C22×C7⋊C8C2311yescharacteristic
130C2×#1131—24no—
131C2×#1131—24no—
132C2×#1131—24no—
133C2×#1131C2314yes—
134C2×#1131C2314yes—
135C2×#1131C2314yes—
136C2×C8×D7—24no—
137C2×C8×D7C2314yes—
138#6461C2×C418yes—
139#6459C2×C418yes—
140#6457C2×C418yes—
141#6452C2×C418yes—
142#6448C2×C418yes—
143#6447C2×C418yes—
144#6446C2×C418yes—
145#6442C2×C418yes—
146C4×D28C2×C414yes—
147C4×D28C2314yes—
148#6435C2×C414yes—
149#6435C2314yes—
150C42×D7C2×C414yes—
151C42×D7C2314yes—
152C4×Dic14C2×C414yes—
153C4×Dic14C2314yes—
154C7×#97C2314yes—
155C7×#97C2314yes—
156C4×C7×C8C2314yes—
157C4×C7×C8C2314yes—
158C22⋊(C7⋊C8)C2314yes—
159C22⋊(C7⋊C8)C2314yes—
160(C2×D7)⋊C8C2314yes—
161(C2×D7)⋊C8C2314yes—
162(C2×D7)⋊C8C2314yes—
163(C2×D7)⋊C8C2314yes—
164#6389C2314yes—
165#6389C2314yes—
166#6389C2314yes—
167Dic7⋊C8C2314yes—
168Dic7⋊C8C2314yes—
169Dic7⋊C8C2314yes—
170Dic7⋊C8C2314yes—
171C8×Dic7C2314yes—
172C4⋊(C7⋊C8)C2314yes—
173C4⋊(C7⋊C8)C2314yes—
174#6377C2314yes—
175C4×C7⋊C8C2314yes—
176C2×#529—71no—
177#2967—716no—
178C2×#446—71no—
179C2×#446—71no—
180C2×#436—71no—
181C2×#436—71no—
182C2×#435—71no—
183C2×#435—71no—
184C2×#435—71no—
185C2×#435—71no—
186C2×#433—71no—
187C2×#433—71no—
188C2×#432—71no—
189C2×#405—71no—
190C2×#405D711yescharacteristic, complemented
191C2×C4×M16—71no—
192C24×C7C22×C411yescharacteristic
193C23×D7C22×C411yescharacteristic
194C23×D7C22×C411yescharacteristic
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7C22×C411yescharacteristic
198C22×C4×C7C22×C411yescharacteristic
199C22×C4×C7C22×C411yescharacteristic
200C22×C4×C7C22×C411yescharacteristic
201C22×C4×C7C22×C411yescharacteristic
202C22×C4×C7C22×C412yes—
203C22×C4×C7C2412yes—
204C22×C4×C7C2411yescharacteristic
205C2×C22⋊D7—42no—
206C2×C22⋊D7—42no—
207C2×C22⋊D7C22×C414yes—
208C2×C22⋊D7C22×C414yes—
209C22×Dic7C22×C411yescharacteristic
210C22×Dic7C22×C411yescharacteristic
211C22×Dic7C22×C411yescharacteristic
212C22×Dic7C22×C411yescharacteristic
213C22×Dic7C22×C411yescharacteristic
214C22×Dic7C22×C411yescharacteristic
215C2×D28—42no—
216C2×D28C22×C414yes—
217C2×C4×D7—22no—
218C2×C4×D7—22no—
219C2×C4×D7—22no—
220C2×C4×D7—22no—
221C2×C4×D7—42no—
222C2×C4×D7—42no—
223C2×C4×D7C22×C412yes—
224C2×C4×D7C22×C412yes—
225C2×C4×D7C22×C414yes—
226C2×C4×D7C22×C414yes—
227C2×C4×D7C2412yes—
228C2×C4×D7C2412yes—
229C2×Dic14—42no—
230C2×Dic14C22×C414yes—
231C7×M16—28no—
232C2×C7×C8—22no—
233C2×C7×C8—22no—
234C2×C7×C8—28no—
235C2×C7×C8#4114yes—
236C2×C7×C8#4114yes—
237C2×C7×C8C2412yes—
238C2×C7×C8C2412yes—
239C2×C7×C8C2412yes—
240C2×C7×C8C2412yes—
241C7×C4⋊C4C22×C414yes—
242C7×C4⋊C4C22×C414yes—
243C7×C22⋊C4C22×C414yes—
244C7×C22⋊C4C22×C414yes—
245C42×C7C22×C412yes—
246C42×C7C22×C412yes—
247C42×C7C2412yes—
248C42×C7C2412yes—
249C22⋊Dic7C22×C414yes—
250C22⋊Dic7C22×C414yes—
251(C2×D7)⋊C4C22×C414yes—
252(C2×D7)⋊C4C22×C414yes—
253(C2×D7)⋊C4C22×C414yes—
254(C2×D7)⋊C4C22×C414yes—
255(C2×D7)⋊C4C22×C414yes—
256(C2×D7)⋊C4C22×C414yes—
257C4⋊Dic7C22×C414yes—
258C4⋊Dic7C22×C414yes—
259Dic7⋊C4C22×C414yes—
260Dic7⋊C4C22×C414yes—
261Dic7⋊C4C22×C414yes—
262Dic7⋊C4C22×C414yes—
263Dic7⋊C4C22×C414yes—
264Dic7⋊C4C22×C414yes—
265C4×Dic7C22×C412yes—
266C4×Dic7C22×C412yes—
267C4×Dic7C22×C414yes—
268C4×Dic7C22×C414yes—
269C4×Dic7C2412yes—
270C4×Dic7C2412yes—
271C2×C7⋊C8—22no—
272C2×C7⋊C8—22no—
273C2×C7⋊C8—22no—
274C2×C7⋊C8—22no—
275C2×C7⋊C8C2412yes—
276C2×C7⋊C8C2412yes—
277C2×C7⋊C8C2412yes—
278C2×C7⋊C8C2412yes—
279#1131—28no—
280#1131—28no—
281#1131—28no—
282C8×D7—28no—
283C22×M16—71no—
284C22×M16—71no—
285C22×M16—71no—
286C22×M16C2×D711yescharacteristic
287C23×C8—71no—
288C23×C8C2×D711yescharacteristic
289#529—78no—
290#529—78no—
291C2×#126—71no—
292C2×#126—71no—
293C2×#125—71no—
294C2×#124—71no—
295C2×#123—71no—
296C2×#123—71no—
297C2×C22⋊Q8—71no—
298C2×#121—71no—
299C2×C4×Q8—71no—
300C2×C4×D4—71no—
301C2×C4×D4—71no—
302C2×C4×D4—71no—
303C2×#117—71no—
304C2×#117C2×D711yescharacteristic
305C22×C42—71no—
306#446—78no—
307#446—78no—
308#436—78no—
309#436—78no—
310#435—78no—
311#435—78no—
312#435—78no—
313#435—78no—
314#433—78no—
315#433—78no—
316#432—78no—
317C2×C4⋊C8—71no—
318C2×C4⋊C8—71no—
319C2×C4⋊C8—71no—
320C2×C4⋊C8—71no—
321C2×C4⋊C8—71no—
322C2×C4⋊C8—71no—
323C2×C22⋊C8—71no—
324C2×C22⋊C8—71no—
325C2×C22⋊C8—71no—
326C2×C22⋊C8—71no—
327C2×C22⋊C8—71no—
328C2×C22⋊C8—71no—
329#405—78no—
330#405C2×D718yescomplemented
331C4×M16—78no—
332C2×#97—71no—
333C2×#97—71no—
334C2×#97—71no—
335C2×#97—71no—
336C2×#97C2×D711yescharacteristic
337C2×#97C2×D711yescharacteristic
338C2×C4×C8—71no—
339C2×C4×C8—71no—
340C2×C4×C8C2×D711yescharacteristic
341C2×C4×C8C2×D711yescharacteristic
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7C23×C412yes—
346C23×C7C23×C411yescharacteristic
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7C23×C412yes—
354C22×D7C23×C412yes—
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×C7C23×C412yes—
364C2×C4×C7C23×C412yes—
365C2×C4×C7C23×C412yes—
366C2×C4×C7C23×C412yes—
367C2×C4×C7C23×C412yes—
368C2×C4×C7C23×C411yescharacteristic
369C2×C4×C7C2×#4112yes—
370C2×C4×C7C2×#4112yes—
371C2×C4×C7C2511yescharacteristic
372C22⋊D7—44no—
373C22⋊D7—44no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—22no—
378C2×Dic7—22no—
379C2×Dic7—22no—
380C2×Dic7C23×C412yes—
381C2×Dic7C23×C412yes—
382C2×Dic7C23×C412yes—
383C2×Dic7C23×C412yes—
384C2×Dic7C23×C412yes—
385C2×Dic7C23×C412yes—
386D28—44no—
387C4×D7—24no—
388C4×D7—24no—
389C4×D7—22no—
390C4×D7—22no—
391C4×D7—22no—
392C4×D7—22no—
393C4×D7—44no—
394C4×D7—44no—
395Dic14—44no—
396C7×C8—22no—
397C7×C8—22no—
398C7×C8C2×#4114yes—
399C7×C8C2×#4114yes—
400C7⋊C8—22no—
401C7⋊C8—22no—
402C7⋊C8—22no—
403C7⋊C8—22no—
404C22×Q8—71no—
405C22×D4—71no—
406C22×D4—71no—
407C22×D4—71no—
408C23×C4—71no—
409C23×C4—71no—
410C23×C4—71no—
411C23×C4—71no—
412C23×C4C22×D711yescharacteristic
413C2×M16—24no—
414C2×M16—74no—
415C2×M16—74no—
416C2×M16—74no—
417C2×M16—144no—
418C2×M16—144no—
419C2×M16—144no—
420C2×M16C22×D714yes—
421C22×C8—24no—
422C22×C8—71no—
423C22×C8—71no—
424C22×C8—71no—
425C22×C8—71no—
426C22×C8—74no—
427C22×C8—144no—
428C22×C8C22×D714yes—
429C22×C8C22×D711yescharacteristic
430C22×C8C22×D711yescharacteristic
431C22×C8C22×D711yescharacteristic
432C22×C8C22×D711yescharacteristic
433#126—78no—
434#126—78no—
435#125—78no—
436#124—78no—
437#123—78no—
438#123—78no—
439C22⋊Q8—78no—
440#121—78no—
441C4×Q8—74no—
442C4×Q8—74no—
443C4×D4—74no—
444C4×D4—74no—
445C4×D4—74no—
446C4×D4—74no—
447C4×D4—74no—
448C4×D4—74no—
449#117—74no—
450#117—74no—
451#117C4×D714yes—
452#117C22×D714yes—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—71no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—71no—
457C2×C4⋊C4—71no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—71no—
461C2×C4⋊C4C4×D711yescharacteristic
462C2×C4⋊C4C4×D711yescharacteristic
463C2×C22⋊C4—71no—
464C2×C22⋊C4—71no—
465C2×C22⋊C4—71no—
466C2×C22⋊C4—71no—
467C2×C22⋊C4—71no—
468C2×C22⋊C4—71no—
469C2×C22⋊C4—71no—
470C2×C22⋊C4—71no—
471C2×C22⋊C4C4×D711yescharacteristic
472C2×C22⋊C4C4×D711yescharacteristic
473C2×C42—71no—
474C2×C42—71no—
475C2×C42—71no—
476C2×C42—71no—
477C2×C42—74no—
478C2×C42—74no—
479C2×C42C22×D711yescharacteristic
480C2×C42C22×D711yescharacteristic
481C4⋊C8—74no—
482C4⋊C8—74no—
483C4⋊C8—74no—
484C4⋊C8—74no—
485C4⋊C8—74no—
486C4⋊C8—74no—
487C22⋊C8—74no—
488C22⋊C8—74no—
489C22⋊C8—74no—
490C22⋊C8—74no—
491C22⋊C8—74no—
492C22⋊C8—74no—
493#97—74no—
494#97—74no—
495#97—74no—
496#97—74no—
497#97C22×D714yes—
498#97C22×D714yes—
499C4×C8—74no—
500C4×C8—74no—
501C4×C8C22×D714yes—
502C4×C8C22×D714yes—
503C22×C7—22no—
504C22×C7—22no—
505C22×C7—22no—
506C22×C7—44no—
507C22×C7C4×#4112yes—
508C22×C7#56812yes—
509C22×C7#56812yes—
510C22×C7C24×C411yescharacteristic
511C2×D7—22no—
512C2×D7—22no—
513C2×D7—22no—
514C2×D7—22no—
515C2×D7—22no—
516C2×D7—22no—
517C2×D7—44no—
518C2×D7—44no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—22no—
523C4×C7—22no—
524C4×C7C4×#4112yes—
525C4×C7C22×#4111yescharacteristic
526C4×C7C22×#4111yescharacteristic
527Dic7—22no—
528Dic7—22no—
529Dic7—22no—
530Dic7—22no—
531Dic7—22no—
532Dic7—22no—
533C24—71no—
534C24—71no—
535C24C2×C4×D711yescharacteristic
536C2×Q8—74no—
537C2×Q8—282no—
538C2×D4—74no—
539C2×D4—74no—
540C2×D4—74no—
541C2×D4—282no—
542C2×D4—282no—
543C2×D4—282no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—71no—
547C22×C4—71no—
548C22×C4—71no—
549C22×C4—71no—
550C22×C4—71no—
551C22×C4—71no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—72no—
555C22×C4—72no—
556C22×C4—74no—
557C22×C4—74no—
558C22×C4—142no—
559C22×C4—142no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—282no—
563C22×C4—282no—
564C22×C4C2×C4×D711yescharacteristic
565C22×C4C2×C4×D711yescharacteristic
566C22×C4C2×C4×D711yescharacteristic
567C22×C4C2×C4×D711yescharacteristic
568C22×C4C2×C4×D711yescharacteristic
569C22×C4C2×C4×D712yes—
570C22×C4C23×D712yes—
571C22×C4C23×D711yescharacteristic
572M16—28no—
573M16—148no—
574M16—148no—
575M16—148no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—28no—
579C2×C8—72no—
580C2×C8—72no—
581C2×C8—72no—
582C2×C8—72no—
583C2×C8—142no—
584C2×C8—142no—
585C2×C8—142no—
586C2×C8—142no—
587C2×C8—148no—
588C2×C8#115714yes—
589C2×C8#115714yes—
590C2×C8C23×D712yes—
591C2×C8C23×D712yes—
592C2×C8C23×D712yes—
593C2×C8C23×D712yes—
594C4⋊C4—74no—
595C4⋊C4—74no—
596C4⋊C4—74no—
597C4⋊C4—74no—
598C4⋊C4—74no—
599C4⋊C4—74no—
600C4⋊C4—74no—
601C4⋊C4—74no—
602C4⋊C4C2×C4×D714yes—
603C4⋊C4C2×C4×D714yes—
604C22⋊C4—74no—
605C22⋊C4—74no—
606C22⋊C4—74no—
607C22⋊C4—74no—
608C22⋊C4—74no—
609C22⋊C4—74no—
610C22⋊C4—74no—
611C22⋊C4—74no—
612C22⋊C4C2×C4×D714yes—
613C22⋊C4C2×C4×D714yes—
614C42—72no—
615C42—74no—
616C42—74no—
617C42—72no—
618C42—72no—
619C42—72no—
620C42C2×C4×D712yes—
621C42C2×C4×D712yes—
622C42C23×D712yes—
623C42C23×D712yes—
624C2×C7—42no—
625C2×C7#296714yescomplemented
626C2×C7C2×C4×#4111yescharacteristic
627C2×C7C2×#56811yescharacteristic
628C2×C7C2×#56811yescharacteristic
629D7—42no—
630D7—42no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—72no—
635C23—72no—
636C23—142no—
637C23—142no—
638C23—142no—
639C23—142no—
640C23—142no—
641C23—142no—
642C23C22×C4×D712yes—
643C23C22×C4×D711yescharacteristic
644Q8—284no—
645D4—284no—
646D4—284no—
647D4—284no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—72no—
657C2×C4—72no—
658C2×C4—72no—
659C2×C4—72no—
660C2×C4—72no—
661C2×C4—72no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—144no—
669C2×C4—144no—
670C2×C4—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—284no—
675C2×C4—284no—
676C2×C4C22×C4×D712yes—
677C2×C4C22×C4×D712yes—
678C2×C4C22×C4×D712yes—
679C2×C4C22×C4×D712yes—
680C2×C4C22×C4×D712yes—
681C2×C4C22×C4×D711yescharacteristic
682C2×C4C2×#115712yes—
683C2×C4C2×#115712yes—
684C2×C4C24×D711yescharacteristic
685C8—22no—
686C8—22no—
687C8—142no—
688C8—142no—
689C8—142no—
690C8—142no—
691C8C2×#115714yes—
692C8C2×#115714yes—
693C7C2×#296711yescharacteristic, complemented, Sylow
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—142no—
699C22—142no—
700C22—142no—
701C22—142no—
702C22—142no—
703C22—142no—
704C22—284no—
705C22—284no—
706C22C4×#115712yes—
707C22#9044112yes—
708C22#9044112yes—
709C22C23×C4×D711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—142no—
716C4—142no—
717C4—142no—
718C4—142no—
719C4—142no—
720C4—142no—
721C4C4×#115712yes—
722C4C22×#115711yescharacteristic
723C4C22×#115711yescharacteristic
724C2—42no—
725C2—282no—
726C2—282no—
727C2#1173600214yesdirect product factor
728C2C2×C4×#115711yescharacteristic
729C2C2×#9044111yescharacteristic
730C2C2×#9044111yescharacteristic
subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C7×#405C2
socleC23×C7C23×C4
prime radicalC2×#6447C4
cosocleC2×C4×C7C25
hypercenterC2×#405D7
hypocenterC7C2×#2967
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×C7×#405C2semidirect
3. C2×#89899C2semidirect
4. C2×#89900C2semidirect
5. C2×#89883C2semidirect
6. C2×#89883C2semidirect
7. C2×#89772C2semidirect
8. #11736002C2direct (N × H)
9. C2×#89478C2semidirect
10. C2×#89481C2semidirect
11. C2×#89477C2semidirect
12. C2×#89473C2semidirect
13. C2×#89460C2semidirect
14. C2×#89461C2semidirect
15. C2×C4×#1131C2semidirect
16. C2×#89451C2semidirect
40. C7×#405C22semidirect
47. #89900C22semidirect
48. #89899C22semidirect
49. #89883C22semidirect
50. #89883C22semidirect
63. #89772C22semidirect
68. #89481C22semidirect
69. #89478C22semidirect
70. #89477C22semidirect
71. #89473C22semidirect
72. #89461C22semidirect
73. #89460C22semidirect
74. C4×#1131C22semidirect
75. #89451C22semidirect
190. C2×#405D7semidirect
330. #405C2×D7semidirect
625. C2×C7#2967semidirect
693. C7C2×#2967semidirect
727. C2#11736002direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902192
C2×C7×#4052
C2×#898992
C2×#899002
C2×#898832
C2×#897722
#117360022
C2×#894782
C2×#894812
C2×#894772
C2×#894732
C2×#894602
C2×#894612
C2×C4×#11312
C2×#894512
C2×#29677